Hi, I think you maybe confusing the term "white" with Gaussian.
In terms of the Rayleigh distribution and Swerling models, that assumption is asserted for the voltage distribution (not power) for the Swerling models 1 and 2. The power distribution for those models is exponential. The Rayleigh distribution comes from taking the square root to obtain the voltage.
Swerling models 1 and 2 are applicable when you have a large number of equal-strength scatterers without having a dominant one. The question you are asking is why in those cases do you get exponential instead of Gaussian (I assume you meant Gaussian when you said white)
Normally, if you sum a number of equally-weak or strong random influences you get something that is Gaussian, but remember in this context you are talking about POWER, and you are really talking about the magnitude squared of a complex number (radar data being assumed to be complex-valued baseband samples). Assume you have a complex number with real and imaginary parts both Gaussian and independent (arising from the situation of a number of equal-strength scatterers), the magnitude squared is the sum of the real part squared and the imaginary part squared. That is exponential with mean two (chi-square with 2 dof).
The difference between Swerling models 1 and 2 comes from the decorrelation time ("scan-to-scan" vs. "pulse-to-pulse")
In terms of MATLAB code, have you looked at the Phased Array System Toolbox.
That toolbox has a number of utilities for simulating Swerling models and for CFAR detection.
