swerling_pd

(rtools/swerling_pd.m)

Function Synopsis

Pd=swerling_pd(ax,SNR,N,model)

Help text

function Pd=swerling_pd(threshold,SNR,No_Pulses,model)
 
 This gives the Probability of Detection given an input of (linear)
 Signal to Noise Ratio for a class of Swerling models. This is the
 ideal fixed threshold case, i.e. it will suffer further CFAR loss.

 fluctuating model should be 1 to 4
 non-fluctuating model is referred to as case 0 or 5, both accepted.

 Some cases are necessarily an approximation, don't rely on the exact value
 but in practice it seems good enough. Anyway, the approximation
 error is far outweighed by the variability in the noise.

 Uses logs for numerical stability.

 NOTE: The Pearson's form of the gamma function in [1], Matlab and
 Mathematica all have different ways of defining the GAMMA(a,b) function
 be _very_ careful - see A & S.
 Conversion from Pearson's form of the Incomplete gamma function in [1].
 I(u,p)=gammainc(p+1,u*sqrt(p+1)) see [3] Sec. 6.5.6

 Source:
 [1] `Probability of Detection for Fluctuating Targets', P. Swerling, 
     (1960), IRE Trans. Inform. Theory IT-6 (271), p273-308.
 [2] A misplaced reference for Swerling 0/5 case - I think it is:
     Meyer & Mayer, "Radar Target Detection Handbook of Theory & Practice", 1973
 [3] `Handbook of Mathematical Functions', M. Abramowitz and I. Stegun, Dover Edition,
     Equivalent to 1970 edition.

 Part of the Matlab Radar Toolbox v0.11 by Glen Davidson at www.radarworks.com
 Please acknowledge use of this toolbox in any publication or software.
 This header must be retained in any derivative work

Cross-Reference Information

cfar_theory_demo              rtools/cfar_theory_demo.m
k_detection_demo              rtools/k_detection_demo.m