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
и
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.