albersheim
Required SNR using Albersheim’s equation
Description
Examples
Compute Required SNR for Probability of Detection
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)")
Compute Required SNR for Probability of Detection of 10 Pulses
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)")
Input Arguments
Pd
— Probability of detection
positive scalar
Probability of detection, specified as a positive scalar.
Data Types: single
| double
Pfa
— Probability of false alarm
positive scalar
Probability of false alarm, specified as a positive scalar.
Data Types: single
| double
N
— Number of pulses for noncoherent integration
1
(default) | positive scalar
Number of pulses for noncoherent integration, specified as a positive scalar.
Data Types: single
| double
More About
Albersheim's Equation
Albersheim's equation uses a closed-form approximation to calculate the SNR. This SNR value is required to achieve the specified detection and false-alarm probabilities for a nonfluctuating target in independent and identically distributed Gaussian noise. The approximation is valid for a linear detector and is extensible to the noncoherent integration of N samples.
Let
and
where PFA and PD are the false-alarm and detection probabilities, respectively
Albersheim's equation for the required SNR in decibels is:
where N is the number of noncoherently integrated samples.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
Does not support variable-size inputs.
References
[1] Richards, M. A. Fundamentals of Radar Signal Processing. New York: McGraw-Hill, 2005.
[2] Skolnik, M. Introduction to Radar Systems, 3rd Ed. New York: McGraw-Hill, 2001.
Version History
Introduced in R2011a
See Also
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