Decision Feedback Equalizer Research Articles

Robust Equalization for Single-Carrier Underwater Acoustic Communications Based on Parameterized Interference Model

There are several sources of artificial and naturally generated impulsive interference in marine environment which could severely degrade the acoustic communication performances. This letter tackles the equalization for single-carrier modulated systems with impulsive interference based on parameterized model, and a two-step equalization algorithm is proposed. In the first step, an iterative interference impulse estimation/cancellation can be performed and initial symbol estimation is obtained by conventional decision feedback equalization. In the second step, a joint channel, impulse, and symbol estimation for single-carrier modulation is applied to enhance the performance. The proposed algorithm is evaluated using partial-band partial-block-duration interference. Simulation results show that the proposed joint estimation algorithm has significant performance advantages over conventional algorithm in various signal-to-interference ratio levels.

Neural Network Equalisation for High-Speed Eye-Safe Optical Wireless Communication with 850 nm SM-VCSELs

In this paper, we experimentally illustrate the effectiveness of neural networks (NNs) as non-linear equalisers for multilevel pulse amplitude modulation (PAM-M) transmission over an optical wireless communication (OWC) link. In our study, we compare the bit-error-rate (BER) performances of two decision feedback equalisers (DFEs)—a multilayer-perceptron-based DFE (MLPDFE), which is the NN equaliser, and a transversal DFE (TRDFE)—under two degrees of non-linear distortion using an eye-safe 850 nm single-mode vertical-cavity surface-emitting laser (SM-VCSEL). Our results consistently show that the MLPDFE delivers superior performance in comparison to the TRDFE, particularly in scenarios involving high non-linear distortion and PAM constellations with eight or more levels. At a forward error correction (FEC) threshold BER of 0.0038, we achieve bit rates of ~28 Gbps, ~29 Gbps, ~22.5 Gbps, and ~5 Gbps using PAM schemes with 2, 4, 8, and 16 levels, respectively, with the MLPDFE. Comparably, the TRDFE yields bit rates of ~28 Gbps and ~29 Gbps with PAM-2 and PAM-4, respectively. Higher PAM levels with the TRDFE result in BERs greater than 0.0038 for bit rates above 2 Gbps. These results highlight the effectiveness of the MLPDFE in optimising the performance of SM-VCSEL-based OWC systems across different modulation schemes and non-linear distortion levels.

Advancing LWIR FSO communication through high-speed multilevel signals and directly modulated quantum cascade lasers

This study investigates the potential of long-wave infrared (LWIR) free-space optical (FSO) transmission using multilevel signals to achieve high spectral efficiency. The FSO transmission system includes a directly modulated-quantum cascade laser (DM-QCL) operating at 9.1 µm and a mercury cadmium telluride (MCT) detector. The laser operated at the temperature settings of 15°C and 20°C. The experiment was conducted over a distance of 1 m and in a lab as a controlled environment. We conduct small-signal characterization of the system, including the DM-QCL chip and MCT detector, evaluating the end-to-end response of both components and all associated electrical elements. For large-signal characterization, we employ a range of modulation formats, including non-return-to-zero on-off keying (NRZ-OOK), 4-level pulse amplitude modulation (PAM4), and 6-level PAM (PAM6), with the objective of optimizing both the bit rate and spectral efficiency of the FSO transmission by applying pre- and post-processing equalization. At 15°C, the studied LWIR FSO system achieves net bitrates of 15 Gbps with an NRZ-OOK signal and 16.9 Gbps with PAM4, both below the 6.25% overhead hard decision-forward error correction (6.25%-OH HD-FEC) limit, and 10 Gbps NRZ-OOK below the 2.7% overhead Reed-Solomon RS(528,514) pre-FEC (KR-FEC limit). At 20°C, we obtained net bitrates of 14.1 Gbps with NRZ-OOK, 16.9 Gbps with PAM4, and 16.4 Gbps with PAM6. Furthermore, we evaluate the BER performance as a function of the decision feedback equalization (DFE) tap number to explore the role of equalization in enhancing signal fidelity and reducing errors in FSO transmission. Our findings accentuate the competitive potential of DM-QCL and MCT detector-based FSO transceivers with digital equalization for the next generation of FSO communication systems.

