Channel Estimation Problem Research Articles

Finding the optimal probe state for multiparameter quantum metrology using conic programming

The ultimate precision in quantum sensing could be achieved using optimal quantum probe states. However, current quantum sensing protocols do not use probe states optimally. Indeed, the calculation of optimal probe states remains an outstanding challenge. Here, we present an algorithm that efficiently calculates a probe state for correlated and uncorrelated measurement strategies. The algorithm involves a conic program, which minimizes a linear objective function subject to conic constraints on a operator-valued variable. Our algorithm outputs a probe state that is a simple function of the optimal variable. We prove that our algorithm finds the optimal probe state for channel estimation problems, even in the multiparameter setting. For many noiseless quantum sensing problems, we prove the optimality of maximally entangled probe states. We also analyze the performance of 3D-field sensing using various probe states. Our work opens the door for a plethora of applications in quantum metrology.

Tensor Based Semi-Blind Channel Estimation for Reconfigurable Intelligent Surface-Aided Multiple-Input Multiple-Output Communication Systems

Reconfigurable intelligent surfaces (RISs) are a promising technology for sixth-generation (6G) wireless networks. However, a fully passive RIS cannot independently process signals. Wireless systems equipped with it often encounter the challenge of large channel matrix dimensions when acquiring channel state information using pilot-assisted algorithms, resulting in high pilot overhead. To address this issue, this article proposes a semi-blind joint channel and symbol estimation receiver without a pilot training stage for RIS-aided multiple-input multiple-output (MIMO) (including massive MIMO) communication systems. In a semi-blind system, a transmission symbol matrix and two channel matrices are coupled within the received signals at the base station (BS). We decouple them by building two parallel factor (PARAFAC) tensor models. Leveraging PARAFAC tensor decomposition, we transform the joint channel and symbol estimation problem into least square (LS) problems, which can be solved by Alternating Least Squares (ALSs). Our proposed scheme allows duplex communication. Compared to recently proposed pilot-based methods and semi-blind receivers, our results demonstrate the superior performance of our proposed algorithm in estimation accuracy and speed.

Bayesian 3D User Localization and Channel Reconstruction with Planar Extremely Large-Scale Antenna Array

An extremely large-scale antenna array (ELAA) can potentially provide significantly increased spatial multiplexing and beamforming gains, as well as enhanced localization capability. While presenting new potential, its near-field propagation and spatial non-stationary properties also impose a great challenge on the receiver design. This paper focuses on the receiver design in an uplink orthogonal frequency-division multiplexing system with a planar ELAA deployed at the base station. To solve the challenging problem of 3D user localization and channel estimation with the planar ELAA, a space-frequency user localization and channel reconstruction (SF-ULCR) receiver is proposed. Under the Bayesian framework, an extended probability model is first established, to capture the channel structural information comprehensively, based on which an iterative receiver consisting of three modules is derived: element-wise line spectrum estimation (ELSE), distance parameter estimation (DPE), and near-field localization (NFL). In particular, the ELSE module handles the line spectrum relationships among multiple subcarriers in the frequency domain, the DPE module extracts and integrates the distance information from the line spectrum parameters, and the NFL module utilizes the messages of distances for user localization based on near-field spatial characteristics. Our numerical results demonstrate that the proposed SF-ULCR algorithm outperforms existing baselines in terms of channel estimation and localization performance, and that it approaches the Cramèr–Rao bound.

A Novel Two-Step Channel Estimation Method for RIS-Assisted mmWave Systems.

In this work, we resolve the cascaded channel estimation problem and the reflected channel estimation problem for the reconfigurable intelligent surface (RIS)-assisted millimeter-wave (mmWave) systems. The novel two-step method contains modified multiple population genetic algorithm (MMPGA), least squares (LS), residual network (ResNet), and multi-task regression model. In the first step, the proposed MMPGA-LS optimizes the crossover strategy and mutation strategy. Besides, the ResNet achieves cascaded channel estimation by learning the relationship between the cascaded channel obtained by the MMPGA-LS and the channel of the user (UE)-RIS-base station (BS). Then, the proposed multi-task-ResNet (MTRnet) is introduced for the reflected channel estimation. Relying on the output of ResNet, the MTRnet with multiple output layers estimates the coefficients of reflected channels and reconstructs the channel of UE-RIS and RIS-BS. Remarkably, the proposed MTRnet is capable of using a lower optimization model to estimate multiple reflected channels compared with the classical neural network with the single output layer. A series of experimental results validate the superiority of the proposed method in terms of a lower norm mean square error (NMSE). Besides, the proposed method also obtains a low NMSE in the RIS with the formulation of the uniform planar array.

