Optimum combining (OC) is a well-known coherent detection technique used to combat fading and suppress cochannel interference. In this dissertation, expressions are developed to evaluate the error probability of OC for systems with multiple interferers and multiple receiving branches. Three approaches are taken to derive the expressions. The first one starts from the decision metrics of OC. It facilitates obtaining closed-form expressions for binary phase-shift keying modulation. The second approach utilizes the moment generating function of the output signal to interference plus noise ratio (SINR) and results in expressions for symbol and bit error probability for multiple phaseshift keying modulation. The third method uses the probability density function of the output SINR and arrives at expressions of symbol error probability for systems where the interferers may have unequal power levels. Throughout the derivation, it is assumed that the channels are independent Rayleigh fading channels. With these expressions, evaluating the error probability of OC is fast, easy and accurate.

Two noncoherent detection schemes based on the multiple symbol differential detection (MSDD) technique are also developed for systems with multiple interferers and multiple receiving branches. The first MSDD scheme is developed for systems where the channel gain of the desired signal is unknown to the receiver, but the covariance matrix of the interference plus noise is known. The maximum-likelihood decision statistic is derived for the detector. The performance of MSDD is demonstrated by analysis and simulation. A sub-optimum decision feedback algorithm is presented to reduce the computation complexity of the MSDD decision statistic. This suboptimum algorithm achieves performance that is very close to that of the optimum algorithm. It can be shown that with an increasing observation interval, the performance of this kind of MSDD approaches that of OC with differential encoding.

The second MSDD scheme is developed for the case in which the only required channel information is the channel gain of the interference. It is shown that when the interference power level is high, this MSDD technique can achieve good performance.