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1

Chen, S., B. Mulgrew, and S. McLaughlin. "Adaptive Bayesian equalizer with decision feedback." IEEE Transactions on Signal Processing 41, no. 9 (1993): 2918–27. http://dx.doi.org/10.1109/78.236513.

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2

Kim, D. W., S. H. Han, M. S. Eun, J. S. Choi, and Y. S. Cho. "An adaptive decision feedback equalizer using error feedback." IEEE Transactions on Consumer Electronics 42, no. 3 (1996): 468–77. http://dx.doi.org/10.1109/30.536144.

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3

Zhang, Sumin, Shu Li, and Donglin Su. "Adaptive support vector machine decision feedback equalizer." Journal of Systems Engineering and Electronics 22, no. 3 (2011): 452–61. http://dx.doi.org/10.3969/j.issn.1004-4132.2011.03.013.

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4

Yu Gong and C. F. N. Cowan. "A self-structured adaptive decision feedback equalizer." IEEE Signal Processing Letters 13, no. 3 (2006): 169–72. http://dx.doi.org/10.1109/lsp.2005.862601.

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5

Le, M. Q., P. J. Hurst, and J. P. Keane. "An adaptive analog noise-predictive decision-feedback equalizer." IEEE Journal of Solid-State Circuits 37, no. 2 (2002): 105–13. http://dx.doi.org/10.1109/4.982416.

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6

Annapurna H. S, Et al. "Performance Analysis of Adaptive Equalizers Over Multipath Faded Channels: Error Vector Magnitudes." International Journal on Recent and Innovation Trends in Computing and Communication 11, no. 10 (2023): 438–44. http://dx.doi.org/10.17762/ijritcc.v11i10.8507.

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Due to the increasing popularity of digital transmission systems, the need for channel equalizers has been acknowledged. These techniques are designed to counteract the effects of the inter-symbol interference (ISI) caused by the communication channels. An adaptive equalizer is used to operate on the output of a channel in order to provide an approximation of the transmission medium. An adaptive equalizer usually requires a training period to operate successfully. This method eliminates the effects of the wireless transmission channel and allows the subsequent symbol modulation. The paper presents an overview of the various adaptive equalizers, such as the least mean squares (LMS), decision feedback equalizers (DFE), and the Recursive least squares (RLS). It also explores their performance in terms of error vector magnitudes (EVM) over Rician and Rayleigh channels. The paper looks into the effects of adaptive equalizers on various digital modulation techniques for rectangular quadrature phase shift, amplitude modulation, such as the BPSK, QPSK, 4-QAM, 16-QAM, 64-QAM and 256-QAM. These modulations are analysed and measured in terms of symbol error rates and number of incorrect symbols.
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Chakraborty, Mrityunjoy, and Suraiya Pervin. "Pipelining the adaptive decision feedback equalizer with zero latency." Signal Processing 83, no. 12 (2003): 2675–81. http://dx.doi.org/10.1016/j.sigpro.2003.07.003.

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8

JIANG, HONG RUI, and KYUNG SUP KWAK. "ON MODIFIED COMPLEX RECURRENT NEURAL NETWORK ADAPTIVE EQUALIZER." Journal of Circuits, Systems and Computers 11, no. 01 (2002): 93–101. http://dx.doi.org/10.1142/s0218126602000276.

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A new modified version called decision feedback complex recurrent neural network equalizer (DFCRNNE) is proposed with the study of complex recurrent neural network equalizer (CRNNE). Based on DFCRNNE, a modified real time recurrent learning (CRTRL) algorithm is developed. Simulation results show that DFCRNNE has better performance than CRNNE based on traditional CRTRL algorithm2 in complex nonlinear channels with severe intersymbol interference (ISI) and nonlinear distortion.
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9

Zerdoumi, Zohra, Djamel Chikouche, and Djamel Benatia. "Multilayer Perceptron Based Equalizer with an Improved Back Propagation Algorithm for Nonlinear Channels." International Journal of Mobile Computing and Multimedia Communications 7, no. 3 (2016): 16–31. http://dx.doi.org/10.4018/ijmcmc.2016070102.