A two-stage slicer employing body biasing for 64-Gb/s PAM4 wireline receiver in 22-nm FDSOI technology

—A 64Gbps 4-level pulse amplitude modulation (PAM4) mixed-signal receiver incorporating a decision-feedback equalizer (DFE) for application in wireline communication is implemented in fully-depleted silicon-on-insulator (FDSOI) 22nm technology. A two-stage slicer with body biasing is proposed to alleviate the stringent timing constraint of the closed-loop DFE. The smaller loading of the first stage shortens the output delay so as to provide a much larger differential input for the second stage. Moreover, body biasing is applied to the proposed slicer to allow higher drive and faster switching capabilities. Simulation results demonstrate that the receiver with body biased two-stage slicer achieves at least 9.9 % and 14.3 % improvements in recovered eye height and eye width over the receiver with StrongArm slicer. The receiver consumes a power of 117.1mW, achieving 1.83pJ/bit energy efficiency.

Low Computational Complexity RLS-Based Decision-Feedback Equalization in Underwater Acoustic Communications

Low Computational Complexity RLS-Based Decision-Feedback Equalization in Underwater Acoustic Communications

A novel variable tap-length adaptive decision feedback equalization in underwater wireless communication

Fix-parameter decision feedback equalization (DFE) is prone to the challenge posed by the time-varying underwater acoustic (UWA) channels. This paper proposes a new adaptively adjusting the DFE’s tap length (TL) algorithm to solve this problem. The number of feedforward filter (FFF) taps of DFE is changed by comparing the fourth-order cumulants and second-order moments related to receiving signals with a threshold value. The feasibility of this approach is verified via theoretical analysis and numerical simulations. Further, the new system has processed the massive experimental data from two lakes. In light of the outcomes, for achieving the same bit error ratio (BER), the signal noise ratio (SNR) that the new algorithm requires is approximately 4 dB less than the variable tap-length method based on the mean square error (MSE). Additionally, this method can improve the system’s flexibility in addressing time-varying channels in underwater wireless communication.

Widely linear RLS equalizer with variable forgetting factor and UD factorization for mud pulse telemetry

To address the problems of time variations and high interferences in continuous-wave mud pulse telemetry channels, a widely linear recursive least squares decision feedback equalizer with a variable forgetting factor was proposed, a smaller steady-state error was achieved, and the tracking performance of the equalizer in time-varying mud channels was enhanced. Furthermore, employing UD factorization in the recursive algorithm improves the computational stability and ensures robust performance. The simulation results indicate that the proposed equalizer enhances the convergence speed by 46 %. The experimental findings demonstrate that within a 3000 m mud pulse telemetry channel, the proposed equalizer reduces the steady-state mean squared error by 3 to 4 dB and increases the error-free transmission rate from 3 bps to 6 bps. These advancements significantly enhance the performance of continuous wave mud pulse telemetry systems.

Design and analysis of CP-free OFDM PDMA transmission system

The paragraph introduces a proposed CP-free OFDM PDMA downlink transmission system. The main focus of the system is to address the capacity limitations caused by the overhead of cyclic prefix in traditional PDMA systems. The transmitter utilizes a pattern mapping unit before CP-free OFDM modulation to enhance system capacity and frequency efficiency. Decision feedback equalization (DFE) is employed in the receiver to eliminate intersymbol interference. The output signals from the DFE are then passed through a CP restoration unit to convert a linear-shifted signal into a cyclic-shifted signals. To assess the system's performance, simulations are conducted, investigating different key parameters such as overload rate, channel condition, and signal-to-noise ratio. The results indicate that, compared to CP OFDM PDMA systems, the proposed CP-free PDMA system significantly enhances system capacity under the same overload rate. Additionally, bit error rate is also evaluated during the simulations. Overall, the paragraph provides an overview of the proposed CP-free OFDM PDMA system, its components, and the simulation-based evaluation of its performance compared to traditional PDMA systems.

