On capacity of non-coherent Rayleigh fading MIMO channels

This paper investigates the capacity of discrete time uncorrelated Rayleigh fading multiple input multiple output (MIMO) channels with no channel state information (CSI) at both the transmitter and the receiver. We prove that to achieve the capacity, the amplitude of the multiple input needs to have a discrete distribution with a finite number of mass points with one of them located at the origin. We show how to compute the capacity numerically in multi antenna configuration at any signal to noise ratio (SNR) with the discrete input using the Kuhn-Tucker condition for optimality. Furthermore, we show that at low SNR, the capacity with two mass points is optimal. Since the first mass point is necessarily located at the origin, we argue that at low SNR, on-off keying is optimal for any antenna number. As the number of receiver antennas increases, the maximum SNR at which two mass points are optimal decreases.