Upper bounds on the bit error rate of optimum combining in wireless systems

This paper presents upper bounds on the bit-error rate (BER) of optimum combining in wireless systems with multiple cochannel interferers in a Rayleigh fading environment. We present closed-form expressions for the upper bound on the bit-error rate with optimum combining, for any number of antennas and interferers, with coherent detection of BPSK and QAM signals, and differential detection of DPSK. We also present bounds on the performance gain of optimum combining over maximal ratio combining. These bounds are asymptotically tight with decreasing BER, and results show that the asymptotic gain is within 2 dB of the gain as determined by computer simulation for a variety of cases at a 10 3 BER. The closed-form expressions for the bound permit rapid calculation of the improvement with optimum combining for any number of interferers and antennas, as compared with the CPU hours previously required by Monte Carlo simulation. Thus these bounds allow calculation of the performance of optimum combining under a variety of conditions where it was not possible previously, including analysis of the outage probability with shadow fading and the combined effect of adaptive arrays and dynamic channel assignment in mobile radio systems.