shnidman

Required SNR using Shnidman's equation

Syntax

SNR = shnidman(Prob_Detect,Prob_FA)
SNR = shnidman(Prob_Detect,Prob_FA,N)
SNR = shnidman(Prob_Detect,Prob_FA,N, Swerling_Num)

Description

SNR = shnidman(Prob_Detect,Prob_FA) returns the required signal-to-noise ratio in decibels for the specified detection and false-alarm probabilities using Shnidman's equation. The SNR is determined for a single pulse and a Swerling case number of 0, a nonfluctuating target.

SNR = shnidman(Prob_Detect,Prob_FA,N) returns the required SNR for a nonfluctuating target based on the noncoherent integration of N pulses.

SNR = shnidman(Prob_Detect,Prob_FA,N, Swerling_Num) returns the required SNR for the Swerling case number Swerling_Num.

Examples

Find and compare the required single-pulse SNR for Swerling cases I and III.

Pfa = 1e-6:1e-5:.001; % False-alarm Probabilities
Pd = 0.9; % Probability of detection
SNR_Sw1 = zeros(1,length(Pfa)); % Preallocate space.
SNR_Sw3 = zeros(1,length(Pfa)); % Preallocate space.
for j=1:length(Pfa)
    % Swerling case I-No dominant scatterer
    SNR_Sw1(j) = shnidman(Pd,Pfa(j),1,1);
    % Swerling case III-Dominant scatterer
    SNR_Sw3(j) = shnidman(Pd,Pfa(j),1,3);
end
semilogx(Pfa,SNR_Sw1,'k','linewidth',2);
hold on;
semilogx(Pfa,SNR_Sw3,'b','linewidth',2);
axis([1e-6 1e-3 5 25]);
xlabel('False-Alarm Probability');
ylabel('SNR');
title('Required Single-Pulse SNR for P_d=0.9');
legend('Swerling Case I','Swerling Case III',...
    'Location','SouthWest');

Note that the presence of a dominant scatterer reduces the required SNR for the specified detection and false-alarm probabilities.

More About

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Shnidman's Equation

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 N pulses. 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 NumberDescription
0 (alternatively designated as 5)Nonfluctuating pulses.
IScan-to-scan decorrelation. Rayleigh/exponential PDF–A number of randomly distributed scatterers with no dominant scatterer.
IIPulse-to-pulse decorrelation. Rayleigh/exponential PDF– A number of randomly distributed scatterers with no dominant scatterer.
IIIScan-to-scan decorrelation. Chi-square PDF with 4 degrees of freedom. A number of scatterers with one dominant.
IVPulse-to-pulse decorrelation. Chi-square PDF with 4 degrees of freedom. A number of scatterers with one dominant.

References

[1] Richards, M. A. Fundamentals of Radar Signal Processing. New York: McGraw-Hill, 2005, p. 337.

See Also

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