A 16-Gb/s 3-tap adaptive DFE in 12-nm FinFET CMOS technology

This paper introduces a 3-tap half-rate adaptive decision feedback equalizer (DFE) and a 2-D eye-opening monitor (EOM). A newly developed regenerating sampler (RG-sampler) with smaller setup time and ck2q time is integrated into the proposed DFE, enhancing its performance. To ensure greater robustness, the sign-sign least-mean-squares (SSLMS) algorithm with a pattern filter is employed to adapt DFE tap coefficients. The proposed 2-D EOM accurately captures the shape of the eye diagram using adjustment steps of 1.95ps and 7 mV in the horizontal and vertical directions, respectively. Additionally, by reusing analog components within the adaptive DFE and 2-D EOM modules, significant reductions in silicon area and power consumption are achieved. Implemented in 12-nm FinFET CMOS technology, the transceiver integrated with adaptive DFE and 2-D EOM operates at a data rate of 16 Gb/s over a channel with 30 dB loss at 8 GHz frequency. The proposed adaptive DFE and 2-D EOM occupy a total area of 0.00808 mm2. Measurement results demonstrate that following DFE adaptation, the eye height is 77 mV, and the eye width is 29.25ps at 16 Gb/s.

A 16 Gb/s serial link transceiver with active inductor based CTLE and 3-tap DFE in 12-nm FinFET CMOS

This paper presents a 16 Gb/s serial link transceiver implemented in 12-nm FinFET CMOS technology. The equalization scheme incorporates a 3-tap feed-forward equalizer (FFE) in the transmitter, a 5-stage continuous time linear equalizer (CTLE), and a 3-tap decision-feedback equalizer (DFE) in the receiver. The proposed FFE structure offers small step size and flexible configuration. The CTLE's high-frequency boost is augmented by integrating an active inductor. A high-accuracy clock and data recovery (CDR) circuit, featuring a cascaded two-step analog phase interpolator (PI) structure, is developed for data retiming. Occupying a footprint of 0.26 mm × 0.63 mm per lane, the transceiver test chip is packaged in a flip chip ball grid array (FC-BGA) module. Measurement results demonstrate a horizontal eye opening of 38 % at a bit error rate (BER) of 10−12 over a channel with 28 dB loss at 8 GHz. Moreover, the power consumption is 68.85 mW per lane at 16 Gb/s.

A sparse adaptive decision feedback equalization approach for the high data rate vertical underwater acoustic communication in deep sea

In underwater acoustic communication (UWAC) environments, multichannel decision feedback equalizer (MDFE) techniques combined with single carrier modulation schemes are widely employed to suppress multipath interference while adapting to time-varying channel response. While MDFE is a powerful technique, the estimation of the numerous filter taps is generally complex problem, and the numerically complexities can lead to the instability of solutions including the occurrence of the burst errors. In this study, we propose a method that introduces L1-norm regularization into the adaptive algorithm of MDFE, considering a sparse channel response environment in the vertical UWAC channel in deep-sea areas. We applied the proposed method to simulation and experimental data, comparing it with conventional methods. As a result, the proposed method demonstrated a clear improvement in bit error rate performance, obtaining sparse filter coefficient estimates and effectively suppressing burst errors.

