Approximating the Partially Coherent Additive White Gaussian Noise Channel in Polar Coordinates

We consider the partially coherent additive white Gaussian noise channel (PCAWGN) in optical communications and review the derivation of the exact channel conditional probability model in a closed-form solution in polar coordinates. In addition, we derive a reduced-complexity approximation by replacing the Rician and Tikhonov distributions describing amplitude and phase components, respectively, with their Gaussian approximation under certain assumptions of high SNR and low phase noise or jitter. Our proposal significantly reduces the hardware complexity by removing the modified Bessel functions involved in the exact solution. Furthermore, we compare the proposed approximation with a different metric previously found in the literature and observe that for maximum-likelihood hard symbol decision, both models are in perfect agreement with the optimal detector. However, our model not only reduces the required number of multiplications from 12 to 8 and additions from 9 to 3 (per computed symbol) but also reduces the information loss by at least one and up to several orders of magnitude with respect to the previously published metric when used to compute the channel achievable information rate (AIR). In all the simulation cases, we use QAM constellations of orders 4, 8, 16 and 32 as test input symbol sets.