On the Sum Rate of MIMO Nakagami-m Fading Channels with Linear Receivers

We investigate the ergodic sum rate of multiple-input multiple-output Nakagami-m fading channels with linear receivers. In particular, both mean square error and zero-forcing receivers are considered. For dual transmit antenna configurations, we present new, closed-form upper bounds on the ergodic sum rate of both receivers. Moreover, we derive exact expressions for the two key parameters dictating the sum rate behavior in the low signal to noise ratio regime, namely the minimum energy per information bit to reliably convey any positive rate and the wideband slope. By doing so, we are able to explicitly demonstrate the sub-optimality of linear receivers compared to optimal receivers, and draw useful insights into the impact of model parameters (e.g., number of antennas, fading parameters).