Performance prediction of the incoherent detector for a weibull fluctuating target

We deal with performance prediction of the incoherent radar receiver (i.e., squared law plus integrator) in the presence of independent nonidentically distributed (non-id)Weibull target echoes. First, we provide the probability density function (pdf) for the sum of independent but non-idWeibull random variables in terms of an infinite sum of Gamma pdfs. Then we develop an analytic expression for the detection probability as a fast converging series of functions. Finally, we study the approximation error and convergence rate of the quoted series, and evaluate the impacts on the detection performance of non-id Weibull target parameters.