Reconfigurable Intelligent Surfaces (RISs) offer a promising means of reshaping the wireless propagation environment, yet practical methods for configuring large passive arrays to achieve reliable signal equalization remain limited. Equalization is essential in wideband links to counteract multipath-induced pulse distortion that otherwise degrades symbol recovery. This work investigates RIS-assisted pulse response equalization and signal boosting using both classical adaptive filtering and model-free deep reinforcement learning (DRL). We develop a steepest descent (SD) method that exploits cascaded BS-RIS-UE channel information to configure RIS coefficients for multipath mitigation and SNR enhancement, and we show that the tradeoffs between SD and DRL primarily arise from the extensive channel estimation required for accurate equalization with passive RIS hardware. Unlike traditional adaptive filtering, which updates delayed filter coefficients after signal reception, our approach uses the RIS positioned within the cascaded channel to perform equalization without delay elements, prior to reception at the UE. In this framework, the channel is estimated before equalization, forming the basis of what we term adaptive RIS equalization (ARISE). To overcome the reliance on channel estimation required for ARISE, we explore several DRL algorithms -- DDPG, TD3, and SAC -- that optimize RIS coefficients directly from the received pulse response without explicit channel estimation. Through extensive simulations across diverse channel conditions and RIS sizes, we show that SAC achieves fast, stable convergence and equalization performance comparable to ARISE while offering significantly lower implementation complexity. These results highlight the potential of DRL as a practical and scalable solution for real-time RIS control in future wireless systems.
We investigate the potential of adaptive equalization techniques to mitigate inter-channel nonlinear interference noise (NLIN). We derive a lower bound on the mutual information of a system using adaptive equalization, showing that the channel estimation error determines the equalizer's performance. We develop an adaptive equalization scheme which uses the statistics of the NLIN to obtain optimal detection, based on Kalman filtering and maximum likelihood sequence estimation (MLSE). This scheme outperforms commonly used equalizers and significantly increases performance.
Nonlinearities can be introduced into communication systems by the physical components such as the power amplifier, or during signal propagation through a nonlinear channel. These nonlinearities can be compensated by a nonlinear equalizer at the receiver side. The nonlinear equalizer also operates on the additive noise, which can lead to noise enhancement. In this work we evaluate this trade-off between distortion reduction and noise-enhancement via nonlinear equalization techniques. We first, evaluate the trade-off between nonlinearity compensation and noise enhancement for the Volterra equal…
A new maximum likelihood estimation approach for blind channel equalization, using variational autoencoders (VAEs), is introduced. Significant and consistent improvements in the error rate of the reconstructed symbols, compared to constant modulus equalizers, are demonstrated. In fact, for the channels that were examined, the performance of the new VAE blind channel equalizer was close to the performance of a nonblind adaptive linear minimum mean square error equalizer. The new equalization method enables a significantly lower latency channel acquisition compared to the constant modulus algori…
This paper deals with linear equalization in massive multi-user multiple-input multiple-output (MU-MIMO) wireless systems. We first provide simple conditions on the antenna configuration for which the well-known linear minimum mean-square error (L-MMSE) equalizer provides near-optimal spectral efficiency, and we analyze its performance in the presence of parameter mismatches in the signal and/or noise powers. We then propose a novel, optimally-tuned NOnParametric Equalizer (NOPE) for massive MU-MIMO systems, which avoids knowledge of the transmit signal and noise powers altogether. We show tha…
Bilkent University（比尔肯特大学）；Massachusetts Institute of Technology (MIT)（麻省理工学院）
We investigate underwater acoustic (UWA) channel equalization and introduce hierarchical and adaptive nonlinear channel equalization algorithms that are highly efficient and provide significantly improved bit error rate (BER) performance. Due to the high complexity of nonlinear equalizers and poor performance of linear ones, to equalize highly difficult underwater acoustic channels, we employ piecewise linear equalizers. However, in order to achieve the performance of the best piecewise linear model, we use a tree structure to hierarchically partition the space of the received signal. Furtherm…
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Nokia（诺基亚）
We investigate the potential of adaptive blind equalizers based on variational inference for carrier recovery in optical communications. These equalizers are based on a low-complexity approximation of maximum likelihood channel estimation. We generalize the concept of variational autoencoder (VAE) equalizers to higher order modulation formats encompassing probabilistic constellation shaping (PCS), ubiquitous in optical communications, oversampling at the receiver, and dual-polarization transmission. Besides black-box equalizers based on convolutional neural networks, we propose a model-based e…
