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On the design of linear arrays of fixed length for diversity reception in Rayleigh fading and cochannel interference

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.