Hardware efficient frequency domain equalization in few-mode fiber coherent transmission systems

Few-mode fiber (FMF) transmission system has become an emerging technology to overcome next capacity crunch. To compensate the large accumulated differential mode group delay (DMGD) and random mode coupling in FMF transmission systems, frequency domain least mean square (FD-LMS) algorithm has been proposed and proven as the most hardware efficient approach. Except for the hardware complexity, convergence speed is another major consideration of adaptive FD-LMS algorithm, especially in FMF system with large accumulated DMGD. We propose two algorithms to improve the convergence speed of the adaptive FD-LMS in FMF transmission systems. One is signal power spectrum density (PSD) dependent adaptive algorithm, which adopts variable step size that is the reciprocal of the power level in each frequency bin. The other is noise power directed adaptive FD-LMS algorithm, which adopts the step size of each frequency bin rendering the posterior errors that will converge to background noise in additive white Gaussian noise channel. Our simulation results show that, in a 3000 km FMF transmission system with 35-ps/km DMGD and optical signal to noise ratio (OSNR) of 14 dB, the noise power directed algorithm and PSD dependent algorithm can improve the convergence speed by 54% and 35% over conventional adaptive FD-LMS algorithm with negligible increase in hardware complexity. We also proposed a complexity reduced single-stage adaptive equalizer for compensating both chromatic dispersion (CD) and DMGD simultaneously. The single-stage method can save 6% complex multiplication over conventional two-stage equalization method in a 1000 km FMF transmission system with 76-ps/km DMGD.