On Capacity of Fading Channels with no Channel State Information

The rapid development of communication systems with mobile receivers at higher data rates has lead to the importance of studies on information transfer over highly time varying channels. Under such circumstances, the channel variations become fast and the receiver is unable to track the channel during the predefined block length. Here existing results for the channel capacity and the optimal input distribution, under the assumption of knowledge of the channel state information (CSI) are no longer valid. In reality the capacity is significantly reduced in the absence of the CSI at both the transmitter and the receiver. Furthermore, finding the optimal input distribution with no CSI is considered an important problem in information theory. This thesis first considers the important case of Gaussian signalling in both single input single output (SISO) and multiple input multiple output (MIMO) fading channels with no CSI. For such a signalling scheme we develop closed form solutions for the mutual information at any signal to noise ratio (SNR) for any number of antennas. Furthermore, we use these new expressions to identify the bounds at high SNR and particularly the use of optimal antennas at both ends of a communication system. To overcome the existing difficulties in calculating the optimal input and the capacity, a novel approach is shown to identify the key characteristics of the optimal input in non-coherent Rayleigh fading MIMO channels. Unlike most work in the literature, this leads to a capacity upper bound which can be obtained without extensive simulations for any antenna number at any SNR. Furthermore, the capacity is shown numerically, deriving the optimal input distribution for any antenna number using a scaler channel model. In particular, some key properties of the optimal input distribution at low SNR is investigated studying the loss in information transfer due to unknown CSI in MIMO wireless communication systems.