The problem of optimizing the placement of the antennas for an optimum combining receiver equipped with a linear antenna array of fixed length is addressed. A Rayleigh fading model is considered where the complex channel gains of both the desired user and the interfering users are assumed to be correlated due to the mutual proximity of the antennas. The average output signal-to-interference-plus-noise ratio is adopted as a measure of the system's performance and is maximized over the number and the arrangement of the antennas in the array. The optimization problem is formulated as a quadratic convex optimization problem in an infinite dimensional space where finite dimensional approximations of the problem are numerically solved using a convex optimization method. For the special case of an exponential correlation function the optimal arrangement is also derived analytically. It is shown for an exponential correlation model that the optimal number of antennas is infinite meaning that adding more antennas is always beneficial. Perhaps unexpectedly, the best arrangement of antennas in this case is not uniform, in general. On the contrary, it is shown through numerical results that for a two dimensional omnidirectional scattering correlation model the optimal number of antennas is a finite number and the optimum placement is uniform.

An analytical expression is derived for the average output signal-to-interference-plus-noise ratio of optimum combining for a spatially correlated array of antennas in the presence of a single interferer and Rayleigh fading. Using the derived expression and based on an asymptotic analysis of the eigenvalues of dense correlation matrices, the asymptotic performance of optimum combining is evaluated as the number of the antennas increases while the total physical size of the array is fixed. Two different scenarios are considered, 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 asymptotic line in the former scenario as well as 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 behaviour to the case of one interferer.

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.

Exact closed-form expressions are derived for the bit error rate of binary phase shift keying in Rayleigh fading channels with maximal ratio combining diversity in the presence of cochannel interference and additive white Gaussian noise. The desired signal and the interferer signals are subject to correlated Rayleigh fading and binary phase shift keying modulation is used by all users.

Exact closed-form expressions are derived for the bit error rate of binary phase shift keying in Rayleigh fading channels with maximal ratio combining diversity in the presence of cochannel interference and additive white Gaussian noise. The desired signal and the interferer signals are subject to correlated Rayleigh fading and binary phase shift keying modulation is used by all users. Using the derived expressions, it is shown through some numerical examples that for a fixed number of antennas, there is a best radius for a uniform circular array at which the array performance is almost as if all antennas in the array were uncorrelated. Counterintuitively, at this radius, the adjacent antennas in the array are not uncorrelated.