Exact error probability analysis of rectangular QAM for single- and multichannel reception in nakagami-m fading channels

Abstract

In this contribution, we derive exact closed-form expressions for the average symbol error probability (SEP) of arbitrary rectangular quadrature amplitude modulation (QAM) for single- and multichannel diversity reception over independent but not-necessarily identically distributed Nakagami-m fading channels. The diversity branches may hence exhibit identical or distinctive power levels and their associated Nakagami indexes need not be the same. Our work extends previous results pertaining to nondiversity reception of M-ary rectangular QAM over Rayleigh fading channels and multichannel reception of M-ary square QAM over Nakagami-m fading channels. For a given number L of diversity branches and a corresponding set of arbitrary real-valued Nakagami indexes not less than 1/2, our SEP results are expressed in terms of Gauss's hypergeometric function <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and Lauricella's multivariate hypergeometric function F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(L)</sup> of L variables, both of which can be efficiently evaluated using standard numerical softwares.