A simplified exact expression of SEP for cross QAM in AWGN channel from M × N rectangular QAM and its usefulness in Nakagami-m fading channel

This paper derives a simple exact expression of symbol error probability (SEP) for general order cross QAM constellation in the presence of additive white Gaussian noise (AWGN) channel. The key idea is to obtain this novel expression from a simple analysis of the corresponding rectangular QAM. The analysis of the expression involves simple one dimensional Gaussian Q functions unlike other complex SEP expressions. A simple tight bound approximation of the proposed exact SEP is also given, which provides performance improvement over the existing SEP approximations, particularly for low signal to noise ratios (SNRs). Also, with the help of simulation results, we show that the proposed approximation is in excellent agreement with the exact SEP curve. Moreover, the proposed expressions prove to be useful for accurate estimation of the SEP in Nakagami-m fading channel, including the special case of Rayleigh fading (m = 1).