Channel estimation for fiber-terahertz communication based on conditional generative adversarial networks

Fiber-terahertz communication is regarded as one of the best candidates for future 6G mobile communication systems. Using fiber optic-assisted terahertz communication can solve the problem of large-capacity terahertz coverage. Still, it also leads to more complex and variable channel environments. This makes channel estimation for fiber terahertz communication challenging. In this paper, we use the conditional generative adversarial networks (CGAN) to solve channel estimation problems with their excellent mapping ability to complex relationships. Meanwhile, we further improved the performance of the network by using a residual structure and an unrolled structure. Compared with the traditional recurrent neural networks (RNN) and convolutional neural networks (CNN), the normalized mean squared error (NMSE) of CGAN-based fiber terahertz channel estimation is reduced by up to 1.93 dB and 1.02 dB, respectively.

Parametric channel estimation for RIS-assisted mmWave MIMO-OFDM systems with low pilot overhead

We consider the channel estimation problem in a millimeter-wave (mmWave) multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) system aided by a passive reconfigurable intelligent surface (RIS). Initially, leveraging the inherent sparsity of mmWave channels, we decouple the channel estimation into the recovery of multipath parameters, including spatial frequencies of angles, delays, and complex gains. Subsequently, we employ two training schemes: the first involves a full row rank constrained RIS phase shift pattern, and the second incorporates a Kronecker structure constrained RIS phase shift pattern. These schemes reform channel estimation into estimating parameters from two fifth-order tensor signals, which admit constrained Canonical Polyadic decomposition. Moreover, both tensor signals share Vandermonde-constrained factor matrices, enabling algebraic algorithms for tensor decomposition problems and recovering channel multipath parameters. Theoretical analyses show that the first training scheme has a lower signal processing complexity for channel estimation, while the second attains a higher estimation accuracy. Also, we prove that our proposed two schemes have the same minimum pilot overhead, which is as low as proportional to the product of the number of paths in the two MIMO channels (transmitter-RIS and RIS-receiver). Numerical results validate the effectiveness of our proposed methods.

Temporally-correlated massive access: joint user activity detection and channel estimation via vector approximate message passing

In the paper, we investigate a massive machine-type communication (mMTC), where numerous single-antenna users communicate with a single-antenna base station while being active. However, the status of user can undergoes multiple transitions between active and inactive states across whole consecutive intervals. Then, we formulate the problem of joint user activity detection and channel estimation within the dynamic compressed sensing (DCS) framework, considering the temporally-correlated user activity across the entire consecutive intervals. To be specific, we introduce a new hybrid vector approximate message passing algorithm for DCS (HyVAMP-DCS). The proposed algorithm comprises a VAMP block for estimating channel and a loopy belief propagation (LBP) block for detecting user activity. Moreover, these two blocks can exchange messages, enhancing the performance of both channel estimation and user activity detection. Importantly, compared to the fragile GAMP algorithm, VAMP is robust and applicable to a much broader class of large random matrices. Furthermore, the fixed points of VAMP’s state evolution align with the replica prediction of the minimum mean-squared error. The simulation results illustrate the superiority of HyVAMP-DCS, demonstrating its significant outperformance over HyGAMP-DCS.

Doppler frequency analysis for sound-field sampling with moving microphones

Moving microphones allow for the fast acquisition of sound-field data that encode acoustic impulse responses in time-invariant environments. Corresponding decoding algorithms use the knowledge of instantaneous microphone positions for relating the dynamic samples to a positional context and solving the involved spatio-temporal channel estimation problem subject to the particular parameterization model. Usually, the resulting parameter estimates are supposed to remain widely unaffected by the Doppler effect despite the continuously moving sensor. However, this assumption raises issues from the physical point of view. So far, mathematical investigations into the actual meaning of the Doppler effect for such dynamic sampling procedures have been barely provided. Therefore, in this paper, we propose a new generic concept for the dynamic sampling model, introducing a channel representation that is explicitly based on the instantaneous Doppler shift according to the microphone trajectory. Within this model, it can be clearly seen that exact trajectory tracking implies exact Doppler-shift rendering and, thus, enables unbiased parameter recovery. Further, we investigate the impact of non-perfect trajectory data and the resulting Doppler-shift mismatches. Also, we derive a general analysis scheme that decomposes the microphone signal along with the encoded parameters into particular subbands of Doppler-shifted frequency components. Finally, for periodic excitation, we exactly characterize the Doppler-shift influences in the sampled signal by convolution operations in the frequency domain with trajectory-dependent filters.

