Abstract:Abstract. Adaptive time-domain equalizer (TDE) is an important module for digital optical coherent receivers. From an implementation perspective, we analyze and compare in detail the effects of error signal feedback delay on the convergence performance of TDE using either least-mean square (LMS) or constant modulus algorithm (CMA). For this purpose, a simplified theoretical model is proposed based on which iterative equations on the mean value and the variance of the tap coefficient are derived with or without… Show more
“…ey show that the RLS has the superior convergence properties. e authors of [23] considered the effects of error feedback delay, using CMA, on the performance of the coherent receiver in the presence of CD. e work done in [24] shows how pipelining and efficient implementation of the adaptive filter's feedback loop in the receiver help reducing the delay of the error signal used in the LMS tap weight updates by 18%.…”
Section: Overview Of Adaptive Filters In Optical Coherent Receiversmentioning
In this article, we analyze the performance of adaptive filtering in the context of dual-polarization coherent optical flexible bit-rate transceivers. We investigate the ability of different adaptive algorithms to track fast state-of-polarization (SOP) transients in the presence of colored noise. Colored noise exists due to the concatenation of Wavelength Selective Switches (WSSs) and polarization dependent loss (PDL) which can be considered as spatially dependent noise. We consider the use of different modulation formats, and the practical limitation of error signal feedback delay in decision-directed adaptive filters is also taken into account. The back-to-back required signal-to-noise ratio (RSNR) penalty that can be tolerated determines the maximum SOP rate of change that can be tracked by the adaptive filters as well as the filter’s adaptive step size. We show that the recursive least squares algorithm, using the covariance matrix as an aggressive “step size,” has a much better convergence speed compared to the least mean squares (LMS) and normalized LMS (NLMS) algorithms in the presence of colored noise in the fiber. However, the three algorithms have similar tracking capabilities in the absence of colored noise.
“…ey show that the RLS has the superior convergence properties. e authors of [23] considered the effects of error feedback delay, using CMA, on the performance of the coherent receiver in the presence of CD. e work done in [24] shows how pipelining and efficient implementation of the adaptive filter's feedback loop in the receiver help reducing the delay of the error signal used in the LMS tap weight updates by 18%.…”
Section: Overview Of Adaptive Filters In Optical Coherent Receiversmentioning
In this article, we analyze the performance of adaptive filtering in the context of dual-polarization coherent optical flexible bit-rate transceivers. We investigate the ability of different adaptive algorithms to track fast state-of-polarization (SOP) transients in the presence of colored noise. Colored noise exists due to the concatenation of Wavelength Selective Switches (WSSs) and polarization dependent loss (PDL) which can be considered as spatially dependent noise. We consider the use of different modulation formats, and the practical limitation of error signal feedback delay in decision-directed adaptive filters is also taken into account. The back-to-back required signal-to-noise ratio (RSNR) penalty that can be tolerated determines the maximum SOP rate of change that can be tracked by the adaptive filters as well as the filter’s adaptive step size. We show that the recursive least squares algorithm, using the covariance matrix as an aggressive “step size,” has a much better convergence speed compared to the least mean squares (LMS) and normalized LMS (NLMS) algorithms in the presence of colored noise in the fiber. However, the three algorithms have similar tracking capabilities in the absence of colored noise.
“…It has been shown that frequency-domain (FD) equalization, utilizing the fast Fourier transform (FFT), is more efficient than time-domain (TD) implementation [6][7][8][9][10]. However, in a practical real-time implementation of an adaptive equalizer with block-based processing, filter update delays will be induced due to the FFTs and other DSP operations in the feedback loop, which can degrade the equalizer's tracking ability, particularly during rapid SOP fluctuations [11][12][13][14].…”
A frequency-domain multiple-input multiple-output (FD-MIMO) equalizer employing a momentum-based gradient descent update algorithm is proposed for polarization multiplexing coherent receivers. Its performance in operation with dynamically varying optical channels is investigated and the impact of filter update delays, arising from the latency of the fast Fourier transforms (FFTs) and other digital signal processing (DSP) operations in the feedback loop, is assessed. We show that the proposed momentum-based gradient descent algorithm used to control the equalizer response has significantly greater tolerance to feedback delay than the conventional gradient descent algorithm. We considered a 92 Gbaud dual-polarization 64 QAM receiver, with DSP operating at two samples per symbol, and with the equalizer operating on blocks of 512 and 1024 samples (i.e., 512/1024-point FFT). We found that at an optical signal-to-noise power ratio (OSNR) of 35 dB, the momentum-based gradient descent algorithm can successfully track state-of-polarization (SOP) rotation at frequencies of up to 50 kHz and with filter update delays of up to 14 blocks (39 ns). In comparison, using the conventional gradient descent algorithm in an otherwise identical receiver, the equalizer performance starts to deteriorate at SOP rotation frequencies above 20 kHz.
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