NOAA Technical Report ERL 373-WPL 47 Implementation of Coastal Current-Mapping HF Radar System Progress Report No. 1 D.E. Barrick M.W. Evans July 1976 U.S. DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration Environmental Research Laboratories NOAA Technical Report ERL 373-WPL 47 Implementation of Coastal 4fflfr. Current-Mapping HF Radar System Progress Report No. 1 c c a D.E. Barrick M.W. Evans Wave Propagation Laboratory Boulder, Colorado July 1976 U. S. DEPARTMENT OF COMMERCE Elliot Richardson, Secretary National Oceanic and Atmospheric Administration ,tJ Robert M. White, Administrator Environmental Research Laboratories Wilmot Hess, Director For solo by tho Superintendent of Documents, U.8. Government Printing Office, Washington, D.C. 20402 NOTICE The Environmental Research Laboratories do not approve, recommend, or endorse any proprietary product or proprietary material mentioned in this publication. No reference shall be made to the Environmental Research Laboratories or to this publication furnished by the Environmental Research Labora- tories in any advertising or sales promotion which would in- dicate or imply that the Environmental Research Laboratories approve, recommend, or endorse any proprietary product or proprietary material mentioned herein, or which has as its purpose an intent to cause directly or indirectly the adver- tised product to be used or purchased because of this Envi- ronmental Research Laboratories publication. 11 FOREWORD This report was written to serve a variety of users. The project has been sponsored over the past eighteen months by the National Oceanic and Atmospheric Administration (NOAA) , the Outer Continental Shelf Environmental Assessment Program (OCSEAP) , the U.S. Coast Guard, and the Energy Research and Development Administration (ERDA) . Each of these sponsors has its own reporting requirements — typically 4-6 page summaries issued at specified periods and in a specified format — and hence we cannot hope to describe the technical content of our developmental program in those reports. Therefore, the present document is not specifically a sponsor report. On the other hand, many within the remote-sensing community, the oceanographic community, from universities, institutes, and private industry have been requesting technical details on the system we are developing. Up to now, no formal publication has been prepared on our radar system for the applications intended here, even though the physics behind the scatter process have been analyzed in the various research papers cited in our report. This report is therefore the first in a series, intended to supply technical details to our many scientific colleagues who have been patiently awaiting further information on our system. A single reader having a given technical area of specialization will undoubtedly find certain sections easy, while other sections will be diffi- cult or even incomprehensible without additional background reading. A reader who desires a cursory understanding of the sea-scatter physics, fundamentals of the operation of our system, its capabilities, limitations, and expected performance should read Sections 1, 2, and 6. One interested in the engineering details of the hardware should read Section 3. Discussion of digital system software — both the software written to control the operation of the radar and the software written to mathematically process the sea-echo signals — is undertaken in Section 4. A technical specialist who wants the detailed mathematics behind the operation of the radar and signal processing should concentrate on Sections 4.3 and S. Finally, the systems analyst who desires details of the mathematics behind our projected system performance and optimizations should read Section 5. in CONTENTS Page FOREWORD iii ABSTRACT vii 1. INTRODUCTION 1 1.1 The Need 1 2. AN HF RADAR SYSTEM FOR MEASURING SURFACE CURRENTS 2 2.1 Sea-Scatter Physics 2 2.2 Background 4 2.3 Description of the Concept 3. SYSTEM HARDWARE 13 3.1 Digital Components 13 3.1.1 A/D Hardware $ System Timing Module 14 3.1.2 Semiconductor Mass-Storage Module 16 3.1.3 Fast-Fourier Transform (FFT) Processor 17 3.1.4 Line-Tape Recorder 17 3.1.5 PDP 11/04 Minicomputer 17 3.1.6 Keyboard/Printer Terminal 20 3.1.7 Graphic System 20 3.2 Transmitter 21 3.3 Receiver 24 3.4 Antennas 27 3.4.1 Transmitting Antennas 27 3.4.2 Receiving Antennas 29 4. SYSTEM SOFTWARE 31 4.1 Radar Signal Generation/Processing Timing 31 4.2 Control Software 34 4.2.1 Interfacing Items Necessary for Understanding of Software 34 4.2.2 Prelude 35 4.2.3 Interlude 35 4.2.4 Postlude 36 4.3 Signal-Processing Software 37 4.3.1 Functional Description 37 4.3.2 Software Description 42 Page 5. SYSTEM ANALYSES AND SIMULATION STUDIES 44 5.1 Signal-to-Noise Ratio (S/N) 44 5.1.1 Basic Radar Performance Criterion 44 5.1.2 Sampled Data and Digital Signal Processing 46 5.1.3 Sea-Echo Radar Cross Section 50 5.1.4 System Signal-to-Noise Ratio vs. Range 52 5.2 Optimization of Radar-Pair Spacing 53 5.3 Accuracies vs. Noise and Signal Statistics 55 5.3.1 Azimuthal (Direct ion-of -Arrival) Accuracy vs. Noise 55 5.3.2 Simulation of Current Map Using Actual Data-Process- ing Software 59 6 . SUMMARY 62 7. ACKNOWLEDGEMENTS 63 8 . REFERENCES 64 VI IMPLEMENTATION OF COASTAL CURRENT-MAPPING HF RADAR SYSTEM PROGRESS REPORT NO. 1 D. E. Barrick and M. W. Evans A concept for radar remote- sensing of near-surface ocean currents in coastal regions is described, and progress is re- viewed on the design and construction of the first operational units. The system employs pairs of low-power (50 W) , trans- portable, HF (30 MHz) radars whose signals from the shore are scattered from ocean waves that serve as tracers, i.e., under- lying currents impart a slight change in velocity to the ocean waves, which is detected by the radar receiver. Signals from each of the two geographically separated radar units of the pair, scattered from the same point on the sea, are used to construct a complete current vector for that point. In an operational system a radar pair will take simultaneous measurements over an ocean area with a grid having a 3-km spacing. Vectors will be con- structed for each 3-km-square section, and a map of the near- surface current field will be output in real-time by a mini- computer on-site. All radar and digital gear is contained in two shock-mounted fiberglass cases, only 44 inches high and weighing under 200 pounds. The radar antennas are easily erectable frames holding three vertical aluminum pipes; the entire system can be set up in less than an hour. All of the individual components of the system have been designed and constructed. The system soft- ware has been essentially completed and checked out in the lab- oratory. Only a small amount of final assembly remains to be done before checkout and use in the field. System performance and simulation studies show that a radar pair can provide current data to a range from the coast of about 70 km. The optimum spacing between paired radars is nominally 40 km. Error analyses show that probable azimuthal position errors are less than 5° for signal-to-noise ratios exceeding 10 dB. Simulations using random sea-echo and noise signals indicate that probable rms current- velocity errors are not more than 5 cm/s. VII Digitized by the Internet Archive in 2013 http://archive.org/details/implementationofOObarr I INTRODUCTION 1. 1 The Need Surface currents are defined as the mean horizontal flow of water within the uppermost layer of the ocean. The thickness of this layer can be nominally taken as 20 to 50 centimeters. On the open oceans, the heights of the waves present will almost always be many times greater than the thickness of this top layer; in addition, the phase velocities of these waves will also be much larger than the speeds of the mean surface currents (e.g., 10 to 100 times greater). Because of these two facts, the moored current meter — which is used successfully at greater depths — is rela- tively useless for measuring surface currents. Yet the currents in the uppermost layer of the ocean are of great importance, especially in near-coastal regions. Anything that floats on the surface is transported by these currents, waves notwithstanding. (The wind may also impart some velocity component to an object with appreciable vertical surface area above the water.) Thus the trajectory and fate of an oil spill or a leak from an offshore rig will depend upon the patterns of the near-surface currents in the area, as will the destination of hot water and pollutant effluents discharged near the shore. And the rescue of a person in the water, especially in conditions of poor visibility, could be aided considerably by real-time observations of surface currents over the area and relevant trajectory predictions. The Bureau of Land Management (BLM) , the Energy Research and Develop- ment Administration (ERDA) , the U.S. Coast Guard, and private oil companies are expending a great deal of resources to assess the impact on the environ- ment of massive offshore oil operations. Although a wide spectrum of scientific disciplines must be involved in such investigations, the under- lying question of paramount importance in all of these studies is: Where does floating oil released near a drilling platform go? The transport of pollutants, whether in toward shore or out to sea, will depend upon many factors, such as winds, waves, storms, tides, the coastline contour, and geophysical forces such as gravity and the Coriolis force (due to Earth rotation). Thus near-surface offshore currents will be highly variable from area to area and at different times. While the ultimate objective is to predict these currents as a function of the driving forces, their accurate measurement is the necessary first step in the development and testing of such a prediction model. In fact, when the near- surface currents are known, it is theoretically possible to (numerically) calculate the currents and circulation all the way to the ocean floor. Yet these near- surface currents are the most difficult to measure. Nearly all available techniques are Lagrangian in nature, meaning that they measure the trajectory of a parcel of water near the surface, thus obtain- ing one or more (current) streamlines vs. time. The most common technique consists of visually or photographically observing a dye marker's dispersal or the movement of timed-release floats from an airplane. Such experiments are expensive and hence limited in area and time. Drogued free-floating buoys, tracked either by radar or optically (from land, ship, and possibly in the future by satellite) represent an alternative technique. Satellite tracking of several such buoys will ultimately provide valuable information on general oceanic circulation patterns and thence, surface wind and ocean/ atmosphere energy exchange, but can hardly be useful for the finer grid- scale requirements for coastal waters over the continental shelves. 2. AN HF RADAR SYSTEM FOR MEASURING SURFACE CURRENTS Approximately two years ago, we identified a remote-sensing concept that appears to be ideally suited to measuring near-surface currents in coastal areas. The system we have designed and developed uses two HF shore-based transportable radars to measure current patterns, and it pro- vides, in real time, a map- like record of the currents. These currents are determined for 3 km x 3 km areas of ocean out to 70 km from shore, and are displayed at the centers of each such area within a rectangular grid. 2.1 Sea-Scatter Physics The mechanism behind the radar under construction here — permitting the measurement of near- surface currents — involves the physics of scatter from ocean waves. Ocean waves (and one in particular) are the "target" for the radar system. Since this target is moving, it produces a "Doppler shift" on the received echo; this merely means that the signal returns at a slightly different frequency than that transmitted, because of the radial rate of closure of the target. The radar receiver/processor measures this Doppler shift, and this permits the determination of the radial component of the current velocity by the following process. The ocean wave motion — producing the measured Doppler shift — consists of two linear combinations of velocity. One is due to the "intrinsic" velocity of any deep-water gravity surface wave; from hydro dynami c theory, this phase velocity to first order is precisely v , = /gL/2TT, where g - 9.81 ms~ 2 (the acceleration of gravity), and L is the wavelength of the water wavetrain. The second velocity component of the wave is due to the current; it is as though the wave were being transported in a Cartesian coordinate system attached to the mean water transport. Thus, by measuring the total Doppler shift (and hence the total radial ocean-wave velocity) , and precisely knowing the first component (due to the intrinsic wave velocity) , one determines the second term, which is the desired radial component of surface current. The logical question at this point is: How does one know precisely which wavetrain out of the entire spectrum constituting the ocean surface is doing the scattering? The physical mechanism behind HF scatter from the sea was discovered over twenty years ago by Crombie [1955]. By looking at ocean waves with a shore-based HF radar and spectrally analyzing the re- ceived echoes, he observed two dominant "spikes" or peaks, symmetrically spaced about the carrier frequency (Fig. 1). These spikes indicated that of all the randomly time- varying ocean waves being observed by the radar, /-A-/ &*£«»* velocity Ocean wavetrain advancing toward radar * Sea echo heights depend upon wave heights RECEIVED SEA ECHO SIGNAL STRENGTH Receding wave echo II RECEIVED FREQUENCY Transmitted signal I I I.I Advancing wave echo Transmitter frequency Figure 1. Sketch of first-order Bragg- scattering process and schematic of sea-echo Doppler spectrum. only two sets were significant (to first order) , just as though two dis- crete targets were producing all of the scatter. By deducing the velocity of these "target" ocean waves from their symmetrical Doppler shifts, and thence the wavelength of the scattering wavetrains, he found that the wavelength was precisely one-half the radar wavelength (for backscatter at grazing incidence along the sea). This is shown schematically in Fig. 1. Thus Bragg scatter — or the diffraction- grating effect — is the respon- sible interaction mechanism. Therefore, out of all the wavetrains present on the ocean surface, only the two wavetrains (or gratings) with a period precisely one- half the radar wavelength and moving radially toward and away from the radar produce the scatter. Crombie confirmed this explanation experimentally by noting that the unique "square-root" relationship between this Doppler shift and the radar carrier frequency followed the square-root water-wave dispersion relationship (between its phase velocity and its wavelength). A theoretical study [Wait, 1966] based upon a deterministic, periodic sea surface, and a different study [Barrick, 1972a] based upon a random sea- surface description both confirmed the empirically discovered scatter mechanism and also gave expressions for the echo amplitude. Crombie also first observed [Crombie, et al., 1970] that these echo peaks are often offset by a discrete amount from their symmetrical positions about the carrier frequency. This is illustrated in the measurements made from San Clemente Island and reported elsewhere [Barrick et al., 1974]. Fig. 2 shows a typical sample spectrum observed at 9.4 MHz. In these measurements, A represents the normalized Doppler-offset contribution due to the radial component of the near- surface currents, where ± 1 are the expected (normalized) positions of the first-order peaks. Thus, the radial component of current is deduc ed fro m such a radar record using the equation v = A • v , , where v , (= /gX/4Tr) is the phase velocity of the first- order Bragg- scattering waves (A being the radar wavelength, = c/f > where c is the free-space radio wave velocity and f is the carrier frequency). For the case shown in Fig. 2, v =22.5 cm/s in the direction toward the to cr radar, using these relationships. 2 . 2 Background Crombie [Crombie et al., 1970; Barrick et al . , 1974] and Stewart and Joy [1974] have been studying radar-deduced near-surface currents, both theoretically and experimentally. In Barrick et al . , [1974], Crombie shows 80 70- -A First-order sea echo -2 I Figure 2. Typical 9-sample average of 200-seoond surface-wave HF sea-echo power spectra at 9.4 MHz. Doppler frequency is normalized with respect to the expected position of the first-order Bragg peaks (here 0.313 Hz); A is the normalized shift of the record due to an underlying current. Narrow-beam radar is looking due west from San Clemente Island. 