A Fast Convergence Frequency Domain Least Mean Square Algorithm for Compensation of Differential Mode Group Delay in Few Mode Fibers

A Step-Size Controlled Method for Fast Convergent Adaptive FD-LMS Algorithm in Few-Mode Fiber Communication Systems

“…As demonstrated in [20] and [21], the convergence speed can be increased by choosing adaptive step size based on the PSD of input signal as shown in (7). Here, α is the adaptation rate, which determines both the convergence speed and equalization performance of the signal PSD dependent algorithm.…”

“…It also needs 2MN complex multiplications in the PSD estimation of M prior error blocks as shown in (20), and 2M 2 ·2N complex multiplications between prior error blocks and conjugate transpose of input frequency domain blocks in cross-correlation estimation of error blocks as shown in (21). The algorithm also additionally needs 2M 2 ·2N divisions and 2M 2 ·2N square roots.…”

“…In addition, the MIMO equalizer should also be able to track the fast-changing channels of FMF transmission systems during initial channel estimation. Our previous simulation results have shown that, in the FMF system with larger accumulated DMGD, the adaptive FD-LMS method requires more training symbols for equalizer convergence [20]. It has been proposed that signal power spectral density (PSD) dependent adaptive FD-LMS algorithm can effectively increase the convergence speed of equalizers over the conventional adaptive FD-LMS method by adopting variable bin-wise step size inverse to its power level in signal power spectrum [20], [21].…”

“…Our previous simulation results have shown that, in the FMF system with larger accumulated DMGD, the adaptive FD-LMS method requires more training symbols for equalizer convergence [20]. It has been proposed that signal power spectral density (PSD) dependent adaptive FD-LMS algorithm can effectively increase the convergence speed of equalizers over the conventional adaptive FD-LMS method by adopting variable bin-wise step size inverse to its power level in signal power spectrum [20], [21]. However, the signal PSD dependent method did not consider the channel background noise, so it is only the optimal solution in noise-free channels, where the adaptive estimation errors should converge to zero.…”

“…We compare its equalization performance and convergence speed with the signal PSD dependent adaptive FD-LMS algorithm in [20] and the conventional adaptive FD-LMS algorithm in [14]. It is shown that, at low optical signal-to-noise ratio (OSNR), the noise PSD directed adaptive FD-LMS method could achieve a faster convergence speed than both the signal PSD dependent method and the conventional method.…”