Performance improvement of transmit beamforming MISO system using optimum codebook indexing over feedback error channel

Transmit beamforming is simple method to achieve the full diversity gain that is available in multiple antenna (MIMO) wireless systems. Unfortunately, the prior condition to achieve this gain requires perfect channel knowledge at both transmitter and receiver, which is impractical on account of limited feedback link. Therefore, for the practical system, codebook based feedback scheme is often employed, where the beamforming vector is selected from the codebook to maximize the output signal-to-noise ratio (SNR) at receiver, and the receiver only sends back the index of the best beamforming vector to the transmitter. In this paper we derive analytical expression of average bit error rate (BER) for the codebook based transmit beamforming MISO system over the feedback error channel. Using this analytical result, we present optimum codebook indexing scheme to improve the performance of this system. From some selected numerical examples we show that our proposed codebook indexing scheme can provide nonnegligible performance improvements in terms of average BER over the severe feedback error channel.