This paper studies the optimum combining (OC) system with multiple arbitrary-power interferers and thermal noise in a flat Rayleigh fading environment. The main contribution of the paper is a concise performance analysis for the overload OC system where the number of interferers exceeds or is equal to the number of antennas elements. Simple closed-form formulas are derived for the moment generating function (m.g.f) of the output signal-to-interference-plus-noise ratio (SINR) and the symbol error rate (SER) with M-ary phase shift keying (M-PSK). These formulas are expressed as a finite sum involving polynomial, exponential and exponential integral terms. Based on the derived m.g.f, the closed-form explicit expressions for the moments of the output SINR are determined. Finally, asymptotic analysis illustrates that employing distinguished power control is an effective approach to combat the SER floor for the overload OC system.

This paper presents the approximate error rates of M-ary phase shift keying (MPSK) for optimum combining (OC) with multiple interferers in a flat Rayleigh fading channel. The approximations, which have been used to evaluate the performance of binary PSK for OC, are extended to the performance analysis of MPSK for OC in the presence of arbitrary numbers of antennas and interferers. The mean eigenvalues of interference-plus-noise covariance matrix are analyzed to compare the approximation techniques, i.e., first-order approximation and the orthongal approximation. Using the moment generating function (MGF)-based method, the approximate error rates of MPSK for OC are derived as the closed-form expressions in terms of the exact error rates of MPSK for MRC. The approximate analytical results show the simple and accurate way to assess the average symbol error rate of MPSK for OC with arbitrary numbers of antennas and interferers.