4 that the depths of the current flow that influence the Doppler offset produced by first-order scatter from the Bragg wavetrain lie within one twenty- fifth radar wavelength of the mean water surface. Hence to measure currents even closer to the surface, one would use a shorter-wavelength (higher- frequency) radar. At 30 MHz, for example, currents to a depth of about one foot would be detected by first-order Bragg scatter. Since the currents closest to the surface are most responsive to atmospheric driving forces — as well as being the most difficult to measure — our present system is designed to radiate near 30 MHz. Besides theoretical analyses, several experiments have already been performed to prove that not only is the concept feasible, but also suffi- cient accuracy is possible that a powerful but simple remote-sensing tool based on this concept can be developed. Both Crombie [in Barrick et al . , 1974] and Stewart and Joy [1974] have shown that the radial component of surface current can be measured to a reasonable precision; we cite results from the latter reference here. Using the joint NOAA/NAVY surface-wave radar facility on San Clemente Island and a drogue buoy operated by Scripps , verification of the concept was obtained. The buoy — drogued to drift with currents at a mean depth of about one meter — was tracked by a micro- wave radar as it drifted across the area observed by the HF radar, as shown in Fig. 3. The observing radar had a directional antenna that could look simultaneously in the two directions shown; many frequencies could also be utilized simultaneously. Fig. 4 shows the actual geographic track of the 340° T PACIFIC OCEAN X INDICATES POSITION OF CURRENT DROGUE SAN CLEMENTE ISLAND TRANSMITTER AND RECEIVER 20 km Figure 3. Configuration of HF surface-wave radar and its two beams on San Clemente Island. "X" shows initial position of drifting buoy. NORTH 1800- i P TIME M40 1600- • / 1400- / 1200- / Be 3 UJ U z 1000- 800- 600- •TIME 1350 400- 200- i TIME 1235 . . 200 400 600 DISTANCE (METERS) Figure 4. Drift of drogued buoy vs. time, starting at 1235 on 24 May 1972 at shown in Fig. 3 buoy (on May 24, 1973) vs. time, starting from the "X" in Fig. 3 at 1235. The current vectors radial to the HF radar along the two beam directions were deduced from this plot. Since this current — at a mean depth of one meter — would (according to the theory) be sensed by an HF radar at a frequency of 12 MHz, this mean radial velocity of the buoy was plotted in Figs. 5 and 6 at that frequency as the circle-dot; the other points are the radar-deduced radial current speeds. The error bars on the current speeds correspond to a Doppler resolution of 0.005 Hz (requiring a 200-second coherent integration time) . The buoy currents compare favorably with the radar- deduced currents. Also, it is expected that the currents very near the surface will be the greatest, since they are influenced most by the atmosphere. Under such a current shear, the higher radar frequencies should "see" greater currents than lower radar frequencies; this phenomenon is reflected in the plots of observed current vs. radar frequency shown in these figures. 5-1 -5- I I 10 FREQUENCY (MHz) 20-, _ 15- T I I I TIME: 1235- 1326 24 MAY 1973 5 10 15 FREQUENCY (MHz) 20 15-r E " 10- 5- Figure 5. Radar- deduced radial current velocities along the two beams corny or ed with buoy measurements . A i -i 0-| !| TIME: 1400- 1434 24 MAY 1973 -i 1 1 1- 5 10 15 20 FREQUENCY (MHz) 25-t =i 10- .j I TIME 1400- 1434 24 MAY 1973 1 10 FREQUENCY (MHz) 20 Figure 6. Radar-deduced radial current velocities along the two beams compared with buoy measurements . Our transportable radar under construction here differs from the San Clemente Island radar used in the above experiment in the method by which the azimuthal direction-of-arrival of the sea-scattered signal is determined. The San Clemente Island radar used the "brute- force" approach of employing a long antenna array (about 800 ft) to form a fairly narrow azimuthal beam. The system under development here, on the other hand, measures this direction of arrival by comparing the phase difference of the scattered signal at two or more closely spaced simple antenna elements (i.e., about 15 feet apart J. Although in principle it should be possible to sort out the directions-of- arrival of signals having differing Doppler shifts, the development of an operational station pair based upon this rather novel concept should have some preliminary experimental verification. Crombie et al. [1970] in fact performed such an experiment, in which they used two simple receiving antennas in Florida near Cape Kennedy to look east across the Gulf Stream. The concept was thus tested against the well-known gross features of the Gulf Stream in its south- to-north flow. For a semicircular radar resolu- tion cell (corresponding to a given echo time delay) the current to the south should produce positive Doppler shifts (with respect to the expected first-order Doppler position); the currents to the east, zero relative Doppler shift; the currents to the north, a negative relative Doppler shift. By measuring the echo phase difference, $(Af), between both antennas at each Doppler shift, Af, from the first-order peak, a, we should be able to determine the direction-of-arrival from the equation $ = k d sin a, where d is the (known) spacing between the two receiving antennas, and k is the (known) radar wavenumber, given by 2tt/A, X being the radar wave- length. This correspondence between Af, $, and a is illustrated in typical measurements at 6.92 MHz, shown in Fig. 7. The "spreading" of the normally narrow first- order Doppler peaks by the strong current is shown at the top, where the positive Doppler peak is seen to be stronger. The phase differ- ence, $, is plotted on the lower portion, and one can see the expected correspondence between the direction-of-arrival and Doppler shift (from the center of the first-order peaks) . Hence, research experiments have already demonstrated the validity of the concepts underlying the radar system under development. These prior experiments were research efforts, in the sense that data were recorded in the field and analyzed later. The present development program is aimed at: (i) building a transportable, turn-key system that can produce its final near-real-time output in the field, viz, a current-vector map; and (ii) determining the accuracy of the system in terms of range/azimuthal resolu- tion and current velocity measurement precision. Hence, the development of operational units is the next logical step in the progression of a new remote- sensing concept from the research stage to the routine operational stage. 2.3 Description of the Concept In order to construct a map of current vectors representing water transport near the surface, radar sea-echo signal must be processed in a special manner. Signals are needed from two coastal stations (separated 00 X 1* ' • 'is - — S:'-* *■';■• — I 1 i i i i i 1 1 - •e +2 1 1 -;l ! i i i i — + 1 -s -E -1 -2 - ,iii i i i i -N Figure 7. Upper: Doppler spectrum of current- smeared sea echo from Gulf Stream received by omni- directional antenna. Middle: Normalized magnitude of coherence function between two antennas for these spectra. Lower: Phase of coherence function between two antennas for these spectra (after Crombie et al. 3 1970). -0.4 -0.2 +0.2 +0.4 Doppler Frequency, Hz by tens of kilometers) are required to obtain a complete horizontal vector at any point, since those from one station alone can provide only the current- vector component radial to that station. Three basic quantities, then, are needed from two stations to produce a current map: (i) the range to the point at which the current vector is desired; (ii) the azimuthal angle to the grid point from a specified direc- tion; (iii) the radial component of current velocity. The first two quanti- ties pinpoint the geographical source of the echo, and the third represents the desired geophysical quantity to be extracted from the echo. The range, or distance, to the scattering point (or cell) is determined from the two- way propagation time of the signal; in other words, the time of pulse transmission is noted, and the time of receipt of the echo thereafter is directly proportional to the distance of the scattering patch from the radar. In the system being constructed, this echo sampling vs. time after transmission is done digitally, and the sequential time samples are referred to as "range gates". The radial width of a given range-gated scattering cell, called the range resolution, is directly proportional to the trans- mitted pulse width; for the pulse width of 20 us to be used here, the corresponding range resolution is 3 km. A given range resolution cell is 8 in reality a circular annulus; in all, approximately 24 range gates will be employed to give a maximum range from each station of ^ 75 km. The signal received from each range gate therefore represents the echo from an entire semicircle of sea (assuming the semicircle behind the radar lies over land). The azimuthal direction of arrival of the signal within a given range gate is determined from the phase difference between the signals received at multiple antennas at the same echo Doppler shift. For two antennas parallel to the beach, this phase (at a given Doppler shift from the first-order echo, Af ) , is $(Af) = k d sin a(Af), where k = 2tt/X (X is the radar wavelength), d is the distance between the two antennas, and a(Af) is the angle-of-arrival from the perpendicular to the beach/baseline. In order that the relationship between a and $ be unambiguous as a goes from -90° to +90°, it is necessary that d be less than A/2. At 30 MHz (X = 10 meters) for example, this spacing should be 5 meters or less. The phase comparison is done by digital computer after the echo from a given range gate has been digitized. The use of two receiving antennas can provide unambiguous direction of arrival only if the Doppler shifts due to the current from each point in the semicircular range- resolution cell are different. Such an assumption may not represent the actual current pattern under observation. A uniform current flow parallel to the beach, for example, will produce a different, unique, Doppler shift for each point on the semicircular scattering cell. A uniform current flow perpendicular to the beach, however, will produce a double-valued Doppler pattern, and with only two antennas, it will not be possible to distinguish the echo signal at -a from that at +ot . This double- valued ambiguity can be resolved, however, by using three receiving antennas and solving two sets of equations (digitally) in two unknowns. Likewise, a triple-valued current-pattern ambiguity can be resolved by using four receiving antennas. Since double- valued current patterns are considered possible, whereas triple (and greater) valued functions are considered much less likely, the presently planned system will use three receiving antennas 2-1/2 meters apart, arranged in a straight line. If initial field observations frequently show higher-valued current ambiguities, appropriate expansion of the receiving antenna system will be undertaken to handle these situations. The range and azimuth (and hence the grid-point position on the map) of a given sea-echo signal samplehaving been determined, the current-vector component at that point oriented in the direction of the radar is obtained from the Doppler frequency shift, Af, from the expected first-order echo position, f as v 1 = X Af. /2 (f D = /g/i\\ , with g - 9.81 ms~ ) , where D 1 , Z 1 , I ' D the subscripts refer to the radar station at which the observations are made. Then the total current vector at that point is then determined on the computer as the trigonometric combination of the two radial components for the given grid point. The hardware and software components required to perform all of the radar control, transmission, reception, and signal processing functions will be described in greater detail in subsequent sections o\~ this report. As an introduction to the overall design and operation, the actual flow of a signal through the system based upon the block diagram of Fig. 8 will be traced briefly here. The receiver is the most complex and costly piece of hardware in the system; it performs several functions, including the synthesis of the desired radar operating frequency and the generation of the transmitted RF pulse. A system timing circuit — or "clock" — generates all of the timing signals used in the system. In particular, it generates a digital 10 MHz bit stream and digital pulsing/gating signals (20 us wide, at a 1 kHz rate) and sends both sets of signals to the receiver. There the syn- thesizer divides the 10 MHz stream down, and then multiplies it back up again to arrive at the system operating frequency (between 25 and 35 MHz) selected by the operator. The pulsing signals from the clock are also used to form a low- level (10-dBm) RF pulse every millisecond at the selected operating frequency. This analog pulse stream is the basic transmitted signal; it is sent through the transmitter- driver where it is amplified to a 50-W peak-power level matched to a 50 fl impedance. After power-splitting, amplification through four identical solid-state power amplifiers, and a recombination process, the pulse signals are radiated at 2.4 kW peak (or ^ 48- W average level) through a semi- directive vertically-polarized Yagi V V Receiving Antennas Y, Receiver/STC & Synthesizer S/H & A/D Pre- Averaging 10 MHz Stream Pulse Generation/Gating Timing STC Stepper 1 d BM Pulse Stream, r = 20 \i%, PR F = 1 kHz Telemetry Link Transmitting Antenna V MODEM Coupler Transmitter Driver FFT Processor Main Memory Digital Information Analog Information Mass Storage Graphics Generator Video Monitor Keyboard/ Printer Terminal Digital Plotter Digital Tape Recorder System Computer (PDP 11/04) Figure 8. Overall block diagram of eurrent-maip-ping radar system. 10 monopole antenna array. All components in the transmitter/ antenna chain are matched to 50 Q for maximum power transfer. During the time of pulse radiation, the receiver is switched off by the timing signals to prevent burnout and then switched back on to receive the sea-scattered echoes. These echo signals are received on three simple, short vertical whip antennas designed to have very high (nearly infinite) input impedance. No attempt is made to "match" impedances at the receiver input because the predominant noise in the system is external noise (at < 30 MHz), and hence a low-noise- factor receiver front end achieved through careful matching and balancing is not required. In addition, short high- impedance antenna elements keep the antenna currents very low, minimizing the undesired effects of mutual coupling between receiver antenna elements and also with the transmitter antenna. Both the transmitter and receiver antennas are simple elements only a few feet high that can be erected in a matter of minutes. In actuality, only one receiving antenna is connected to the receiver at a time. In other words, immediately after the transmitter pulse is radiated, antenna #1 will be connected to the receiver input by the pulse timing signals. This antenna will remain connected to the receiver until the echo from the most distant patch of sea has been received (i.e., about 0.7 millisecond after transmission). Then antennas #2 and #3 are each sequentially connected to the receiver for similar periods, after which the process is repeated. The receiver also obtains digital signals from the sensitivity-time control (STC) stepper. This causes attenuation of various levels to be inserted in the recaiver IF gain stages in a pre-programmed manner. Since the maximum signals will be received immediately after transmission, because of the extremely strong echoes scattered at short ranges, the attenuation vs. time after pulse transmission decreases mono- tonically. This STC function is necessary to prevent saturation and undesired nonlinear effects that would occur, since the desired echo-signal dynamic range would greatly exceed the dynamic range of the analog-to- digital convertor if compensation for range were not made. The receiver forms an IF signal in the normal manner by mixing the RF signal with a local oscillator signal generated by the synthesizer. Two IF channels are employed: an "in-phase" channel (designated I) and "quadra- ture" channel (designated Q) . The signals through these channels are "balanced" to have the same amplitude, but are 90° out of phase with each other. This is one of the two usual methods employed when Fourier trans- formation of the signal is ultimately to be performed; it allows the signal to be mixed to a "zero-IF" before digitization, after which the