A joint estimation algorithm for single-input multiple-output underwater acoustic communications

In single-input multiple-output (SIMO) underwater acoustic (UWA) communications, the receiver based on passive time reversal (PTR) combined with decision feedback equalizer (DFE) is widely used but has a limited performance. A multi-channel joint estimation algorithm based on sparse Bayesian learning (MJSBL) is proposed in this paper to exploit the diverse gain from multi-channels, where reasonable prior distribution functions are selected for parameters in the probabilistic model. Afterwards, the algorithm is derived by the mean-field variational inference (VI), iteratively updating the estimation of symbols, channels and noise variation. As a result, the maximum likelihood estimation of the dictionary matrix, as well as the maximum posterior estimation of the channel vectors and noise variance, can be approximated. Simulation and experimental results verify that compared to typical single-channel and multi-channel algorithms, the systems always have lower bit error rates (BERs) and symbol error rates (SERs) with the MJSBL algorithm for different communications distances and symbol block lengths.

Low-complexity and low-latency equalization technique - probabilistic noise cancellation.

Both inside data centers (DCs) and in short optical links between data centers (DC campuses), intensity-modulation and direct-detection (IMDD) systems using four-level pulse amplitude modulation (PAM4) will dominate this decade due to low transceiver price and power consumption. The next DC transceiver generation based on 100 Gbaud PAM4 will require advanced digital signal processing (DSP) algorithms and more powerful forward error correction (FEC) codes. Because of bandwidth limitations, the conventional DC DSP based on a few-tap linear feed-forward equalizer (FFE) is likely to be upgraded to more complex but still low-complexity Volterra equalizers followed by a noise whitening filter and either a maximum likelihood sequence estimation (MLSE) or a maximum a posteriori probability (MAP) algorithm. However, stringent power consumption and latency requirements may limit the use of complex algorithms such as decision feedback equalizer (DFE) or MLSE/MAP in DC networks (DCN). In this paper, we introduce a low-complexity, low-latency algorithm based on a feedforward structure, yielding a performance between DFE and MLSE. We call the novel equalization algorithm probabilistic noise cancellation (PNC), since it weights noise patterns based on their probabilities in the presence of bandwidth limitations. The probabilistic weighting is efficiently exploited in correcting correlated errors caused by noise coloring in the FFE.

Coded GFDM with decision feedback equaliser for enhanced performance in underwater wireless optical communication

Coded GFDM with decision feedback equaliser for enhanced performance in underwater wireless optical communication

Experimental demonstration of low-complexity trigonometric-memory-polynomial decision-feedback equalizer for nonlinear compensation in IM/DD optical systems.

We propose a simple but high-performance trigonometric-memory-polynomial decision-feedback equalizer (TMP-DFE) to cope with the nonlinear distortions in intensity-modulation direct-detection (IM/DD) systems. The proposed method employs sine and cosine operations of received samples, which can be implemented by the efficient CORDIC algorithm using only additions and shifts, to fit odd- and even-order nonlinearities with the effect of different nonlinear orders adjusted by the nonlinear factor. We further propose TMP improved-weighted DFE (TMP-IWDFE) to reduce the error propagation probability of decision feedback. We experimentally evaluate the performance of the proposed schemes in a C-band Erbium-doped-fiber-amplifier-free 56-80Gbit/s four-level pulse-amplitude-modulation (PAM-4) IM/DD system over 30-50 km standard single-mode fiber (SSMF) transmission. The results show that TMP-DFE exhibits better bit error rate performance than Volterra decision-feedback equalizer (V-DFE), diagonally-pruned V-DFE (DP-V-DFE), and diagonally-pruned absolute-term V-DFE (DPAT-V-DFE) while only requiring real multiplications 20.04%, 43.25%, and 74.12% of these conventional schemes. TMP-IWDFE further improves the performance and is better than V-IWDFE, DP-V-IWDFE, and DPAT-V-IWDFE in terms of both performance and complexity. Therefore, the proposed schemes have great potential for high-performance and low-cost IM/DD optical transmission systems.

