Optimal Power Allocation for Multiuser Photon-Counting Underwater Optical Wireless Communications Under Poisson Shot Noise

Photon counting is an effective technique to detect low-power optical signals in underwater optical wireless communications (UOWC), but undergoes signal-dependent Poisson shot noises that lead to intractable data rate expressions and hinder effective power allocation of photon-counting systems. This paper presents a new approach to the optimal power allocation of a multiuser photon-counting UOWC system, where we first derive the asymptotic achievable rate as the background radiation is large under the signal-dependent Poisson shot noises. With the tractability of the asymptotic achievable rate, we formulate a new power allocation problem to maximize the weighted sum-rate of the multiuser photon-counting UOWC system. A new algorithm is developed to decompose the problem into subproblems with deterministic convexity or concavity and accordingly convexified and solved using successive convex approximation. We also propose to pre-select the subproblems, thereby reducing the complexity significantly with negligible loss of the weighted sum-rate. Simulations validate our asymptotic achievable rate, and show that the proposed algorithms can improve the weighted sum-rates of the UOWC systems by orders of magnitude, compared to the existing approaches.