Maximum Likelihood Sequence Estimation Equalizer Research Articles

Joint Linear and Nonlinear Equalization Based on Cascaded ANN-MLSE With a Modified Loss Function for PAM-4 Optical Transmission

High-speed optical transmission systems suffer from severe inter-symbol interferences (ISIs) and nonlinear distortions due to the limited bandwidth and the nonlinear response of optical and electrical components at the transceivers. Previous work has shown the benefits of applying maximum-likelihood sequence estimation (MLSE) to deal with the ISI and using the neural network-based equalizer (NNE) to mitigate strong nonlinearities. However, most of the NNE has a quasi-hard output as the training and validation loss continue to drop to an over-equalized state in which the quasi-hard output sequence loses the symbol-wise soft information of the signal and fails to obtain the BER performance gain from MLSE. In this work, we investigate the cascaded NNE and MLSE equalization scheme to deal with linear and nonlinear impairments. To solve the over-equalized problem, we propose a modified loss function (MLF) assisting NNE to achieve soft-out without entering into the over-equalized state. With the soft output after NNE, joint linear and nonlinear equalization can be realized by cascading the NNE with MLSE. Both numerical simulations and experimental demonstrations confirm the improved performance of our proposed method. With joint linear and nonlinear equalization, improved back-to-back (BtB) and fiber transmission performances of the 220-Gbps PAM-4 signal are demonstrated.

Complexity Reduction of MLSE and MAP Equalizers Using Modified Prolate Basis Expansion

Maximum likelihood sequence estimation (MLSE) and maximum a posteriori probability (MAP) equalizers are optimum receivers for dealing with intersymbol interference (ISI) in time-dispersive channels. However, their high complexity and latency limit their widespread implementation; therefore, research into reducing their complexity is an open topic. This paper proposes a novel modification to reduce the computational complexity of the aforementioned algorithms, which exploits the representation of the communication channels in a time-delay-domain basis expansion model (BEM). It is shown that an appropriate basis is a set of modified prolate functions, in which the transmitter and receiver filters are considered in the kernel construction. Simulation results show that a reduction in sums and multiplications on the order of 55% can be obtained, maintaining the same bit error rate performance as in the traditional implementation.

Approximate MLSE Equalization of SOQPSK-TG in Aeronautical Telemetry

An approximate maximum likelihood sequence estimator (MLSE) equalizer for shaped offset QPSK, version TG (SOQPSK-TG) is derived based on the pulse amplitude modulation (PAM) approximation of SOQPSK-TG using the two principal PAM pulses. The resulting equalizer is a generalization of the equalizer based on the Ungerboeck observation model, where the generalization is to two parallel, cross-correlated symbol streams over parallel intersymbol interference channels. The bit error rate (BER) performance and computational complexity of the approximate MLSE equalizer operating over three example channels, motivated by multipath propagation in aeronautical telemetry and with increasing selectivity, are presented. The BER performance was evaluated using computer simulations and shown to be approximately 5–8 dB better than the best frequency-domain minimum mean-squared error (MMSE) equalizers published in the open literature. The computational complexity, measured by the number of real-valued multiplications, is comparable to that of the frequency-domain MMSE equalizers.

MLSE Equalizer With Channel Shortening for Faster-Than-Nyquist Signaling

Faster-than-Nyquist (FTN) signaling by introducing controlled inter-symbol interference (ISI) has been viewed as a potential technique in future communication systems due to its higher spectrum efficiency. In order to achieve the high transmission rate, the effective receivers have to been designed to suppress the ISI and extract the transmit signals. Therefore, we propose a channel shortening-based maximum-likelihood sequence estimation (MLSE) scheme. In this scheme, the length of the shortening channel can be optimized for the different time-squeezing factor, which determines the transmission rate and ISI in FTN systems, to achieve a good tradeoff between the detection performance and the implementation complexity. The simulation analysis results show that the proposed MLSE equalizer with optimized channel shortening can achieve a good tradeoff between the performance and the complexity.