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Neural network based equalizers can easily compensate channel impairments; such additive noise and inter symbol interference (ISI). The authors present a new approach to improve the training efficiency of the multilayer perceptron (MLP) based equalizer. Their improvement consists on modifying the back propagation (BP) algorithm, by adapting the activation function in addition to the other parameters of the MLP structure. The authors report on experiment results evaluating the performance of the proposed approach namely the back propagation with adaptive activation function (BPAAF) next to the BP algorithm. To further prove its effectiveness, the proposed approach is also compared beside a so known nonlinear equalizer explicitly the multilayer perceptron with decision feedback equalizer MLPDFE. The authors consider various performance measures specifically: signal resorted quality, lower steady state MSE reached and minimum bit error rate (BER) achieved, where nonlinear channel equalization problems are employed.
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10

Sheng Chen, S. McLaughlin, B. Mulgrew, and P. M. Grant. "Adaptive Bayesian decision feedback equalizer for dispersive mobile radio channels." IEEE Transactions on Communications 43, no. 5 (1995): 1937–46. http://dx.doi.org/10.1109/26.387409.

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11

Mastan Sharif, SK, K. Satya Prasad, and D. Venkata Rao. "Adaptive decision feedback equalizer with dynamic principle for echo cancellation." Transactions of the Institute of Measurement and Control 40, no. 16 (2018): 4455–71. http://dx.doi.org/10.1177/0142331218755233.

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Adaptive decision feedback equalizer (ADFE) based on Least Mean square algorithm (LMS) has emerged as a novel tool for signal propagation without noise. However, it has the limitation of computational complexity. Since it has been reported that substantial echo cancellation leads to increased system quality and capacity, this paper proposes a dynamic LMS-based ADFE (DLMS-ADFE) to cancel the generation of the echo signal. The DLMS-ADFE has two dynamic principles in updating the coefficients. The first principle has varying step-size and the second principle has varying degree and magnitude of the signal. The comparison results show that the DLMS-ADFE is outperforming LMS-ADFE.
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12

Chakraborty, Mrityunjoy, and Suraiya Pervin. "A systolic array realization of the adaptive decision feedback equalizer." Signal Processing 80, no. 12 (2000): 2633–40. http://dx.doi.org/10.1016/s0165-1684(00)00145-6.

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13

Al-Taee, Alaa R., Fei Yuan, and Andy Ye. "Adaptive Decision Feedback Equalizer with Hexagon EOM and Jitter Detection." Circuits, Systems, and Signal Processing 35, no. 7 (2015): 2487–501. http://dx.doi.org/10.1007/s00034-015-0147-9.

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14

Raghunath, K. J., and K. K. Parhi. "Parallel adaptive decision feedback equalizers." IEEE Transactions on Signal Processing 41, no. 5 (1993): 1956–61. http://dx.doi.org/10.1109/78.215315.

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15

Lee, K. Y. "Fuzzy adaptive decision feedback equaliser." Electronics Letters 30, no. 10 (1994): 749–51. http://dx.doi.org/10.1049/el:19940434.

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16

Han, Zhen, Weiliang Tao, Dan Zhang, and Peng Jiang. "Virtual Space-Time DiversityTurbo Equalization Using Cluster Sparse Proportional Recursive Least Squares Algorithm for Underwater Acoustic Communications." Applied Sciences 13, no. 19 (2023): 11050. http://dx.doi.org/10.3390/app131911050.

