Performance Evaluation of Simple Feedback Methods for 2x1 Wireless Systems

The objective of this paper is to evaluate the impact of feedback with a few number of information bits about the channel state information (CSI) from the receiver to the transmitter of a two-transmit and single-receive antenna wireless system. We investigate on how to allocate this few bits of feedback to achieve better performance in a Rayleigh fading channel. We examine several schemes using transmit diversity for a 2times1 system. These schemes include the Alamouti´s space-time coding (no feedback), the optimal beamforming (full CSI is sent to the transmitter), the channel selection (the stronger subchannel is selected, i.e., one bit feedback), the partial phase combining (the phase difference of subchannels is fed back with m-bits) and a proposed hybrid scheme. We derive the expression of the average bit error rate (BER) for these methods and compare them. Our comparison reveals that a single bit feedback allows to achieve 1.76 dB gain in average SNR over Alamouti scheme by either selecting the subchannel with the stronger magnitude or by one bit phase adjustment of one of subchannels. The performance of proposed hybrid scheme approaches as close as 0.67 dB in average SNR to that of the the optimal beamforming scheme (OBS), by using only 2 bits of feedback on both the magnitude and phase difference information of subchannels. Using 2 (or more) bits of feedback, the hybrid method outperforms partial phase combining (PPC) method with about 0.5 dB higher gain in SNR while maintaining the simplicity of implementation