A Convex Combination–Variable-Step-Size Least Mean p-Norm Algorithm

Underwater acoustic channels often have to face the interference of impulsive noise, which is usually modeled by α-stable distribution in simulation experiments. To solve the problem of underwater acoustic channel estimation under impulsive noise, this paper proposes a convex combination–variable-step-size least mean p-norm algorithm. The algorithm incorporates a convex combination into the variable-step-size least mean p-norm algorithm and uses the convex combination of different convergence domains provided by changing the parameters of the Gaussian function to further improve the effect after convergence. The simulation results of channel estimation show that the convex combination–variable-step-size least mean p-norm algorithm provides a more stable, robust, and universal solution than the variable-step-size least mean p-norm algorithm.

Estimation of Dispersive High-Doppler Channels in the RIS-Aided mmWave Internet of Vehicles

Reconfigurable intelligent surfaces (RISs) have emerged as a promising candidate for improving the spectral-and energy-efficiency of millimeter-wave (mmWave) Internet of vehicles (IoV) communications, but the conception of their accurate channel estimation poses. Hence the existing estimation methods mainly focus on time-invariant channels, while ignoring the Doppler effect induced by the high-velocity vehicles, which will lead to significant performance degradation. In this paper, we investigate the problem of channel estimation in RIS-aided mmWave IoV systems considering the deleterious Doppler effect. Firstly, we derive the expression of the time-varying cascaded two-hop multiple-path channels, where each delay tap is subject to multiple paths instead of having a simple one-to-one correspondence. In order to decouple the paths, the problem is formulated in the delay-domain by a series of transformations and the cascaded two-hop channel can be estimated at each delay tap. Then we propose a pair of estimation strategies by considering different hardware constraints depending on the number of receiver antennas at the base station (BS). When a large receiver array is employed at the BS, we can exploit its high angular selectivity for distinguishing each resolvable path at a certain delay tap because they arrive from different directions. However, this cannot be achieved for small arrays, given their more limited angular resolution. Thus, the RIS reflection patterns are delicately designed for distinguishing multiple resolvable paths. After separating the paths, Doppler estimation can be performed by calculating the phase difference of the adjacent symbols. Our simulation results demonstrate the superior performance of the proposed methods within a wide range of Doppler shifts.

Deep Residual Learning with Attention Mechanism for OFDM Channel Estimation

In this paper, we apply deep learning to the channel estimation problem of OFDM. Precisely speaking, to reduce the influence of noise on LS channel estimation, we design a channel estimation model based on attention mechanism and residual network. AttRNet-Conv and AttRNet-FC use attentional mechanism to change the weight of the feature to suppress noise. Compared with other channel estimation algorithms based on deep learning, AttRNet-Conv and AttRNet-FC avoid damaging channel information. The simulation results show that AttRNet-Conv and AttRNet-FC are superior to existing channel estimation algorithms based on deep learning in both high and low pilot frequency conditions. Even at low SNR, the estimation accuracy is higher than that of LMMSE. Experimental results show thatAttRNet-Conv and AttRNet-FC has strong robustness. In addition, we find that AttRNet-Conv is more suitable for channel estimation at low SNR in EPA, and the AttRNet-FC model is used in other cases.

Channel Parameter Estimation of mmWave MIMO System in Urban Traffic Scene: A Training Channel-Based Method

In frequency selective channel environment, channel estimation in hybrid precoding millimeter-wave (mmWave) massive multiple input multiple output (MIMO) system is a challenge issue. To solve this problem, we propose an effective channel estimation scheme for frequency selective channel, which is based on the training channel model in urban traffic environment. Considering that the practical mmWave MIMO channel is sparsity and the subcarrier multi-channels have the same sparse structure, we regard the channel estimation problem as the sparse channel recovery, and propose a multipath simultaneous matching tracking estimation method. It is assumed that the noise between the practical channels has a certain correlation, and the noise correlation has an impact on the selection of the optimal atomic support set in the process of channel recovery. Therefore, noise weighting is introduced in our proposed method. The simulation results prove the validity of this proposed method in frequency selective mmWave MIMO channel. Without increasing the complexity of the algorithm, the proposed method can achieve better local performance than the traditional classical methods.