signals from each channel form the real and imaginary arrays of the Fourier trans- form input. The Fourier transform output then contains signal power at both negative and positive Doppler shifts near DC. The zero (or baseband) IF signals out of the receiver have an informa- tion content approximately 1 Hertz in bandwidth (because of the nature of the sea echo), even though the actual signal bandwidth is much greater. These analog signals are "sampled and held" (S/H) every 10 us (the aperture time is less than 2.0 ns, during which the signals are constant). These signals are then digitized, and from this point on, all processing is 11 digital in nature. Even though the signals are digitized every 10 us, only every other sample is ultimately used; these alternate digital samples thus each represent sea echo from consecutive 20 us range gates. Only the signals from the first 32 range gates after every pulse transmission are retained for processing, even though there are actually fifty 20 us time intervals available between consecutive pulse transmissions. Since consecu- tive pulses are received sequentially on each of the three antennas, it takes 3 ms for the signal on a given antenna to be sampled again. Hence 3 x 32 = 96 total samples for both the I and the Q channels are obtained every 3 ms. These signal samples then pass through a digital component that pre- averages them for one-half second. In other words, for the I channel and antenna #1 and, say, range gate #7, two samples arriving every 3 ms for a total of one- half second are added together to form an averaged signal. Thus the digitization process (at a one-third kHz rate per range gate per antenna) and the pre- averaging process effectively reduce the signal band- width to 2 Hz (i.e., -1 Hz to + 1 Hz), or about twice its intrinsic value for ultimate processing. For each of the 32 range gates, for each of the three antennas, and for both the I and the Q channels, there are therefore 167 (rounded from 166 2/3) pulses averaged to form 32 x 3 x 2 = 192 digital samples every half second. Each of these 192 samples being obtained every 0.5 second is stored in a memory component for a total of 256 seconds until a total of 192 x 256/0.5 = 98,304 samples are collected. At the end of 256 seconds, each of the 96 I and Q channels has produced a time- series array of 512 digital samples, and these then ultimately become the real and imaginary parts of the input to the fast- Fourier transform (FFT) processor. Therefore as many as 96 complex Fourier transforms, each of 512-word length, must be calculated every 256 seconds in order for the system computer to keep up with the data input, or to work in "real-time"; this will in fact be accomplished with the system under construction with no difficulty. The computer input /output bus serves as the transfer point between digital hardware components for the processing of all digital data. After FFT processing, the data arrays are ready for the mathematical algorithms that extract the radial current velocity at each of the predetermined set of grid points (roughly 3 x 3 km apart) . The echo signal-to-noise ratio is checked at each Doppler frequency shift for each range gate and antenna; if it does not exceed a predetermined threshold, the signal sample is discarded. If the signal-to-noise ratio exceeds the threshold, the azimuthal angle-of- arrival is extracted from the three antenna samples at each Doppler frequency, and a running average over several 256- second samples is computed. For each range gate, a curve is fit to the data points giving Doppler frequency vs. azimuthal angle- of- arrival. Each grid point on the desired map is then converted to range and azimuth angle for each radar location. Interpola- tion procedures are used to find the proper range gate samples; then from the digital "curve" or array of Doppler frequency vs. azimuth angle, the Doppler is found at the desired grid point. From this, the radial current velocity at that grid point is found. These radial current velocity values are then stored until they can be combined trigonometrically with those from the second site to produce the final output, a current -vector map. The total radar operating time required to produce one such map could range 12 from five minutes to two hours, depending upon a number of factors; the optimum measurement time should ultimately be selected only after field experience. SYSTEM HARDWARE 3.1 Digital Components This section presents a brief description of the properties and functions (as they are seen at the present state of progress) of various digital components of the current-sensing-radar system, as configured in the block diagram of Fig. 8. In some cases, two or more devices represented function- ally as a single block in that figure are actually combined constructional ly on a single chassis board. Certain of the devices to be described here have been designed and constructed "in-house"; others have been purchased from commercial sources. Nearly all of the digital hardware that is to be employed with the system in the field is to fit in one (of two) weatherproof fiberglass cases containing shock-mounted racks. Fig. 9 is a photo of the total field system at one site, with the digital gear contained primarily in the left case and the RF gear in the right case; each case is 40" high x 24" wide and will weigh less than 200 pounds, capable of being handled by two persons. Each of the major digital hardware items is described below: Figure 9. Current-sensing-radar components mounted in their fiberglass oases for field use. 13 3.1.1 A/D Hardware 5 System Timing Module Three functions represented in Fig. 8 have been combined into a single hardware module: (i) the sample and hold (S/H) and analog- to-digital convertor (A/D) functions; (ii) the pre-averaging function; and (iii) the system timing function. This module has been designed and assembled in- house; a photo of the module is shown in Fig. 10, and a block diagram is shown in Fig. 11. The S/H and A/D convertors represent the first digital component in the signal flow through the receiver chain. Two analog signals are output from the receiver into this device, one each from the I (in-phase) and Q (quadrature) channels; these signals are "zero- IF" (centered on DC or zero frequency) with a bandwidth of approximately 50 kHz (the reciprocal of the pulse width). Each then passes into a Philbrick 4855 sample- and-hold circuit with an aperture uncertainty time of 0.25 ns. (This "fast" apertur- ing eliminates the possibility of phase jitter in the subsequent digital samples representing the range- gated signals) . From there, the signals are converted to 10-bit binary digital numbers by two Philbrick 4131 analog-to- digital convertors every 10 us*. The output of the two channels (I § Q) at this point now consists of two streams of 10-bit numbers, which represent samples of the analog signals taken every 10 us. In order to eliminate Figure 10. A/D hardware and system timing module. * The receiver signal is actually sampled every 10 us, even though indepen- dent range gates are obtainable only every 20 ys because of the 20 us pulse width; subsequently, however, only every other sample word is to be retained for processing. 14 Latch Philbrick 4855 S/H Philbrick 4131 A/D I Receiver ■ 1 n. o ' - t -I mi -*o 1 Channel 6 Bit Multiplier Adder Jigitjl Receiver Philbrick 4855 S/H Philbrick 4131 A/D II Q Channel Power Supply ROM Weighting Table ! Float ng Analog Front End 1 Digital Pre-Averaging Device Computer 16 6.1 In erlace Computer I/O 8us | System Timing Circuit HP 10 MHz Oscillator W Comparator n_n Schottky Divider Change S> System Timing Line Driver 10 MHz to Receiver Synth eiizer Figure 11. Block diagram of A/D hardware and system timing module. interference caused by ground current loops through the chassis and elec- tronic components, the analog front end of the module is coupled into the digital hardware by means of solid-state optical isolators. The second function performed within this module is the pre-averaging. This digital operation has the same effect as a filter whose bandwidth is the reciprocal of the pre-averaging time, in this case (nominally) one-half second. To simulate a good filter with a sharp rolloff in the frequency domain, these digital time samples are weighted in a predetermined manner before being averaged. The weighting constants multiplying the digital samples are stored in a read-only memory (ROM). After multiplication, the samples are summed for one-half second by TTL 74181 ALU-chips (arithmetic logic units) and stored in a Type-2102 MOS memory array. The output is then transmitted to the computer I/O bus through a commercial non-processor request (NPR) interface supplied by MDB Systems, Inc. (This interface device is also used in the fast-Fourier transform processor.) The third function performed in this module is system timing. The heart of this device is a temperature-controlled 10.0 MHz Hewlett-Packard oscillator having a drift less than one part in 10 (within one second). All timing signals (for carrier frequency synthesis, pulse generation. IS sample- and- hold, computing sequencing, etc.) are obtained by using this signal in combination with digital dividers and combinatorial logic. The basic precision of the oscillator allows measurement of received Doppler shifts to an accuracy of 0.002 Hz at the 30 MHz carrier frequency. 3.1.2 Semiconductor Mass-Storage Module This unit is shown functionally in Fig. 8. Basically, it accepts and rearranges the output digital data from the A/D Hardware £ System Timing Module in a form that can readily be used to fill the input arrays required of the FFT module. It consists of a 32K by 18-bit-word semiconductor memory that is configured (in conjunction with a Line-Tape digital recorder unit) to operate like a magnetic disk storage device. By storing one- fourth of the data required every 256 seconds for all of the Fourier- transform processing, it will repack this data on magnetic tape in four sets of blocks; hence for each of the three receiving antenna channels and each of the 32 range gates, all 512 words (each) of the I and Q channel data are packed on the digital magnetic tape sequentially. These two sets of 512 words (stored and packed 128 words at a time) represent the real and imaginary parts of the signal time series (each word is one-half second apart in time) that become the input to the FFT. The semiconductor memory cards are manufactured by EMM, Inc., and utilize 4K by 1-bit static memory elements. The module was assembled in-house and is shown in Fig. 12. Figure 12. Semiconductor mass-storage module. 16 3.1.3 Fast- Fourier Transform (FFT) Processor By designing and constructing this module in house, we have arrived at a unit that is extremely fast at a considerably lower cost than commercially available FFT processors. A block diagram of the unit is shown in Fig. 13. A 512-point (complex) Fourier transform requires approximately 7 ms to complete, excluding input/output time. (This time can be reduced to ^ 3 ms by replacing the present Type-2102 MOS memory in the module with Type-93415 bipolar memory). The speed is made possible by a state-of-the-art two-chip 16-bit binary multiplier. This device, manufactured by AMD, Inc., allows a complex-multiply operation to be performed in ^ lys. While only 512-point complex transforms are now currently envisioned, the present module contains sufficient memory storage for a 1024-point complex transform. A photo of the module is shown in Fig. 14. 3.1.4 Line-Tape Recorder This storage device from Computer Operations, Inc., (Fig. 15) was selected over alternatives (e.g., "floppy" disk or large 7- or 9-track tape drives) primarily because of its extreme reliability and compactness. (A dual-track redundant phase-recording technique is employed.) The tape is used in conjunction with the Semiconductor Mass-Storage Module (discussed in Section 3.1.2) during system operation. Its principal function, however, is to store the final output surface-current-vector data required to produce a map (after combination with similar data from the other site) . The unit stores approximately 147K by 16-bit words of digital data on a 300- foot spool of 1-inch magnetic tape. 3.1.5 PDP 11/04 Minicomputer The heart of all of the digital signal processing and radar control programming is the PDP 11/04 minicomputer (Fig. 16); it was purchased from the Digital Equipment Corporation, Inc. One is required at each site. The reader is referred to company manuals for a complete description of this device. The computer mainframe contains additional room for other digital devices. Following are the interfaces that are to be inserted into the computer mainframe and extender chassis for use in the current- sensing radar: a) 28K words of semiconductor parity memory with battery backup. b) Hardware multiply/divide unit. c) ROM diagnostic routines. d) ROM trig- function lookup tables. e) Line-Tape interface. f) Two asynchronous communication interfaces. g) A/D Hardware $ System Timing Modulo interface. 17 F> £ •9 , .Sis k> » T=I>-t *» ^> if eS< =5> «5 E o S/5- E o .#< ^3 I* O CO to cs> t I to g I h CD LA 7T I 3 3L See O'- er X oj to c in to CM o*2 r: in "3" — x \7 — X s 5 oe-B s s B .5 25 E H Is s>s cO O.CJ fc» -_ J- O 3 S !!§ = E g c « a .5 E CD |— a a n to O O DDDDttf co I o CO o c«3 <3i 18 Figure 14. Fast Fourier Transform module. Figure 15. Lino-Tape recorder. 19 Fvgure 16. PDF 11/04 minicomputer. (Front panel to be used is from PDP 11/34 minicomputer.) h) Semiconductor mass- storage interface. i) FFT processor interface. j) Receiver interface. k) Digital plotter interface. 1) Video graphics interface. m) System status interface. 3.1.6 Keyboard/Printer Terminal The operator communicates with the radar system entirely through this device. It was purchased from Texas Instruments, Inc., and is their "Silent 700 Terminal" (Model 735, shown in Fig. 17) . The terminal operates at a rate of 30 characters per second (300 baud) . The printed hard-copy output employs a thermal process to form the characters. 3.1.7 Graphic System •Plots, curves, and other pictorial data (including the final current map) can be displayed for the operator by this 10- inch Conrac rack-mounted video monitor. The input to this scope monitor comes from a graphic generator manufactured by Intermedia Systems, Inc. The overall system is capable of 20 Figure 17. Keyboard/printer terminal. displaying 65K points of data in a 256 x 256 grid on the video scope monitor, Data from the computer, to be displayed, are stored on the graphic generator board in a 4K by 16-bit dynamic memory. A hard- copy map of surface currents (as well as hardcopy of other desired graphic outputs) is obtained from the Zeta Research digital incre- mental pen-plotter (Model 130, capable of 300 steps per second). The plotter — as well as the video graphic system — is driven by a version of Calcomp software developed in-house. 