Page 546 - Fundamentals of Radar Signal Processing

location, as seen in Fig. 7.1b; the actual peak in this realization (expanded in the

inset) is at –0.033 Rayleigh widths. The larger the noise variance, the greater
the likely deviation of the measurement from the noise-free case.
Because of the noise, the measured peak value is now a random variable
(RV). If the peak measurement is repeated on noisy data many times, the PDF of
that RV can be estimated. Figure 7.2 shows two histograms for the observed
peak location when complex Gaussian noise at two values of peak SNR is

added to the received signal prior to the detector. The black curves are zero-
mean Gaussian PDFs with the same variance as the simulated data. In Fig. 7.2b,
the SNR is 20 dB lower (a factor of 100× in power) than in 7.2a, resulting in a
wider angle error distribution than in the higher SNR case. In this example, the
variance of the distribution in Fig. 7.2b is 9.54 times that of the distribution in
Fig. 7.2a. This factor is approximately the square root of the 100× change in
SNR.