Digital equalisation at 10.7 Gb/s using maximum likelihood sequence estimation - a present and future technology

This article proposes a low-complexity maximum likelihood sequence estimation (MLSE) algorithm tailored for non-return-to-zero (NRZ) high-speed transceivers. In particle physics experiments, data transmission volumes are continually increasing, with transceivers assuming pivotal roles. MLSE has garnered significant attention due to its notable advantages in eliminating intersymbol interference (ISI) and its capability to replace decision feedback equalizers (DFEs). However, MLSE complexity exponentially escalates with the increment of traceback length and equalizer order. Hence, reducing MLSE complexity while preserving performance is imperative. This article simplifies MLSE transition metric calculations, obviating the necessity for intricate state computations and result storage. A configurable and highly adaptable transceiver simulation system is developed, utilizing a field-programmable gate array (FPGA), and the proposed algorithm is evaluated using this system. Synthesis results demonstrate that the proposed algorithm significantly reduces resource utilization while maintaining algorithm performance.

The performance of a high-speed intensity-modulation (IM)/direct-detection (DD) transmission system could be limited by the bandwidth of optical transceivers. One popular way to cope with this performance limitation is to utilize the maximum likelihood sequence estimation (MLSE) at the receiver. However, a practical problem of MLSE is its high implementation complexity. Even though the channel impulse response can be truncated by using a two-tap filter before applying the MLSE, it still faces an implementation problem when used for multi-level modulation formats. In this paper, we propose and demonstrate a reduced-state MLSE for band-limited IM/DD transmission systems using M-ary pulse amplitude modulation (PAM-M) formats. We use a conventional Viterbi algorithm to search a reduced-state trellis, which is constructed by using the coarse pre-decision of the signal equalized by a feed-forward equalizer. Thus, the proposed MLSE reduces the implementation complexity significantly. We evaluate the performance of the proposed reduced-state MLSE over 100∼140-Gb/s PAM-4/6/8 transmission systems implemented by using a 1.3-µm directly modulated laser. The results show that the proposed MLSE achieves almost the same performance as the conventional MLSE but reduces the implementation complexity by a factor of 4∼10 when the complexity is assessed by the number of multiplications and additions.

A maximum-likelihood sequence estimation (MLSE) based equalizer with Viterbi algorithm is designed in this paper. It can effectively compensate the intersymbol interference (ISI) caused by the polarization mode dispersion (PMD).The simulation results prove that the electronic equalizer, in 40Gbit/s non-return-to-zero (NRZ) optical system with Gaussian noise, can mitigate the polarization mode dispersion (PMD) and improve performance of the communication system. At the last, we compared the MLSE equalizers and DFE(FFE),we can come to the conclusion that the MLSE equalizer is the best way to combat polarization mode dispersion(PMD) and it can improve performance of system effectly.

We propose a blind sequence estimator (BSE) that is well suited for short burst communication formats used in many wireless TDMA systems. It is based on per survivor processing (PSP) maximum likelihood sequence estimation (MLSE). However, the initial channel estimates needed for conventional MLSE, are obtained blindly from the on-set of a burst. This provides PSP with near-convergence initial channel estimates without the help of training sequences. Thus, this approach is effective for short burst TDMA wireless communication, since it eliminates the overhead associated with training which is significant in short burst formats. For fast time-varying frequency selective wireless channels, the proposed BSE performs similarly compared to conventional PSP MLSE with training sequences. This is mainly because the need for channel tracking limits the usefulness of training sequences.

The performance of different electronic equalization and processing schemes for 40- and 10-Gb/s optical transmission over single-mode fiber (SMF) are discussed, from the point of their ability to compensate chromatic dispersion (CD) and polarization mode dispersion (PMD). In addition, the impact of fiber nonlinearity and modulation format on equalization is also investigated. The main objective of this paper is to present an overview and a comparison of the performances rather than a detailed explanation of the principles of the different equalization schemes. The equalizers which will be covered are analog equalizer (feedforward and decision feedback type), maximum likelihood sequence estimator (MLSE), electronic precompensation, coherent/intradyne detection with digital signal processing (DSP) equalization, DSP-based optical orthogonal frequency division multiplexing (OFDM), and turbo equalization.