3.2 Transmitter The transmitter system was designed in-house because a suitable device could not be found commercially; currently available transmitters are both too large and too expensive. The transmitter chain designed and built here consists of three submodules (see Fig. 18 for a transmitter block diagram): (i) the control and power submodule; (ii) a low-level driver amplifier; (iii) four high-level final amplifiers. The input to the driver amplifier is a +10-dBm, carrier- frequency, 20 us RF pulse from the synthesizer portion of the receiver. The RF pulse has been "pre- shaped" in the time domain to effect a bandpass filtering of the signal, in order to contain the signal energy within specified frequency limits. The driver utilizes three stages of broadband (capable of operating 21 A/V^ Input lOdBM Attenuator son 0-10dB 1 Driver Amplifier 1 Low- 12W 50 W (<40MHz) 12W 12W 12W Breaker for Output Overload 30V IDA ^ Protection Control Module 2h Storage Capacitor 12000 /if Power Amplifier Power Amplifier 600 W 600 W Power Amplifier 600 W Power Amplifier 600 W 2.4 kW Low-Pass Filter «40 MHz) o cc S Power to Amplifers Figure 18. Transmitter /Amplifier block diagram. from 2 to 35 MHz) linear push-pull amplifiers, operated photo of the driver unit is shown in Fig. 19. •Class AB". Output power from the driver is to be a minimum of 50 watts across the band from 25 to 35 MHz. This driver output is applied to a low-pass filter with a cutoff of 40 MHz in order to prevent transmission of spurious har- monic interference (at 2, 3, 4, ... times the carrier frequency). The low- pass filter output is then coupled to a 4:1 power splitter, which in turn is connected to the input of each of four final-power amplifiers. The final amplifiers utilize four TRW PT9780 transistors configured in two push-pull pairs. A fifth transistor (a TRW PT9780) is used as a tempera- ture sensor in the AB bias system to prevent thermal runaway. The amplifiers employ ferrite- loaded brass tubes as broadband transformers. (The ferrite loading is required only at the lower frequencies.) The amplifier gain is ^ 16 dB at a peak-power output level (per final amplifier) of ^ 600 W from 25 to 30 MHz. This level is obtainable only under the low duty- factor operation of the present system (i.e., a 20 us pulse at a 1 kHz pulse- repetition frequency gives a duty factor of 2%) . The positive temperature coefficient of the PT9780 emitter-ballast resistor causes the power output to drop as the device temperature rises. The heat sink for these amplifiers has been designed to handle the normal 2% duty- factor operation, but a high-level sustained CW output cannot be tolerated. The present unit has 22 f / Figure 19. Prototype transmitter driver-amplifier. shown no tendency toward instability in laboratory tests, and has shown an ability td survive both open and short circuits on the amplifier output. A photo of the amplifier is shown in Fig. 20. In order to generate over 2000 W peak power at 30 V (for all four amplifiers), a power supply must be capable of delivering almost 100 amps of current during the pulse duration; a unique power supply was developed for this purpose. This supply operates by charging a special Sprague low- impedance, high-current capacitor from a 30-V, 10-amp switching regulator at a controlled current level. During the 20-us pulse passage (through the amplifier), the required high current is supplied by discharging the capaci- tor. In the event of a timing failure, in which a CW signal (instead of a pulse) would appear at the amplifier input, the capacitor would simply discharge to a low level to prevent sustained large currents that would produce overheating. Also, if a voltage standing-wave ratio (VSWR) detector at the transmitter output senses the presence of either an open or short circuit across the antenna system, a relay opens so that the capacitor cannot be charged, causing the system to shut down. Either of these fail- ures will cause an error condition message to be sent to the computer, which in turn notifies the operator by means of the system console. Final ly, additional circuitry is included to provide a hard "shutdown" of the trans- mitters between pulses in order to prevent amplification and radiation of broadband noise; if unchecked, this can be a problem with linear amplifiers. 23 Figvcre 20. Final transmitter -power- amplifier. 3.3 Receiver The receiver is by far the most sophisticated RF component in the current- sensing-radar system. For lack of time and experience, we have contracted out the design and construction of this item to Barry Research, Inc. It will be discussed here, therefore, from the standpoint of a func- tional block diagram and the parameter specifications that the contractor is meeting. Fig. 21 shows the receiver block diagram. The heart of the receiver is the frequency synthesizer. It generates both the (selected) transmitter carrier frequency, as well as all of the frequencies required for mixing in the receiving process. Let us start first with the transmitted signal. The frequency synthesizer receives a 10 MHz stream of square pulses from the A/D Hardware £ System Timing Module. The 10 MHz frequency of this input is divided down to 200 kHz within the synthesizer, so that any frequency between 25 and 35 MHz can be selected in 200 kHz increments. The operator in fact determines the frequency by means of a thumbwheel "channel selector." The CW signal from the synthesizer then passes through a gate, whose duration and timing is also controlled digitally by the A/D Hardware S System Timing Module. This gate forms and shapes the pulse-modulated carrier signal (at a +10 dBm level) which then passes into the transmitter driver. Part of the CW carrier signal from the synthesizer passes through the calibration box, which square-wave modulates the carrier at a 0.5-Hz rate. The signal is then available at the receiver input for calibration purposes; 24 «-1 CO it will emerge from the receiver with energy at the usual 0.5-Hz sidebands of a square-wave signal. The operator can select the power level of this calibrate signal to be either -17 dBm or -57 dBm; these power levels will produce 0.5 Hz sidebands at the output of -37 dBm and -77 dBm, respectively, for reference purposes. The actual receiving process starts some 20-40 us after radiation of the transmitted pulse. During transmission, the receiver front end is shorted by a blanking signal (also from the A/D Hardware § System Timing Module) in order to prevent damage from the intense transmitted signal. Then one of the three antennas is switched to the receiver front end by PIN diodes for a duration of ^ 940 us; the digital switching signals also come from the same timing submodule. Because the received sea-echo signal power on the average decreases with range, R, (or time after transmission, T) at a rate greater than R (or T ), the received signal dynamic range will greatly exceed the 60 dB dynamic range of the A/D converter. (The radar receiver has a dynamic range of 100 dB at a 20-dB signal-to-noise ratio.) The usual radar technique employed to make the received signal's large dynamic range compatible with the limited A/D converter dynamic range is to use what is referred to as a sensitivity-time control (STC) . This means that the effective receiver gain is switched in pre-programmed steps as a function of time, to remove the signal falloff with time. In our Barry receiver, this is accomplished in two stages. In the first, PIN-diode attenuation steps are switched in, providing attenuation from -1 dB to -40 dB vs. time. The second stage switches in amplification steps, from -5 dB to +75 dB vs. time. The stepping sequence for both of these STC stages originates with a 7-bit binary code originating in the computer; this passes into a digital-to-analog (D/a) convertor which converts the digital signals to attenuation/amplification steps for the two STC stages. The actual attenuation/amplification steps are stored in random- access memory (RAM) buffers of a computer interface, and are transmitted to the D/A convertor as a 7-bit code; the step- change rate (i.e., every 20 us, corresponding to the pulse/range-gate resolution) originates from the system timing submodule. Before each "map-run" begins, the computer determines the attenuation/amplification steps vs. time by sampling the returns from each of the first 32, 20-us range gates during a test transmission. The entire STC process allows greater signal dynamic range, thereby allowing maximum signal resolution by the A/D convertors and subsequent FFT processor. The received frequency at the transmitter and receiver front end will in practice be selected from the region between 25 and 30 MHz (although the receiver is capable of operating between 2 and 35 MHz) . Subsequently, the signal is mixed to a fixed IF value of 40 MHz. After the second STC stage, the signal is mixed to a second fixed IF value of 500 kHz; the signal is band-pass limited at 40 MHz with a crystal IF filter bandwidth of 50 kHz, the reciprocal of the pulse width. Finally, two channels at a zero IF frequency value are generated by mixing two 500 kHz reference signals (from the synthesizer) — one shifted by 90° with respect to the other — to form the receiver output I (in-phase) and Q (quadrature) signals required for subsequent complex Fourier transforms. 26 An AM output channel is also provided (50 kHz wide) to allow the operator to switch off the transmitter and "listen" at various possible frequencies to make sure he is selecting a channel free of interference. The receiver front end has been designed with a noise figure of 10 dB; this is adequate below 30 MHz because the dominant noise is external to the system. The receiver has also been designed to provide "status" signals from various locations within the module to indicate to the operator the integrity of the receiver. 3.4 Antennas Radar systems that can scan and map the echo return over areas with reasonably good resolution are typically many wavelengths in physical size. At HF, this often involves antenna lengths of hundreds of meters, which in turn requires leasing large amounts of land. Therefore, the antenna for many previous HF radar systems has been the major factor limiting mobility and driving up the cost. The azimuthal mapping techniques discussed pre- viously were selected so that the antenna size and complexity could be reduced. Our antenna systems have dimensions no more than a few meters, and consist of simple elements — resembling the "vertical whip" automobile antenna — which can be erected and dissembled on the beach in a matter of minutes. As it turns out, the antennas are one of the lowest-cost com- ponents of the system. 3.4.1 Transmitting Antennas The transmitting antenna is to be partially directional. Fig. 22 shows a photo of this antenna. It is known as a vertically-polarized Yagi monopole array, and is to consist of three or four vertical elements. Only one vertical element in this type of antenna receives the input power from the transmitter; the others are known as parasitics, and serve to direct the radiated power forward. It is anticipated that the radar system will be allocated approximately six frequencies slightly below 30 MHz by the Interdepartmental Radio Advisory Committee (IRAC) ; the operator will select the particular frequency for a given operating period at the site, choosing the "cleanest" channel (free from noise and interference) . Therefore the transmitting antenna must be capable of being "matched" to the particular frequency selected by the operator. Matching is a problem at HF that is germane to transmitting antennas only. The ultimate objective of the transmitter portion of the system is to illuminate the desired sea area with the greatest possible power. This is possible only if the radiation resistance of the transmitting antenna is equal to (or matched to) the output resistance of the transmitters and characteristic impedance of the transmission line; in addition, the total reactive portions of the impedance in the antenna and transmission line/ transmitter outputs must cancel. Antennas of the type shown in Fig. 2 J, 27 Figure 22. Transmit antenna. with the advantage of being simple and compact, nonetheless have the dis- advantage that their input impedance varies with frequency. Therefore, although the antenna can be readily designed to be matched at one frequency, it can be badly mismatched .at another operating frequency selected later, only two or three megahertz away, and hence radiate poorly. Optimal match- ing can be achieved at a given frequency (while retaining the desired radiation pattern) by varying the heights of and spacings between the vertical whips. Thus the mechanical design calls for telescoping whips and sliding sections of the metallic basebar. It is intended that the antenna will be precalibrated by tuning it to each of the frequencies allocated by IRAC. The spacings and whip heights corresponding to the matched condition at each of these frequencies will then be marked on the sliding elements. Hence the operator in the field — upon selection of his operating fre- quency — would slide the various antenna elements to their respective "matched" positions. The general Yagi antenna has been used for many years, and much is known about its performance. It has the desirable properties of maximum gain (at a given frequency) for minimum size. We need to know the precise quantitative relationships between the number of elements, their heights, spacings, and the electrical properties of the nearby ground, as these 28 affect the radiation pattern, input impedance, and bandwidth of the antenna. To this end, we are having a team at LLL (Lawrence Livermore Laboratories) — leaders in the field of digital antenna design/optimization — do a study of these parameters. Preliminary results from the LLL study have shown that the input impedance can be designed to be 50 Q (purely resistive, and hence matched to the transmitter output/transmission line system) by varying the element lengths. For example, at 25 MHz, using one-inch diameter vertical elements, we can construct a three-element Yagi having 50 Q, input resistance with the following dimensions: reflector height = 3.19 meters; driver height = 3.19 meters; director height = 2.57 meters; reflector-driver spacing = 2.70 meters; driver-director spacing = 0.627 meter; the 3 dB beamwidth of such an antenna is. 150°. A four-element Yagi matched to 50 9, at 25 MHz has the following dimensions: reflector height = 3.19 meters; driver height = 3.19 meters; first director height = 2.57 meters; second director height = 2.57 meters; reflector-driver spacing = 2.70 meters; driver-first director spacing = 0.75 meter; first-second director spacing = 4.624 meters; the 3 dB beamwidth of such an antenna is 88°. At 30 MHz, the 50 Q input resistance is achieved for the above three and four- element Yagis by merely changing the heights of the vertical elements, but leaving the spacings the same (the beamwidths remain essentially the same also). The input impedances for the above antennas vary less than 1 Q (about the nominal 50 9, input) across a band ± 50 kHz about the carrier; since the total signal bandwidth is 50 kHz, the antenna bandwidth will not distort the signal in any signi- ficant manner. The implications of the above on the mechanical design and field utilization are important. Essentially, the only thing that needs to change based upon the selected operating frequency is the element heights; the remainder of the antenna mount is fixed. Thus, elements having different heights would be cut for each operating frequency; the proper set would be screwed into the base upon selection of this frequency. The decision as to whether to use a three or four-element antenna would be made in the field by the operator, depending upon whether the particular coastline geometry would call for a wide or a narrow antenna beam pattern. Other results of the LLL study concern the configuration of an acceptable ground screen beneath the Yagi array. By plotting the magnitudes and directions of the electrical currents that would be induced in a perfectly conducting earth, ground screen wires can be configured beneath the antenna in the proper directions, especially where the currents are strong. LLL studies show that our several radial wires shown in Fig. 22 in front of the antenna (running into the sea) are important; those behind the antenna are less important, and can either be shortened or eliminated. 3.4.2 Receiving Antennas The receiving system consists of three separate antenna elements whose signals are processed and recorded independently. By computing the phase 29 differences between the signals at the three antennas, the azimuthal direc- tion of arrival is obtained in the digital processing system following the receiver. The mathematics of the present computer software calls for the three antennas to be arranged along a line, with an equidistant spacing no more than one-half wavelength. Fifteen feet between elements, for a total length of 30 feet, is planned. The elements are switched on sequentially, during consecutive pulse transmissions (every millisecond). Hence, each receiving element — acting alone — has an omni-directional (azimuthal) receiving pattern. The receiving antenna system has already been built, and a photograph is shown in Fig. 23. The exact spacing and antenna baseline orientation are parameters entered by the operator during measurements. There are no stringent criteria for the hardware design involved in an HF receiving antenna, as there are for the transmitting antenna. The effect of a mismatch at the receiving antenna terminals will cause the internal noise (generated at random electron motion) in the receiver front end to increase relative to the externally received signal power. At HF, however, (in contrast to the microwave region) , external noise (from atmospheric sources) dominates internal noise typically by 30 dB. There- fore, even if the front-end internal receiver noise were to increase by 20 dB relative to the total externally received signal, the external noise would still dominate internal. noise by 10 dB. Hence most HF receiving antenna systems will merely connect the element to (essentially) an infinite imped- ance receiver front end. This technique is planned for our system also, where the whip elements are to be kept electrically short (e.g., 3 feet) with a high (reactive) intrinsic impedance feeding into a high- impedance receiver input. Such high impedances also have the desirable effect of Figure 23. Receiving antenna system. 