Solutions for 100/400-Gb/s Ethernet Systems Based on Multimode Photonic Technologies

In this paper, we experimentally demonstrate the transmission of 112 Gb/s four-level pulse amplitude modulation over 100-m OM4 multimode fiber employing a multimode 850-nm vertical-cavity surface-emitting laser (VCSEL) at the transmitter side and equalization techniques at the receiver's digital signal processing (DSP). The penalties imposed by the strong bandwidth limitations due to the optical components as well as the low modal bandwidth of the fiber are compensated by three variant DSP schemes at the receiver, i.e., 1) a finite-impulse response (FIR) filter, 2) a maximum likelihood sequence estimation equalizer (MLSE), and 3) an FIR filter followed by an MLSE equalizer (FIR/MLSE) in a cascaded form. We evaluate all three aforementioned equalization schemes under two different transmitter implementations, i.e., employing a 30-GHz arbitrary waveform generator and a lower bandwidth 15-GHz commercially available digital-to-analog converter and we infer about the applicability of each DSP scheme under these implementations. We show that the hybrid implementation of an FIR followed by a 16-state MLSE can enable the 100-m transmission below the 7% hard decision (HD) forward error correction (FEC) threshold limit and outperforms its other two counterparts for the back-to-back case as well as after 100-m transmission for the high-bandwidth transmitter implementation. On the other hand, lower bandwidth DAC implementations, i.e., 15 GHz, require an increased state MLSE without the need for a preceding FIR filter to bring the bit error rate (BER) below the HD-FEC limit after 100-m OM4 fiber transmission. DSP complexity versus BER performance is assessed for all the aforementioned scenarios evaluating the impact of the transmitter's bandwidth on the overall system's performance. Our proposed solutions show that 112 Gb/s 100-m OM4 multimode links based on VCSELs and standard OM4 fiber can enable next generation 100 and 400 Gb/s wavelength division multiplexed optical interconnects.

Performance Comparison Between 4D Trellis Coded Modulation and PAM-4 for Low-Cost 400 Gbps WDM Optical Networks

We investigate two trellis-coded modulation (TCM) schemes for use in next-generation low-cost 400G optical networks. Their performance is evaluated against that of four-level pulse amplitude modulation (PAM-4). We experimentally demonstrate that TCM outperforms PAM-4 at bit rates between 56 and 80 Gbps and thus is a valid candidate for $\text{8}\lambda \times \text{50G}$ implementations of future 400G wave division multiplexing (WDM) networks. Due to the severe bandwidth limitations of the experimental setup, the feed-forward equalizer and the maximum likelihood sequence estimation equalizer are employed in order to achieve bit error rates below the KP4 threshold of $3\times 10^{-4}$ . We also show that, at 56 Gbps and 1300 nm wavelength, TCM enables optical links of up to 40 km, whereas PAM-4 can only provide transmissions of up to 30 km. We observe that TCM performance degrades faster than that of PAM-4 when we increase the bit rate. For rates higher than 80 Gbps, TCM is not able to improve upon PAM-4 anymore. Thus, only PAM-4 is fit for $\text{4}\lambda \times \text{100G}$ WDM networks, unless higher bandwidth components are used.

1.55-μm Long-Wavelength VCSEL-Based Optical Interconnects for Short-Reach Networks

