On the BEP analysis of M-QAM and R-QAM under cascaded double η-μ, κ-μ or α-μ fading channels

Abstract

This article presents new expressions for the bit error probability (BEP) of the M-ary quadrature amplitude modulation (M-QAM) and rectangular QAM (R-QAM) scheme in a frequency non-selective channel model with cascaded double fading, characterized in the links by the distributions η-μ, κ-μ or α-μ. In this paper, the probability density function (PDF) of the signal-to-noise ratio (SNR) of the double link is written in terms of an integral of the product of the PDF of the envelope of the first link by the PDF of the SNR of the second link. With this procedure, expressions for the BEP of the M-QAM and R-QAM scheme, with and without a maximum ratio combiner (MRC) associated, are obtained by means of the general expressions of Cho and Yoon, calculated with the help of the Gauss-Laguerre quadrature. The new expressions are written in terms of the integral of the moment generating function (MGF) of the instantaneous SNR from the second link, which are simpler than using expressions involving infinite series in terms of special functions like hypergeometric functions and the Meijer G-function. In addition, insights regarding the expressions obtained and comments about their complexity are provided. Several curves for the BEP are presented, for different parameters that characterize the channel and different numbers of branches of the MRC. All analytical expressions obtained in this paper are corroborated by computer simulations performed with the Monte Carlo method.