Power spectrum of Uplink Array signals with random phase and delay errors

Uplink Array signals emanating from different antennas must be compensated for Doppler and delay in order to achieve the N² array gain predicted by theory¹. However compensation is never perfect, leaving residual errors that cause losses in array gain and degradation in signal quality. Here we develop a mathematical model for Uplink Array signals in the presence of phase and delay errors, similar to well-known multipath analyses but with features unique to this problem. The resulting losses and distortions are described, and the power spectral density of the array signal derived first conditioned on a given error vector, then averaged over distributions deemed suitable for Uplink Array applications. The impact of phase and delay errors on array gain and signal distortion are addressed, and the maximum data throughput is quantified in terms of the assumed error statistics.