Time Series (I&Q) (Signal with enhanced SNR) Cohere with current tx phase - first trip. Cohere with previous tx phase - second trip

Transcription

1 RANDOM PHASE PROCESSING FOR THE RECOVERY OF SECOND TRIP ECHOES Paul Joe, Richard Passarelli Jr., Alan Siggia and John Scott AES and SIGMET 1 Introduction The introduction of Doppler technology into operational weather radar networks is now commonplace. For reasons to be explained in the following section, Doppler radars provide ambiguous estimates of target velocity and range that can potentially confound the interpretation of the received information. This is commonly known as the range and velocity folding problem. These eects are intimately intertwined. This paper will describe signal processing techniques to mitigate these eects. The focus will be primarily on the problem of range folding. 2 The Velocity-Range Dilemma In weather radars, the Doppler velocity (V r ) of the target is measured by the pulse to pulse dierence in the phase of the received signal. To measure reasonable unambiguous velocities, the time between transmitted pulses () is kept small by transmitting the radar pulses quickly. The maximum range of a radar (r max ) is determined by the distance that a radar pulse can travel to and return from in the time between successive pulse transmissions. Targets beyond r max will still return a signal (echo) back to the radar. The signal will be received after the next pulse is transmitted. Since, the radar processing assumes that the echo should be located with respect to the most recently transmitted pulse, the target will be incorrectly located and the target has been termed to have been range folded. Large Nyquist velocities require high pulse repetition frequencies while large maximum ranges require low pulse repetition frequencies. This tradeo is described by the following equation. V Nyquist r max = c 8 (1) 3 Eect of Multiple Trip Echo Eects The eect of range folded echoes depends on the type of transmitter. Coherent systems (e.g., klystron) transmit pulses that are consistent in phase from pulse to pulse. Coherenton-receive systems (e.g., magnetron) transmit pulses that are random in phase. Since the phase of each transmitted pulse is the same for coherent systems, the Doppler shift for multiple trip echoes can be retrieved. For coherent-on-receive systems, the multiple trip echo signal is processed with a transmitted pulse that is unrelated and therefore the resulting Doppler shift is essentially random. When several pulses are averaged to improve parameter estimation, the random Doppler shifts from the multiple trip echoes will statistically have an expected value of zero. Therefore, the Doppler information from second trip echoes cannot be recovered. This has the advantage in that they are eectively eliminated and do not confound echoes within the rst trip. However, there will still be a power (zero moment) contribution. 1

2 4 Second Trip When echoes beyond the maximum range are recorded in such a position to coincide with the location of rst trip echoes, the echoes are said to be overlaid. The range folding problem can completely obscure radar echoes and/or confound the Doppler imagery for coherent systems. It is also desirable to extend the range of the radar to increase the areal coverage, despite the type of Doppler radar. For a coherent-on-receive radar, the random phase of system can be exploited to range unfold the data. With these systems, the second trip echoes do not obscure the echoes in the rst trip because statistical averaging eliminates the eect of echoes from the second trip. A logical consequence is that if the echoes were processed with respect to the previously transmitted pulse, then the processing will yield echoes from the second trip and the rst trip echoes are statistically eliminated. For coherent systems, a pseudo-random phase sequence could be statistically constructed and introduced to the transmitter pulse through a phase shifter. Laird (1981) tested this phase coding concept and concluded that the second trip echo could be recovered if it was greater than -10 db of the rst trip echo. The rst trip echo appears as "white" noise and the -10 db represents the minimum usable signal to noise ratio. Sachidanana and Zrnic (1986) constructed a pseudo-random phase sequence that splits the spectrum of the unwanted signal and allows for autocovariance signal processing eective to about -15 db. Siggia (1983) relaxed the constraint by using an adaptive whitening lter to reduce the contribution of the rst trip power. A rst order maximum entropy and unit-vector lters were tested and demonstrated by numerical simulation that -30 db dierence could be tolerated. Analysis by Zrnic and Mahapatra (1984) concluded that narrow spectra widths are needed to get these results and that the overlaid echo power must be at least -3dB. Siggia (1983) shows the actual recovery of a second trip weather echo using the maximum entropy approach. The restriction in signal power is signcant when considering reectivity values that have been range normalized (Joe et al, 1994). A tolerance of -10dB means that the second trip echo must be at least 30dBZ higher than the rst trip echo to recover and this explains why second trip echo eects do not aect rst trip echoes unless there are strong echoes in the second trip. 5 Implementation Issues Random phase processing is under development at the King Weather radar stations (Crozier et al, 1991). The phase of the current and previously transmitted pulse must be digitally recorded and stored in the signal processor. The signal processor must be programmed to store and to process received echo phases with respect to this information. The COHO is not needed to lock to the phase of the transmitted pulse since it is now done digitally in the signal processor. The COHO is allowed to run freely which may improve the stability of the system. There are three signicant issues in implementing this phase coding scheme. The rst issue involves introducing a pseudo-random phase coding to coherent radar systems or measuring the phase of the transmitted pulse for coherent-onreceive systems. For coherent radar systems, phase diversity must be introduced since for these radars the phase is consistent from pulse to pulse (Chakrabarti and Tomlinson, 1976). This can be done by adding a phase shifter after the coherent oscillator (COHO) and before the transmitter (Siggia, 1983). For a coherent-onreceive system, the natural random phase of the system can be exploited. The ability to get an accurate digital sample the phase of the transmitted pulse without adding additional phase noise is crucial to recovering the second trip. Phase stability was measured by pointing the radar at a stationary targets, in this case, an isolated tower. It should be kept in mind that even under moderate winds, 2

