Capacity bounds for a Gaussian optical wireless relay channel

Capacity of a radio relay channel has been extensively studied. Although general solution to the capacity problem is still elusive, solution for a physically degraded relay channel is available. This paper presents the original results for lower and upper bounds on the capacity of an optical wireless relay channel. Optical intensity communication uses signals that are inherently non-negative and are governed by average and peak power constraints dictated by the considerations of battery life and safety of human eye. The component optical wireless links of the relay channel are assumed to be Gaussian, a valid assumption for intensity modulation direct detection model. The decode-and-forward inner bounds are developed through entropy power inequality. The concept of duality of capacity is employed for determining the min-max cut upper bound. Two sets of upper bounds have been worked out using a non-zero mean Gaussian and a piecewise continuous measure comprising Gaussian and exponential components on the channel output. As maximum entropy measure for a peak and mean power-constrained channel depends on mean-to-peak power ratio , separate set of bounds have been computed for and . It is shown that high signal asymptotes of upper and lower bounds tend to converge. The maximum gap between the two asymptotic bounds is half a bit. Copyright (c) 2014 John Wiley & Sons, Ltd.