Recently, deep learning methods have shown significant improvements in communication systems. In this paper, we study the equalization problem over the nonlinear channel using neural networks. The joint equalizer and decoder based on neural networks are proposed to realize blind equalization and decoding process without the knowledge of channel state information (CSI). Different from previous methods, we use two neural networks instead of one. First, convolutional neural network (CNN) is used to adaptively recover the transmitted signal from channel impairment and nonlinear distortions. Then t…
Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院）；University of Kaiserslautern（凯泽斯劳滕大学）
Due to the rapid development of autonomous driving, the Internet of Things and streaming services, modern communication systems have to cope with varying channel conditions and a steadily rising number of users and devices. This, and the still rising bandwidth demands, can only be met by intelligent network automation, which requires highly flexible and blind transceiver algorithms. To tackle those challenges, we propose a novel adaptive equalization scheme, which exploits the prosperous advances in deep learning by training an equalizer with an adversarial network. The learning is only based …
This paper deals with turbo-equalization for coded data transmission over intersymbol interference (ISI) channels. We propose a message-passing algorithm that uses the expectation-propagation rule to convert messages passed from the demodulator-decoder to the equalizer and computes messages returned by the equalizer by using a partial Gaussian approximation (PGA). Results from Monte Carlo simulations show that this approach leads to a significant performance improvement compared to state-of-the-art turbo-equalizers and allows for trading performance with complexity. We exploit the specific str…
Reconfigurable intelligent surfaces (RISs), which enable tunable anomalous reflection, have appeared as a promising method to enhance wireless systems. In this paper, we propose to use an RIS as a spatial equalizer to address the well-known multi-path fading phenomenon. By introducing some controllable paths artificially against the multi-path fading through the RIS, we can perform equalization during the transmission process instead of at the receiver, and thus all the users can share the same equalizer. Unlike the beamforming application of the RIS, which aims to maximize the received energy…
In this paper, the performance of adaptive turbo equalization for nonlinearity compensation (NLC) is investigated. A turbo equalization scheme is proposed where a recursive least-squares (RLS) algorithm is used as an adaptive channel estimator to track the time-varying intersymbol interference (ISI) coefficients associated with inter-channel nonlinear interference (NLI) model. The estimated channel coefficients are used by a MIMO 2x2 soft-input soft-output (SISO) linear minimum mean square error (LMMSE) equalizer to compensate for the time-varying ISI. The SISO LMMSE equalizer and the SISO for…
Linear minimum mean-square error (L-MMSE) equalization is among the most popular methods for data detection in massive multi-user multiple-input multiple-output (MU-MIMO) wireless systems. While L-MMSE equalization enables near-optimal spectral efficiency, accurate knowledge of the signal and noise powers is necessary. Furthermore, corresponding VLSI designs must solve linear systems of equations, which requires high arithmetic precision, exhibits stringent data dependencies, and results in high circuit complexity. This paper proposes the first VLSI design of the NOnParametric Equalizer (NOPE)…
In this paper, we propose a novel approach for downlink transmission from a satellite swarm towards a ground station (GS). These swarms have the benefit of much higher spatial separation in the transmit antennas than traditional satellites with antenna arrays, promising a massive increase in spectral efficiency. The resulting precoder and equalizer have very low demands on computational complexity, inter-satellite coordination and channel estimation. This is achieved by taking knowledge about the geometry between satellites and GS into account. For precoding, each satellite only requires its a…
The problem of channel shortening equalization for optimal detection in ISI channels is considered. The problem is to choose a linear equalizer and a partial response target filter such that the combination produces the best detection performance. Instead of using the traditional approach of MMSE equalization, we directly seek all equalizer and target pairs that yield optimal detection performance in terms of the sequence or symbol error rate. This leads to a new notion of a posteriori equivalence between the equalized and target channels with a simple characterization in terms of their underl…
Channel equalization is the process of reducing amplitude, frequency and phase distortion in a radio channel with the intent of improving transmission performance. Different types of equalizers, their applications and some practical example is given. Especially, in the digital communication scenario how equalization works is shown. This paper presents a vivid description on channel equalization in digital transmission system.
