albersheim

Signal-to-noise ratio (SNR) usage of Albersheim’s equation.

Library

EngeePhased.

Syntax

Function call

You can call the albersheim function in the following ways:

SNR = albersheim(Pd,Pfa) returns the signal-to-noise ratio (SNR), in dB. This value indicates the ratio required to achieve the specified probabilities of detection (argument Pd) and false alarm (argument Pfa) for a single signal.
SNR = albersheim(Pd,Pfa,N) specifies the required signal-to-noise ratio (SNR) for the non-coherent integration of N samples.

Arguments

Input

Pd — detection probability
`positive scalar

Details

The probability of detection given as a positive scalar.

Data types: single | Float64

Pfa — false alarm probability
`positive scalar

Details

The probability of a false alarm, given as a positive scalar.

Data types: single | Float64

N - number of pulses for incoherent integration
1 (by default) | positive scalar

Details

The number of pulses for incoherent integration, set as a positive scalar.

Data types: single | Float64

Examples

Calculating SNR for detection probability

Details

Calculate the required signal-to-noise ratio (SNR) value for a single pulse to obtain a detection probability equal to 0.9, depending on the probability of false alarm.

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

Pd = 0.9
Pfa = 0.0001:0.0001:0.01
snr = albersheim.(Pd, Pfa) # Выполнение цикла уравнения Альберсгейма для всех вероятностей ложной тревоги.
plot(Pfa, snr, xaxis = :log10, title = "Required SNR for P_D = $Pd (N = 1)", ylabel = "Required SNR (dB)", xlabel = "Probbility of False Alarm", legend = false, minorgrid = true)

Calculating SNR for detection probability of 10 pulses

Details

Calculate the required signal-to-noise ratio (SNR) value from 10 incoherently integrated pulses to obtain a detection probability equal to 0.9, depending on the probability of false alarm.

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

Pd = 0.9
Pfa = 0.0001:0.0001:0.01
Npulses = 10
snr = albersheim.(Pd, Pfa, Npulses) # Выполнение цикла по уравнению Альберсхайма для всех вероятностей ложной тревоги.
plot(Pfa, snr, xaxis = :log10, title = "Required SNR for P_D = $Pd (N = $Npulses)", ylabel = "Required SNR (dB)", xlabel = "Probbility of False Alarm", legend = false, minorgrid = true)

Additional Info

Albersheim equation

Details

The Albersheim equation uses a closed form approximation to calculate the signal-to-noise ratio (SNR). This SNR value is required to achieve specified detection and false alarm probabilities for a static target in the presence of independent and identically distributed Gaussian noise. The approximation is valid for a linear detector and can be extended to incoherent integration of N samples.

Let

where and are false alarm and detection probabilities, respectively.

Albersheim equation for the required SNR in dB:

where N is the number of incoherently integrated samples.