Performance Analysis and Array Design for Size Constrained Multiple Antenna Reception

Future generations of wireless cellular networks will vastly benefit from the various advantages of multiple antenna techniques. It is, however, well known that signal correlation among a closely spaced set of antennas deployed on a small wireless mobile device can dramatically degrade the performance of such multiple antenna techniques. The performances of two multiple antenna reception schemes for a size limited array of antennas are investigated. Exact closed-form expressions are derived for the bit error rate of binary phase shift keying (BPSK) in Rayleigh fading with maximal ratio combining (MRC) diversity in the presence of cochannel interference (CCI) and additive white Gaussian noise (AWGN). The desired signal and the interferer signals are all subject to correlated Rayleigh fading. In the next contribution, an analytical expression is derived for the average output signal-to-interference-plus-noise ratio (SINR) of optimum combining (OC) 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. The case of multiple interferers is examined by simulation and is shown to exhibit similar asymptotic behavior to the case of one interferer. Finally, a general analytical framework for the optimal design of a size constrained array of antennas is developed. It is shown that the problem of optimizing the number and the positions of the antennas within a size limited array can be formulated as a quadratic convex optimization problem which can be solved efficiently using the available numerical methods for convex optimization. Moreover, an analytical solution to this convex problem is obtained for the special case of a linear array under exponential correlation model. Several one-dimensional (1D) and two-dimensional (2D) array design examples are presented within the proposed framework.