The impact of feedback on linear precoding for the two-user uplink MIMO channel with a zero forcing equalizer

This work considers a two-user uplink MIMO channel, where the receiving node applies a zero forcing equalizer to jointly estimate the transmitted symbols. The goal is to design linear precoders at the two users in order to improve the performance of the equalizer. In one part of this work, assuming local channel knowledge at each user, we quantify the minimum amount of feedback from the receiving node necessary for construction of optimal precoders at the users. In contrast to common feedback procedures, where the precoders are fed back to the users, we show that the amount of complex numbers to feedback is at most half when compared to feeding back the precoders. Furthermore, we investigate construction of precoders when limited feedback is available from the receiving node. Numerical results are presented that quantify the loss due to absence of optimal feedback, as well as the gain obtained from limited feedback with local channel knowledge compared to precoding without feedback and channel knowledge at the users.