Summary: Capacity of non-coherent Rayleigh fading MIMO
channels
R.R. Perera, K. Nguyen, T.S. Pollock and T.D. Abhayapala
Abstract: The capacity of discrete time uncorrelated Rayleigh fading multiple input multiple
output (MIMO) channels was investigated without channel state information (CSI) at either the
transmitter or the receiver. 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. It is shown how to compute the capacity numerically in multi-antenna configuration at any
signal-to-noise ratio (SNR), with the discrete input using the Kuhn­Tucker condition for
optimality. Furthermore, it is shown that at low SNR, the capacity with two mass points is
optimal. As the number of receiver antennas increases, the maximum SNR at which two mass
points are optimal decreases. Using this result it is argued that on­off keying is optimal in non-
coherent Rayleigh fading MIMO channels at low SNR.
1 Introduction
In wireless communications, the knowledge of channel state
information (CSI) at either the receiver or at the transmitter,
or at both, is considered to be a vital part in information
transfer across the channel. It appears from the results of [1]
that it is possible to obtain accurate CSI using pilots in
slowly changing channels. It is also beneficial if the statistics

Source: Abhayapala, Thushara D. - Department of Information Engineering, Australian National University

Collections: Computer Technologies and Information Sciences