Underwater Photon-Counting Systems Under Poisson Shot Noise: Rate Analysis and Power Allocation

Photon counting is an effective detection technique for weak optical signals in underwater optical wireless communications (UOWC). This paper proposes a new approach for power allocation in an uplink M-ary pulse position modulation (PPM), photo-counting non-orthogonal multiple-access (PhC-NOMA) system. Different from existing techniques in photon-counting systems, the new approach supports consistent duty cycles across underwater devices and adjusts the transmit rates of the devices through their transmit powers, thereby avoiding the delays of duty cycle adjustments and supporting high-speed transmissions. Power allocation is non-trivial in photon-counting systems due to signal-dependent Poisson shot noises. As a key contribution, we derive the exact and asymptotic expressions for the achievable rate of the M-ary PPM PhC-NOMA system with the signal-dependent Poisson shot noise and multiuser interference considered. With the expressions, we reveal the received power at the base station (BS) is minimized when their minimum data rate requirements are delivered and can be solved using an incremental algorithm. We also asymptotically maximize the photon efficiency of the devices while preventing the saturation of the receiving photon detector, using Karush-Kuhn-Tucker (KKT) conditions. Simulations show that our approach can reduce the received power at the BS by up to 25% and double the photon efficiency, as compared to the existing techniques.