Error probabilities for QAM systems on partially coherent channels with intersymbol interference and crosstalk

We describe an efficient procedure to calculate the probability of error P_e for a quadrature amplitude modulation (QAM) communications system operating over a channel that introduces distortion, interference, and noise. The method is an extension of the saddlepoint integration technique introduced by Helstrom (1986) to efficiently evaluate P_e for one-dimensional pulse-amplitude modulation (PAM) systems with intersymbol interference (ISI) and crosstalk. We consider the effects of noise, random carrier phase offset, ISI, and crosstalk between the I and Q channels. The error probability is written as a double Laplace inversion integral and can be easily applied to any rectangular constellation. This integral is calculated by extending the saddlepoint integration technique to two complex dimensions. Results are presented for QAM systems with 16, 64, and 256 symbols. The technique can be directly extended to environments with cochannel interference consisting of other QAM signals