BER analysis of arbitrary rectangular QAM

M-ary quadrature amplitude modulation (M-ary QAM) is an attractive technique to achieve high rate transmission without increasing the bandwidth in wireless communication systems. A great deal of attention has been devoted to the study of bit error rate (BER) performance of M-ary square QAM constellations. Approximate expressions for bit error probabilities of M-ary square QAM have recently been developed by J.J. Lu et al. (1999) and L. Yang and L. Hanzo (2000) based on signal-space concepts and recursive algorithms, respectively. However, it is only recently that an exact generalized closed form expression for the BER of M-ary square QAM constellation has been developed (see Yoon, D. et al., IEEE VTC Fall 2000, vol.5, p.2422-7, 2000). We extend that previous work of ours to an arbitrary I/spl times/J rectangular QAM (R-QAM) scheme. A general closed form expression for the exact BER performance of an arbitrary I/spl times/J R-QAM with Gray code mapping is derived and analyzed under an additive white Gaussian noise (AWGN) channel. The BER performance is also analyzed under fading channels. It is shown that there is a noticeable deviation in the BER performance between the approximation and exact expression over low SNR values.