Optimization and tradeoff analysis of two-way limited feedback beamforming systems

In a two-way system where two users transmit data to each other, limited feedback beamforming is a simple method to supply channel state information to the transmitter (CSIT) for a multiple-input-multiple-output (MIMO) system when channel reciprocity is unavailable. For analytical tractability, most existing papers assume the existence of an ideal fixed-rate feedback channel to assist the transmitter to adapt to instantaneous channel conditions. The relationship between the feedback rate and data rate is typically analyzed in a unidirectional manner. In reality, judicious resource allocation to transmitting feedback and data leads to a tradeoff between the effective forward and reverse data rates. In this paper, we represent the achievable rate by effective SNRs, and we present a framework to analyze the tradeoff. We find that the forward and reverse rate tradeoff can be decomposed into two local tradeoffs, resulting from the resource allocation policy of each user. The local tradeoff region for each user is found in closed-form, whereas the overall tradeoff region is approximated for the special case when the two users have equal hardware configurations.