Maximum Likelihood Sequence Estimation Algorithm Research Articles

Burst-Error-Propagation Suppression for Decision-Feedback Equalizer in Field-Trial Submarine Fiber-Optic Communications

In this paper, we present a field-trial C-band 72Gbit/s optical on-off keying (OOK) system over 18.8km dispersion-uncompensated submarine optical cable in the South China Sea. Chromatic dispersion (CD) of 18.8km submarine optical cable causes four spectral nulls on the 36GHz bandwidth of 72Gbit/s OOK signal, which is the main obstacle for achieving an acceptable bit-error-rate (BER) performance. Decision feedback equalizer (DFE) is effective to compensate for the spectral nulls. However, DFE has a serious defect of burst-error propagation when the burst errors emerge due to the unstable submarine environment. Weighted DFE (WDFE) can be used to mitigate the burst-error propagation, but it cannot fully compensate for the spectral nulls because only a part of feedback symbols is directly decided. Fortunately, maximum likelihood sequence estimation (MLSE) can be added after the WDFE to simultaneously eliminate the resisting spectral distortions and implement optimal detection. Compared to the joint DFE and MLSE algorithm, the joint WDFE and MLSE algorithm can effectively suppress the burst-error propagation to obtain a maximum 2.9dB improvement of $\boldsymbol{Q}$ factor and eliminate the phenomenon of BER floor. In conclusion, the joint WDFE and MLSE algorithm can solve the burst-error propagation for the field-trial fiber-optic communications.

Zero-guard band dual-SSB PAM4 signal transmission with joint equalization scheme.

We propose and experimentally demonstrate a joint equalization scheme to recover a zero-guard band dual-single sideband (dual-SSB) four-level pulse amplitude modulation (PAM4) signal in a system with moderate bandwidth limitation. In the joint equalization scheme, a multiple-input multiple-output feedforward equalizer (MIMO-FFE) is first used to mitigate the residual crosstalk resulting from non-ideal optical filtering. Then, a modified post filter (PF) is placed after the MIMO-FFE to suppress the MIMO-FFE-enhanced low-frequency noise, whereas the known inter-symbol interference introduced by the modified PF is further eliminated with the maximum likelihood sequence estimation algorithm. Based on the proposed scheme, we experimentally demonstrate a 112-Gb/s zero-guard band dual-SSB PAM4 signal transmission over an 80-km single mode fiber with the averaged bit error ratio of two sidebands below 3.8×10-3. We also achieve, to the best of our knowledge, a record electrical spectral efficiency of 7.1 b/s/Hz for single polarization direct detection systems using a dual-SSB PAM4 or dual-SSB 16-quadrature amplitude modulation format.

Single‐channel blind source separation for paired carrier multiple access signals

Paired carrier multiple access (PCMA) is one of the most common single-channel mixtures. It is still a great challenge to recover the transmitted bits from non-cooperative received PCMA signals, due to the high complexity of existing single-channel blind source separation (SCBSS) algorithms. Hence, a double-direction delayed-decision-feedback sequence estimation (DD-DDFSE) algorithm for non-causal high-order channel is proposed to realise the separation of PCMA signals. The proposed algorithm employs the Viterbi algorithm (VA) with low-order channel twice instead of conventional VA with high-order channel once. The symbols estimated by the initial VA are utilised to equalise the causal and non-causal taps of the channel beyond the trellis state in the second VA. The relationship between the decision-feedback error from the initial VA and the performance of the second VA is also derived. Compared with state-of-the-art maximum likelihood sequence estimation algorithms, DD-DDFSE algorithm can not only decrease the computation complexity but also improve the separation performance.

MLSE-Based DQPSK Transmission in 43$~$Gb/s DWDM Long-Haul Dispersion-Managed Optical Systems

We analyze by simulation the performance of the differential quadrature phase-shift keying (DQPSK) modulation format in dispersion-managed multi-span WDM optical systems at 43 Gb/s, with 50 GHz channel spacing, in the presence of fiber nonlinearity. We show that the use of maximum-likelihood sequence-estimation (MLSE) receivers significantly helps to increase tolerance to dispersion map design. We also show that the use of an MLSE algorithm which takes into account the correlation of samples allows to improve system performance, partially mitigating the impact of fiber non-linearity. Some of the results presented here hint at a possible use of similar techniques in the context of coherent systems as well.

An MLSE Receiver for Electronic Dispersion Compensation of OC-192 Fiber Links

A maximum-likelihood sequence estimation (MLSE) receiver is fabricated to combat dispersion/intersymbol interference (chromatic and polarization mode), noise (optical and electrical), and nonlinearities (e.g., fiber, receiver photodiode, or laser) in OC-192 metro and long-haul links. The MLSE receiver includes a variable gain amplifier with 40-dB gain range and 7.5-GHz 3-dB bandwidth, a 12.5-Gb/s 4-bit analog-to-digital converter, a dispersion-tolerant phase-locked loop, a 1:8 demultiplexer, and a digital equalizer implementing the MLSE algorithm. The MLSE receiver achieves more than 50% reach extension at signal-to-noise levels of interest as compared to conventional clock data recovery systems

On MLSE algorithms for unknown fast time-varying channels

We consider maximum-likelihood sequence estimation (MLSE) algorithms for unknown, time-varying intersymbol interference communication channels. We assume a statistical channel model, and marginalize over model parameters to derive expectation-maximization (EM) algorithms for both time-independent Gaussian and Gauss-Markov models, and we contrast these with direct MLSE and computationally efficient per-survivor processing implementations. We identify a general concern associated with the convergence of EM-based discrete parameter (e.g., symbol) estimators.

A Bayesian maximum-likelihood sequence estimation algorithm for a priori unknown channels and symbol timing

It is shown that the optimum demodulator for the case of an a priori unknown channel and symbol timing can be approximated using a modified Viterbi algorithm (VA), in which the branch metrics are obtained from the conditional innovations of a bank of extended Kalman filters (EKFs). Each EKF computes channel and timing estimates conditioned on one of the survivor sequences in the trellis. It is also shown that the minimum-variance channel and timing estimates can be approximated by a sum of conditional EKF estimates, weighted by the VA metrics. Simulated bit error rate (BER) results and averaged-squared channel/timing error trajectories are presented, with estimation errors compared to the Cramer-Rao lower bound. The BER performance of the modified VA is also shown to be superior to that obtained using a decision-directed channel/timing estimation algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Computational savings and implementation of maximum likelihood detectors (Corresp.)

A further analysis of maximum likelihood sequence estimation algorithms for Gaussian channels with finite intersymbol interference is presented. It is shown that several maximum likelihood survivor paths cannot occur simultaneously, and hence that searching some of the nodes of the state trellis diagram can be avoided. An efficient algorithm is given that updates the metrics while avoiding redundant parts of the search.