Channel Estimation Scheme Research Articles

Leakage Suppression in Pulse-Shaped OTFS Delay-Doppler-Pilot Channel Estimation

In this letter, we propose a novel channel estimation scheme with leakage suppression for orthogonal time frequency and space (OTFS) modulation. In OTFS, data and pilot symbols are placed in the delay-Doppler (DD) domain and spread over the time-frequency (TF) domain. This increases the achievable accuracy in estimating linear time-varying (LTV) channels. Unfortunately, leakage effects reduce the measurement precision significantly. Therefore, we propose a scheme that exploits smoothness regularization in TF to suppress the leakage observed in the DD domain. It allows us to improve the channel estimation accuracy while reducing signaling overhead.

Anchor-Assisted Channel Estimation for Intelligent Reflecting Surface Aided Multiuser Communication

Channel estimation is a practical challenge for intelligent reflecting surface (IRS) aided wireless communication. As the number of IRS reflecting elements or IRS-aided users increases, the channel training overhead becomes excessively high, which results in long delay and low throughput in data transmission. To tackle this challenge, we propose in this paper a new anchor-assisted channel estimation approach, where two anchor nodes, namely A1 and A2, are deployed near the IRS for facilitating its aided base station (BS) in acquiring the cascaded BS-IRS-user channels required for data transmission. Specifically, in the first scheme, the partial channel state information (CSI) on the element-wise channel gain square of the common BS-IRS link for all users is first obtained at the BS via the anchor-assisted training and feedback. Then, by leveraging such partial CSI, the cascaded BS-IRS-user channels are efficiently resolved at the BS with additional training by the users. While in the second scheme, the BS-IRS-A1 and A1-IRS-A2 channels are first estimated via the training by A1. Then, with additional training by A2, all users estimate their individual cascaded A2-IRS-user channels simultaneously. Based on the CSI fed back from A2 and all users, the BS resolves the cascaded BS-IRS-user channels efficiently. In both schemes, the channels among the fixed BS, IRS, and two anchors are estimated in a large timescale, which greatly reduces the real-time training overhead. Simulation results demonstrate that our proposed anchor-assisted channel estimation schemes achieve superior performance as compared to existing IRS channel estimation schemes, under various practical setups. In addition, the first proposed scheme outperforms the second one when the number of antennas at the BS is sufficiently large, and vice versa.

Sparse Bayesian Learning Aided Estimation of Doubly-Selective MIMO Channels for Filter Bank Multicarrier Systems

Sparse Bayesian learning (SBL)-based channel state information (CSI) estimation schemes are developed for filter bank multicarrier (FBMC) systems using offset quadrature amplitude modulation (OQAM). Initially, an SBL-based channel estimation scheme is designed for a frequency-selective quasi-static single-input single-output (SISO)-FBMC system, relying on the interference approximation method (IAM). The IAM technique, although has low complexity, is only suitable for channels exhibiting mild frequency-selectivity. Hence, an alternative time-domain (TD) model based sparse channel estimation framework is developed for highly frequency-selective channels. Subsequently, the Kalman filtering (KF)-based IAM and its TD counterpart are developed for sparse doubly-selective CSI estimation in SISO-FBMC systems. These schemes are also extended to FBMC-based multiple-input multiple-output (MIMO) systems, for both quasi-static and doubly-selective channels, after demonstrating the special block and group-sparse structures of the IAM and TD-based models respectively, which are the characteristic features of such channels. The Bayesian Cramér-Rao lower bounds (BCRLBs) and the time-recursive BCRLBs are derived for the proposed quasi-static as well as doubly-selective sparse CSI estimation models, respectively. Our numerical results closely match the analytical findings, demonstrating the enhanced performance of the proposed schemes over the existing techniques.

Federated Learning for Channel Estimation in Conventional and RIS-Assisted Massive MIMO

Machine learning (ML) has attracted a great research interest for physical layer design problems, such as channel estimation, thanks to its low complexity and robustness. Channel estimation via ML requires model training on a dataset, which usually includes the received pilot signals as input and channel data as output. In previous works, model training is mostly done via centralized learning (CL), where the whole training dataset is collected from the users at the base station (BS). This approach introduces huge communication overhead for data collection. In this paper, to address this challenge, we propose a federated learning (FL) framework for channel estimation. We design a convolutional neural network (CNN) trained on the local datasets of the users without sending them to the BS. We develop FL-based channel estimation schemes for both conventional and RIS (intelligent reflecting surface) assisted massive MIMO (multiple-input multiple-output) systems, where a single CNN is trained for two different datasets for both scenarios. We evaluate the performance for noisy and quantized model transmission and show that the proposed approach provides approximately 16 times lower overhead than CL, while maintaining satisfactory performance close to CL. Furthermore, the proposed architecture exhibits lower estimation error than the state-of-the-art ML-based schemes.

Deep Learning for Joint Pilot Design and Channel Estimation in MIMO-OFDM Systems.