We demonstrate the generation and transmission of a 28-Gb/s intensity modulated optical signal over single mode fiber (SMF) links up to 1, 2, 5, and 10 km employing a 18-GHz 3-dB bandwidth monolithic vertical-cavity surface-emitting laser (VCSEL) based on buried tunnel junction technology with regrown n -doped InP material. Inexpensive technologies such as nonreturn-to-zero on–off keying modulation format, direct detection as well as digital signal processing-based receivers make the transmission feasible for chromatic dispersion (CD) uncompensated SMF links up to 10 km at the 7% hard-decision (HD) forward error correction (FEC) limit. Three different equalizers for the receiver side are investigated in this paper in terms of performance optimization, i.e., the maximum likelihood sequence estimation equalizer (MLSE), the feed-forward equalizer (FFE) and a hybrid scheme that comprises of an FFE and an MLSE equalizer (FFE/MLSE) in cascaded form. Our experimental results indicate that MLSE scheme outperforms the other two counterparts in all transmission scenarios. Performance optimization in terms of MLSE complexity is also presented. Less complex implementations like FFE equalizer can provide reliable transmission below the 7% HD-FEC limit for links up to 5 km. The FFE/MLSE scheme provides similar performance as MLSE for links up to 5 km, while its performance deteriorates for 10 and 15 km links as signal distortion due to CD becomes too severe to recover the signal. A timing recovery unit is employed before the equalizers in order to compensate for phase offsets and improve the signal quality. Our proposed scheme proves a promising candidate to enable VCSEL-based short reach optical interconnects in data centers and metro-access area.

Coherent Compensation for 100G DP-QPSK With One Sample per Symbol Based on Antialiasing Filtering and Blind Equalization MLSE

We propose coherent detection with one sample/symbol. Maximum-likelihood sequence estimation (MLSE) is used to compensate for intersymbol interference introduced by antialiasing filtering. The 100 000-ps/nm chromatic dispersion and 100-ps differential group delay are compensated with 1.5-dB penalty. Blind MLSE equalization is proposed.

Low Complexity MLSE Equalization in Highly Dispersive Rayleigh Fading Channels

A soft output low complexity maximum likelihood sequence estimation (MLSE) equalizer is proposed to equalize M-QAM signals in systems with extremely long memory. The computational complexity of the proposed equalizer is quadratic in the data block length and approximately independent of the channel memory length, due to high parallelism of its underlying Hopfield neural network structure. The superior complexity of the proposed equalizer allows it to equalize signals with hundreds of memory elements at a fraction of the computational cost of conventional optimal equalizer, which has complexity linear in the data block length but exponential in die channel memory length. The proposed equalizer is evaluated in extremely long sparse and dense Rayleigh fading channels for uncoded BPSK and 16-QAM-modulated systems and remarkable performance gains are achieved.

Electrical Dispersion Compensation for Multichip DPSK Detection Utilizing MISO DFE

Multichip differential phase-shift keying (MC-DPSK) is a promising method to improve the performance of DPSK signal. It has been proposed that a joint maximum likelihood sequence estimation (MLSE) equalizer can be utilized after MC-DPSK detection to further improve the chromatic dispersion (CD) and polarization-mode dispersion (PMD) tolerance in optical fiber transmission system. In this letter, we investigate electrical CD and PMD compensation for MC-DPSK detection with different chip numbers utilizing multiple-input-single-output (MISO) decision-feedback equalizers, which has less computation complexity than joint MLSE equalizers. Moreover, we propose the MISO equalization scheme after separate-photodiode MC-DPSK detection, which will further improve the distortion tolerance.

Equalization of nonlinear transmission impairments by maximum-likelihood-sequence estimation in digital coherent receivers

We describe a successful introduction of maximum-likelihood-sequence estimation (MLSE) into digital coherent receivers together with finite-impulse response (FIR) filters in order to equalize both linear and nonlinear fiber impairments. The MLSE equalizer based on the Viterbi algorithm is implemented in the offline digital signal processing (DSP) core. We transmit 20-Gbit/s quadrature phase-shift keying (QPSK) signals through a 200-km-long standard single-mode fiber. The bit-error rate performance shows that the MLSE equalizer outperforms the conventional adaptive FIR filter, especially when nonlinear impairments are predominant.

A Comparative Study on Time Domain Sequential Equalizer with MLD and MLSE Equalizer on MIMO Frequency Selective Channels

In this paper, we investigate two receiver structures for spatially multiplexed transmission on MIMO frequency selective fading channels. Those receivers compensate the IAI (Inter-Antenna Interference) and ISI (Inter-Symbol Interference) in the time domain. We first propose the MIMO sequential equalizer in which the block of several receives symbols is processed symbol by symbol by MLD (Maximum Likelihood Detection). Next we investigate the MIMO MLSE (Maximum Likelihood Sequence Estimation) receiver in which the terminated block trellis is decoded by the Viterbi algorithm. The bit error rates of two time domain receivers are examined through computer simulations and we also compare their BER characteristics to those of the conventional MIMO SC-FDE.