Bilkent University（比尔肯特大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We introduce a novel family of adaptive robust equalizers for highly challenging underwater acoustic (UWA) channel equalization. Since the underwater environment is highly non-stationary and subjected to impulsive noise, we use adaptive filtering techniques based on a relative logarithmic cost function inspired by the competitive methods from the online learning literature. To improve the convergence performance of the conventional linear equalization methods, while mitigating the stability issues, we intrinsically combine different norms of the error in the cost function, using logarithmic fu…
In this theoretical work, the DSP-perceived channel in optical coherent communications is first simplified, based on which we categorize linear MIMO equalizers into four classes according to their reference locations. The entire channel inverse can be represented by a complex conjugate-dependent system, coinciding with the widely linear equalization theory. Suboptimally removing FO dynamics, relatively static channel inverses parameterized with common device and channel parameters are presented for monitoring or calibration purposes.
Power line communication continues to draw increasing interest by promising a wide range of applications including cost-free last-mile communication solution. However, signal transmitted through the power lines deteriorates badly due to the presence of severe inter-symbol interference (ISI) and harsh random pulse noise. This work proposes a new precoded turbo equalization scheme specifically designed for the PLC channels. By introducing useful precoding to reshape ISI, optimizing maximum {\it a posteriori} (MAP) detection to address the non-Gaussian pulse noise, and performing soft iterative d…
A self-iterating soft equalizer (SISE) consisting of a few relatively weak constituent equalizers is shown to provide robust performance even in severe intersymbol interference (ISI) channels that exhibit deep nulls and valleys within the signal band. Constituent equalizers are allowed to exchange soft information in the absence of interleavers based on the method that are designed to suppress significant correlation among their soft outputs. The resulting SISE works well as a stand-alone equalizer or as the equalizer component of a turbo equalization system. The performance advantages over ex…
All-digital basestation (BS) architectures for millimeter-wave (mmWave) massive multi-user multiple-input multiple-output (MU-MIMO), which equip each radio-frequency chain with dedicated data converters, have advantages in spectral efficiency, flexibility, and baseband-processing simplicity over hybrid analog-digital solutions. For all-digital architectures to be competitive with hybrid solutions in terms of power consumption, novel signal-processing methods and baseband architectures are necessary. In this paper, we demonstrate that adapting the resolution of the analog-to-digital converters …
Future services demand high data rate and quality. Thus, it is necessary to define new and robust algorithms to equalize channels and reduce noise in communications. Nowadays, new equalization algorithms are being developed to optimize the channel bandwidth and reduce noise, namely, Blind Channel Equalization. Conventional equalizations minimizing mean-square error generally require a training sequence accompanying the data sequence. In this study, the result of Least Mean Square (LMS) algorithm applied on two given communication channels is analyzed. Considering the fact that blind equalizers…
In this article, a fractional-norm constrained blind adaptive algorithm is presented for sparse channel equalization. In essence, the algorithm improves on the minimization of the constant modulus (CM) criteria by adding a sparsity inducing \(\ell_p\)-norm penalty. Simulation results demonstrate that the proposed regularized equalizer exploits the inherent channel sparsity effectively and exhibits faster convergence compared to its counterparts.