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The oceanic positioning, navigation and timing (PNT) network requires high-quality underwater acoustic message transmission. Turbo equalization technology has exhibited superior performance for underwater acoustic (UWA) communications compared with conventional channel equalizers. To overcome the performance reduction caused by severe doubly selective UWA channels, the virtual space-time diversity soft direct-adaptation turbo equalization is proposed for UWA communications. The proposed scheme improves the ability of the typical turbo equalizer to deal with both Doppler and multipath effects for time varying channels. We utilize a fractionally spaced soft interference cancellation equalizer (FS-SE) instead of a hard decision to constitute the soft-input soft-output (SISO) equalizer. Combined with another virtual time-reversal mirror equalizer component, we can obtain virtual space and time diversity with only a single receiving transducer and mitigate the error propagation phenomenon of the feedback filter. To satisfy the sparse UWA channel, the ℓp,q-PRLS algorithm is applied to adaptive updates for FS-SE. In the proposed scheme, an adjustable interpolator and digital phase-locked loop are embedded into the equalizer to overcome the residual Doppler frequency shift and recover the timing distortion. Results of simulations and field lake trial show that the proposed scheme achieves better performance than existing ones under the same equalizer order.
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17

Chung, G. C., Mohamad Yusoff Alias, and T. C. Chuah. "An adaptive minimum bit-error decision-feedback equalizer for UWB systems." IEICE Electronics Express 4, no. 14 (2007): 435–41. http://dx.doi.org/10.1587/elex.4.435.

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18

Lingyan Fan, Chen He, Dongjian Wang, and Lingge Jiang. "Efficient robust adaptive decision feedback equalizer for large delay sparse channel." IEEE Transactions on Consumer Electronics 51, no. 2 (2005): 449–56. http://dx.doi.org/10.1109/tce.2005.1467986.

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19

Kohli, Amit Kumar, and D. K. Mehra. "Adaptive MMSE decision feedback equalizer for asynchronous CDMA with erasure algorithm." Digital Signal Processing 15, no. 6 (2005): 621–30. http://dx.doi.org/10.1016/j.dsp.2005.02.004.

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20

Vishwakarma, Shubham, and ,. Prof Neelam Sharma. "Channel State Information Based Equalizer Design for Frequency Selective Channels." INTERANTIONAL JOURNAL OF SCIENTIFIC RESEARCH IN ENGINEERING AND MANAGEMENT 07, no. 10 (2023): 1–11. http://dx.doi.org/10.55041/ijsrem26138.

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Abstract—Equalizer design is an extremely critical aspect for wireless networks. This paper presents an approach combining the decision feedback mechanism and successive signal detection to equalize frequency selective channel effects for signals traversing different run-lengths. In this approach, the errors on comparison between the transmitted signal and received signal are fed to the equalizer to adjust the tap weights. Still the irreversible nature of inter symbol interference is a huge challenge due to multi path propagation mechanisms in wireless channels. It is a common observation that signals traversing a smaller path reach the receiver earlier compared to the multi-path component traversing a longer path. Assuming similar shadowing effects, it is seen that fading effects make it difficult to accurately receive long distance MPCs, thereby degrading the BER performance. It has been shown that the proposed system attains almost similar BER performance irrespective of the shadowing effect or run length of the MPCs. Keywords— Multi Path Component (MPC), Inter Symbol Interference (ISI), Adaptive Equalizer, Channel State Information (CSI), , Bit Error Rate (BER), Probability of Error
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21

Diana, D. C., and R. Hema. "Swarm Intelligence Based MMSE Frequency Domain Equalization for MIMO Systems." ECTI Transactions on Electrical Engineering, Electronics, and Communications 21, no. 2 (2023): 249824. http://dx.doi.org/10.37936/ecti-eec.2023212.249824.