MLSE and MAP Equalization for Transmission Over Doubly Selective Channels

In this paper, equalization for transmission over doubly selective channels is discussed. The symbol-by-symbol maximum a posteriori probability (MAP) equalizer and the maximum-likelihood sequence estimation (MLSE) are discussed. The doubly selective channel is modeled using the basis expansion model (BEM). Using the BEM allows for an easy and low-complexity mechanism for constructing the channel trellis to implement the MLSE and the MAP equalizer. The MLSE and the MAP equalizer are implemented for single-carrier transmission and for multicarrier transmission implemented using orthogonal frequency-division multiplexing (OFDM). In this scenario, a complexity-diversity tradeoff can be observed. In addition, we propose a joint estimation and equalization technique for doubly selective channels. In this joint estimation and equalization technique, the channel state information (CSI) is obtained in an iterative manner. Simulation results show that the performance of the joint channel estimation and equalization approaches the performance when perfect CSI is available at the receiver.

Iterative Minimum Mean Square Error Equalization for Optical Fiber Communication Systems

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this letter, considering the photodetector- induced nonlinearity and non-Gaussian noise in optical fiber communication systems, a new iterative equalization algorithm based on the minimum mean square error criterion, called iterative minimum mean square error equalization, is derived to effectively mitigate the intersymbol interference caused by polarization-mode dispersion and chromatic dispersion. Compared with maximum-likelihood sequence estimation equalization, the proposed algorithm presents a better capability of improving the performance of the receiver. </para>

On the least-squares performance of a novel efficient center estimation method for clustering-based MLSE equalization

Recently, a novel maximum-likelihood sequence estimation (MLSE) equalizer was reported that avoids the explicit estimation of the channel impulse response. Instead, it is based on the fact that the (noise-free) channel outputs, needed by the Viterbi algorithm, coincide with the points around which the received (noisy) samples are clustered and can thus be estimated directly with the aid of a supervised clustering method. Moreover, this is achieved in a computationally efficient manner that exploits the channel linearity and the symmetries underlying the transmitted signal constellation. The resulting computational savings over the conventional MLSE equalization scheme are significant even in the case of relatively short channels where MLSE equalization is practically applicable. It was demonstrated, via simulations, that the performance of this algorithm is close to that using a least-squares (LS) channel estimator, although its computational complexity is even lower than that of the least-mean squares (LMS)-trained MLSE equalizer. This paper investigates the relationship of the center estimation (CE) part of the proposed equalizer with the LS method. It is proved that, when using LS with the training sequence employed by CE, the two methods lead to the same solution. However, when LS is trained with random data, it outperforms CE, with the performance difference being proportional to the channel length. A modified CE method, called MCE, is thus developed, that attains the performance of LS with perfectly random data, while still being much simpler computationally than classical LS estimation. Through the results of this paper, CE is confirmed as a methodology that combines high performance, simplicity, and low computational cost, as required in a practical equalization task. An alternative, algebraic viewpoint on the CE method is also provided.

Adaptive MLSE Equalizer with Per-Survivor QR Decomposition for Trellis-Coded MIMO Transmission

A trellis-coded multiple-input multiple-output (MIMO) transmission technique, which exploits multiple-antenna elements at both transmitter and receiver sides and employs trellis-coded modulations (TCMs), has potential to significantly increase spectral efficiency in wireless communications. At the receiver, an adaptive equalizer based on maximum-likelihood sequence estimation (MLSE) deals with intersymbol interference (ISI) incurred in wideband transmissions and jointly decodes multiplexed TCM signals. Recently, a sphere-constrained maximum-likelihood detection, so-called sphere decoding, has drawn much attention for reducing the computational burden in MIMO transmission systems. This paper describes the super-trellis structured Viterbi algorithm applying per-survivor sphere decoding, and evaluates the effect of the complexity reduction in branch metric computations.

