albersheim

Required SNR using Albersheim’s equation

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Syntax

SNR = albersheim(Pd,Pfa)
SNR = albersheim(Pd,Pfa,N)

Description

SNR = albersheim(Pd,Pfa) returns the signal-to-noise ratio in decibels. This value indicates the ratio required to achieve the given probabilities of detection Pd and false alarm Pfa for a single sample.

example

SNR = albersheim(Pd,Pfa,N) determines the required SNR for the noncoherent integration of N samples.

example

Examples

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Open Live Script

Compute the required SNR of a single pulse to achieve a detection probability of 0.9 as a function of the fals- alarm probability.

Set the probability of detection to 0.9 and the probabilities of false alarm from 0.0001 to 0.01.

Pd = 0.9;
Pfa = 0.0001:0.0001:.01;

Loop the Albersheim equation over all false-alarm probabilities.

snr = zeros(1,length(Pfa));
for j = 1:length(Pfa)
    snr(j) = albersheim(Pd,Pfa(j));
end

Plot the SNR as a function of false-alarm probability.

semilogx(Pfa,snr)

grid
axis tight
xlabel("Probability of False Alarm")
ylabel("Required SNR (dB)")
title("Required SNR for P_D = "+Pd+" (N = 1)")

Figure contains an axes object. The axes object with title Required SNR for P_D = blank 0 . 9 blank (N blank = blank 1 ), xlabel Probability of False Alarm, ylabel Required SNR (dB) contains an object of type line.

Open Live Script

Compute the required SNR of 10 noncoherently integrated pulse to achieve a detection probability of 0.9 as a function of the false-alarm probability.

Set the probability of detection to 0.9 and the probabilities of false alarm from 0.0001 to 0.01.

Pd = 0.9;
Pfa = 0.0001:0.0001:.01;
Npulses = 10;

Loop over the Albersheim equation over all the false-alarm probabilities.

snr = zeros(1,length(Pfa));
for j = 1:length(Pfa)
    snr(j) = albersheim(Pd,Pfa(j),Npulses);
end

Plot the SNR as a function of the false-alarm probability.

semilogx(Pfa,snr)

grid
axis tight
xlabel("Probability of False Alarm")
ylabel("Required SNR (dB)")
title("Required SNR for P_D = "+Pd+" (N = 10)")

Figure contains an axes object. The axes object with title Required SNR for P_D = blank 0 . 9 blank (N blank = blank 10 ), xlabel Probability of False Alarm, ylabel Required SNR (dB) contains an object of type line.

Input Arguments

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Probability of detection, specified as a positive scalar.

Data Types: single | double

Probability of false alarm, specified as a positive scalar.

Data Types: single | double

Number of pulses for noncoherent integration, specified as a positive scalar.

Data Types: single | double

More About

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Extended Capabilities

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Version History

Introduced in R2011a

See Also