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The automatic upgradation of equalizer weights in channel equalization demands a low-complexity, highly accurate estimation of recovery at the minimum possible time. The low-complexity frequency domain equalization improves the minimum mean square error (MMSE) of the equalization process. Adding the superiority of particle swarm optimization (PSO) to the equalizer coefficient selection process enhances the MMSE. This work proposes frequency-domain channel equalization along with a modified PSO (MPSO) as an adaptive algorithm for equalizer weight selection in MIMO systems. The simulation results validate the performance with the time domain linear and decision feedback equalizer structures for BPSK and QAM systems. The parameters are carefully selected by analyzing MMSE thoroughly under timevarying channel conditions.
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22

Ali, Farman, Shabbir Ahmad, Fazal Muhammad, Ziaul Haq Abbas, Usman Habib, and Sunghwan Kim. "Adaptive Equalization for Dispersion Mitigation in Multi-Channel Optical Communication Networks." Electronics 8, no. 11 (2019): 1364. http://dx.doi.org/10.3390/electronics8111364.

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Optical communication networks (OCNs) provide promising and cost-effective support for the ultra-fast broadband solutions, thus enabling them to address the ever growing demands of telecommunication industry such as high capacity and end users’ data rate. OCNs are used in both wired and wireless access networks as they offer many advantages over conventional copper wire transmission such as low power consumption, low cost, ultra-high bandwidth, and high transmission rates. Channel effects caused by light propagation through the fiber limits the performance, hence the data rate of the overall transmission. To achieve the maximum performance gain in terms of transmission rate through the OCN, an optical downlink system is investigated in this paper using feed forward equalizer (FFE) along with decision feedback equalizer (DFE). The simulation results show that the proposed technique plays a key role in dispersion mitigation in multi-channel optical transmission to uphold multi-Gb/s transmission. Moreover, bit error rate (BER) and quality factor (Q-factor) below 10 − 5 and above 5, respectively, are achieved with electrical domain equalizers for the OCN in the presence of multiple distortion effects showing the effectiveness of the proposed adaptive equalization techniques.
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23

Sheng-Sung Yang, Chia-Lu Ho, and Chien-Min Lee. "HBP: improvement in BP algorithm for an adaptive MLP decision feedback equalizer." IEEE Transactions on Circuits and Systems II: Express Briefs 53, no. 3 (2006): 240–44. http://dx.doi.org/10.1109/tcsii.2005.858494.

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24

Berberidis, K., and P. Karaivazoglou. "An efficient block adaptive decision feedback equalizer implemented in the frequency domain." IEEE Transactions on Signal Processing 50, no. 9 (2002): 2273–85. http://dx.doi.org/10.1109/tsp.2002.801884.

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25

Labat, J., and C. Laot. "Blind adaptive multiple-input decision-feedback equalizer with a self-optimized configuration." IEEE Transactions on Communications 49, no. 4 (2001): 646–54. http://dx.doi.org/10.1109/26.917771.

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26

Yang, Xiaoxia, Jun Wang, and Haibin Wang. "Blind adaptive correlation-based decision feedback equalizer (DFE) for underwater acoustic communications." Journal of the Acoustical Society of America 141, no. 5 (2017): 3988. http://dx.doi.org/10.1121/1.4989125.

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27

Dong Kyoo Kim and PooGyeon Park. "Adaptive self-orthogonalizing per-tone decision feedback equalizer for single carrier modulations." IEEE Signal Processing Letters 13, no. 1 (2006): 21–24. http://dx.doi.org/10.1109/lsp.2005.860548.

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28

AL-Taee, Alaa R., Matthew Dolan, and Fei Yuan. "An edge-based dual adaptive decision feedback equalizer for Gbps serial links." Analog Integrated Circuits and Signal Processing 90, no. 2 (2016): 399–409. http://dx.doi.org/10.1007/s10470-016-0804-3.

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29

Al-Kanan, Haider. "An Enhanced Deployment Approach of Adaptive Equalizer for Multipath Fading Channels." Iraqi Journal for Electrical and Electronic Engineering 21, no. 1 (2025): 264–73. https://doi.org/10.37917/ijeee.21.1.25.

