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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 maximumlikelihood 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