High data-rate upstream transmission in wavelength division multiplexed passive optical network (WDM-PON) based on reflective semiconductor optical amplifier (RSOA) is limited by severe inter-symbol interference (ISI), owing to low-bandwidth transmitter and fiber dispersion. To overcome the limitations in RSOA-based WDM-PON, we propose a novel receiver based on partial response maximum likelihood (PRML) equalization which combines the use of partial response (PR) signaling with maximum likelihood sequence estimation (MLSE). MLSE has been long considered as the optimal reception technique to overcome various types of impairment in optical transmission such as dispersions. It is demonstrated in this paper that PRML surpasses standard MLSE in ISI and reflection suppression with reduced complexity for RSOA-based WDM-PON system. 150 km unidirectional distance is demonstrated for 10 Gb/s uplink, while bidirectional uplinks up to 50 km and 20 km are achieved for data rate of 10 Gb/s and 20 Gb/s respectively, in WDM-PON using PRML. Furthermore, the impacts of discrete reflections on various equalization techniques are investigated, where PRML also shows superiority over MLSE.

The authors present a maximum likelihood sequence estimation (MLSE) receiver structure for both linear and hard-limited 16-quadrature pulse overlapping modulation (QPOM) schemes. Using this structure, the performance of these schemes over shadowed Rician fading channels is studied. The structure of linear 16-QPOM schemes allowed the use of independent decoding for in-phase and quadrature components of the transmitted signal, thus reducing considerably the complexity of the MLSE receiver. The hard-limited 16-QPOM scheme used two hard-limited QPOM schemes in parallel. It is shown that an optimum MLSE receiver for this type of signal needs to consider both in-phase and quadrature components at the same time. Using the MLSE receiver, both schemes outperform conventional coherent 16-quadrature amplitude modulation (QAM). >

Maximum likelihood sequence estimation in high-speed PONs using machine learning-based pre-equalizers

By embedding a decision-feedback equalizer (DFE) into the structure of a maximum-likelihood sequence estimator (MLSE), an adaptive combined DFE/MLSE scheme is proposed. In this combined DFE/MLSE, the embedded DFE has three functions: (i) prefiltering the received signals and truncating the equivalent channel response into the desired one, (ii) compensating for channel distortions, and (iii) providing the MLSE detector with predicted values of input signals. Since the embedded MLSE detector operates on the predicted signals the detected symbols at the output of the DFE/MLSE do not suffer any delay and can be directly fed back into the embedded DFE so that the error propagation, which usually takes place in a conventional DFE, can be greatly reduced. Analytical and simulation results indicate that the performance is significantly improved by the DFE/MLSE compared to the conventional DFE while its computation complexity is much less than that of the conventional MLSE receiver. The combined DFE/MLSE can use different adaptive structures (block-updating, sliding window updating or symbol-by-symbol updating) to meet different performance objectives. Moreover, the proposed DFE/MLSE provides a trade-off between performance and complexity with a parameter m representing the MLSE detection depth as well as the number of predicting steps of the embedded DFE. For some particular values of m, this scheme is capable of emulating the conventional DFE, MLSE-VA, adaptive LE-MLSE equalizer, adaptive DDFSE, and adaptive BDFE without detection delay.

We propose a path diversity reception technique that uses steering vector arrays and Viterbi algorithm-based sequence estimation techniques to cope with severe intersymbol interference (ISI). The proposed scheme suppresses some delayed paths with spatial and temporal processing based on the single constraint sample matrix inversion algorithm to reduce excess ISI for sequence estimation. The path diversity branches are weighted in proportion to the quality of the array output signals and then combined via the branch-metric-combining (BMC) Viterbi algorithm to estimate the most likely transmitted sequence. Maximum likelihood sequence estimation, limited-state sequence estimation, and decision-feedback sequence estimation are examined for their suitability as estimation techniques. Consequently, the proposed scheme is sufficient for managing various kinds of channel models. Thus, the proposed scheme is suitable for high-speed time-division multiple access (TDMA) mobile radio systems, because, in this kind of transmission, fading can be presumed to be nearly quasi-static during the burst, and the delayed paths are spread over several symbols.