3 3 Figure 1: Random Phase Signal. See text for details. The shaded boxes indicate standard processing. the objects will sway and will appear as phase noise in these tests. The IF magnetron sample burst derived from the AFC mixer is switched into the quad phase detector in order to bypass the receiver. The I and Q values are sampled by the signal processor and the phases are corrected digitally. This required additional circuitry consisting of a high speed switch and IF amplier to by-pass the linear receiver. In addition, a one shot trigger delay was added to help position the sample. Testing showed that the digital phase locking yielded results with the same accuracy as the analog approach. Phase noise values of about 1:2 o were observed at pulse widths of 0.5 and 2.0 microseconds. This allows approximately 30 db of signal difference needed for clutter cancellation or for second trip echo recovery. Testing on a more modern (that is, more stable) S-band system at the EEC factory using a dummy load and a microwave echo delay line, instead of a stationary target, a phase noise value of 0:8 o for a 0.8 microsecond pulse could be achieved. Another key issue for the implementation of random phase processing is that the performance of the phase diversity processing must be improved to recover second trip echoes in a broad range of weather conditions. The adaptive whitening lter approach, applied by Siggia (1983) showed considerable potential, able to retrieve the second trip echo within 30 db of the rst trip echo. Table 2 is a list of potential candidates for the adpative whitening lter. The main message from this list is that there are a variety of possible heurstic approaches. An important property of the whitening Table 1: Adaptive Whiteners - Frequency Domain Name Description No Filter Re-cohere for second trip with no whitening. Unit Normalize to 1, each frequency Vector component. Fixed 2.5W Half Nyquist Unit Vector A xed notch 2.5 W wide centred about the mean. The components in the notch are replaced by the magnitude of the noise outside the notch, preserving the phase. Replace V Nyquist / 2 about the mean velocity with the noise level preserving the phase. ComponentReplace all com- greater than twice the thresholdingponents noise level with the noise level, preserving the phase. Dynamic Compute the width of the lter based on the spectrum Filter and Noise width and signal power and ll the lter region with noise power, preserving the phase. Fill Dynamic Filter and Zero Fill As above, except zero ll the lter region. lter is that in the event that there is not coherent power to remove, the whitening lter must pass the signal without change. Simulations indicate that the Dynamic Filter with zero ll produces the best results. Even at 30 db signal dierence, the second trip moment recovery is shown in Fig. 2. The mean velocities were 0.10 and -0.25, spectral widths were 0.10 and 0.20, as a fraction of the Nyquist interval and the SQI were 0.95 and 0.68 for the rst and second trip echoes respectively. Fig. 2 contrasts the performance of the no