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Inter-symbol interference (ISI) exhibits major distortion effect often appears in digital storage and wireless communication channels. The traditional decision feedback equalizer (DFE) is an efficient approach of mitigating the ISI effect using appropriate digital filter to subtract the ISI. However, the error propagation in DFE is a challenging problem that degrades the equalization due to the aliasing distorted symbols in the feedback section of the traditional DFE. The aim of the proposed approach is to minimize the error propagation and improve the modeling stability by incorporating adequate components to control the training and feedback mode of DFE. The proposed enhanced DFE architecture consists of a decision and controller components which are integrated on both the transmitter and receiver sides of communication system to auto alternate the DFE operational modes between training and feedback state based on the quality of the received signal in terms of signal-to-noise ratio SNR. The modeling architecture and performance validation of the proposed DFE are implemented in MATLAB using a raised-cosine pulse filter on the transmitter side and linear time-invariant channel model with additive gaussian noise. The equalizer capability in compensating ISI is evaluated during different operational stages including the training and DFE based on different channel distortion characteristics in terms of SNR using both 0.75 and 1.5 symbol duration in unit delay fraction of FIR filter. The simulation results of eye-diagram pattern showed significant improvement in the DFE equalizer when using a lower unit delay fraction in FIR filter for better suppressing the overlay trails of ISI. Finally, the capability of the proposed approach to mitigate the ISI is improved almost double the number of symbol errors compared to the traditional DFE.
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30

Widiarti, Yuning, and Mohammad Basuki Rahmat. "Implementation Adaptive Decision Feedback Equalizer for Time-Reversal Communication in Shallow Water Environment." SPIRIT OF SOCIETY JOURNAL 6, no. 1 (2022): 12–20. http://dx.doi.org/10.29138/scj.v6i1.2037.

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Underwater wireless communications are growing very fast along with human needs for applications such as defense, state security, underwater control and monitoring systems. Until now, an acoustic signal is a practical way to achieve long distance communication in the ocean. However, the underwater acoustic channel faces many challenges including limited available bandwidth, long delays, time-variability, and Doppler-spread. These challenges can reduce the reliability of the communication system and the achievement of high data-rate becomes a challenge. Adaptive decision feedback equalization is a method to compensate for the distortion of information signals on the underwater acoustic channel. On the other hand, time reversal is an effective method of overcoming intersymbol interference (ISI) problems which is the effect of multipath phenomena in underwater channels. Spatial focusing on time reversal can reduce the co-existing system disturbances and its temporal focusing makes the received power concentrated within a few taps so that the equalizer design work becomes much simpler. The temporal focusing can also increase the transmission rate. This paper shows that the combination of time reversal and adaptive DFE (TR-DFE) has superior performance than TR and DFE itself. By modifying the step-size parameters in the adaptive DFE, the TR-DFE level of convergence and performance can be improved. The geometry-based modeling which is used proves that distance and multipath variation greatly affect the quality of time reversal communication on the underwater acoustic channel.
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31

Chen, Fangjiong, Shaoe Lin, Beixiong Zheng, et al. "Minimum Symbol-Error Rate Based Adaptive Decision Feedback Equalizer in Underwater Acoustic Channels." IEEE Access 5 (2017): 25147–57. http://dx.doi.org/10.1109/access.2017.2772302.

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32

Raji, T. I., and Z. K. Adeyemo. "Performance of Binary Phase Shift Keying (BPSK) and Quartenary Phase Shift Keying (QPSK) Signalling Schemes in Fast and Frequency Non-Selective Rayleigh Fading Channel with a Decision Feedback Equalizer (DFE) at the Receiver." Advanced Materials Research 62-64 (February 2009): 99–104. http://dx.doi.org/10.4028/www.scientific.net/amr.62-64.99.

