Week 8 Update

1. Week 8 Update Joe Hoatam Josh Merritt Aaron Nielsen

2. Outline Range Ambiguity Velocity Ambiguity Clutter Filtering

3. Problem: Range Ambiguity • Range Ambiguity: situation in radar signal processing where received signals from different ranges appear to have the same range

4. Problem: Range Ambiguity Pulse Repetition Frequency (PRF) low, range ambiguity decreases, but velocity ambiguity increases Trade off between maximum range and maximum velocity Techniques have been developed to allow higher PRF (thus higher velocity measurements) while not incurring more range ambiguity

5. Solution: Range Ambiguity • One solution to reduce the effects of range ambiguity is a technique called phase coding • Phase Coding has an encoding and a decoding stage • In the encoding stage, transmitted signals from the radar are phase shifted by a code sequence, ak • In the decoding stage, the received signal is phase shifted by ak* to restore the phase

6. Solution: Range Ambiguity Consider the event where a signal is received with a first trip signal (phase coded by ak) and second trip signal (phase coded by ak-1) overlaid When the received signal is multiplied by ak*, the first trip signal will become coherent and the second trip signal will not be phase coded by ck= ak-1 ak* Using certain codes allows one to alter the spectra of the two signals

7. Solution: Range Ambiguity • Two important considerations are needed when choosing a phase code • Spectrum of overlaid signal has the property that R(1) (autocorrelation at lag T) is equal to zero. This allows reconstruction of the stronger signal • Capability to reconstruct signal spectrum from a small part of original spectrum • SZ (Sachidananda-Zrnic) code is constructed as follows

8. Solution: Range Ambiguity • SZ has autocorrelation of one at lags of M/n and zero autocorrelation at any other lag • SZ(n/M) code, M=number of samples, is specified by the following:

9. Solution: Range Ambiguity Velocity is calculated from the autocorrelation function by arg[R(1)] Multiplying the received signal by ak* will make the first trip signal coherent When autocorrelation is calculated, the autocorrelation of the second trip signal will have lag 1 and be equal to zero, thus not affecting the velocity estimation of the first trip signal Velocity of the first trip signal (v1) can now be recovered By use of a notch filter centered at v1, the second trip signal velocity can also be recovered

10. Solution: Range Ambiguity • Other phase codes exist • Random Phase Coding • Systematic Coding: • Simulations show SZ code more effective than these codes

11. Plans For Next Semester Implement phase coding techniques on received data from CHILL Simulate phase codes in Matlab Study phase coding techniques more in depth “Phase Coding for the Resolution of Range Ambiguities in Doppler Weather Radar” by M.Sachidananda and Dusan S. Zrnic

12. Problem: Velocity Ambiguity • Velocity Ambiguity: problem in radar data processing where received signals from different velocities have a phase shift of greater than 2π • If the wait between pulses is too long, the velocity of the object in question may exceed this maximum velocity, thereby overlapping our data and giving us a negative velocity

13. Problem: Velocity Ambiguity Pulse Repetition Frequency (PRF) high, range ambiguity increases, but velocity ambiguity decreases Various techniques have been developed to help increase both velocity and range measurements with little to no trade-off

14. Solution: Velocity Ambiguity • Use the Maximum Likelihood technique to help decrease both range and velocity ambiguities at medium- to high-PRF waveforms. • ML technique • Takes a data set and discriminates between real targets and ghost targets generated by range errors • Uses the clustering algorithm to process data

15. Solution: Velocity Ambiguity For high-PRF waveforms, a favorite algorithm was the Chinese Remainder Theorem Does not require a relationship between different PRF signals However, could yield very large errors in calculations from received signals The clustering algorithm presents a better alternative Can be used to resolve either range or velocity ambiguities

