PDF of the sum of Rician signals and Gaussian noise

We derive a general probability density function (PDF) expression for the envelope of the sum of L Rician signals and an additive white Gaussian noise (AWGN) process. This PDF is often required for analyzing the error probability performance of several multiple access systems adopting the M-ary frequency-shift-keying (MFSK) and non-coherent detection. The derived exact PDF is in the form of a definite integral of a rather complicated function. We therefore present a closed-form formula for the exact PDF by employing a generating function for the Laguerre polynomials. We also propose an approximation of the PDF, which is accurate when the number of Rician signals, L, is sufficiently large. Finally, we examine and compare the accuracies of the closed-form formula and the proposed approximation for the PDF.