Error Performance Analysis of $M$ -ary $\theta$ -QAM

In this paper, we derive new exact and general expressions for the symbol error rate (SER) and bit error rate (BER) of M-ary θ-quadrature amplitude modulation (QAM) for M = 2^l , I ≥ 4, based on not only square-QAM (SQAM) for M = 2^2l, I ≥ 2 but cross-QAM (CQAM) as well, for M = 2^2l+1, I ≥ 2 in additive white Gaussian noise (AWGN) and various fading channels; we also present the optimum angle and constellation of M-ary θ-QAM. Through computer simulations, we confirm the results of the theoretical analysis. Because the SER and BER expressions are provided in terms of 2-D Gaussian Q-function in AWGN and various fading channels, they will be very useful for numerical evaluations in various cases of practical interest in QAM systems.