30 keeping currents on the antenna elements low, minimizing the coupling between receiving elements and also with the nearby transmitting antenna. SYSTEM SOFTWARE 4.1 Radar Signal Generation/Processing Timing In Section 2.3 we briefly explained the signal and information flow through the system, using the overall block diagram of Fig. 8 to explain the operation of the radar. In this section — as a prelude to discussions of the system software — we describe in detail the sequence of events that occurs within the system during normal radar operation. This sequence of functions must occur automatically and routinely; individual operations in this sequence take place in almost every component of the system (e.g., at the receiving antenna terminals, in the receiver, transmitter, A/D hardware, pre-averaging subsystem, FFT processor, computer, mass storage device). Digital signals from a single system timing unit (specifically, the 10 MHz pulse stream originating in the A/D Hardware § System Timing Module) represent the basic source that controls the timing of all of these events. The sequence of events is best illustrated schematically by the system timing diagram shown in Fig. 24. The sequence can be assumed to begin at t = when receiving antenna whip #1 is connected to the input of the receiver through a three-way PIN-diode switch. At this time, a 20-us shaped pulse is provided by the receiver and passes (instantaneously) through the transmitter amplifiers. It is broadcast from the Yagi trans- mitting antenna at ^ 2 kW power level. During this transmission time, the receiver input is shorted to prevent damage from the intense radiated pulse. Shortly after t = 40 us, the receiver is reconnected to the antenna system and begins detecting the echo pulse. At t = 60 us the two A/D convertors digitize the zero- IF, I and Q channel outputs from the receiver. Thus two "blank" pulse periods are left after the transmitted pulse clears the antennas but before signal processing begins. This process therefore ignores the scatter from a circle around each radar out to 6 km, and hence eliminates echoes from unwanted strong "reflectors" (such as towers or buildings), but results in loss of very little sea current information on the basis of a geographic grid of points every 3 x 3 km. The sampling and digitizing process continues, with digital samples being weighted and retained in the pre-averaging memory every 20 ys until 32 such samples are collected (at t = 700 ys) . Each sample represents the instantaneous echo from one "range gate", with contiguous range gates separated by 3 km. The total range extent from the radar unit permitted by 700 ys delay is 'v. 105 km. (It is not expected that sea echoes will be received above the noise beyond about 70-80 km because of the extreme path loss at greater ranges.) Since both I and Q channel data for 52 range 51 s CO 0) C5i 1*4 32 gates are being collected, a total of 64 locations is reserved in the pre- averaging memory for these samples from antenna whip #1 within t < 1 ms. At t = 1 ms, the above process is repeated (beginning with the trans- mission of another 20-ys pulse) , but now antenna whip #2 is connected to the receiver. These samples are stored in I and Q memory locations 65 through 128 within the pre-averager. At t = 2 ms, the same process is repeated, but with antenna whip #3 feeding the receiver; the corresponding pre-averaging memory locations reserved for these samples are 129 through 192. The entire scan sequence switching through the three antennas is now repeated, beginning at t = 3 ms. The resulting 192 samples from t = 3 ms to t = 6 ms are weighted and added to the previous 192 samples stored in the pre-averaging memory. This sequence repeats itself every 3 ms , with running, weighted sums being stored in each of the 192 pre-averaging memory locations. It ceases after one-half second (at t = 501 ms, to be exact); at this point, 167 samples have been collected and added for each range gate and each receiving element to form the 192 weighted sums remaining in the pre-averaging memory. At t = 501 ms, the 192 samples in the pre- averaging memory are transferred through the computer input/output bus to the semiconductor mass storage device. The I and Q channel samples for each of the 32 range gates and for each of the three antennas thus each forms the first complex point in the array of time samples to be Fourier transformed. A total of 96 Fourier transforms are to be taken ultimately (32 range gates times 3 antennas). At t = 501 ms, the process described in the preceding paragraphs repeats itself, terminating at t = 1.002 s, after which time the second complex point of each of the 96 Fourier transform input arrays has been collected. This entire sequence repeats itself every 501 ms, until 512 complex time-series points have been collected as the input for each of the 96 Fourier transform arrays. This collection is completed at t = 256.512 s (after ^ 4.27 minutes). At this time ( t > 256.512 s), the 96 complex 512-point Fourier trans- forms are taken sequentially in the FFT processor. Allowing at most 10 ms for one 512-point transform means that all transforms can be completed in ^ 1 second. Theoretically, a current map can be constructed with one set of such samples (i.e., after only one 256.512-s run of radar operating data). If any portion of the radar signal is random, however (e.g., be- cause of the random amplitude of the sea echo, or the random noise signal, or the random fluctuations in the surface current) , it may prove desirable to "average" the results of several such 256-second transforms, to obtain an "average" current map. In this event — which is an option available to the operator — the radar continues with new Fourier- transform cycles being repeated every 256 seconds ( 4-1/4 minutes) until the operator judges that an adequate data run has been completed, at which point he terminates operation of the system. Note that no "complete" current vector map is possible until the data from the second site (operating simultaneously but at a second, non-inter- ferring frequency) are combined with the data from the first. The computer processing required for this combination and final map production will most 33 likely be performed immediately after cessation of the radar operation, although there is no reason this cannot be done during radar operation. In fact a map in fact can be produced as soon as the data from one site can be transmitted (e.g., by telephone or telemetry) to the other. 4.2 Control Software 4.2.1 Interfacing Items Necessary for Understanding of Software Control software designates the programs (mainly machine language) that permit the operator to interact effectively with and control the operation of the entire current -sensing- radar system. No attempt will be made here to provide a detailed listing of the software; several of the programs have not yet been completed, and some are currently undergoing modification. Rather, the following three subsections will describe the typical functional interactions between the operator and the radar system for which the software is being written. The present subsection discusses the fundamental tools upon which the use of the control software is based. RSX11S is the designation of the "operating system" (supplied by the Digital Equipment Corporation, the manufacturer of the PDP 11/04 minicom- puters to be used in the radar units) selected for use in the field. The operating system is' the fundamental software that controls the operations performed by the computer; it permits real-time multi-tasking within the machine. Since there are many tasks to be performed within the computer — both simultaneously and sequentially — the operating system interleaves and schedules these required tasks. The tasks themselves may have been preprogrammed in assembly language, FORTRAN, or Basic. The required portions of RSX11S — along with the control, processing, and display software tasks — are loaded into the PDP 11/04 memory from the Line-Tape unit before the operator begins a radar run in the field. The Line-Tape recorder is used for two other functions during radar operation. After RSX11S and the associated tasks have been loaded into the machine memory, a blank tape reel is placed on the drive. This reel is first employed simultaneously with the radar operation and real-time data processing as a temporary storage medium; in conjunction with the semi- conductor mass- storage device, data are rearranged in array form to be used as the complex input to the FFT processor. Finally, the tape is utilized to store a permanent copy of the current map. All communication between the operator and the system occurs through the Texas Instruments "Silent 700" terminal and the video display monitor (a cathode ray tube) . The former unit not only provides a keyboard from which the operator enters commands, but also gives a permanent hardcopy printed output of these commands and the routine status of the system (similar to a "log") . The video display monitor will display graphic data for the operator, such as sea-echo Doppler spectra and current-map data; if 34 he desires, the operator can obtain a permanent hardcopy of such graphic output on the Zeta digital plotter. A MODEM with an acoustic coupler provides digital communication between the radar sites by way of either a 172-MHz telemetry link or a normal telephone (where the latter service is available). Thus, map data can be transferred between sites so that a complete map can be constructed. In addition, the site operators can communicate with each other (by voice) using either the radio or telephone. 4.2.2 Prelude For the sake of discussion, the system control software is divided into three groups, depending upon when it is being executed. The prelude group includes those functions performed between man and machine before the actual radar data- taking begins. Software for these functions is best described by illustrating the interactions that occur between the field operator and the system at the keyboard terminal. First, the operator turns on the system power, the computer, and then loads RSX11S (and the associated system tasks) from tape into the PDP 11/04 extended memory; he immediately replaces the tape reel with a blank. The computer then automatically performs diagnostics on itself and on other system hardware to make sure everything is running as per design; if any fault occurs, the computer will print out (at the terminal) where the fault occurred and what happened. When everything in the system has been automatically checked out, the computer will query the operator for pertinent processing data. These data include: (i) time and date; (ii) geographic position (latitude and longitude of the two sites); (iii) receiving antenna baseline orientation; (iv) radar frequency selected for operation; (v) relevant meteorological data (such as wind speed, direction, tidal phase) for later referral and correlation; (vi) planned length of operation. After completion of this exchange (which is recorded in hardcopy form as a permanent record) , the machine, upon command from the operator, initiates its first 256- second radar data run. 4.2.3 Interlude The interlude group of computer functions includes all those that take place during the operation of the radar (i.e., during transmission and reception). These tasks may be divided into two categories: foreground and background processing. Foreground processing includes all of the real-time data manipulation and mathematics required to obtain the final output current map; by real-time we mean those tasks that run simultaneously with radar transmission and reception. Most of the foreground tasks will be described in the subsequent section on signal-processing software. 35 Background processing involves "housekeeping" tasks not obviously related to digital radar signal processing. Under RSX11S, various tasks falling under foreground and/or background can be running simultaneously on the PDP 11/04 minicomputers, in a time- share mode. Background tasks will include routine system checks and diagnostics; for example, the transmitter output power level will be monitored, and a message will be printed if it falls below a given threshold. Another check will be made on noise and/or interference; if it exceeds a given threshold, the operator will be notified, at which point he has the option of switching to another frequency. The computer will print routine messages for the operator (without requiring the system to pause), such as one indicating when a given 256-second run is completed. It is important to emphasize that the evolution of the various inter- lude tasks and messages will be an ongoing process; as more experience in the field is acquired, it will become obvious what changes can reduce the complexity of the work for the operator and produce a more effective output product. In fact, it will even be possible to program in many functions during operations in the field. 4.2.4 Postlude At the termination of actual radar operation (whether after one or several 256-second coherent integration periods), an array of digital data stored on the magnetic Line Tape has been acquired at both stations. Each array contains information regarding the mean component of surface current radial to that station, at a variety of geographic points within the radar coverage area. The information in these arrays may be "raw", i.e., Doppler spectra (including phase) as output from the FFT, or it may have been processed further during the interlude; the actual decision as to how much to pre-process during the interlude has not been finalized. Certainly during the first field tests, very little pre-processing will be done during interlude in order to allow maximum flexibility to examine the data during all phases of the processing. As operation of the system becomes more routine, it is planned that nearly all of this pre-processing be done during interlude, so that a minimum amount of final processing need be done in postlude. At any rate, a certain amount of data processing must be done at the termination of radar operation before an actual current map is produced. The details of the mathematics behind this data processing will be covered in the next section. Among the functions that may be performed under either interlude or postlude operations include: (i) an averaging of data points; (ii) determination of azimuth angle of arrival (at each Doppler shift); (iii) further averaging of data points; (iv) elimination of points for which the signal-to-noise ratio falls below a predetermined threshold; (iv) interpolation and/or extrapolation for regions where there are no data points; (v) for each range gate, the fitting of a curve where Doppler shift is made a function of azimuth angle-of- arrival; (vi) conversion from Doppler shift vs. range and azimuth (polar coordinates) to Doppler shift vs. x-y 36 distances to each selected map grid point (rectangular coordinates); (vii) conversion from Doppler shift at each map grid point to radial current velocity at that point; (viii) trigonometric combination of radial current velocities from the two sites to obtain the total current vector at each grid point; (ix) display and/or hardcopy plotting and/or (magnetic) record- ing of the actual current- vector map, including the coastline and any desired information labels. All of these steps have been run on our PUP computer systems using the software that is to go in the field systems, and the total running time for these processes to the output of the map is expected to take less than ten minutes. 4.3 Signal-Processing Software 4.3.1 Functional Description The ultimate purpose of the software described here is to convert the received radar signals into a map of current vectors. The processing begins by definition after the completion of the digital FFTs . All digital processing before that is done in real-time by special digital hardware components, as discussed in previous sections. Thus — referring to Fig. 25 — we are excluding from consideration here all of the functions done in the upper left section called RADAR DATA. Two functional inputs are required to produce a current map: (i) received sea-echo radar data in the form of completed digital FFT arrays, and (ii) geographic data, which are input by the operator. The radar data and their processing will be described here, while the geographic data will be described subsequently. Recall that the radar data for each of the two sites consist of 512-point complex Fourier transforms (i.e., 1024 words per transform) for each of 32 range gates for each of three receiving antennas; such a set of data is collected and available every 256 seconds. In reality, it is expected that only the first 24 range gates will contain adequate sea-echo signal strength to be useable (these gates extend to a range from each site of ^ 78 km). Hence, processing for purposes of making a map will be conducted only on the data from the first 24 of the 32 range gates*. Initially, the computer determines the total mean signal power level in each range gate by (complex) squaring and summing all of the 512 output FFT points for each range gate. This value is used to set automatically the receiver gain for that range gate, which we discussed previously as part of the receiver "sensitivity-time control" components. This ensures that full receiver analog and digital processing dynamic ranges are being utilized for the signals from each range gate. The "feedback" manner in * The contents of the 32nd range gate will be used for monitoring purposes as a measure of the noise and/or interference present, since the sea echo at this distance will always be well below the noise. 