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.

<p> Multiple-subcarrier modulated (MSM) indoor wireless optical systems provide highspeed bandwidth-efficient communication as well as multi-access capability at low cost. A major drawback of such systems is the high average optical power requirement. To address this problem, trellis codes are designed for data transmission realizing an average optical power reduction as high as 0.95 dB. A simultaneous peak optical power reduction up to 0.44 dB is also possible by employing this technique.</p> <p> Moreover, the unregulated bandwidth available in wireless optical channels is exploited to reduce the average optical power in MSM wireless optical systems. Data transmission is confined in a bandwidth located near DC, while reserved carrier signals are designed outside the data bandwidth to reduce the average optical power. Distorted out-of-band signals at higher frequency are removed at the receiver by low-pass filtering and not used for detection. To design the out-of-band carrier amplitudes, both a standard optimization algorithm over the set of real numbers and an exhaustive search over discrete constellation are proposed. It is shown that significant average optical power reduction as high as 2.56 dB is achieved.</p> <p> It is assumed that a symbol-by-symbol bias is used in MSM wireless optical systems since it offers significant optical power reduction. The received DC bias level provides a degree of diversity and is used at the receiver to improve detection. It is also used to design trellis codes with better distance properties. In this manner, an additional average optical power reduction up to 0.50 dB is achieved with a simultaneous peak power reduction of 0.46 dB for MSM wireless optical systems.</p> / Thesis / Master of Applied Science (MASc)