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 order to improve the sensitivity of an optical receiver, the gain and the collection area of the photo-detectors within the receiver should be increased. Detectors with internal gain such as avalanche photodiodes (APD) are usually used to increase the sensitivity of the receiver. One problem with APDs is the sensitivity of their gain to their bias voltage, which makes them challenging to be fabricated in a standard CMOS process due to variations in their gain. However, when an APD is biased over its breakdown voltage, it is sensitive to a single photon, hence, referred to as a single photon avalanche diodes (SPAD). The SPADs are photon-counting detectors, which are less sensitive to their bias voltage, and can be integrated with rest of the electronic circuitry that form an optical receiver. An avalanche diode requires dedicated circuits to be operated in the SPAD mode. These circuits make the diode insensitive to an incident photon for a duration that is known as deadtime. Unfortunately, The collection area of the PD, APD, and SPADs are limited to their capacitance. Hence, a large photo-detector leads to a larger capacitance, which reduces the bandwidth of the receiver. In this thesis, a photon counting optical receiver based on an array of SPADs is proposed which increases the collection area with a low output capacitance. The avalanche diode and peripheral circuits which operate and readout-out the SPAD array are fabricated in the commercially available UMC 0.18 μm CMOS process. Initially, the avalanche diode is tested and characterised. A high performance circuit is then designed and tested which is able to achieve short deadtimes up to 4 ns. Once the photon counting operation of the SPAD is verified, a numerical model is developed to investigate the influence of several factors, including the deadtime, on the performance of the photon-counting detector in a communication link. Based on the simulation results, which show the advantages of an array over a single detector, a prototype detector array of 64 asynchronous SPADs is designed and tested. This array uses a high-speed readout mechanism which is inspired by the current steering digital-to-analogue converters. Bit error ratio tests (BERT) verify the photon counting capability of the proposed detector, and a bit error rate of 1E-3 has been achieved at data rate of 100 Mbps. In addition, the array of SPAD is compatible with a front-end of conventional optical receiver which uses a photodiode as a photo detector.