Sum Rate Analysis for Multi-User Massive MIMO Relay Networks

The performance of multi-user massive MIMO amplify-and-forward relay networks with linear zero-forcing detectors is investigated by deriving closed-form sum rate upper bounds for finitely many antennas and asymptotic approximations for infinitely many antennas at the relay and destination. The acquisition of channel state information (CSI) is investigated by using minimum mean square error channel estimation, and thereby, the impact of imperfect CSI on transmit power scaling laws at the user nodes and relay is studied. For genie-aided perfect CSI case, the transmit power at the user nodes and/or relay can be scaled down inversely proportional to the number of destination antennas. Nevertheless, for the imperfect CSI case, the transmit power can only be scaled down inversely proportional to the square-root of the destination antenna count. Specifically, asymptotic signal-to-interference-plus-noise ratio (SINR) expressions are derived for three transmit power scaling laws for both perfect and imperfect CSI cases and are used for deriving the corresponding asymptotic sum rates for the case in which the antenna counts at the relay and destination grow without bound while keeping a fixed ratio. Notably, these asymptotic SINRs and sum rates become independent of the fast fading component of the wireless channel for infinitely many relay and destination antennas, and consequently, paving the way to low-complexity medium access control layer operations and reduced latency in the air interface.