A Hypergeometric View on Diversity Combining

Hypergeometry of objects in K dimensions is used to determine the optimum dimension of signal-to-noise ratio adaptive receivers. Previously, it is shown that the volume and surface area of many A´-dimensional objects are maximized for a particular dimension. In this paper, this observation is used to conjecture that the average performance measures of signal-to- noise ratio adaptive receivers reach a maximum for a particular dimension. The performance analysis is obtained assuming a generic two-stage diversity combining structure at the receiver front-end. Although the diversity combining schemes increase the output channel amplitude by adding more receiver antennas for any branch fading statistics, the subsequent signal-to-noise ratio adaptive signal processing creates an optimum in the number of receiver antennas. This is confirmed by numerical examples assuming a bank of detectors operating over erasure subchannels. The optimum dimension of the receiver has significant impact on the overall receiver complexity.