Information Theory Gaussian inputs: performance limits over non-coherent SISO and MIMO channels

Performance limits of information transfer over a discrete time memoryless Rayleigh fading channel with neither the receiver nor the transmitter knowing the fading coefficients except its statistics is an important problem in information theory. We derive closed form expressions for the mutual information of single input single output (SISO) and multiple input multiple output (MIMO) Rayleigh fading channels for any antenna number at any signal to noise ratio (SNR). Using these expressions, we show that the maximum mutual information of non-coherent Rayleigh fading MIMO channels is achieved with a single transmitter and multiple receivers when the input distribution is Gaussian. We show that the addition of transmit antennas for a fixed number of receivers result in a reduction of mutual information. Furthermore, we argue that the mutual information is bounded by the SNR in both SISO and MIMO systems showing the sub-optimality of Gaussian signalling in non-coherent Rayleigh fading channels. Copyright © 2006 AEIT