In this paper, we study the equalization design for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems with insufficient cyclic prefix (CP). In particular, the signal detection performance is severely impaired by inter-carrier interference (ICI) and inter-symbol interference (ISI) when the multipath delay spread exceeding the length of CP. To tackle this problem, a deep learning-based equalizer is proposed for approximating the maximum likelihood detection. Inspired by the dependency between the adjacent subcarriers, a computationally efficient join…
In optical transport networks, signal lightpaths between two terminal nodes can be different due to current network conditions. Thus the transmission distance and accumulated dispersion in the lightpath cannot be predicted. Therefore, the adaptive compensation of dynamic dispersion is necessary in such networks to enable flexible routing and switching. In this paper, we present a detailed analysis on the adaptive dispersion compensation using the least-mean-square (LMS) algorithm in coherent optical communication networks. It is found that the variable-step-size LMS equalizer can achieve the s…
We investigate channel equalization for Rayleigh fading channels under bounded channel uncertainties. We analyze three robust methods to estimate an unknown signal transmitted through a Rayleigh fading channel, where we avoid directly tuning the equalizer parameters to the available inaccurate channel information. These methods are based on minimizing certain mean-square error criteria that incorporate the channel uncertainties into the problem formulations. We present closed-form solutions to the channel equalization problems for each method and for both zero mean and nonzero mean signals. We…
In this paper we propose a smoothing turbo equalizer based on the expectation propagation (EP) algorithm with quite improved performance compared to the Kalman smoother, at similar complexity. In scenarios where high-order modulations or/and large memory channels are employed, the optimal BCJR algorithm is computationally unfeasible. In this situation, low-cost but suboptimal solutions, such as the linear minimum mean square error (LMMSE), are commonly used. Recently, EP has been proposed as a tool to improve the Kalman smoothing performance. In this paper we review these solutions to apply th…
Affine Frequency Division Multiplexing (AFDM), which is based on discrete affine Fourier transform (DAFT), has recently been proposed for reliable communication in high-mobility scenarios. Two low complexity detectors for AFDM are introduced here. Approximating the channel matrix as a band matrix via placing null symbols in the AFDM frame in the DAFT domain, a low complexity MMSE detection is proposed by means of the $\rm{LDL}$ factorization. Furthermore, exploiting the sparsity of the channel matrix, we propose a low complexity iterative decision feedback equalizer (DFE) based on weighted max…
We compare the potential of neural network (NN)-based channel estimation with classical linear minimum mean square error (LMMSE)-based estimators, also known as Wiener filtering. For this, we propose a low-complexity recurrent neural network (RNN)-based estimator that allows channel equalization of a sequence of channel observations based on independent time- and frequency-domain long short-term memory (LSTM) cells. Motivated by Vehicle-to-Everything (V2X) applications, we simulate time- and frequency-selective channels with orthogonal frequency division multiplex (OFDM) and extend our channel…
In the transmission of digital data at a relatively high rate over a particular band limited channel, it is normally necessary to employ an equalizer at the receiver in order to correct the signal distortion introduced by the channel .ISI (inter symbol interference) leads to large error probability if it is not suppressed .The possible solutions for coping with ISI such as equalization technique. Maximum Likelihood Sequence Estimation (MLSE) implemented with Viterbi algorithm is the optimal equalizer for this ISI problem sense it minimizes the sequence of error rate. This estimator involves a …
A new approach for blind channel equalization and decoding, variational inference, and variational autoencoders (VAEs) in particular, is introduced. We first consider the reconstruction of uncoded data symbols transmitted over a noisy linear intersymbol interference (ISI) channel, with an unknown impulse response, without using pilot symbols. We derive an approximate maximum likelihood estimate to the channel parameters and reconstruct the transmitted data. We demonstrate significant and consistent improvements in the error rate of the reconstructed symbols, compared to existing blind equaliza…
We perform an asymptotic study of the performance of filter bank multicarrier (FBMC) in the context of massive multi-input multi-output (MIMO). We show that the effects of channel distortions, i.e., intersymbol interference and intercarrier interference, do not vanish as the base station (BS) array size increases. As a result, the signal-to-interference-plus-noise ratio (SINR) cannot grow unboundedly by increasing the number of BS antennas, and is upper bounded by a certain deterministic value. We show that this phenomenon is a result of the correlation between the multi-antenna combining tap …
In diffusion-based communication, as for molecular systems, the achievable data rate is low due to the stochastic nature of diffusion which exhibits a severe inter-symbol-interference (ISI). Multiple-Input Multiple-Output (MIMO) multiplexing improves the data rate at the expense of an inter-link interference (ILI). This paper investigates training-based channel estimation schemes for diffusive MIMO (D-MIMO) systems and corresponding equalization methods. Maximum likelihood and least-squares estimators of mean channel are derived, and the training sequence is designed to minimize the mean squar…
Mitsubishi Electric Research Laboratories（三菱电机研究实验室）
