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Congested and expensive radio spectrum coupled with an insatiable demand for higher throughput in the last mile makes optical wireless an attractive alternative. The limitation of coverage area of optical wireless links is compensated by their ultrahigh bandwidth and unregulated spectrum. Cooperative relay strategies can further enhance the capacity and availability of optical wireless. A number of researchers have studied how the capacity of an optical relay channel is effected by fading processes. However, the capacity of an optical wireless relay channel (OWRC) has received little attention. This paper attempts to delineate the achievable capacity region of a Gaussian OWRC. Decode and forward, compress and forward, and amplify and forward relay strategies are used to determine the capacity bounds that constitute the achievable region. High and low signal asymptotes of the bounds are developed. The probability of outage under fading induced by turbulence and pointing error is also discussed. The results presented in this paper will facilitate the design of optical wireless relay networks in terms of choice of relaying strategy and input distribution.Index Terms-Achievable rate region; Amplify and forward (AF) capacity bound; Compress and forward (CF) capacity bound; Decode and forward (DF) capacity bound; Gaussian optical wireless channel; Min-max cut bound; Optical wireless (OW) channel; Optical wireless relay channel (OWRC); Peak and mean power constrained channel; Relay channel; Relay channel capacity.

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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 0 <˛6 1 2 and 1 2 6˛6 1. 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.