Performance Improvements From Decision-Delay Adaption in Adaptive MLSE Equalizers

This paper analyzes a fully adaptive maximum-likelihood sequence estimator (MLSE) equalizer in fast fading channel conditions. The receiver adaptively estimates the channel state information, and also adapts to learn the channel fading statistics. The equalizer is analyzed using pairwise error probabilities to derive lower bounds on performance. A decision delay adaption rule is proposed, based on the bit-error rate analysis. With this new rule, the fully adaptive MLSE equalizer is shown to outperform existing fixed-delay equalizers when channel statistics are unknown. Simulation studies confirm that the performance is close to the analytic bounds.

MLSE receiver for direct-sequence spread-spectrum systems on a multipath fading channel

To accommodate high-speed data transmissions, it may be necessary to substantially reduce the processing gain of a direct-sequence spread-spectrum (DSSS) system. As a result, intersymbol interference effects may become more severe. In this paper, we present a new structure for maximum-likelihood sequence estimation equalization of DSSS signals on a multipath fading channel that performs the function of despreading and equalization simultaneously. Analytical upper bounds are derived for the bit-error probability when random spreading sequences are used, and comparisons to simulation results show that the bounds are quite accurate. The results also show that significant performance improvement over the conventional RAKE receiver is obtained.

A robust noncoherent equalizer receiver for fading channels with short memory . II. Modified structure

For pt. I see ibid., vol.5, no.5, p.1040-54 (2002). In Part I, we introduced a robust noncoherent maximum likelihood sequence estimation (MLSE) equalizer receiver structure applicable to radio channels with impulse responses spanning less than two bit intervals. The distinct characteristic of this receiver was its robustness to carrier frequency offsets. However, due to the differential operation prior to the MLSE equalization, we observed some performance degradation, resulting in a delay spread range significantly smaller than an equivalent coherent MLSE equalizer. We propose techniques to significantly improve the performance of the noncoherent equalizer by using a second, complementary differential processor. The performance assessment of the new receiver is presented. In particular, using the Digital Enhanced Cordless Telecommunications system as an example, it is shown that the modified receiver's dispersive channel operation range is almost twice as much as the basic structure, with a multipath diversity gain comparable to a coherent equalizer receiver. On the other hand, unlike coherent structures, it retains low sensitivity to both frequency offsets and modulation index drifts. Finally, we introduce an approach to further extend the receiver's frequency offset tolerance to that of a standard differential detector receiver.

A robust noncoherent equalizer receiver for fading channels with short memory .I. Basic structure

Traditional equalizers are very sensitive to carrier frequency offsets between the transmitter and receiver. Coherent receivers with frequency estimation algorithms can remove the offset to prevent the equalizer breakdown, but with a penalty in receiver complexity. On the other hand, noncoherent receivers such as differential detectors are inherently robust to the frequency offsets but cannot employ standard equalization techniques due to their nonlinear front-end. We introduce a simple noncoherent equalizer receiver structure for fading channel environments with short memory (up to two-bit intervals). The receiver consists of a whitened matched filter followed by a differential detector and a maximum likelihood sequence estimation (MLSE) equalizer. We examine the performance of this noncoherent equalizer by both analysis and simulation. It is shown that despite the simplicity, this receiver structure is capable of significant performance improvement as compared to an ordinary differential detector while operating with receiver frequency offsets two orders of magnitude greater than a traditional MLSE equalizer. This structure offers an attractive solution for high-bit-rate cordless transmission systems such as Digital Enhanced Cordless Telecommunications (DECT) that use simple noncoherent receivers whose performance can be constrained by channel dispersion. Using DECT as a case study, we show that the equalizer's performance limits are caused by the receiver nonlinearity and can be improved by adaptation of this nonlinearity to channel conditions.