A simplified decision feedback Chebyshev function link neural network with intelligent initialization for underwater acoustic channel equalization

IntroductionIn shallow-water environments, the reliability of underwater communication links is often compromised by significant multipath effects. Some equalization techniques such as decision feedback equalizer, and deep neural network equalizer suffer from slow convergence and high computational complexity.MethodsTo address this challenge, this paper proposes a simplified decision feedback Chebyshev function link neural network equalizer (SDF-CFLNNE). The structure of the SDF-CFLNNE employs Chebyshev polynomial function expansion modules to directly and non-linearly transform the input signals into the output layer, without the inclusion of hidden layers. Additionally, it feeds the decision signal back to the input layer rather than the function expansion module, which significantly reduces computational complexity. Considering that, in the training phase of neural networks, the random initialization of weights and biases can substantially impact the training process and the ultimate performance of the network, this paper proposes a chaotic sparrow search algorithm combining the osprey optimization algorithm and Cauchy mutation (OCCSSA) to optimize the initial weights and thresholds of the proposed equalizer. The OCCSSA utilizes the Piecewise chaotic population initialization and combines the exploration strategy of the ospreywith the Cauchy mutation strategy to enhance both global and local search capabilities. RseultsSimulations were conducted using underwater multipath signals generated by the Bellhop Acoustic Toolbox. The results demonstrate that the performance of the SDFCFLNNE initialized by OCCSSA surpasses that of CFLNN-based and traditional nonlinear equalizers, with a notable improvement of 2-6 dB in terms of signal-to-noise ratio at a bit error rate (BER) of 10−4 and a reduced mean square error (MSE). Furthermore, the effectiveness of the proposed equalizer was validated using the lake experimental data, demonstrating lower BER and MSE with improved stability. DiscussionThis underscores thepromise of employing the SDFCFLNNE initialized by OCCSSA as a promising solution to enhance the robustness of underwater communication in challenging environments.

Spatial diversity processing mechanism based on the distributed underwater acoustic communication system.

To address the problem of unreliable single-link underwater acoustic communication caused by large signal delays and strong multipath effects in shallow water environments, this paper proposes a distributed underwater acoustic diversity communication system (DUA-DCS). DUA-DCS employs a maneuverable distributed cross-medium buoy network to form multiple distributed, non-coherent, and parallel communication links. In the uplink, a receiving diversity processing mechanism of joint decision feedback equalizer embedded phase-locked loop and maximum signal-to-interference ratio combining (DFE-PLL-MSIRC) is proposed to achieve waveform-level diversity combining of underwater signals. A phase-locked loop module is embedded in each branch of the decision feedback equalizer to eliminate the residual frequency and phase errors after Doppler compensation. Meanwhile, the combining coefficients are determined based on the maximum signal-to-interference ratio criterion, taking into account the residual inter-symbol interference after equalization, resulting in efficient and accurate computation. Additionally, the combined decision values are fed back to the feedback filters in each branch to ensure more accurate feedback output. Simulation and lake experiment results demonstrate that, compared to the single-link communication system, DFE-PLL-MSIRC can achieve a diversity gain of more than 5.2 dB and obtain about 3 dB more diversity gain than the comparison algorithm. And the BER of DFE-PLL-MSIRC can be reduced by at least one order of magnitude, which is lower by at least 0.6 order of magnitude compared to the comparison algorithm. In the downlink, a transmitting diversity processing mechanism of complex orthogonal space-time block coding (COSTBC) is proposed. By utilizing a newly designed generalized complex orthogonal transmission matrix, complete transmission diversity can be achieved at the coding rate of 3/4. Compared to the single-link communication system, the system can achieve a diversity gain of more than 6 dB.

Multi-standard speculative decision feedback equalizer for PAMN wireline receiver

Multi-standard speculative decision feedback equalizer for PAMN wireline receiver

A Loop-Break Decision Feedback Equalizer for DAC/ADC-DSP-Based Wireline Transceivers

A Loop-Break Decision Feedback Equalizer for DAC/ADC-DSP-Based Wireline Transceivers

MLSE-assisted decision feedback equalizer for error-propagation suppression in high-speed IM-DD transmission systems

MLSE-assisted decision feedback equalizer for error-propagation suppression in high-speed IM-DD transmission systems