57 RADAR DATA GEOGRAPHIC DATA Field Radar Time Data: 2 Radar Sites 3 Receiving Antennas 24 Range Cells FFT: 512 Point Complex REAL TIME i cs PROCESSING Signal and Noise Levels: (Each Range Cell) Window FFT: Select 1st Order Scatter Angle— Of— Arrival and Signal Amplitude: 1 or 2 Signals (Each Doppler Cell) Operator: Site Locations Calibration: Antenna Boresight Angles Current Map Coordinate System MAP PRODUCTION Vector Current Field: At Grid Points Current Map: With Coastline and Sites Coastline Data Figure 25. Functional diagram of data processing required to produce a current map. 38 which the sensitivity-time-control function is performed here is similar to what is called "automatic gain control" (AGC) in radio receivers. Next, the spectra (i.e., the sum of the square of the real and imaginary parts of the FFT at each frequency point) are available for display to the operator on the video monitor. The operator then (i) selects the stronger of the two first-order echoes, and (ii) imposes a "window" around the portion of this echo that he considers to be truly first-order (excluding second-order regions and/or noise); this he does on the keyboard. He will probably not do this for all 24 range gates, but only for a few interspersed across the 24. On the basis of initial experience gained by "operator windowing" it is planned that ultimately this windowing function will be done automatically. Therefore, the only data points that will be retained for subsequent processing are those contained within the window; all others will be excluded. The width of this window — and hence the number of points of data retained for processing — is directly proportional to the radial current shear around the circular range gate. With no current, for example, the width is infinitesimal and the total number of included points is only two or three. Next, the angle- of- arrival of the signals is computed for each Doppler- frequency included within the window. For the receiving antennas along a line separated by a distance A/4, the angle a is defined with respect to the perpendicular to the baseline (see Fig. 26) . Assuming that (i) the surface current is not a random variable with time (i.e., for time periods less than 256 seconds), and that (ii) there is no noise present (i.e., only the desired first-order sea echo is present), we can obtain the angle, a, of a signal arriving from only one direction at a given Doppler frequency uniquely and deterministically using two antennas. Likewise, the angles a, and a of two signals arriving at the same frequency from different directions can be uniquely determined with three antennas. The relation- ship used to obtain these angles is: Signal No 1 Jk Signal No 2 radio frequency of 30 MHz lengt of 3c Illustrated n the cite of two signals •rriving with the same doppler shift but it two different ingles of arrival a, and a,. Figure 26. Diagram of three- antenna resolution of signals arriving from two directions. 39 a i,2 = Sin -1 ■tan Im(x l,2 ) Re(x lj2 ) H 2 CD where x „ are defined in terms of the complex Fourier transforms of the signals V. , V , V„ at antennas A, B, and C (for a given Doppler frequency) as 1,2 flV I 2 - IV I 2 ") ± i >4lv V* - V V*| 2 - flV I 2 - IV l 2 1 2 C B 2 t V C V B " W B A 1 (2) The amplitude of the signals arriving from the two directions is given by 1,2 _ y 2 ,i- v b (X 2,1 " X l,2^ (3) This system can handle the situation of only one signal arriving from a single direction a (i.e., a = a») . It cannot resolve signals arriving from three (or more) directions at the same Doppler frequency; it can recognize this situation, however, and eliminate the data point. In practice, it is unlikely that current patterns occurring in nature will produce more than a double-valued ambiguity. Therefore it was decided that the three- antenna system (and related software) would be used unless field experience shows that more are needed. Furthermore, when noise (or second-order sea echo, which is considered noise for our purposes) is included in V A , V D , and V_,, the angles a, and a,, determined in the above manner will not define exactly the direction- of - arrival of the desired first-order signal. In other words, there will be some error, Aa, and Aa ? , between the true directions and those defined from Eqs. (1) and (2). The error will depend upon the signal-to-noise ratio; the higher the signal-to-noise ratio, the smaller the errors Aa ] and Aa„. The fact that low signal-to-noise ratios will produce greater errors can be used to eliminate such points; one merely computes A and A_, and compares them with a predefined noise threshold to decide whether to retain these points. Averaging is also used to help smooth the data. Various types of averaging are presently being tested in software simulations. One type will be described here. Assume that there are data points from several 40 256-second FFT runs. For each value of Doppler frequency, Af., that is retained within the window, there will be several values of azimuth angle estimates, a.(Af.). We could treat Af. as the independent variable, averag- ing over a for a given Af., or we could treat a as the independent variable, averaging over Af. We have chosen the latter. We divide the azimuthal sector over which surface currents are sought (e.g., -90° < a < 90°) into specified increments, Act. Then we average all of the Doppler frequency points falling within the n-th azimuthal bin, nAa, as - 1 M Af(nAa) = ^ Z Af (nAa) , 1=1 where M is the total number of Doppler frequency points in that bin. In certain situations, there may be no frequency points to average in a given azimuth bin; this must be noted for subsequent processing. Thus we arrive at an array of averaged Doppler frequencies vs. azimuth angle, i.e., Af(a ), where a = nAa. An interpolating curve is now fitted to these n n r points so that Doppler frequency can be estimated at any desired value of a. Among the interpolating curves being tried are a spline fit, a linear interpolation, and least-squares fits; the latter method at present appears to be working the best. The final process that must be done at each site preparatory to the map graphics is to convert the Doppler shift vs. polar coordinates (i.e., vs. range gate and azimuth angle) to Doppler shift vs. the rectangular coordinates at each selected map grid point. With a map grid specified, the x-y distances from each site are converted to R, a; by interpolation, the Doppler shift at that grid point is determined. Finally, the Doppler shift at that point is converted to a current velocity radial to the given site by using the equation V (x,y) = y [f R - Af(x,y)], where f is the first-order Bragg frequency and X is the radar wavelength. When the data points from both sites are available, the two sets of radial current velocities at each grid point are combined trigonometrical ly to obtain the total current vector at each grid point (i.e., length and direction). These vectors are available for storage on magnetic tape (for subsequent analyses) or for graphic display on the video monitor and/or hardcopy digital plotter. In order to establish the angles at each grid point with respect to the two sites (required for the trigonometric vector combination) , geographic input data are required as shown in Fig. 24. It is planned that these will ■be entered by the operators at both sites. The latitude and longitude at each site will be determined by locating the site on a local topographic map. Positional accuracies need not exceed one-half kilometer. Finally, the boresight angle of the linear receiving antenna array must be determined and entered at each site by the operators. This can be done either with a compass or by using transmitted signals from the other site and measuring the phase differences at the separate antennas; both methods will be tried initially in the field. 41 We intend to show a contour of the coastline on the current- vector map. This will help the user to orient himself and also to assess on the spot the practical impact of a current-borne spill on the beach. At present, we have coastline data from the entire continental U.S.A. and Alaska; these data are stored as latitude- longitude points on magnetic tape. It is anticipated that smaller digital tape subsets containing portions of the coastline near our planned operating areas will be prepared ahead of time in the laboratory so that they can be readily used in the field. 4.3.2 Software Description The preceding section described functionally the mathematical steps necessary to convert the digital radar signals at the output of the FFT into current vectors. This section describes in greater detail the actual computer programs and subroutines for accomplishing this. Not all of the programs correspond one-to-one with the functional blocks of Fig. 25; hence we show in Fig. 27 the actual computer software used for these tasks. All of this software currently exists and has been checked out in FORTRAN against simulated current -modulated sea-echo signals. Site Location Data (Input from operator) Program Manage (Interface between hardware and other software) Subroutine CRDNT (Defines current-map coordinate system) Subroutine SRCH (Automatically selects first-order spectral data for processing) Subroutine COMP (Computes radial velocity versus angle of arrival) Subroutine SGNL (Monitors signal and noise power levels) Subroutine ARRAY (Generates current-velocity vector data for plotting current map) Figure 27. Current- sensing- radar data-processing software. 42 Three types of data are shown here as inputs required for the data processing: (i) site location data, (ii) radar sea-echo backscatter data, and (iii) receiver gain-control data. The site location data consist of the latitudes and longitudes of both radar sites and the angular orienta- tions of the linear receiving antenna arrays at both sites. As described in the preceding section, topographic maps will be used to determine the site locations; most likely, one-way transmissions between the two sites will be used to establish the receiving antenna angles. The radar sea-echo backscatter data consist of the complex array of signal vs. (Doppler) frequency for each range gate and each antenna, as output by the hardware FFT device. These radar backscatter data can either originate from actual signals received in the field or simulated signals; the latter are presently being used in the laboratory to check out the software. Finally, gain- control information is provided for each range gate (i.e., the attenuations and/or gains set in the receiver STC) so that the quality of the data can be ascertained. The main program MANAGE interfaces the computer hardware with the remaining software subroutines as to the manipulation and processing of the input data; it routes the various data to the proper subroutines for each processing step. Site location data are used within subroutine CRDNT to establish the coordinate system grid for the current map. Subroutine SRCH automatically determines what portion of a spectrum (FFT output power vs. Doppler frequency) will be retained as the first- order echo. It performs this "automatic windowing" by searching for the higher of the two maxima, and then including everything lying above a preset threshold so many decibels below this peak. A "manual override" will of course be available so that the operator — as he views the spectra on the video display — can set the window and threshold to the position he judges to be optimum. Undoubtedly during most of the initial field opera- tions, human decision processes will be used in lieu of automatic decisions; as more experience is accrued and operation becomes more routine, more and more of these decisions will be made automatically. After windowing by subroutine SRCH, the data points retained are processed by subroutine COMP. This routine computes the angle-of-arrival of the signal at each Doppler frequency, performs averaging and curve fitting to these Doppler frequency- vs- azimuth points, converts Doppler frequency to radial current velocity, and finally computes the radial current velocity at each of the preselected x-y map grid points. Finally, this information is passed along to subroutine ARRAY — along with similar data from the other site — where a total current-velocity vector is com- puted at each map grid point by a trigonometric combination of the radial currents from the two sites. Subroutine SGNL is designed to monitor the received sea-echo signal- power level (i.e., the summation of total power at each FFT frequency) for each range gate so that the gain setting for the receiver STC system can be automatically programmed. One range gate (in which the transmitter signal echo is absent) is reserved for measuring noise and interference power in this same fashion; this information is necessary (i) for operating fre- 43 quency selection, (ii) for continued operator monitoring, and (iii) for ascertaining the mean signal-to-noise ratio for purposes of retaining only meaningful data points. SYSTEM ANALYSES AND SIMULATION STUDIES 5.1 Signal- to-Noise Ratio (S/N) 5.1.1 Basic Radar Performance Criterion The signal-to-noise ratio (S/N) is the basic measure of radar perfor- mance. It indicates not only whether the desired signal is likely to be seen above the noise (the detection problem) , but also how closely the parameters of the desired signal can be determined as a result of the noise degradation (the precision/accuracy problem) . It is obvious that S/N must be greater than unity in order for one to see and identify the desired echo signal. Noise is always a randomly varying quantity; hence it makes sense to talk only about the average noise power at the output of the receiver. The desired echo signal may or may not vary randomly over time, depending upon the nature of the target. An HF ship echo, for example, is likely to be non- fluctuating. First-order sea echo, on the other hand, is very definitely a random variable [see Barrick and Snider, 1977] whose (voltage) signal fluctuations are Gaussian in nature and which is uncorrelated with itself for consecutive observation times longer than about 25 seconds. When the signal is a random variable independent of the noise, S/N is normally defined by averaging the signal echo power independently from the noise echo power. Noise at HF originates from external sources. Handbooks [CCIR-322, 1964] of noise have been prepared from extensive, world-wide seasonal/diurnal measurements made in the 1940 's and 1950' s. Such a noise-voltage signal is a random variable which is spectrally flat over bandwidths less than 100 kHz. This means that if one were to look at the average spectrum of noise (the output of a receiver FFT, squared and averaged) , one would observe a constant value as a function of spectral frequency. This constant is defined as N (watts per Hertz bandwidth, or joules). At 30 MHz, CCIR tables show that total average noise power spectral density referred to the receiver input is: N o = [kT] dB + F AM (in decibels )> ( 4 ) where kT is the internal noise in the front end of the receiver (at room -23 temperature, T - 300 K, k = Boltzmann's constant = 1.38 x 10 , and hence [kT] , - -204 dBJ). F. M is the median atmospheric noise factor. At 30 MHz, this quantity typically originates from man-made noise; at a reasonably 44 quiet location, F is 20 dB, meaning that external noise is two orders of magnitude higher than kT (i.e., the theoretically lowest possible internal noise at room temperature). This means N = 184 dBJ. Let us first assume that the desired signal is originating from a target moving at a uniform velocity*. This target echo will — after spectral processing in the receiver — appear as a discrete spike at a Doppler frequency proportional to its velocity. The height of the echo peak and the reciprocal of its width will then vary in direct proportion to the coherent spectral