Minimum BER beamforming in the RF domain for OFDM transmissions and linear receivers

In this paper, we study transmission schemes for a novel OFDM-based MIMO system which performs adaptive signal combining in radio-frequency (RF). Specifically, we consider the problem of selecting the linear precoder and the transmit and receive RF weights (or beamformers) for minimizing the bit error rate (BER) under the assumption of perfect channel knowledge and linear receivers. Firstly, it is shown that the optimal precoder amounts to uniformly distribute the overall mean square error (MSE) among the information symbols. Secondly, we propose a gradient search algorithm to obtain the optimal pair of beamformers. Interestingly, in the case of low signal to noise ratios (SNR), the proposed beamforming criterion is equivalent to the maximization of the received SNR. However, for moderate and high SNRs, part of the received SNR is sacrificed in order to improve the channel response of the worst subcarriers, which translates into significant advantages over other previously proposed approaches. Finally, the performance of the proposed scheme is illustrated by means of some numerical examples.