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In this paper, we study the performance of Binary phase shift keying (BPSK) and Quartenary phase shift keying (QPSK) modulation signalling over fast and frequency non-selective Rayleigh fading channel with mobile digital communication and usually a decision feedback equalizer (DFE) at the receiver. Mobile communication is generally a complex process in which the input modulated signals propagate to the receiver over many different paths resulting in what is known as multipath propagation. Its main effects are delay spread and Doppler spread. These effects result in the channel being classified as fast and frequency non selective. Performances in terms of Bit Error Rate (BER) with respect to the Signal-to-Noise Ratio (SNR) at different selected velocities of 10, 40, 70 and 100km/hr are investigated with Adaptive Equalizer. Simulation results are obtained using MATLAB 7.0 programming language. The results indicate that at all the velocities considered; there is an excessive degradation in the BER performance due to fading with both the BPSK and QPSK modulation schemes. However, the BER improves for BPSK modulation signalling scheme when a decision feedback equalizer is used at the receiver
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33

Zhao, Haiquan, Xiangping Zeng, Jiashu Zhang, and Tianrui Li. "Nonlinear Adaptive Equalizer Using a Pipelined Decision Feedback Recurrent Neural Network in Communication Systems." IEEE Transactions on Communications 58, no. 8 (2010): 2193–98. http://dx.doi.org/10.1109/tcomm.2010.08.080612.

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34

Zhao, Haiquan, Xiangping Zeng, Xiaoqiang Zhang, Jiashu Zhang, Yangguang Liu, and Tiao Wei. "An adaptive decision feedback equalizer based on the combination of the FIR and FLNN." Digital Signal Processing 21, no. 6 (2011): 679–89. http://dx.doi.org/10.1016/j.dsp.2011.05.004.

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35

Chung, W. "Soft decision approaches in adaptive blind decision feedback equalisers." Electronics Letters 44, no. 22 (2008): 1328. http://dx.doi.org/10.1049/el:20082379.

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36

Lin, Y. C., S. J. Jou, and M. T. Shiue. "High throughput concurrent lookahead adaptive decision feedback equaliser." IET Circuits, Devices & Systems 6, no. 1 (2012): 52. http://dx.doi.org/10.1049/iet-cds.2010.0445.

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37

Kanaan, Amenah I. "Optimization of Eye Diagram Based on Adaptive Decision Feedback Equalizer for High Speed Digital System." Tikrit Journal of Engineering Sciences 23, no. 3 (2016): 105–15. http://dx.doi.org/10.25130/tjes.23.3.12.

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Eye diagram used in a lot of radio and telecommunication application, but it can also be used in digital signal integrity. This kind of analysis is a common indicator of performance in digital transmission systems. As integration density and data rates increase, dispersive losses, reflections and crosstalk can severely degrade signal integrity. Fortunately, these effects are linear processes. Accordingly, simple, on-chip signal processing techniques can compensate for them. In this paper we introduce an approach to improve eye diagram for data transmission that indicate the signal strength by using adaptive Decision Feedback Equalizer (DFE) in receiver circuits of digital system. The simulation results are presented to validate the efficiency of the proposed method.
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38

Yee, M. S., and L. Hanzo. "A wide-band radial basis function decision feedback equalizer-assisted burst-by-burst adaptive modem." IEEE Transactions on Communications 50, no. 5 (2002): 693–97. http://dx.doi.org/10.1109/tcomm.2002.1006548.

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39

Shaik, Rafi Ahamed, and Mrityunjoy Chakraborty. "A block floating point treatment to finite precision realization of the adaptive decision feedback equalizer." Signal Processing 93, no. 5 (2013): 1162–71. http://dx.doi.org/10.1016/j.sigpro.2012.11.024.

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40

Seong, Chang-Kyung, Jinsoo Rhim, and Woo-Young Choi. "A 10-Gb/s Adaptive Look-Ahead Decision Feedback Equalizer With an Eye-Opening Monitor." IEEE Transactions on Circuits and Systems II: Express Briefs 59, no. 4 (2012): 209–13. http://dx.doi.org/10.1109/tcsii.2012.2186366.

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41

Kou, Xu, Yanbo Wu, and Min Zhu. "Iterative decision feedback equalization using a variable step-size hyperbolic secant adaptive filter algorithm for under-ice acoustic communication." Journal of the Acoustical Society of America 157, no. 5 (2025): 3946–57. https://doi.org/10.1121/10.0036776.