processing (or observation) time, T . One can then define S/N as the height of this signal peak compared with the averaged, flat noise level across the same spectral band. Standard radar textbooks [e.g., Cook and Bernfeld, 1967] show that the best one can do with matched receiver conditions in terms of S/N for this case is given by** P T S/N = -jLi. , (5) o where P is the average power available at the receiver front end. The standard radar range equation [Barrick, 1972a, b; Skolnik, 1962] in turn relate the received power to the transmitted peak power P pT , antenna gains G , G , range to the target R, and radar cross section, a, of the target as 1 K follows c/„ P PT TT I G T G / S/N - -nr— • — 7v • ° ■ (6) r o (4tt) R where F is the voltage path- loss attenuation factor; if the path were free space, F = 1. In general for surface-wave propagation beyond the horizon (as in our system above the sea) F - 1 at short ranges (less than 10 km), but decreases — eventually exponentially — with increasing range. Barrick [1971] has provided extensive calculations of this factor vs. frequency, range, and sea state; these in turn have been verified by measurements and will be used for subsequent calculations here. The quan- tities t and T are pulse width and the pulse-repetition interval (as seen at each of the receiving antennas) . Since the three receiving antennas are operated sequentially, T is three times as long as it would have been had there been only one receiving antenna (i.e., T =3x1 ms =3 ms) . * The actual situation where the received signal is due to first-order sea echo is only slightly different, and will be considered subsequently. ** Since two-sided Doppler processing (i.e., including negative frequencies) is to be employed here, we henceforth use^.a two-sided definition of average noise spectral density, defined as N = N /2. r y o • o 45 5.1.2 Sampled Data and Digital Signal Processing Equation (6) gives a general guideline as to the best signal-to-noise ratio one can hope to realize with any receiver/processor system. It is therefore incumbent upon us to show that the system which we have designed — consisting of both analog and digital circuitry — does in fact achieve this optimum S/N; anything which falls considerably short of this target indicates that our design is inefficient. Let us start at the output of the sample-and-hold (S/H) and analog-to- digital convertor (A/D) circuits, as shown in Fig. 8. The receiver has an IF bandwidth that is the reciprocal of the pulse width, i.e., B - 1/t. (Here T = 20 usee; hence B D * 50 kHz) . Within each pulse at the receiver I K and Q channel output, the zero- IF (baseband) sea-echo voltage signals (assumed at present to occur at a single frequency, w ) are given as v gI (t) = A cos(w s t + <})) ; v SQ (t) = A sin ("s* + ^ " ^ Note that the intrinsic Doppler frequency w /2tt of the first-order sea echo is ^ 0.56 Hz at 30 MHz, even though the actual pulsed signal through the receiver has a bandwidth of 1/t - 50 kHz. The sampling gate has a sampling uncertainty time - 0.25 ns, so that for range gate j, we obtain a series of discrete values from the A/D convertor of V SI (nT r } = A l C0S K; nT r + *x) > v SQ (nT r } = A l sin ( w s nT r + ^ > ( 8 ) where T is the pulse repetition frequency per antenna channel (here, r -j T = 3 ms), and A, is related to A by a constant, K, . r J 1 J 1 Select a time t p at the input of the pre-averager. (The pre-averaging time T is fixed here at one-half second.) Therefore, M = T /T (=166 ■=- - 167) values are to be added to obtain* (M-l)/2 . v si ( V ■ I ,- V si^ - n V K Mv si or ■Tj/2 SQ' (10) i(j). sin(a)-u) )T T /2 V S^ ■ OT lV (co- M Jt i /2 The actual digital FFT processor approximates the Fourier integral transform by a Fourier series. Thus the output, rather than being a con- tinuous function of w, is an array corresponding to discrete frequency values a) = Mu) = 2ttM/T ,; for the parameters selected for our system, there- fore, the frequency resolution (or distance between adjacent frequency points) is f = 1/T = 1/256 = 0.0039 Hz. The output array lies spaced over a frequency window extending from -1.0 Hertz to +1.0 Hertz. The use of inphase and quadrature data to fill both the real and imaginary parts of the input FFT array allows us to define a non- ambiguous transform over both positive and negative frequency values, a result not possible had we used only inphase (real) values at the FFT input. Note that for a large trans- form with considerable resolution, the peak value (from Eq. 10) occurs at 47 u)_ = MpO) - 03 , at which point the peak signal amplitude (from the FFT) is |vJ(Mp)| = MTjA^ Before examining the processing of noise by our system, let us relate the signal amplitude to the received power. Since the average received power was denoted as P the peak received power (per pulse) has the value P pR = — P R . We assigned the voltage signal level at the I and Q receiver output channels as amplitude A. The voltage signal at the receiver input can be written v„(t) = /2PI7r7 cos(o) t + ceived power per pulse is thus merely the amplitude of v q squared and divided by twice the input resistance, R. . If we assume a constant receiver voltage amplification gain K D , then A = K D /2P DD R. = K D /2R.P D T /t , or K K FK 1 K 1 K r A^ = K,K D /2R.P D T /T . 1 1 R l R r Let us now examine the noise at the I and Q output channels of the receiver. Since all signals — including noise — have been filtered upon passage through the receiver (with an IF bandwidth B - 1/t = 50 kHz) , the signal at the first IF offset of 40 MHz can be considered a narrow-band Gaussian process; hence let us write the baseband IF at the receiver output as v NI (t) = Ajj(t) cos <|> N (t) ; v m ^ = \(t) sin ^(t). (11) As before, we can relate A^ to the average effective noise power at the receiver input; the latter is N B R . Hence, using our previous notation, 2. _ 2 . n .2 . ., _ „ „ „2. 'NQ' = 2 = 2 = K_2R.N B D = K_2R.N /t , T4 NI NO R l o R Rio In a fashion similar to Eqs. (9) , we obtain the following expression for the digital output of the pre-averaging circuit: (M-l)/2 _. (M-l)/2 V NI ( V = I v NI ( V nT r ) J V N0 C V = I V NQ ( H - nT r ); (12) -(M-l)/2 N ^ -(M-l)/2 N * * r here, the bar over the voltages denotes the sample sum of M numbers; hence this sample sum is still a random variable. We can relate it to a noise correlation function defined as R^T) E = , (13a) or 48 i R N (T) E (K^R.N o /T)p(T) fl3bj where p(T) is a dimensionless correlation coefficient whose maximum value, unity, occurs at T = 0. Therefore, the sample voltage-squared average from the pre-averager is ■ , (M-l)/2 (M-l)/2 <[V NI ( V ] > = I I < WV mT r )v NI ( V n V > m * -(M-l)/2 -(M-l)/2 NL * r Nl * r (14) (M-l)/2 (M-l)/2 I I R N ((m-n)T), -(M-l)/2 -(M-l)/2 with an identical . expression for the quadrature channel output. The essence of the simplification of the above equation lies in the following argument. The voltages v T (t) and v Nn (t) have bandwidths B - 1/t = 50 kHz. The Fourier transform of any average spectrum with a K nominal width B is a correlation function whose peak width (near T = 0) has a width 1/B - t; for time arguments considerably larger than t, the correlation coefficient becomes negligibly small. Therefore, when m / n in the above equation, we see that (m-n)T » t, and hence the double summation is negligible except for m = n. Thus Eq. (14) becomes -i 2 -i 2 (M-D/2 ? ? <[vi I (t £ )] > - <[vJ Q (t £ )] > = R N (0) J 1 = M Vl R.N o /T. (15) - (M-IJ/Z The actual noise signal v^ T (t p ) + iv^ (t p ) at the input to the FFT processor is a random variable; however, the assumption that this noise is. "white" or spectrally flat (on the average) means that the noise power |v^(a))| ' is spread uniformly across the spectral window of width 1/T. after averaging. Hence, the average noise-power spectral-density height at the FFT output is given by = «I^(t t )] 2 > * <[vj Q (t £ )] 2 » • T A = 2MKJ^R.N T A /T. (161 Using the fact that we can define the power spectral density of the desired echo signal at its peak as S^(u> ) = |V^(a) ) | /T = M"T \" 2 2 2 = M TI K • 2R.P T /t, we can form the signal-to- (average) noise ratio at the processor output as 49 «A.I |V S ( V |2 M2T I K R K 1 • 2R i P R T r /T P R T I P < Vj( 2MIC1CR.N T a /t o 1 N v ^ l RlioA where we have used the fact that M = T./T . A r Hence we see that the signal-to-noise ratio at the output of our spectral processor, S/N | , is in fact identically that predicted by Eq. (5) as the optimum that one can expect for a matched receiver /processor. There- fore, our digital signal processing system does indeed provide the best possible processing of the signal from a moving target in the presence of white (random) noise. 5.1.3 Sea-Echo Radar Cross Section In the previous section, we treated the radar target echo as a non- random CW signal (see Eqs. 7), as though it originated from a discrete target. First-order sea echo in practice is a Gaussian random variable [Barrick and Snider, 1977] . Hence it makes sense to speak of the average sea-echo received power, or alternately, of the average sea-echo radar cross section. Barrick [1972a, 1972b] shows that the average first-order sea-echo radar cross section, a, is proportional to a A, where A is the mean sea-surface area within the radar resolution cell and a is the average sea-echo backscattering cross section per unit area. The above references show that Q° = 2 6 irk 4 S(2k ,0), (18) where S(K ,K ) is the average ocean waveheight directional (spatial) spec- trum evaluated at spatial wavenumbers K , K , and k is the radar wavenumber. r x y o This expression is valid for vertically polarized backscatter at grazing i ncidence (i.e., for surface-wave geometries such as ours). For /2 2 2 2 /K + K > g/u (g = 9.81 m/s , u = wind speed, m/s) , the waves with wave- x y numbers K , K are usually developed to their maximum possible heights, and an empirical expression found valid by oceanographers in this saturated region of the spectrum [Barrick, 1972b] is S(K , K ) = .005/ [2*0^ + kV]. a y a y Using this expression in the above equation, we obtain a =0.01; this saturation condition at 30 MHz requires that > 2.8 m/s, or the waveheight be greater than approximately one-half, foot, a condition that is nearly always true on the open sea. Even when the sea is actually calmer than 50 this, some waves of the required scattering length (i.e., 5 meters) will always be present. If their heights are less than 6 inches, this simply means that the received echo signal will be proportionately weaker. For our analysis here, we will assume a =0.01 (a saturated condition). The area within the resolution cell, A, we take to be that of a semi- 8 circular annulus of width cx/2 (c = 3 x 10 m/s, x is the pulse width), and half- circumference ttR (R being the range from the radar to the semi -circular range gate). Thus A = ttctR/2. For our first radar system, t = 20 us, and 3 hence the range-gate width, ct/2, is 3 km = 3 x 10 m. The total expression for the radar cross section of the sea — to be used in Eq. (6) — is a = 30ttR, (19) with a having the dimensions of square meters and R in meters. The equations stated in (5) and derived in (17) for signal-to-noise ratio of a moving target show a peak in the frequency domain whose height varies directly with, and width varies inversely with the spectral coherent integration time, T_ (or Fourier transform window time) . These expressions are valid for any stationary target or target moving at a uniform radial velocity, whose echo signal can be expressed as a pure sinusoid, as assumed in Eq. (7) . Barrick [1972a] has shown that this is true of sea echo to first order, in the absence of an underlying current shear . The entire principle of operation of the present system, however, assumes that the radial current-velocity component is not uniform around the semicircular ring, but varies according to some pattern (to be measured by the system) . This "shear" will not produce a target signal at a single frequency, but will result in an echo signal with several frequencies (merging into a continuum) whose spread is related to the total variation in radial current velocity around the semicircle. In order to study quantitatively the expected system signal-to-noise ratio under average conditions, we postulate the following model as a modification to the results of the preceding section, to account for current shear. In that section, we saw that the height of the spectral power peak was proportional to received power, P , times processing time T ; the K 1 former quantity is proportional to the radar cross section of the target. The width of the spectral peak is inversely proportional to T . We now assume that the current shear broadens this peak to a width B , instead of the original width 1/T_. Since the total received backscattered power from the sea from the same semicircular ring remains the same, this means that the peak of the first-order sea-echo power spectrum must decrease propor- tionately. Thus, the signal-to-noise ratio decreases by a current-shear factor, F , given by F = 1/(B T T ) . Let us assume a current-shear radial- cs ° • cs c I velocity variation across the semicircle from -100 cm/s to +100 cm/s (probably an extreme situation for coastal waters) in order to be somewhat conservative in our S/N calculations. Then at 30 MHz, B = 0.4 Hz. Then for our first- generation radar system with T = 256 seconds, we have F = 1/102.4 = 0.01. 51 5.1.4 System Signal- to-Noise Ratio vs. Range At this point, we can re-write Eq. (6) for signal-to-noise ratio, using the parameters discussed in the preceding section. P tT G G F 4 S/N = rh 1 ' ffv a ' F " ' or (20a) r o (4it) R P TT G G F 4 (.3) S/n = — — - • -^ . (20b) ' TN ,3 2.3 K J r o 4 tt R The system under design is to radiate a total of P pT = 2400 W peak; also, t = 20us, T = 3 ms, and T T = 256s. We use N = -184 dBJ at 30 MHz ' r I o 19 (or N - 4 x 10 joules). The antenna gains used in the above used in the above equations must be referenced to free space, since the effect of ground imaging is included in the sea-echo radar cross section. For the receiving monopoles, this gives G - 0.75. The transmitting antenna is more directional, and at its beam maximum, should have a "free-space** gain G - 3.28 (based on the fact that the free-space Yagi half-wave dipole equivalent is to have a gain of 4 x 1.64). Substituting all of these factors into Eq. (20), we obtain for our system: S/N = 7.557 x 10 21 x F 4 /R 3 . (21) Again, R is the range from the radar, given in meters. F is the dimension- less "Norton attenuation factor" for ground-wave propagation; it is unity at short ranges, but decreases (eventually exponentially) at longer ranges. It is also a function of frequency, surface conductivity, and surface rough- ness (sea state). It can be obtained from Barrick [1971]. We tabulate its average value below vs. range for sea water, a spherical Earth model, 30 MHz, and Sea State #2. Figure 28 also shows the S/N relationship graphically. R(km) F 4 S/N (decibels)* 5 .6210 105.7 10 .2512 92.8 20 .3981 x 10" 2 65.8 30 .3311 x 10~ 3 49.7 40 .4571 x 10 _lf 37.3 50 .9550 x 10" 5 27.6 60 .2512 x 10" 5 19.4 70 .7586 x 10" 6 12.2 80 .2399 x 10" 6 5.5 * S/N is usually given in decibels, where in terms of absolute (S/N) , it is defined as S/N = lOLog (S/N) . 52 110 100 90 BO £ 70 -a 6 '§ 60 so g 40 E a 30 to 20 10 ■10 WPL current -mapping radar system Expected signal-to-noise ratio _ P PT = 2.4kw t = 20ps T r = 3ms T, = 256s G T = 3.28 G R - 0.75 u° = 0.01 f = 30MH/ N = 4x10" " J watts/Hz Sea State "2 Current Shear -100cm/s S(co) = Lim — -^ , (25a) N(co) = Lim — ! =-= , (25b) T-k» ., r , nr > - t- aT t»T v \ r( .i -j(co) ro ~ C(co) = Lim - = |C(co)|e . (26) T-m» Upon substituting Eqs. (24) into this definition and using the Eqs. (25) , we obtain -jco(d/c)sina 2tt^ -joo(d/c)sina |C(co)|e J l } = S(co)e + / N(w,a)e da. (27) In obtaining this expression, we have used the fact that the signal and noise voltages are uncorrelated, and hence their cross-product terms vanish in the averaging process. Also, if the signal is actually mono- chromatic at frequency co , we can replace co by co in the first term; in the exponential, therefore, we have co(d/c) = co (d/c) = k d. If the noise has been narrow-band- filtered about co and is spectrally flat (or "white") o r j 57 across this filter bandwidth, we can make this substitution for w in the second term also. Finally, we postulated that the signal amplitude was a non- random constant; this does not affect the spectrum S(u)), for the average of a constant is the constant itself. The assumption that the average noise is isotropic in angle means that N(w ,a) is not a function of a; hence we can make the substitution N(oj ,a) = N(uj )/2tt and remove this factor from the integrand. The re- maining integral containing only the exponential then gives rise to the zero-order Bessel function. Hence we have -j$(w ) -jk d sina |C(u o )|e" ° = S(w o )e " s + N(u) o )J o (k o d). (28) Since S(w) and N(w) are pure real quantities, we can write the phase difference $(w ) from the averaged cospectrum above. Note that in the absence of noise, this phase is exactly the expression we discussed at the outset of this section in terms of the signal arrival direction a . With noise, however, $ depends upon the average signal-to-noise ratio (S/N = S(w )/N(o) )) also. Thus we can write , sin(k dsina ) -1 OS $(w ) = tan T , — r-: r — T . — ,. . ..