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

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.

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.

Unified low-complexity decision feedback equalizer with adjustable double radius constraint

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.

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.

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.

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.

In this work, a sequential estimation algorithm based on branch metric is used as channel equalizer to combat intersymbol interference in frequency-selective wireless communication channels. The bit error rate (BER) and computational complexity of the algorithm are compared with those of the maximum likelihood sequence estimation (MLSE), the recursive least squares (RLS) algorithm, the Fano sequential algorithm, the stack sequential algorithm, list-type MAP equalizer, soft-output sequential algorithm (SOSA) and maximum-likelihood soft-decision sequential decoding algorithm (MLSDA). The BER results have shown that whilst the sequential estimation algorithm has a close performance to the MLSE using the Viterbi algorithm, its performance is better than the other algorithms. Beside, the sequential estimation algorithm is the best in terms of computational complexity among the algorithms mentioned above, so it performs the channel equalization faster. Especially in M-ary modulated systems, the equalization speed of the algorithm increases exponentially when compared to those of the other algorithms.

We reviews optical access technologies for 5G mobile communication networks such as mobile data compression, high-speed passive optical network (PON), and analog radio over fiber (RoF) technologies. Recent feasibility studies for future optical access network with optical mobile convergence are discussed.

This chapter discusses fundamentals of information theory and channel coding (error correction coding ECC, Forward error correction FEC). First, key results of Shannon, including channel capacity and the relationship between transmit power and bandwidth, are discussed. Block codes multiply a block of data with an encoding matrix. For systematic codes, the resulting codeword consists of systematic bits and parity check bits. Decoding is achieved by multiplication with a parity check matrix and determination of the syndrome vector. Correction of errors within the correction sphere can be done, e.g., through lookup tables. Convolutional codes send the source data stream through shift registers and adders, a process described by a trellis diagram. Maximum-likelihood sequence estimation (Viterbi algorithm) determines the (transmit) bit sequence with best distance metric (Hamming or Euclidean) from the received signal. Methods for combining coding and higher-order modulation include trellis coded modulation (using set partitioning for code design) and bit-interleaved coded modulation (BICM). Turbo codes are close to capacity-achieving. They are based on transmitting differently interleaved convolutional codes; receivers use soft decoding of the constituent codes and iterative exchange of soft information (log-likelihood ratios). Low-density parity check codes (LDPCC) are decoded by belief propagation (message passing), where variable nodes and constraint nodes exchange beliefs about the codeword. In fading channels, (block or convolutional) interleaving is essential to provide diversity. From an information-theoretic point of view, in fading channels we can distinguish between the ergodic capacity and the outage capacity. If the channel state information is known at the transmitter, waterfilling is the optimum power allocation strategy. Automatic Repeat Request ARQ) and Hybrid ARQ (including chase combining or incremental redundancy) are described in the appendix.

This paper investigates the combination of partial-response (PR) shaping and trellis coded modulation (TCM), for high-bit-rate wireline data transmission. Combining PR and TCM, we attempt to reduce the normalized bandwidth of the transmitted signal, without imposing a penalty on its minimum distance. The optimum detection method for such signals is the maximum likelihood sequence estimator (MLSE), using a Viterbi algorithm which operates on the combined PR/TCM trellis. Since the large number of states makes the MLSE computationally prohibitive, we investigate the performance of suboptimum reduced-complexity detectors, namely the M-, T- and RSSE/DFSE algorithms, and show that we can obtain near-MLSE performance at a much lower computational cost. Considerations about the PR pulse shape and the trade-off between bandwidth and performance are also given.

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.

Decision feedback sequence estimation (DFSE), which is a reduced-complexity alternative to maximum likelihood sequence estimation (MLSE), can be used effectively for equalization of intersymbol interference (ISI) as well as for multiuser detection. The algorithm performs very well for whitened (minimum-phase) channels. For nonminimum-phase channels, however, the algorithm is not very effective. Moreover, DFSE requires a noise-whitening filter, which may not be feasible to compute for time-varying channels such as a multiuser direct-sequence code division multiple access (DS-CDMA) channel. Noise-whitening is also cumbersome for applications that involve bidirectional equalization such as the global system for mobile communication (GSM) system. In such conditions, it is desirable to use the Ungerboeck (1974) formulation for sequence estimation, which operates directly on the discrete-time unwhitened statistic obtained from conventional matched filtering. Unfortunately, DFSE based on matched filter statistics is severely limited by untreated interference components. We identify the anticausal interference components, using an error probability analysis. This leads us to a modified unwhitened decision feedback sequence estimator (MUDFSE) in which the components are canceled, using tentative decisions. We obtain approximate error probability bounds for the proposed algorithm. Performance results indicate that the modified algorithm, used on unwhitened channels with relatively small channel correlations, provides similar performance/complexity tradeoffs as the DFSE used on the corresponding whitened minimum-phase channels. The algorithm is especially attractive for multiuser detection for asynchronous DS-CDMA channels with long spreading codes, where it can achieve near-MLSE performance with exponentially lower complexity.

The prohibitive cost of dedicated fiber local loops for residential customers led to the development of passive optical networks (PONs) for access to broadband services. However the passive splitting of optical signals which gives flexibility, low cost and robustness creates a broadcast physical topology compromising customer privacy. Encryption is the only cost-effective way to prohibit global reception and create the required point-to point logical links restoring confidentiality to the desirable degree. Because of the very high speed of such networks, only solutions amenable to hardware implementations are acceptable. ATM cells are allocated to the system users on a time division basis each encrypted with a different key. A suitable for the PON environment encryption solution based on the summation generator stream cipher is presented with an outline of its hardware implementation.