Week 9 Update

Your NameYour Title

Your Organization (Line #1)Your Organization (Line #2)

Week 9 UpdateJoe HoatamJosh Merritt

Aaron Nielsen

Outline

Aaron: Analysis of Systematic and Random coding

Josh: Maximum Likelihood

Joe: GMAP

Average Power Calculations

Average power as a function of distance was calculated and plotted for four modes

No coding (VH mode)No coding (VHS mode)Random codingSystematic (SZ) coding

Figure 1: Average power received (VH mode)

Comparison of Coding Techniques

Scatter plots were completed illustrating actual average received power (VH mode, no coding) versus measured average received power for different coding techniques

Linear regression was completed on the scatter plotsIf slope = 1, then measured results were equal to the theoretical results

The “norm of the residuals” was calculated to illustrate the deviation of points from the linear regression model

If norm = 0, then all points lie on the line of linear regression

n

iiddnorm

1

2)2,(

Comparison of Coding Techniques: SZ coding (n=128)

Comparison of Coding Techniques: Random coding

Comparison of Coding Techniques: No coding

Comparison of Coding Techniques

Signal-to-noise ratio (SNR) is the ratio of a signal power to the noise power corrupting the signal

SNR was analyzed and plotted using a RHI (row height indicator) plot for three cases

No coding (VH mode)Random codingSZ coding

Comparison of Coding Techniques: No coding (VH mode)

Figure 4: RHI plot of no coding (VH mode)

Comparison of Coding Techniques: SZ coding (n=128)

Figure 5: RHI plot of SZ coding (n=128)

Comparison of Coding Techniques: Random coding

Figure 6: RHI plot of random coding

Summarized results

Linear regression completed on scatter plotsBest: SZ coding (norm = 26.44)Middle: Random coding (norm = 27.39)Worst: No coding, VHS (norm = 29.79)

RHI plots of signal-to-noise ratioBest: SZ codingMiddle: Random codingWorst: No coding, VHS mode

Conclusions

Data collected on December 28, 2006 indicated systematic (SZ) coding outperformed both random coding and no coding techniques

Previous simulations (Sachidananda, Zrnic 1998) also indicated SZ coding outperformed other coding techniques using two performance metrics

Region of recovery of weaker signalStandard errors in mean velocity

Maximum Likelihood

Miscellaneous Questions

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.

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

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 targetsWhen time-domain windows are applied such as Hamming or Blackman the number of samples that are processed are reduced

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

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

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).


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”


Replace Clutter pointsDynamic 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 caseSimilar to dynamic noise case except the spectrum points that are larger than the noise level are used


Recompute GMAP with optimal windowDetermin 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.

Gmap With Data From CASA

Power from PRF1


Power from PRF2


Velocity from PRF1


Velocity from PRF2

Documents

Week 9 Update