The implementations of super-Nyquist pulse generation, both in a digital field using a digital-to-analog converter (DAC) or an optical filter at transmitter side, are introduced. Three corresponding signal processing algorithms at receiver are presented and compared for high spectral-efficiency (SE) optical systems employing the spectral prefiltering. Those algorithms are designed for the mitigation towards inter-symbol-interference (ISI) and inter-channel-interference (ICI) impairments by the bandwidth constraint, including 1-tap constant modulus algorithm (CMA) and 3-tap maximum likelihood sequence estimation (MLSE), regular CMA and digital filter with 2-tap MLSE, and constant multi-modulus algorithm (CMMA) with 2-tap MLSE. The principles and prefiltering tolerance are given through numerical and experimental results.

We experimentally demonstrate uncompensated 8-channel wavelength division multiplexing (WDM) and single channel transmission at 10.7 Gb/s over a 470 km hybrid fiber link with in-line semiconductor optical amplifiers (SOAs). Two different forms of the duobinary modulation format are investigated and compared. Maximum Likelihood Sequence Estimation (MLSE) receiver technology is found to significantly mitigate nonlinear effects from the SOAs and to enable the long transmission, especially for optical duobinary signals derived from differential phase shift keying (DPSK) signals directly detected after narrowband optical filter demodulation. The MLSE also helps to compensate for a non-optimal Fabry-Perot optical filter demodulator.

In this paper, we propose a joint feedforward equalizer (FFE) and an error-based feedforward equalizer (Err-FFE) to eliminate the serious inter-symbol interference and high-frequency colored noise for 100 Gb/s 4-level pulse-amplitude modulation (PAM4) optical systems. The proposed Err-FFE is first designed to replace the joint post-filter (PF) and maximum likelihood sequence estimation (MLSE). The Err-FFE algorithm has only 15% computational complexity compared to the joint PF and MLSE. Moreover, experimental results show that the performance of joint FFE and Err-FFE algorithm is much better than that conventional FFE, and is comparable with that of FFE joint with PF and MLSE. In conclusion, the proposed Err-FFE has both low computational complexity and excellent performance for PAM4-based optical systems, which indicates its potential for applications in low-cost and low-power short-reach optical interconnects.

Combining a channel memory-shortening filter with maximum likelihood sequence estimation (MLSE) effectively reduces MLSE complexity in low-bandwidth optical fiber communication systems. In this paper, we propose an enhanced decision feedback equalizer (DFE)-MLSE for high-speed fiber optic communication systems. This enhanced algorithm builds on our previous work by introducing a dispersion filter that adjusts channel memory length and by directly applying feedback filter coefficients in MLSE branch metric calculations. These advancements improve channel equalization performance, which we experimentally validate in a pulse-amplitude modulation level-4 (PAM-4) system. At a transmission rate of 112 GBd and a distance of 2 km, the enhanced DFE-MLSE achieves an approximate 0.5 dB improvement over the previous DFE-MLSE at a bit error rate of 3.8·10-3, demonstrating its potential for 200 Gbps transmission in short-reach optical networks.

We propose a channel classification method that identifies the delay path profile of Rayleigh fading channels, which can be used in conjunction with conventional maximum-likelihood sequence estimation (MLSE) receivers. The proposed method determines the appropriate number of delay taps for the MLSE trellis, based on a decision variable obtained from multiple traffic bursts. By formulating the decision variable using the F-distribution, we derive exact expressions for misclassification probability. A new MLSE receiver structure that utilizes the channel classification method is described, and bit error rate (BER) simulation results are presented to demonstrate the performance improvement. The particular application which is discussed is the IS-136 TDMA standard.