Gaussian inputs: Performance limits over non-coherentSISO and MIMQ channels

Performance limits of information transfer over a discrete time memoryless Rayleigh fading channel withneither the receiver nor the transmitter knowing the fading coefficients except its statistics is an importantproblem in information theory. We derive closed form expressions for the mutual information of single inputsingle output (SISO) and multiple input multiple output (MIMO) Rayleigh fading channels for any antennanumber at any signal to noise ratio (SNR). Using these expressions, we show that the maximum mutualinformation of non-coherent Rayleigh fading MIMO channels is achieved with a single transmitter andmultiple receivers when the input distribution is Gaussian. We show that the addition of transmit antennasfor a fixed number of receivers result in a reduction of mutual information. Furthermore, we argue that themutual information is bounded by the SNR in both SISO and MIMO systems showing the sub-optimalityof Gaussian signalling in non-coherent Rayleigh fading channels.