Capacity Bounds for MIMO Nakagami-$m$ Fading Channels

Abstract

This paper studies the ergodic capacity limits of multiple-input multiple-output (MIMO) antenna systems with arbitrary finite number of antennas operating on general fading environments. Through the use of majorization theory, we first investigate in detail the ergodic capacity of Nakagami-m fading channels, for which we derive several ergodic capacity upper and lower bounds. We then show that a simple expression for the capacity upper bound is possible for high signal-to-noise ratio (SNR), which permits to analyze the impact of the channel fading parameter m on the ergodic capacity. The asymptotic behavior of the capacity in the large-system limit in which the number of antennas at one or both side(s) goes to infinity, is also addressed. Results demonstrate that the capacity scaling laws for Nakagami-m and Rayleigh-fading MIMO channels are identical. Finally, we employ the same technique to distributed MIMO (D-MIMO) systems undergoing composite log-normal and Nakagami fading, where we derive similar ergodic capacity upper and lower bounds. Monte Carlo simulation results are provided to verify the tightness of the proposed bounds.