RT_Kcdf_noise

(rtools/RT_Kcdf_noise.m)

Function Synopsis

[p,q] = RT_Kcdf_noise(Ivec,nu,mu,rho,tol)

Help text

function [p,q] = RT_Kcdf_noise(I,nu,mu,rho,tol)

 Gives the CDF of the K distribution in noise, this is a double integral.
 The intensity integral [0,I] dI was evaluated via mathematica.
 The remaining integral [0,inf] d(rho) is numerically calculated

 The K distribution has mean mu and shape parameter nu 
 in the presence of thermal noise with variance rho.

 Overall mean = mu + rho

 The singularity at 0 was removed using an integral transform, the
 integration limits are expanded towards infinity as a power of 2.
 The initialisation limit is determined from those suitable for the
 limit distribution of rho->0.

 The numerical integration to infinity is sensitive to
 extreme values for the mean clutter (mu) and noise component (rho).
 The routine rescales the input but if rho >> mu or mu >> rho by a
 factor of 1e3, the corresponding limit distribution is used (and
 a warning is produced).

 This limit of +/- 30dB is not good enough (see [1] for example), but
 without it numerical convergence is slow/unreliable. Modify the
 code and send me the result if this is a problem.

 Source: Direct Evaluation

 [1] `Effect of noise on order parameter estimation for K-distributed clutter', 
 P. Lombardo, C.J. Oliver and R.J.A. Tough, IEE Proc. Radar, Sonar and Navigation,
 1995, 142(1) pp 33-40


 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

RT_Kcdf                       rtools/RT_Kcdf.m
RT_gamcdf                     rtools/RT_gamcdf.m
aux_Kcdf_noise_Zlog           rtools/aux_Kcdf_noise_Zlog.m

k_noise_demo                  rtools/k_noise_demo.m