On the Capacity of an Average and Peak Power Constrained Optical Wireless Relay Channel

Abstract

Ever evolving bandwidth hungry applications present a gigantic challenge and an unprecedented opportunity for wireless communication. Radio spectrum is already congested. The researchers are vigorously pursuing efficient utilisation of radio spectrum and use of alternate media. Optical wireless is an attractive alternative media that can provide ultra high bandwidth and unregulated spectrum. However, its area of coverage is severely restricted by atmospheric turbulence and misalignment errors. Cooperative relaying can enhance the coverage and availability of optical wireless. This motivates the present study of an optical wireless relay channel (OWRC). Whereas radio frequency wireless relay channel has been widely investigated, study of an OWRC is a novel subject. Focus of this thesis is to develop capacity region by defining upper and lower bounds, the minimum energy per bit required for reliable communication and the outage capacity due to fading induced by scintillation and misalignment errors. An OWRC is the classical three node network comprising source, relay and destination nodes. The nodes are interconnected by optical wireless. The optical wireless links of the OWRC are assumed to be Gaussian. The upper bounds are based on the principle of min-max cut flow. Expectation of the information divergence between an output measure and the channel law over the joint input probability measure is used to derive the bounds. The choice of output measure is critical in obtaining a tight upper bound. The lower bounds are computed in terms of entropy of the input probability measures. Capacity approaching measures are used for obtaining tight lower bounds. The lower bounds also depend on the relaying strategy. Decode and forward, compress and forward, and amplify and forward relaying is considered in this thesis. It is shown that upper and lower bounds tend to converge when peak signal to noise ratio is high. Fading due to scintillation and misalignment is investigated for different relaying strategies. Probability of outage is derived in closed form for the above mentioned relaying strategies. Bounds on the minimum energy per bit required for reliable communication over an OWRC are defined as a function of peak signal level. They are closely related to the lower and upper bounds on the capacity. It is shown that the minimum energy per bit is inversely proportional to the square root of the low signal asymptotic capacity. The results of this thesis provide a comprehensive and novel study of an optical wireless relay channel. It will help in estimating the capacity, coverage and availability issues of optical wireless relay networks in general and relay channels in particular for positioning optical wireless to augment the wireless infrastructure to meet the growing customer needs.