- tt= = k dsina , (29) o J cos(k dsina ) + J (k d)/(S/N) o e' v J where a is the estimated direction-of- arrival and a is the true e s direction- of- signal- arrival. The angular estimation error is then e = a - a . e s In order to obtain a feeling for the dependence of e upon S/N, we choose several parameter values for a and k d for the above model and plot e vs. S/N. These curves are shown in Fig. 30. The curves plotted from Eq. (29) indicate that — for the signal and noise model examined here — the mean angular error in estimating direction of arrival is always less than 3° for S/N > 10 dB, but this angular error increases rapidly as S/N drops below 10 dB. This is consistent with other analyses on this subject also. While the system being implemented differs from the model analyzed here (both in the fact that three antennas are used instead of two and in the fact that the estimated angle is extracted before averaging), the results obtained here are expected to be generally applicable to our system also. More precise angular error analyses for our system will be performed in a subsequent report; such an analysis must of necessity be done digitally, using the actual system software along with Monte-Carlo techniques for signal and noise. An example of a simulated current plot using these techniques is shown in the next section. 58 Ll) c o 41 5 I W- a> Q 2 \ a ■45*, d -X/2 V a-O'. 90*; d -X/2 a-0°; d -X/4 Isotropic External Noise Direction of Arrival of Desired Signal =a ' J.BW" a- 45°; d-X/4 a- 90° d-X/4 5 10 15 20 25 Signal-to-Noise Ratio, Decibels 30 Figure SO. Mean azimuth-angle mea- surement errors for two-antenna system and various signal arrival directions , a , and antenna spao^ngSj d. 5.3.2 Simulation of Current Map Using Actual Data-Proc3ssing Software As mentioned in the preceding section, it is impossible to develop a closed- form mathematical model for our current- vector errors for several reasons: (i) Thresholding is used to eliminate data points originating at low signal-to-noise ratio values; this is a nonlinear process making the analysis very complex. (ii) The equations giving the two angles-of-arrival in a three-antenna system (i.e., Eqs. 1-3) are quite involved transcendental relationships. (iii) Averaging is done after angular extraction from the signals. (iv) This averaging is done on the Doppler frequency (or radial current velocity), rather than on the azimuth angle. Hence the only practi- cable way of obtaining a feeling for current-vector errors is by simulating the random sea-echo signals and noise signals, employing the Doppler- shift distribution on the sea-echo signal produced by a predetermined current pattern. Another reason for doing such simulations is to check out the system data-processing software before actually operating in the field. In this manner, "bugs" in the programming can be found in the laboratory. Also, by varying the current-pattern geometries and system parameters, we can anti- cipate trouble areas in system operation before going into the field, and modifications can be made where appropriate. In Fig. 25, two possible sets of signals were shown at the upper left as inputs to the data-processing software. The first set represents actual sea-echo signals as they would pass through the receiver in the field and exist in digital time-series form at the input to the FFT. The second set are simulated signals of the type being discussed here for laboratory studies and analyses. Both sets of signals pass through the same software, and hence the software (with the underlying mathematical processes and attendant accuracies) can be checked with properly simulated signals. 59 An entirely separate computer program is being used to generate simu- lated signal data tapes for use with the system software. These simulated signals for a given range gate consist of two components: (i) the random sea- echo signals, and (ii) random noise signals. The random sea-echo signal for the I and Q channel time series is assumed to originate from 180°/Aa different scattering directions. Typically we have used Aa = 1°, meaning that the sea- echo is assumed to be different every degree in azimuth over a 180° semicircle. This difference manifests itself in three ways: (i) The I and Q channel amplitudes X . and Y . of the signals from each direction, a. (a. = iAa) are assumed to be uncorrelated Gaussian random variables, (ii) The frequency of the signal is assumed to be f + f . , where f R is the first-order Bragg-scatter frequency and f . is the Doppler frequency due to the radial velocity component of the assumed current pattern at the i-th azimuthal point around the range semicircle. (iii) The iirAa phase of the signal is (Ji-l)k d sin( ., Qr . ), where 1=1, 2, or 3 for each O loU of the three receiving antennas, and iAa = a. is the angle in degrees of the signal with respect to the perpendicular to the antenna baseline. Hence the total I and Q channel sea-echo signal at a given time t. is the summation of 180°/Aa terms, each representing the signal from a different azimuthal direction iAa. The simulated noise signal is also the summation of 180°/Aa, I and Q channel terms. However, at each sampling time, t., these amplitudes, X N - . and Y >T . ., are assumed to be uncorrelated Gaussian random variables (as well Nij as uncorrelated for each azimuthal direction as represented by different i). This has the effect of giving the noise power a bandwidth B - 0.5/(t. . - t.), where t. , - t. is the time between the time-series signal samples at the output of the pre- averaging circuit and input to the FFT. Thus the average noise power will be spread uniformly over the output FFT window from -B to + B Hz. The noise signal originating from each of the a. different azimuthal directions is given the phase factor discussed in (iii) of the preceding paragraph, corresponding to the receiving antenna element being considered. This latter fact and the independence of the X . . over i has the physical meaning that the noise is essentially isotropic in direc- tion, i.e., the noise originates with equal average power levels from all directions. Using these models for simulated sea-echo and noise signals, we have exercised the system software for different current patterns and signal parameters. Figure 31 is an example of one such early simulation. The input current pattern employed here was a one-half- knot uniform field flowing away from a line joining two sites (40 km apart) straddling Yakutat Bay in Alaska. Had there been no noise or sea-echo signal randomness, the output pattern would have had all of the arrows straight and of the same length. For this particular simulation, the following additional assumptions were made: (i) Frequency is 30 MHz. (ii) Only one FFT sample was employed (i.e., one 256-second run only). (iii) The antenna baselines at the two sites lie parallel to the line shown joining the sites. (iv) The signal- to-noise ratio defined as / is 20 dB. This corresponds to an si Nij r 60 YflKUTAT BflT rrer mum BRTT 3ITI It WLfWIMR SJi BMC O IBTITTJOBttAJfc «■- 43 4* LWOIWCEOWtSfc -140- 12 It RLTWDCCSfc -80 aiTTOo 10 dB) ratio should be attainable to a distance of 70 kilometers from each station. On the basis of this distance, an optimization study has shown that for a straight coastline, a desirable site separation would be near 40 km. Error analyses show that for signal-to-noise ratios greater than 10 dB, azimuthal position errors should be less than 3°. Simulations using random sea-echo and noise signals are being conducted to check out, exercise, and improve the data- processing software in the laboratory, before operating in the field. These simulations thus far reaffirm our expectation that rms current- velocity errors will not exceed 5 cm/s. 7. ACKNOWLEDGMENTS In a governmental research laboratory like ours, a task such as this, namely the design and construction of a new system from ground up — in a period of only eighteen months — is made especially difficult because of Federal Civil Service personnel regulations. We could not recruit new full-time experienced engineers as we would have done elsewhere. The entire design and construction efforts were done mainly with transient student and part-time personnel. Bob Weber was responsible for deriving and programming all of the signal processing and simulation software. Karl Sutterfield not only organized and maintained all of the computer components used on the project, but also developed all of the control and interface software. Jack Riley very competently developed much of the mathematical graphics and display software. The "transient" hardware engineers who accomplished the "impossible" in the way of design and construction included Roger Andrews, Dan Law, Craig Blasingame, Jack Hawkins, Bill Everard, and Scott Spettel. Untold unpaid hours have resulted in the system being completed nearly on schedule. Don Lund assisted in the design and construc- tion of the radar antennas. Many thanks go to the contractors and vendors who supplied both components and services essential to the radar system. These include Barry Research, the Digital Equipment Corporation, the Lawrence Livermore Laboratories, and locally, Astro Engineering, Incorporated, and ERBTEC. Their responsiveness consistently extended far beyond the formal terms obligated by their contracts. The project could not have reached its present status so quickly and successfully without the support and understanding of Drs . C. G. Little and W. N. Hess. Finally we owe much to our sponsors, and especially to OCSEAP, whose patience and willingness to provide flexible financial support permitted us to maintain a schedule drawn up nearly two years ago in spite of numerous minor crises along the way. 63 8. REFERENCES Barrick, D. E., (1971), Theory of HF/VHF propagation across the rough sea, Parts I and II, Radio Science , Vol. 6 , pp. 517-533. Barrick, D. E., (1972a), First-order theory and analysis of MF/HF/VHF scatter from the sea, IEEE Transactions on Antennas and Propagation , Vol. AP-20 , pp. 2-10. Barrick, D. E., (1972b), Remote sensing of sea state by radar, Chapter 12 in Remote Sensing of the Troposphere , edited by V. E. Derr, U.S. Govt. Printing Office. Barrick, D. E., J. M. Headrick, R. W. Bogle, and D. D. Crombie, (1974), Sea backscatter at HF: interpretation and utilization of the echo, Proc. IEEE , Vol. 62 , pp. 673-680. Barrick, D. E., and J. B. Snider, (1977), The statistics of HF sea-echo Doppler spectra, accepted for publication in IEEE Transactions on Antennas and Propagation . C.C.I.R. (International Radio Consultative Committee) Report No. 322 (1964) "World Distribution and Characteristics of Atmospheric Radio Noise", International Telecommunication Union, Geneva, M64, 78 pp. Cook, C. E., and M. Bernfeld, (1967), Radar Signals. An Introduction to Theory and Application , Academic Press, New York, 531 pp. Crombie, D. D., (1955), Doppler spectrum of sea echo at 13.56 Mc/s, Nature Vol. 175, pp. 681-682. Crombie, D. D., J. M. Watts, and W. M. Beery, (1970), Spectral characteris- tics of HF ground wave signals backscattered from the sea, Electro- magnetics of the Sea , AGARD Conference Proceedings No. 77. National Technical Information Service, Springfield, Virginia; Accession No. AD 716 305. Skolnik, M. I., (1962), Introduction to Radar Systems , McGraw-Hill, New York, pp. 3-5 (648 pp.) Stewart, R. H., and J. W. Joy, (1974), HF radio measurements of surface currents, Deep Sea Research , Vol. 21 , pp. 1039-1049. Wait, J. R., (1966), Theory of HF ground wave backscatter from sea waves, J . Geophys . Res . , Vol. 71 , pp. 4839-4842. 64 OU.S. Government Printing Office: 19 76-6 7 7-34 7/128 5 Region 8 LABOR AT ORIES The mission of the Environmental Research Laboratories is to study the oceans, inland waters, the lower and upper atmosphere, the space environment, and the Earth, in search of the understanding needed to provide more useful services in improving man's prospects for survival as influenced by the physical environment The following laboratories contribute to this mission. MESA Marine EcoSystems Analysis Program Office Plans and coordinates regional programs of. basic and applied research directed toward the solution of environmental problems which involve the functioning, health and restoration of marine ecosystems OCSEA Outer Continental Shell Environmental Assessment Program Office Plans and directs assessments of the primary environmental impact of energy development along broad areas of the outer continental shelf of the United States, coordinates related research activities of federal, state and private institutions W/M Weather Modification Program Office Plans and directs ERL weather modification research for precipitation enhancement and severe storms mitigation, operates ERL s research aircraft NHEML National Hurricane and Experimental Meteorology Laboratory Develops techniques for more effective understanding and forecasting of tropical weather Research areas include hurricanes and tropical cumulus systems, experimental methods for their beneficial modification RFC Research Facilities Center Provides aircraft and related instrumentation for environmental research programs Maintains liaison with user and provides required operations or measurement tools, logged data, and related information for airborne or selected surface research programs (CIRES) Theoretical Studies Group Provides NOAA participation in the Cooperative Institute for Research in Environmental Sciences (CIRES). a joint activity with the University of Colorado Conducts cooperative research studies of a theoretical nature on environmental problems AOML Atlantic Oceanographic and Meteorological Laboratories Research areas include geology and geophysics of ocean basins and borders, oceanic processes, sea-air interactions and remote sensing of ocean processes and characteristics (Miami. Florida) PMEL Pacific Marine Environmental Laboratory Research areas include environmental processes with emphasis on monitoring and predicting the effects of man s activities on estuanne. coastal, and near-shore marine processes (Seattle. Washington) GLERL GFDL APCL Great Lakes Environmental Research Laboratory Research areas include physical chemical, and biological limnology lake-air interactions, lake hydrology, lake level forecasting, and lake ice studies (Ann Arbor Michigan) Geophysical Fluid Dynamics Laboratory Research areas include dynamics and physics of geophysical fluid systems, development of a theoretical basis, through mathematical modeling and computer simulation, lor the behavior and properties of the atmosphere and the oceans (Princeton New Jersey) Atmospheric Physics and Chemistry Laboratory Research areas include processes of cloud and precipitation physics, chemical composition and nucleating substances in the lower atmosphere, laboratory and field experiments toward developing feasible methods of weather modification NSSL National Severe Storms Laboratory Research is directed toward improved methods of predicting and detecting tornadoes, squall lines, thunderstorms, and other severe local convective phenomena (Norman. Oklahoma) Wave Propagation Laboratory Research areas include theoretical research on radio waves. optical waves, and acoustic gravity waves experimental research and development on new forms of remote sensing WPL >:¥:«:::¥:¥::v ARL AL SEL Air Resources Laboratories Research areas include diffusion, transport, and dissipation of atmospheric contaminants development of methods for prediction and control of atmospheric pollution geophysical monitoring for climatic change (Silver Spring. Maryland! Aeronomy Laboratory Research areas include theoretical, laboratory rocket and satellite studies of the physical and chemical processes controlling the ionosphere and exosphere of the Earth and other planets, and of the dynamics of their interactions with high-altitude meteorology Space Environment Laboratory Research areas include solar-terrestial physics, service and technique development in the areas of environmental monitoring and forecasting NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION BOULDER. COLORADO 80302