Required SNR using Shnidman’s equation
Compute Single-Pulse SNR
Find and compare the required single-pulse SNR for Swerling cases I and III. The Swerling case I has no dominant scatterer while the Swerling case III has a dominant scatterer.
Specify the false-alarm and detection probabilities.
pfa = 1e-6:1e-5:.001; Pd = 0.9;
Allocate arrays for plotting.
SNR_Sw1 = zeros(1,length(pfa)); SNR_Sw3 = zeros(1,length(pfa));
Loop over PFAs for both scatterer cases.
for j=1:length(pfa) SNR_Sw1(j) = shnidman(Pd,pfa(j),1,1); SNR_Sw3(j) = shnidman(Pd,pfa(j),1,3); end
Plot the SNR vs PFA.
semilogx(pfa,SNR_Sw1) hold on semilogx(pfa,SNR_Sw3) hold off xlabel("False-Alarm Probability") ylabel("SNR") title("Required Single-Pulse SNR for Pd = "+Pd) legend("Swerling Case "+["I" "III"],Location="southwest")
The presence of a dominant scatterer reduces the required SNR for the specified detection and false-alarm probabilities.
Pd — Probability of detection
Probability of detection, specified as a positive scalar.
Pfa — Probability of false alarm
Probability of false alarm, specified as a positive scalar.
N — Number of pulses for noncoherent integration
1 (default) | positive scalar
Number of pulses for noncoherent integration, specified as a positive scalar.
Shnidman's equation is a series of equations that yield an estimate
of the SNR required for a specified false-alarm and detection probability.
Like Albersheim's equation, Shnidman's equation is applicable to a
single pulse or the noncoherent integration of
Unlike Albersheim's equation, Shnidman's equation holds for square-law
detectors and is applicable to fluctuating targets. An important parameter
in Shnidman's equation is the Swerling case number.
Swerling Case Number
The Swerling case numbers characterize the detection problem for fluctuating pulses in terms of:
A decorrelation model for the received pulses
The distribution of scatterers affecting the probability density function (PDF) of the target radar cross section (RCS).
The Swerling case numbers consider all combinations of two decorrelation models (scan-to-scan; pulse-to-pulse) and two RCS PDFs (based on the presence or absence of a dominant scatterer).
|Swerling Case Number||Description|
|0 (alternatively designated as 5)||Nonfluctuating pulses.|
|I||Scan-to-scan decorrelation. Rayleigh/exponential PDF–A number of randomly distributed scatterers with no dominant scatterer.|
|II||Pulse-to-pulse decorrelation. Rayleigh/exponential PDF– A number of randomly distributed scatterers with no dominant scatterer.|
|III||Scan-to-scan decorrelation. Chi-square PDF with 4 degrees of freedom. A number of scatterers with one dominant.|
|IV||Pulse-to-pulse decorrelation. Chi-square PDF with 4 degrees of freedom. A number of scatterers with one dominant.|
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
Does not support variable-size inputs.
 Richards, M. A. Fundamentals of Radar Signal Processing. New York: McGraw-Hill, 2005.
Introduced in R2011a