Bit-error probability for optimum combining of binary signals in the presence of interference and noise

We derive an exact bit-error probability (BEP) expression for coherent detection of binary signals with optimum combining in wireless systems in the presence of multiple cochannel interferers and thermal noise. A flat Rayleigh fading environment with space diversity, uncorrelated equal-power interferers, and additive white Gaussian noise is considered. The approach is to use the chain rule of conditional expectation together with the joint probability density function (pdf) of the eigenvalues of the interference correlation matrix. This joint pdf is related to the Vandermonde determinant. Let N_A denote the number of antennas and N_I the number of interferers. We consider both the cases of an overloaded system, in which N_I≥N_A, and an underloaded system, in which N_IA. Using averaging techniques that make use of the properties of the Vandermonde determinant, we obtain in each of the two cases a closed-form BEP expression as a finite sum, and the only special function that this expression contains is the Gaussian Q-function. This makes it a powerful tool for analysis and computation.