An Improved GOMP Sparse Channel Estimation for Vehicle-to-Vehicle Communications

Reliable channel estimation is critical for wireless communication performance, especially in vehicle-to-vehicle (V2V) communication scenarios. Aiming at the major challenges of channel tracking and estimating as the highly dynamic nature of vehicle environments, an improved generalized orthogonal matching pursuit (iGOMP) is proposed for V2V channel estimation. The iGOMP algorithm transforms the channel estimation problem into a sparse signal recovery problem and replaces the classical inner product criterion with the Dice atom matching criterion. Additionally, the atomic weak progressive selection method is integrated to avoid the suboptimal selection of atoms from the redundant dictionary using the inner product criterion. The proposed iGOMP method can achieve optimal channel estimation by iterating feedback results. Simulation results demonstrate that the iGOMP method has superior estimation accuracy, mean square error (MSE), and bit error rate (BER) performance compared with traditional channel estimation methods in V2V communications.

Common structured sparsity based multi-user channel estimation for double-RIS assisted millimeter wave systems

Compared to a single reconfigurable intelligent surface (RIS) system, a double RIS system can achieve better passive beamforming gain, while requiring more accurate channel state information (CSI). However, due to the presence of double-reflection links, channel estimation with low pilot overhead is quite challenging. In this paper, we investigate channel estimation of double-RIS assisted multi-user millimeter wave (mmWave) communication systems. Firstly, the channel estimation problem for double-reflection links is formulated as a sparse signal recovery problem. Then, we analyze and exploit the common structured sparsity of the cascaded channel among multiple users, i.e., the common row and column sparsity in the angular channel matrix, and the corresponding common sparsity after being transformed into the channel vector. Inspired by this, we further propose a novel common structured sparsity based orthogonal matching pursuit (CSS-OMP) algorithm for multi-user joint channel estimation. Simulation results show that CSS-OMP algorithm can provide more accurate channel estimation with reduced pilot overhead compared to the conventional OMP algorithm.

OFDM-Based Massive Connectivity for LEO Satellite Internet of Things

Low earth orbit (LEO) satellite has been considered as a potential supplement for the terrestrial Internet of Things (IoT). In this paper, we consider grant-free non-orthogonal random access (GF-NORA) in the orthogonal frequency division multiplexing (OFDM) system to increase access capacity and reduce access latency for LEO satellite-IoT. We focus on the joint device activity detection (DAD) and channel estimation (CE) problem at the satellite access point. The delay and the Doppler effect of the LEO satellite channel are assumed to be partially compensated. We propose an OFDM-symbol repetition technique to better distinguish the residual Doppler frequency shifts, and present a grid-based parametric probability model to characterize channel sparsity in the delay-Doppler-user domain, as well as to characterize the relationship between the channel states and the device activity. Based on that, we develop a robust Bay esian message-passing algorithm named modified variance state propagation (MVSP) for joint DAD and CE. Moreover, to tackle the mismatch between the real channel and its on-grid representation, an expectation–maximization (EM) framework is proposed to learn the grid parameters. Simulation results demonstrate that our proposed algorithms significantly outperform the existing approaches in both activity detection probability and channel estimation accuracy.

Joint channel and impulse noise estimation based on compressed sensing and Kalman filter for OFDM system

Impulse noise (IN) widely exists in many communication systems, which seriously affects the performance of OFDM communication systems. A joint channel and IN estimation method based on all subcarriers is designed. This method uses a sparse Bayesian learning (SBL) algorithm incorporating forward–backward Kalman filter (FB-Kalman) to tackle the problem of joint channel and IN estimation and data detection for OFDM systems. Firstly, the channel impulse response and IN are regarded as unknown sparse vectors, and a SBL framework using all subcarriers is proposed to estimate the unknown vector. The SBL theory is used based on the prior distribution of variables, and then the forward–backward joint system is established, which applies the data detection simultaneously. We also propose the FB-Kalman implementation algorithm by using the expectation maximization updates. Explicit expressions of mean and covariance matrix of the posterior distribution are derived in the E-step. Simulation results show that the proposed algorithm improves the normalized mean square error and bit error rate performance of OFDM system in the presence of IN communication environment.

