detectability

Radar detectability factor

Since R2021a

Syntax

D = detectability(PD,PFA)

D = detectability(PD,PFA,N)

D = detectability(PD,PFA,N,SW)

Description

D = detectability(PD,PFA) returns the detectability factor of a single radar pulse given the probability of detection PD and probability of false alarm PFA.The function assumes that you are using a square-law detector and a nonfluctuating target.

D = detectability(PD,PFA,N) returns the detectability factor using the number of pulses for noncoherent integration N. .The function assumes that you are using a nonfluctuating target.

D = detectability(PD,PFA,N,SW) returns detectability factor using the Swerling case number SW. The function assumes you are using a chi-square distributed target.

Examples

Detectability Factor for Swerling 1 Case Target

Calculate the detectability factor for a Swerling 1 case target. Assume a probability of detection from 0.01–0.99, probability of false alarm of 1e-6, and 24 received pulses.

PFA = 1e-6; 
PD = 0.01:0.01:0.99;
N = 24;  
D = detectability(PD,PFA,N,'Swerling1');       

Plot the detectability factor.

plot(PD,D)
xlabel('Probability of Detection');
ylabel('Detectability (dB)');
grid on

Input Arguments

PD — Probability of detection

positive scalar | length-J vector

Probability of detection, specified as a positive scalar in the range (0,1) or as a length-J vector with each element in the range (0,1).

PFA — Probability of false alarm

positive scalar | length-K vector

Probability of false alarm, specified as a positive scalar in the range (0,1) or as a length-K vector with each element in the range (0,1).

N — Number of pulses for noncoherent integration

1 (default) | positive scalar

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

SW — Swerling case number

'Swerling0' (default) | 'Swerling1' | 'Swerling2' | 'Swerling3' | 'Swerling4' | 'Swerling5'

Swerling case number, specified as one of these

• 'Swerling0'

• 'Swerling1'

• 'Swerling2'

• 'Swerling3'

• 'Swerling4'

• 'Swerling5'

Output Arguments

D — Detectability factor

J-by-K matrix

Detectability factor, returned as a J-by-K matrix in dB with rows corresponding to the number of elements in PD and columns corresponding to the number of elements in PFA.

Algorithms

Computation methods used in detectability function

The function computes detectability using the computation methods summarized in this table.

Swerling Case Number	PD is in the range [0.2, 1-1e-6] and PFA < 1e-4	PD outside the range [0.2, 1-1e-6] or PFA ≥ 1e-4
0 or 5	Shnidman's approximation	Exact computation
1, 2, 3, 4	Barton's universal equation	Exact computation

For Swerling1 and N = 1 and Swerling2 and N set to any positive scalar, the function computes the radar detectability factor with no approximation errors using Barton's universal equation. For other Swerling cases, there are small approximation errors when PD is in the range [0.2, 1-1e-6] and PFA < 1e-4.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2021a