In this thesis channel capacity of a special type of multiple-input multiple-output (MIMO) Rayleigh fading channels is studied, where the transmitters are subject to a finite phase-shift keying (PSK) input alphabet. The constraint on the input alphabet makes an analytical solution for the capacity beyond reach. However we are able to simplify the final expression, which requires a single expectation and thus can be evaluated easily through simulation. To facilitate simulations, analytical expressions are derived for the eigenvalues and eigenvectors of a covariance matrix involved in the simplified capacity expression. The simplified expression is used to provide some good approximations to the capacity at low signal-to-noise ratios (SNRs). Involved in derivation of the capacity is the capacity-achieving input distribution. It is proved that a uniform prior distribution is capacity achieving. We also show that it is the only capacity-achieving distribution for our channel model. On top of that we generalize the uniqueness case for an input distribution to a broader range of channels.

<h2 id="x-x-x-bp_categories-h"> </h2> / <p>The discrete-time Poisson (DTP) channel models a wide range of optical communication channels. The channel capacity and capacity-achieving distributions are generally unknown. This thesis addresses system design of DTP channels and presents novel contributions to the capacity of DTP channel, properties and closed-form expression of the capacity-achieving distribution under peak and average constraints, signalling design, and sum-capacity-achieving distributions of DTP multiple access channel (MAC) with peak amplitude constraints.</p> <p>Two algorithms are developed to compute the channel capacity of DTP channel as well as the capacity-achieving distribution with average and peak amplitude constraints. Tight lower bounds based on input distributions with simple forms are presented. Non-uniform signalling algorithms to achieve the channel capacity are also demonstrated. Fundamental properties of capacity-achieving distributions for DTP channels are established. Furthermore, necessary and sufficient conditions on the optimality of binary distributions are presented. Analytical expressions for the capacity-achieving distributions of the DTP channel are derived when there is no dark current and when the dark current is large enough. A two-user DTP multiple access channel model is proposed and it is shown that the sum-capacity-achieving distributions under peak amplitude constraints are discrete with a finite number of mass points.</p> / Doctor of Philosophy (PhD)