Channel Estimation for Reconfigurable Intelligent Surface-Assisted Full-Duplex MIMO With Hardware Impairments

We consider the problem of channel estimation in a multiple-input-multiple-output (MIMO) full-duplex (FD) wireless communication system assisted by a reconfigurable intelligent surface (RIS) with hardware impairments (HI) occurring at the transceivers and RIS elements. We propose an unbiased channel estimator that requires knowledge of only the first and second order statistics of the HI, for which we derive closed form expressions. The proposed estimator reduces to the maximum likelihood estimator (MLE) in the case of ideal hardware. We also describe FD and HD orthogonal pilot schemes that minimize the mean square error of the MLE in the case of ideal hardware. We verify the performance of the estimator under varying conditions of transceiver and RIS HI via numerical simulations.

Channel Estimation for Reconfigurable Intelligent Surface Aided Multi-User mmWave MIMO Systems

Channel acquisition is one of the main challenges for the deployment of reconfigurable intelligent surface (RIS) aided communication systems. This is because an RIS has a large number of reflective elements, which are passive devices with no active transmitting/receiving abilities. In this paper, we study the channel estimation problem for the RIS aided multi-user millimeter-wave (mmWave) multi-input multi-output (MIMO) system. Specifically, we propose a novel channel estimation protocol for the above system to estimate the cascaded channels, which are the products of the channels from the base station (BS) to the RIS and from the RIS to the users. Further, since the cascaded channels are typically sparse, this allows us to formulate the channel estimation problem as a sparse recovery problem using compressive sensing (CS) techniques, thereby allowing the channels to be estimated with less training overhead. Moreover, the sparse channel matrices of the cascaded channels of all users have a common block sparsity structure due to the common channel between the BS and the RIS. To take advantage of the common sparsity pattern, we propose a two-step multi-user joint channel estimation procedure. In the first step, we make use of the common column-block sparsity and project the received signals onto the common column subspace. In the second step, we make use of the row-block sparsity of the projected signals and propose a multi-user joint sparse matrix recovery algorithm that takes into account the common channel between the BS and the RIS.

Variance state propagation for uplink channel estimation in LEO satellite systems

AbstractThis paper, considers the channel estimation problem of the uplink low Earth orbit (LEO) satellite orthogonal frequency division multiplexing (OFDM) system. By exploiting the channel structured sparsity in the delay‐Doppler‐angle domain, the channel estimation problem is formulated as a block‐sparse signal recovery problem. The variance state propagation (VSP) framework is extended to solve such a problem. Considering that the delay, Doppler shift, and angle of departure (AoD) of each propagation path may not exactly fall on the presumed discrete grid points, an expectation maximization (EM) based parameter learning scheme in VSP to iteratively update the grid parameters is introduced. Simulation results demonstrate that the proposed approach achieves a substantial performance gain over the existing methods.

Channel Estimation for XL-RIS-Aided Millimeter-Wave Systems

Reconfigurable intelligent surface (RIS) is able to enhance the capacity of wireless communication systems with low overhead. Extremely large (XL)-RIS-aided millimeter-wave (mmWave) communication has become a promising key technique for future 6-th Generation (6G) systems. The performance gain brought in by XL-RIS relies on the accurate channel state information (CSI). However, channel estimation requires huge training overhead and high computational complexity due to the XL number of passive elements at RIS. Moreover, the unknown visual region (VR) infomation caused by the sensitivity of mmWave signal to random blockages makes the channel estimation more difficult. In this paper, we consider the channel estmation for XL-RIS-aided mmWave uplink system. We firstly model the XL-RIS-aided channel as a hybrid one composed of near-field RIS-to-user channel and far-field RIS-to-base station (BS) channel, where the VR issue of XL-RIS has been taken into consideration. Then we formulate the channel estimation problem as a sparse recovery problem. To solve this problem, we propose a two-stage algorithm for joint channel estimation and VR detection. Finally numerical results show that the proposed algorithms outperform the existing benchmark schemes in terms of normalized mean-squared error (NMSE) due to the VR detection and the utilization of shift common-support property among sub-channels.