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Small man-portable unmanned underwater vehicles enhance exploration in under-ice environments while reducing deployment costs. Single-input single-output underwater acoustic communication systems are advantageous for these unmanned underwater vehicles due to their low power consumption, compact design, and user-friendliness. However, the lack of diversity gain in single-input single-output systems presents challenges in complex oceanic environments. Although under-ice underwater acoustic channels typically exhibit stability, impulsive noise severely degrades signal quality. Conventional Gaussian noise-based underwater acoustic communication equalizers may experience performance degradation even under moderate signal-to-noise ratio. To address the challenges of sparse multipath underwater acoustic channels and impulsive noise, this paper proposed an iterative decision feedback equalizer (DFE) based on a variable step-size sparse hyperbolic secant adaptive filtering (AF) algorithm. The key to this DFE is to make filter coefficient updates insensitive to outliers, while also introducing correntropy-induced metric to AF algorithm with norm constraints, and then optimizing trade-off between convergence speed and stability by a variable step-size method. Furthermore, the performance of the DFE is further improved by iterative fine-tuning of filter coefficients. Numerical simulations and under-ice experiments validate the superiority of the proposed equalization scheme, achieving approximately 2 dB improvement over alternative AF algorithm-based DFEs at a 1000 m communication distance.
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42

Kim, Do-Hoon, and Heung-Gyoon Ryu. "Adaptive Decision Feedback Equalizer Based on LDPC Code for the Phase Noise Suppression and Performance Improvement." Journal of Korean Institute of Communications and Information Sciences 37, no. 3A (2012): 179–87. http://dx.doi.org/10.7840/kics.2012.37a.3.179.

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43

Mulgrew, B., and S. Chen. "Adaptive minimum-BER decision feedback equalisers for binary signalling." Signal Processing 81, no. 7 (2001): 1479–89. http://dx.doi.org/10.1016/s0165-1684(01)00035-4.

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44

Han, Ruigang, Ning Jia, Yunfei Li, Dong Xiao, Shengming Guo, and Li Ma. "Iterative-detection–based time-domain adaptive decision feedback equalization for continuous phase modulation of underwater acoustic communication." Journal of the Acoustical Society of America 157, no. 3 (2025): 1912–25. https://doi.org/10.1121/10.0036145.

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Continuous phase modulation (CPM), which is widely used in aviation telemetry and satellite communications, may help improve the performance of underwater acoustic (UWA) communication systems owing to its high spectral and power efficiency. However, applying conventional frequency-domain equalization (FDE) algorithms to CPM signals over time-varying UWA channels considerably degrades performance. Moreover, time-domain equalization algorithms often rely on excessive approximations for symbol detection, compromising overall reception. This study presents an iterative-detection–based time-domain adaptive decision feedback equalization (ID-TDADFE) algorithm that tracks channel variations through symbol-by-symbol detection. The symbol detection in ID-TDADFE fully considers the inherent coding gain of CPM signals can be cascaded with an adaptive equalizer, and enhances symbol detection performance by utilizing joint probability estimation. Numerical simulations with minimum-shift keying (MSK) and Gaussian MSK signals demonstrated that ID-TDADFE significantly improved communication performance over a time-varying UWA channel within one or two iterations. In a sea trial for experimental verification, ID-TDADFE reduced bit errors by 45.08% and 51.8% in the first and second iterations, respectively, compared to FDE.
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45

Meng-Da Yang, An-Yeu Wu, and Jyh-Ting Lai. "High-performance VLSI architecture of adaptive decision feedback equalizer based on predictive parallel branch slicer (PPBS) scheme." IEEE Transactions on Very Large Scale Integration (VLSI) Systems 12, no. 2 (2004): 218–26. http://dx.doi.org/10.1109/tvlsi.2003.820521.