4 4 Cohere with current tx phase - first trip Build Adaptive whitener for 1st trip Whiten 1st trip Recohere for other trip Time Series (I&Q) Cohere with previous tx phase - second trip Build Adaptive whitener for 2nd trip Whiten 2nd trip Recohere for other trip (Signal with enhanced SNR) 2nd trip echo st trip echo Figure 2: Random Phase Signal. See text for details. The shaded boxes indicate standard processing. lter approach with the dynamic width lter with zero ll for the recovery of the second trip echo velocity. Each marker represents a separate simulation. The no lter approach can not retrieve the second trip echo velocity when the rst trip is greater than the second trip echo power. However, with the dynamic lter with zero ll approach, the simulation shows that it is successful even when the rst trip exceeds the second trip power by up to 30 db. The third issue is the need for sucient processing power and speed to keep up with the data acquisition. Fig. 3 shows that there is about a four fold increase in computation. It is only recently that commercially available digital signal processing hardware could perform the necessary computations in real-time. The system requires FFT processing of the received signal to simplify the development of the algorithms. FFT (as opposed to autocovariance) processing allows for nonlinear heuristic algorithms to be evaluated that may have superior performance - as with ground clutter lters (Passarelli et al, 1981; Crozier et al, 1991). 6 Conclusions Phase diversity or coding of the transmitted pulse can be used to retrieve multiple trip echoes, doubling the useful range of the radar. An implementation of this is under way at the King Weather Radar facility. Tests have shown that digital sampling of the main bang on two conherent-on-receive Doppler radar system has proven to be sucient to recover second trip echoes or to cancel clutter with 30dB dierence. Appropriate candidates for the whitening lter have been identied for velocity retrieval and wait for real-time testing. Signal strength estimation algorithms remain to be developed. It must be kept in mind that the adaptive whitening process has its own characteristics (contributes to the noise) that must be considered. The adaptive whitener must be able to remove coherent power with minimal distortion of the 'hidden' other echo. It is important to mention that the implementation of random phase processing for the retrieval of the second trip echo is a no-loss proposition. The retrieval of rst trip echo is unaected. When there is a large power dierence between the trips, the weaker echo (usually second trip) will appear 'white' and the whitening lter also will be 'white'. The weaker trip will pass through the processing unaected and further processing will recover the stronger signal. This case occurs when there is a strong rst trip and a weak second trip overlaying echo or when there is no rst trip echo. In the rst case, the processing identical with standard processing and in the latter case, the second trip echo is recovered and correctly located in range. In the case of a strong signal (usually rst trip) with very broad spectrum, the other trip information is lost, since the strong signal (noise) will dominate the weak noise (signal), and the technique eectively reverts to standard processing.

5 7 Acknowledgements The Doppler Project Oce of the Atmospheric Environment Service under the leadership of Eric Aldcroft provided support and partial funding for the project. The engineers at Enterprise Electronic Corporation were very cooperative in providing a radar and facilities to conduct some of the tests. 8 References 1. Bergen, W.R. and S.C. Albers, 1988: Two and three dimensional de-aliasing of Doppler radar velocities, JTech, 5, Sachidananda, M. and D.S. Zrnic, 1986: Recovery of spectral moments from overlaid echoes in a Doppler weather radar, IEEE Trans. on Geosci. Remote Sens., GE-24, No. 5, Siggia, A.D., 1983: phase coded radar signals with adaptive digital lters, 21st Conf. Radar Met., AMS, Zrnic, D.S. and P. Mahapatra, 1985: Two methods of ambiguity resolution in pulse Doppler weather radars, IEEE Trans. on Aerospace and Electronic Systems, AES- 21, Chakrabarti, N. and M. Tomlinson, 1976: Design of sequences with specied autocorrelation and cross-correlation, IEEE Trans. on Communications, COM-24, 3. Crozier, C.L., P. Joe, J.W. Scott, H.N. Herscovitch and T.R. Nichols, 1991: The King City operational Doppler radar: development, all season applications and forecasting, Atmosphere-Ocean, 29, Eilts, M.D. and S.D. Smith, 1990: Ecient dealiasing of Doppler velocities using local environment constraints, JTech, 7, Joe, P. and M. Leduc, 1990: Radar signatures and severe weather forecasting, in The Tornado: Its structure, dynamics, prediction and hazards, Church, C., D.Burgess, C. Doswell and R. Davies- Jones, Editors, 1993: Amer. Geoph. Union, Geophysical Mono. 79, Laird, B.G., 1981: On ambiguity resolution by random phase processing, 20th Conf. Radar Met., AMS, Passarelli, R., P. Romanik, S.G. Geotis and A.D. Siggia, 1981: Ground clutter rejection in the frequency domain, 20th Conf. Radar Me., AMS,