Diversity order gain with noisy feedback in multiple access channels

In this paper, we study the effect of feedback channel noise on the diversity-multiplexing tradeoff in multiuser MIMO systems using quantized feedback, where each user has m transmit antennas and the base-station receiver has n antennas. We derive an achievable tradeoff and use it to show that in SNR-symmetric channels, a single bit of imperfect feedback is sufficient to double the maximum diversity order to 2 mn compared to when there is no feedback (maximum is mn at multiplexing gain of zero). Further, additional feedback bits do not increase this maximum diversity order beyond 2 mn. Finally, the above diversity order gain of mn over non-feedback systems can also be achieved for higher multiplexing gains, albeit requiring more than one bit of feedback.