In this paper, we introduce a simple geometric approach that is based on signal-space concepts to efficiently evaluate the performance of M-ary phase-shift keying (M-PSK) and M-ary quadrature amplitude modulation (M-QAM) schemes over an additive white Gaussian noise channel. In particular, new bit error rate approximations are derived and shown to be in excellent agreement with Monte Carlo simulation results.
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Lu et al. (1999) studied this question.