16. Solution: Velocity Ambiguity Clustering Algorithm Given a velocity measurement vector Ri, all possible range values can be given by: After arranging the vector from smallest to largest, we can find the average squared error Cv(j) for m number of consecutive ranges as: The best cluster occurs with a data set where Cv(j) is at a minimum value By taking the ratio of the second lowest Cv(j) value to the minimum, we can find the probability that they're correct

17. Plans for Next Semester If possible, test with data collected from CSU CHILL Implement the Maximum Likelihood algorithm

18. Problem: Ground Clutter • Clutter:There is always clutter in signals and it distorts the purposeful component of the signal. Getting rid of clutter, or compensating for the loss caused by clutter might be possible by applying appropriate filtering and enhancing techniques. • Ground Clutter: Ground clutter is the return from the ground. The returns from ground scatters are usually very large with respect to other echoes, and so can be easily recognized Ground-based obstacles may be immediately in the line of site of the main radar beam, for instance hills, tall buildings, or towers.

19. Solution: IIR/Pulse-Pair approach • Uses a fixed notch-width IIR clutter filter followed by time-domain autocorrelation processing (pulse-pair processing) • Drawbacks to using this approach: • Perturbations that are encountered will effect the filter output for many pulses, effecting the output for several beamwidths • The filter width has to change accordingly with clutter strength • Have to manually select a filter that is sufficiently wide to remove the clutter without being to wide so it doesn’t affect wanted data

20. Solution: FFT processing • FFT: is essentially a finite impulse response block processing approach that does not have the transient behavior problems of the IIR filter. It minimizes the effects of filter bias. • Drawbacks to this approach: • Spectrum resolution is limited by the number of points in the FFT. If the number points is to low it will obscure weather targets • When time-domain windows are applied such as Hamming or Blackman the number of samples that are processed are reduced

21. Solution: GMAP • GMAP: GMAP is a frequency domain approach that uses a Gaussian clutter model to remove ground clutter over a variable number of spectral components that is dependent on the assumed clutter width, signal power, nyquist interval and number of samples. Then a Gaussian weather model is used to iteratively interpolate over the components that were removed, restoring any of the overlapped weather spectrum with minimal bias

22. Solution: GMAP • GMAP assumptions: • Spectrum width of the weather signal is greater then clutter. • Doppler spectrum consists of ground clutter, a single weather target and noise. • The width of the clutter is approximately known. • The shape of the clutter is a Gaussian. • The shape of the weather is a Gaussian

23. GMAP Algorithm Description • First a Hamming window weighting function is applied to the In phase and quadrature phase (IQ) values and a discrete Fourier transform (DFT) is then performed. • The Hamming window is used as the first guess after analysis is complete a decision is made to either accept results or use a more aggressive window based on the clutter to signal ratio (CSR).

24. GMAP Algorithm Description • Remove Clutter points • The power in the three central spectrum components is summed and compared to the power that would be in the three central components of a normalized Gaussian spectrum. • Normalizes the power of the Gaussian to the observed power the Gaussian is extended down to the noise level and all spectral components that fall within the gaussian curve are removed. The removed components are the “clutter power”

25. GMAP Algorithm Description • Replace Clutter points • Dynamic noise case • Fit a Gaussian and fill-in the clutter points that were removed earlier keep doing this until the computed power does not change more then .2dB and the velocity does not change by more than .5% of the Nyquist velocity. • Fixed noise case • Similar to dynamic noise case except the spectrum points that are larger than the noise level are used

26. GMAP Algorithm Description • Recompute GMAP with optimal window • Determin if the optimal window was used based on the CSR • IF CSR > 40 dB repeat GMAP using a Blackman window and dynamic noise calculation. • IF CSR > 20 dB repeat GMAP using a Blackman window. Then if CSR>25dB use Blackman results. • IF CSR < 2.5 dB repeat GMAP using a rectangular window. Then if CSR < 1 dB use rectangular results. • ELSE accept the Hamming window result.

27. Plans For Next Semester • Implement new GMAP codes • Test GMAP coding on received data from CHILL