Visible Light Communications (VLC) has recently emerged as a viable solution for solving the spectrum shortage problem. The idea is to use artificial light sources as medium to communicate with portable devices. In particular, the light sources can be switched on and off with a very high-frequency corresponding to 1s and 0s of digital communication. The high-frequency on-off switching can be detected by electronic devices but not the human eyes, and hence will not affect the light sources' illumination functions. In VLC, if a receiver is equipped with photodiodes that count the number of arriving photons, the channels can be modeled as Poisson channels. Unlike Gaussian channels that are suitable for radio spectrum and have been intensively investigated, Poisson channels are more challenging and are not that well understood. The goal of this thesis is to characterize the fundamental limits of various Poisson channels that models different scenarios in VLC. We first focus on single user Poisson fading channels with time-varying background lights. Our model is motivated by indoor optical wireless communication systems, in which the noise level is affected by the strength of the background light. We study both the single-input single-output (SISO) and the multiple-input and multiple-output (MIMO) channels. For each channel, we consider scenarios with and without delay constraints. For the case without a delay constraint, we characterize the optimal power allocation scheme that maximizes the ergodic capacity. For the case with a strict delay constraint, we characterize the optimal power allocation scheme that minimizes the outage probability. We then extend the study to the multi-user Poisson channels and analyze the sum-rate capacity of two-user Poisson multiple access channels (MAC). We first characterize the sum-rate capacity of the non-symmetric Poisson MAC when each transmitter has a single antenna. We show that, for certain channel parameters, it is optimal for a single-user to transmit to achieve the sum-rate capacity. This is in sharp contrast to the Gaussian MAC, in which both users must transmit, either simultaneously or at different times, in order to achieve the sum-rate capacity. We then characterize the sum-rate capacity of the Poisson MAC with multiple antennas at each transmitter. By converting a non-convex optimization problem with a large number of variables into a non-convex optimization problem with two variables, we show that the sum-rate capacity of the Poisson MAC with multiple transmit antennas is equivalent to a properly constructed Poisson MAC with a single antenna at each transmitter. We further analyze the sum-rate capacity of two-user Poisson MIMO multiple-access channels (MAC), when both the transmitters and the receiver are equipped with multiple antennas. We first characterize the sum-rate capacity of the Poisson MAC when each transmitter has a single antenna and the receiver has multiple antennas. We show that similar to Poisson MISO-MAC channels, for certain channel parameters, it is optimal for a single user to transmit to achieve the sum-rate capacity, and for certain channel parameters, it is optimal for both users to transmit. We then characterize the sum-rate capacity of the channel where both the transmitters and the receiver are equipped with multiple antennas. We show that the sum-rate capacity of the Poisson MAC with multiple transmit antennas is equivalent to a properly constructed Poisson MAC with a single antenna at each transmitter.

In this thesis we investigate how to improve the performance of MU-MIMO wireless system in terms of achieving Shannon capacity limit and efficient use of precious resource of radio spectrum in wireless communication. First a new suboptimal volume-based scheduling algorithm is presented, which can be applied in MU-MIMO downlink system to transmit signals concurrently to multiple users under the assumption of perfect channel information at transmitter and receiver. The volume-based scheduling algorithm utilises Block Diagonalisation precoding and Householder reduction procedure of QR factorisation. In comparison with capacity-based suboptimal scheduling algorithm, the volume-based algorithm has much reduced computational complexity with only a fraction of sum-rate capacity penalty from the upper bound of system capacity limit. In comparison with semi-orthogonal user selection suboptimal scheduling algorithm, the volume-based scheduling algorithm can be implemented with less computational complexity. Furthermore, the sum-rate capacity achieved via volume-based scheduling algorithm is higher than that achieved by SUS scheduling algorithm in the MIMO case. Then, a two-step scheduling algorithm is proposed, which can be used in the MU-MIMO system and under the assumption that channel state information is known to the receiver, but it is not known to the transmitter and the system under the feedback resource constraint. Assume that low bits codebook and high bits codebook are stored at the transmitter and receiver. The users are selected by using the low bits codebook; subsequently the BD precoding vectors for selected users are designed by employing high bits codebook. The first step of the algorithm can alleviate the load on feedback uplink channel in the MU-MIMO wireless system while the second step can aid precoding design to improve system sum-rate capacity. Next, a MU-MIMO cognitive radio (CR) wireless system has been studied. In such system, a primary wireless network and secondary wireless network coexist and the transmitters and receivers are equipped with multiple antennas. Spectrum sensing methods by which a portion of spectrum can be utilised by a secondary user when the spectrum is detected not in use by a primary user were investigated. A Free Probability Theory (FPT) spectrum sensing method that is a blind spectrum sensing method is proposed. By utilizing the asymptotic behaviour of random matrix based on FPT, the covariance matrix of transmitted signals can be estimated through a large number of observations of the received signals. The method performs better than traditional energy spectrum sensing method. We also consider cooperative spectrum sensing by using the FPT method in MU-MIMO CR system. Cooperative spectrum sensing can improve the performance of signal detection. Furthermore, with the selective cooperative spectrum sensing approach, high probability of detection can be achieved when the system is under false alarm constraint. Finally, spectrum sensing method based on the bispectrum of high-order statistics (HOS) and receive diversity in SIMO CR system is proposed. Multiple antennas on the receiver can improve received SNR value and therefore enhance spectrum sensing performance in terms of increase of system-level probability of detection. Discussions on cooperative spectrum sensing by using the spectrum sensing method based on HOS and receive diversity are presented.