Recently, data-driven approaches motivated by modern deep learning have been applied to optical communications in place of traditional model-based counterparts. The application of deep neural networks (DNN) allows flexible statistical analysis of complicated fiber-optic systems without relying on any specific physical models. Due to the inherent nonlinearity in DNN, various equalizers based on DNN have shown significant potentials to mitigate fiber nonlinearity. In this paper, we propose a turbo equalization (TEQ) based on DNN as a new alternative framework to deal with nonlinear fiber impairm…
Deep neural networks (DNNs) based digital receivers can potentially operate in complex environments. However, the dynamic nature of communication channels implies that in some scenarios, DNN-based receivers should be periodically retrained in order to track temporal variations in the channel conditions. To this aim, frequent transmissions of lengthy pilot sequences are generally required, at the cost of substantial overhead. In this work we propose a DNN-aided symbol detector, Meta-ViterbiNet, that tracks channel variations with reduced overhead by integrating three complementary techniques: 1…
Orthogonal Frequency Division Multiplexing (OFDM) has recently been applied in wireless communication systems due to its high data rate transmission capability with high bandwidth efficiency and its robustness to multi-path delay. Fading is the one of the major aspect which is considered in the receiver. To cancel the effect of fading, channel estimation and equalization procedure must be done at the receiver before data demodulation. This paper mainly deals with pilot based channel estimation techniques for OFDM communication over frequency selective fading channels. This paper proposes a spe…
Reconfigurable intelligent surface (RIS)-empowered communications is on the rise and is a promising technology envisioned to aid in 6G and beyond wireless communication networks. RISs can manipulate impinging waves through their electromagnetic elements enabling some sort of control over the wireless channel. In this paper, the potential of RIS technology is explored to perform a sort of virtual equalization over-the-air for frequency-selective channels whereas, equalization is generally conducted at either the transmitter or receiver in conventional communication systems. Specifically, with t…
Sparse intersymbol-interference (ISI) channels are encountered in a variety of high-data-rate communication systems. Such channels have a large channel memory length, but only a small number of significant channel coefficients. In this paper, trellis-based equalization of sparse ISI channels is revisited. Due to the large channel memory length, the complexity of maximum-likelihood detection, e.g., by means of the Viterbi algorithm (VA), is normally prohibitive. In the first part of the paper, a unified framework based on factor graphs is presented for complexity reduction without loss of optim…
Semantic Channel Equalization Strategies for Deep Joint Source-Channel Coding
DIAG Department, Sapienza University of Rome（罗马大学DIAG系）；Consorzio Nazionale Interuniversitario per le Telecomunicazioni (CNIT)（国家跨大学电信合作机构）；CEA Leti, University Grenoble Alpes（CEA Leti与格勒诺布尔阿尔卑斯大学）；DIET Department, Sapienza University of Rome（罗马大学DIET系）
Low-complexity Equalization of Zak-OTFS Via Neumann Series
Duke University（杜克大学）；Department of Electrical Engineering, Indian Institute of Technology Delhi（德里印度理工学院电气工程系）；Cohere Technologies Inc.（Cohere科技有限公司）；Department of Mathematics, University of Texas at Austin（德克萨斯大学奥斯汀分校数学系）
To reap the promised gain achieved by distributed reconfigurable intelligent surfaces (RISs)-enhanced communications in a wireless network, timing synchronization among these metasurfaces is an essential prerequisite in practice. This paper proposes a unified framework for the joint estimation of the unknown timing offsets and the RIS channel parameters, as well as the design of cooperative reflection and synchronization algorithm for the distributed multiple-RIS communication. Considering that RIS is usually a passive device with limited capability of signal processing, the individual timing …
Reconfigurable intelligent surface (RIS) has entered the public consciousness as a promising technology for enhancing the performance of future wireless communication systems by dynamically constructing the wireless channels. In this letter, we study a double-RIS aided downlink multi-user multiple-input multiple-output (MIMO) communication system. We investigate the mean-square-error (MSE) minimization problem by jointly optimizing the active transmit beamforming, the receive equalizer and the passive beamforming at each RIS. Different from prior works, for the sake of reducing both communicat…
Programmable radio environments parametrized by reconfigurable intelligent surfaces (RISs) are emerging as a new wireless communications paradigm, but currently used channel models for the design and analysis of signal-processing algorithms cannot include fading in a manner that is faithful to the underlying wave physics. To overcome this roadblock, we introduce a physics-based end-to-end model of RIS-parametrized wireless channels with adjustable fading (coined PhysFad) which is based on a first-principles coupled-dipole formalism. PhysFad naturally incorporates the notions of space and causa…
Over-the-air computation (AirComp) is a promising technology that is capable of achieving fast data aggregation in Internet of Things (IoT) networks. The mean-squared error (MSE) performance of AirComp is bottlenecked by the unfavorable channel conditions. This limitation can be mitigated by deploying a reconfigurable intelligent surface (RIS), which reconfigures the propagation environment to facilitate the receiving power equalization. The achievable performance of RIS relies on the availability of accurate channel state information (CSI), which however is generally difficult to be obtained.…
