Analysis of weight error loss with a multichannel beamformer processor

An analysis is presented which derives the bit error rate (BER) performance achieved by a multiple-channel coherent BPSK receiver subject to noisy multichannel impulse response (MCIR) estimates. The receiver utilises a frequency-independent beamformer processor prior to coherent detection which is subject to weight error owing to imperfect MCIR estimates. It is demonstrated that in the flat static channel at high SNR the fractional increase in BER compared to the perfect MCIR estimation case is equal to [N-1/2]/L_S, where N is the number of antenna elements and L_S is the training sequence length. Similar results are derived for the flat Rayleigh-fading case both for total and for zero correlation between the fading at the antenna elements. These results are then extended to consideration of the degradation in receiver sensitivity, termed the weight error loss, which for the Rayleigh-fading channels at high SNR turns out to be independent of both the mean SNR and N, and is inversely proportional to L_S