Asymptotic Performance Analysis of Optimum Combining for Dense Multiple Antenna Reception Under Rayleigh Fading

Using an asymptotic analysis of the eigenvalues of dense correlation matrices, the asymptotic average output signal-to-interference-plus-noise ratio performance of optimum combining is evaluated as the number of the antennas in the receiver array increases while the total physical size of the array is fixed. As a result of the constraint imposed on the total physical dimensions of the array, the array output signals become more and more spatially correlated as more antennas are introduced to the array. A Rayleigh fading channel model is considered and the desired signal is assumed to be corrupted by a single cochannel interferer and thermal noise. Two different scenarios are investigated, namely, fixed average received power per antenna and fixed total average received power. It is shown that in the former scenario, the average output signal-to-interference-plus-noise ratio is asymptotically a linear function of the number of the antennas, while in the latter scenario it eventually saturates at a certain value. The slope of the asymptote in the former scenario and the value of the saturation limit in the latter scenario are derived in terms of the point spectrum of the underlying array correlation function. The case of multiple interferers is examined by simulation and is shown to exhibit similar asymptotic behavior to the case of one interferer for both power constraint scenarios. Numerical examples show that the receiver exhibits its asymptotic behavior for a practically small number of antennas.