Spatial Channel Degrees of Freedom for Optimum Antenna Arrays

One of the ultimate goals of future wireless networks is to maximize data rates to accommodate bandwidth-hungry services and applications. Thus, extracting the maximum amount of information bits for given spatial constraints when designing wireless systems will be of great importance. In this paper, we present antenna array topologies that maximize the communication channel capacity for given number of array elements while occupying minimum space. Capacity is maximized via the development of an advanced particle swarm optimization (PSO) algorithm devising optimum standardized and arbitrarily-shaped antenna array topologies. Number of array elements and occupied space are informed by novel heuristic spatial degrees of freedom (SDoF) formulations which rigorously generalize existing SDoF formulas. Our generalized SDoF formulations rely on the differential entropy of three-dimensional (3D) angle of arrival (AOA) distributions and can associate the number of array elements and occupied space for any AOA distribution. The proposed analysis departs from novel closed-form spatial correlation functions (SCFs) of arbitrarily-positioned array elements for all classes of 3D multipath propagation channels, namely, isotropic, omnidirectional, and directional. Extensive simulation runs and comparisons with existing trivial solutions verify correctness of our SDoF formulations resulting in optimum antenna array topologies with maximum capacity performance and minimum space occupancy.