In MIMO-OFDM systems, pilot design and estimation algorithm jointly determine the reliability and effectiveness of pilot-based channel estimation methods. In order to improve the channel estimation accuracy with less pilot overhead, a deep learning scheme for joint pilot design and channel estimation is proposed. This new hybrid network structure is named CAGAN, which is composed of a concrete autoencoder (concrete AE) and a conditional generative adversarial network (cGAN). We first use concrete AE to find and select the most informative position in the time-frequency grid to achieve pilot optimization design and then input the optimized pilots to cGAN to complete channel estimation. Simulation experiments show that the CAGAN scheme outperforms the traditional LS and MMSE estimation methods with fewer pilots, and has good robustness to environmental noise.

Transfer learning-based channel estimation in orthogonal frequency division multiplexing systems using data-nulling superimposed pilots.

Data-nulling superimposed pilot (DNSP) effectively alleviates the superimposed interference of superimposed training (ST)-based channel estimation (CE) in orthogonal frequency division multiplexing (OFDM) systems, while facing the challenges of the estimation accuracy and computational complexity. By developing the promising solutions of deep learning (DL) in the physical layer of wireless communication, we fuse the DNSP and DL to tackle these challenges in this paper. Nevertheless, due to the changes of wireless scenarios, the model mismatch of DL leads to the performance degradation of CE, and thus faces the issue of network retraining. To address this issue, a lightweight transfer learning (TL) network is further proposed for the DL-based DNSP scheme, and thus structures a TL-based CE in OFDM systems. Specifically, based on the linear receiver, the least squares estimation is first employed to extract the initial features of CE. With the extracted features, we develop a convolutional neural network (CNN) to fuse the solutions of DL-based CE and the CE of DNSP. Finally, a lightweight TL network is constructed to address the model mismatch. To this end, a novel CE network for the DNSP scheme in OFDM systems is structured, which improves its estimation accuracy and alleviates the model mismatch. The experimental results show that in all signal-to-noise-ratio (SNR) regions, the proposed method achieves lower normalized mean squared error (NMSE) than the existing DNSP schemes with minimum mean square error (MMSE)-based CE. For example, when the SNR is 0 decibel (dB), the proposed scheme achieves similar NMSE as that of the MMSE-based CE scheme at 20 dB, thereby significantly improving the estimation accuracy of CE. In addition, relative to the existing schemes, the improvement of the proposed scheme presents its robustness against the impacts of parameter variations.

Deep Learning-Based Channel Estimation for mmWave Massive MIMO Systems in Mixed-ADC Architecture.

Millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems can significantly reduce the number of radio frequency (RF) chains by using lens antenna arrays, because it is usually the case that the number of RF chains is often much smaller than the number of antennas, so channel estimation becomes very challenging in practical wireless communication. In this paper, we investigated channel estimation for mmWave massive MIMO system with lens antenna array, in which we use a mixed (low/high) resolution analog-to-digital converter (ADC) architecture to trade-off the power consumption and performance of the system. Specifically, most antennas are equipped with low-resolution ADC and the rest of the antennas use high-resolution ADC. By utilizing the sparsity of the mmWave channel, the beamspace channel estimation can be expressed as a sparse signal recovery problem, and the channel can be recovered by the algorithm based on compressed sensing. We compare the traditional channel estimation scheme with the deep learning channel-estimation scheme, which has a better advantage, such as that the estimation scheme based on deep neural network is significantly better than the traditional channel-estimation algorithm.

Efficient Message Passing Receivers for Downlink MIMO-SCMA Systems

Sparse code multiple access (SCMA) and multiple input multiple output (MIMO) are considered as two efficient techniques to provide both massive connectivity and high spectrum efficiency for future machine-type wireless networks. However, the computational complexity of the conventional message passing algorithm (MPA) for the downlink MIMO-SCMA detection increases exponentially with the degree of variable nodes (VNs). To address this issue, two novel fixed low complexity MPA detectors are proposed by utilizing the sparse feature of codewords, which are based on the serial schedule strategy in order to accelerate their convergence. First, a maximum distance MPA (MDMPA) detector is introduced to reduce the number of VNs involved in the message updating procedure in the first <inline-formula><tex-math notation="LaTeX">$T_0$</tex-math></inline-formula> iterations and fix <inline-formula><tex-math notation="LaTeX">$TJ_0$</tex-math></inline-formula> codewords at the <inline-formula><tex-math notation="LaTeX">$L_0$</tex-math></inline-formula> iteration, which subsequently drops the redundant codeword combinations in the remaining iterations. To further improve the bit error ratio (BER) performance, an improved MDMPA (IMDMPA) is proposed, in which, the VNs associated with the target user are always allowed to participate in the iterative propagation of message. An efficient linear squares (LS) channel estimation scheme is also derived based on block pilots by stacking all the received signals at the same subcarrier together. Simulation results illustrate that the proposed MDMPA and IMDMPA detectors significantly reduce the computational complexity of the original MPA, but with comparable decoding capabilities, and the proposed LS channel estimator can closely approach the corresponding lower bound over frequency selective channels.

