Linear and nonlinear impairments in underwater wireless optical communication (UWOC) systems caused by the limited bandwidth and nonlinearity of devices severely degrade the system performance. In this paper, we propose a sparse Volterra series model-based nonlinear post equalizer with greedy algorithms to mitigate the nonlinear impairments and the inter-symbol interference (ISI) in a UWOC system. A variable step size generalized orthogonal matching pursuit (VSgOMP) algorithm that combines generalized orthogonal matching pursuit (gOMP) and adaptive step size method is proposed and employed to compress the Volterra equalizer with low computational cost. A maximum data rate of 500 Mbps is realized with the received optical power of −32.5 dBm in a 7-m water tank. In a 50-m swimming pool, a data rate of 500 Mbps over 200-m underwater transmission is achieved with a BER lower than the forward error correction (FEC) threshold of 3.8 × 10−3. The number of kernels of the sparse Volterra equalizer is reduced to 70% of that of the traditional Volterra equalizer without significant BER performance degradation. Compared with orthogonal matching pursuit (OMP) scheme and regularized orthogonal match pursuit (ROMP) scheme, the VSgOMP scheme reduces the running time by 68.6% and 29.2%, respectively. To the best of our knowledge, this is the first time that a sparse Volterra equalizer combined with VSgOMP algorithm is employed for the nonlinear equalization in a long-distance high-speed UWOC system.

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