BER criterion and codebook construction for finite-rate precoded spatial multiplexing

Precoded spatial multiplexing systems with rate-limited feedback have been studied recently based on various precoder selection criteria. Instead of those based on indirect performance indicators, we in this paper propose a new criterion directly based on the exact bit error rate (BER) of the system. We show that in the asymptotic case of infinite-rate feedback, the optimal precoder design based on the BER criterion is drastically different from the counterparts with other criteria. In the finite-rate case, we apply the generalized Lloyd algorithm used in vector quantization to construct good precoder codebooks. The new found codebooks improve considerably the minimum distance relative to those currently available. Our numerical results compare the BER performance with different codebooks and with different selection criteria.