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46

Hayashi, Kazunori, and Shinsuke Hara. "A spatiotemporal equalization method with cascade configuration of an adaptive antenna array and a decision feedback equalizer." Electronics and Communications in Japan (Part II: Electronics) 86, no. 10 (2003): 25–35. http://dx.doi.org/10.1002/ecjb.10186.

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47

Georgiadis, Apostolos T., and Bernard Mulgrew. "Adaptive Bayesian decision feedback equaliser for alpha-stable noise environments." Signal Processing 81, no. 8 (2001): 1603–23. http://dx.doi.org/10.1016/s0165-1684(01)00075-5.

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48

Rizogiannis, Constantinos, Eleftherios Kofidis, Athanasios A. Rontogiannis, and Sergios Theodoridis. "Adaptive BLAST-type decision-feedback equalizers for DS-CDMA systems." Signal Processing 92, no. 4 (2012): 977–88. http://dx.doi.org/10.1016/j.sigpro.2011.10.010.

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49

Li, Weijie, Min Liu, Xuqiang Zheng, et al. "A 100-Gb/s PAM-4 DSP in 28-nm CMOS for Serdes Receiver." Electronics 12, no. 2 (2023): 257. http://dx.doi.org/10.3390/electronics12020257.

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Abstract:
This paper presents a dedicated digital signal process (DSP) for four pulse amplitude modulation (PAM4) SerDes receivers. It is targeted to implement data recovery and adaptive equalization under ultra-high-speed and large channel attenuation with a small area and high power efficiency. The DSP consists of a clock data recovery (CDR), a 16-tap feed forward equalizer (FFE), a 1-tap decision feedback equalizer (DFE), and an automatic adaptation engine. An adaptive least mean square (LMS) algorithm is utilized to make the system more intelligent in calculating tap coefficients of the FFE and DFE. To address the timing limitation associated with traditional digital DFE that cannot handle large amounts of parallel data at a high speed, speculative techniques and a customized 4-to-1 multiplexer (MUX) unit are employed to remove the summation time and reduce the selection time, respectively. A first-order sigma-delta modulator is used to replace the traditional moving average to calculate average voltages, which could prominently save the hardware resources and power consumption. Additionally, the influence of input quantization resolution on the equalization ability is analyzed. Implemented in a 28-nm CMOS, the DSP could compensate for up to 33-dB loss at 100 Gb/s with a power consumption of 7.22 pJ/bit.
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50

Jing, Lianyou, Qingsong Wang, Qiulong Yang, et al. "Multi-directional decision feedback equalization for orthogonal time frequency space underwater acoustic communication system." Journal of the Acoustical Society of America 157, no. 4 (2025): 2657–70. https://doi.org/10.1121/10.0036370.

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Abstract:
Orthogonal time frequency space (OTFS) modulation is widely recognized for its superior performance in time-varying channels, making it particularly effective in rapidly changing underwater acoustic (UWA) environments. This paper introduces a two-dimensional (2D) adaptive multichannel decision feedback equalization (DFE) technique with a multi-directional structure, specifically designed for OTFS-based UWA communication system. Two distinct multi-directional architectures are designed, each capitalizing on the 2D modulation characteristics of OTFS to mitigate error propagation across different directions, resulting in diverse error patterns and locations. The first architecture employs a parallel combination approach, consolidating outputs from multi-directional DFEs to enhance performance by exploiting the low correlation among different directional DFEs. Optimal weight factors for this multi-directional setup are derived. The second architecture adopts a serial approach, in which the outputs from other directional DFEs inform the symbol decision process of the current directional equalizer, thereby accelerating the convergence of the equalization process. Simulation and experimental results conducted in lake environments validate the efficacy of the proposed multi-directional 2D DFE algorithm. Comparative analyses reveal its significant outperformance over traditional 2D DFE methods, demonstrating superior symbol detection capabilities relative to other equalization strategies, especially under conditions characterized by limited pilot resources and channel estimation accuracy.
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