Channel Modeling and Channel Estimation for Holographic Massive MIMO With Planar Arrays

In a realistic wireless environment, the multi-antenna channel usually exhibits spatially correlated fading. This is more emphasized when a large number of antennas is densely deployed, known as holographic massive MIMO (multiple-input multiple-output). In the first part of this letter, we develop a channel model for holographic massive MIMO by considering both non-isotropic scattering and directive antennas. With a large number of antennas, it is difficult to obtain full knowledge of the spatial correlation matrix. In this case, channel estimation is conventionally done using the least-squares (LS) estimator that requires no prior information of the channel statistics or array geometry. In the second part of this letter, we propose a novel channel estimation scheme that exploits the array geometry to identify a subspace of reduced rank that covers the eigenspace of any spatial correlation matrix. The proposed estimator outperforms the LS estimator, without using any user-specific channel statistics.

Learning-Based Channel Estimation and Phase Noise Compensation in Doubly-Selective Channels

In this letter, we propose a learning based channel estimation scheme for orthogonal frequency division multiplexing (OFDM) systems in the presence of phase noise in doubly-selective fading channels. Two-dimensional (2D) convolutional neural networks (CNNs) are employed for effective training and tracking of channel variation in both frequency as well as time domain. The proposed network learns and estimates the channel coefficients in the entire time-frequency (TF) grid based on pilots sparsely populated in the TF grid. In order to make the network robust to phase noise (PN) impairment, a novel training scheme where the training data is rotated by random phases before being fed to the network is employed. Further, using the estimated channel coefficients, a simple and effective PN estimation and compensation scheme is devised. Numerical results demonstrate that the proposed network and PN compensation scheme achieve robust OFDM performance in the presence of phase noise.

Channel Estimation and Secret Key Rate Analysis of MIMO Terahertz Quantum Key Distribution

We study the secret key rate (SKR) of a multiple-input multiple-output (MIMO) continuous variable quantum key distribution (CVQKD) system operating at terahertz (THz) frequencies, accounting for the effects of channel estimation. We propose a practical channel estimation scheme for the THz MIMO CVQKD system which is necessary to realize transmit-receive beamforming between Alice and Bob. We characterize the input-output relation between Alice and Bob during the key generation phase, by incorporating the effects of additional noise terms arising due to the channel estimation error and detector noise. Furthermore, we analyze the SKR of the system and study the effect of channel estimation error and overhead. Our simulation results reveal that the SKR may degrade significantly as compared to the SKR upper bound that assumes perfect channel state information, particularly at large transmission distances.

Hierarchical-Block Sparse Bayesian Learning for Spatial Non-Stationary Massive MIMO Channel Estimation

This letter provides a novel hierarchical-block channel estimation scheme for massive multiple-input multiple-output (MIMO) systems based on Bayesian learning frameworks. Specifically, considering the spatial non-stationarity of massive MIMO channels introduced by a large-scale antenna array, we first exploit a hierarchical-block prior to characterize the delay-domain sparse channel structure across the antenna array and then develop an iterative Bayesian learning scheme to infer the channel vector as well as its hyperparameters associated with the hierarchical-block prior. Meanwhile, the Cramer-Rao bound (CRB) is derived as a reference line. To evaluate our proposed scheme, we modify the standardized 3GPP channel model with birth-death process to capture the spatial non-stationarity of practical massive MIMO channels. Simulation results demonstrate that our proposed scheme can recover channels effectively and attain a significant performance improvement over comparison methods.

Channel Estimation for Extremely Large-Scale MIMO: Far-Field or Near-Field?

Extremely large-scale multiple-input-multiple-output (XL-MIMO) is promising to meet the high rate requirements for future 6G. To realize efficient precoding, accurate channel state information is essential. Existing channel estimation algorithms with low pilot overhead heavily rely on the channel sparsity in the angular domain, which is achieved by the classical far-field planar-wavefront assumption. However, due to the non-negligible near-field spherical-wavefront property in XL-MIMO, this channel sparsity in the angular domain is not achievable. Therefore, existing far-field channel estimation schemes will suffer from severe performance loss. To address this problem, in this paper, we study the near-field channel estimation by exploiting the polar-domain sparsity. Specifically, unlike the classical angular-domain representation that only considers the angular information, we propose a polar-domain representation, which simultaneously accounts for both the angular and distance information. In this way, the near-field channel also exhibits sparsity in the polar domain, based on which, we propose on-grid and off-grid near-field XL-MIMO channel estimation schemes. Firstly, an on-grid polar-domain simultaneous orthogonal matching pursuit (P-SOMP) algorithm is proposed to efficiently estimate the near-field channel. Furthermore, an off-grid polar-domain simultaneous iterative gridless weighted (P-SIGW) algorithm is proposed to improve the estimation accuracy. Finally, simulations are provided to verify the effectiveness of our schemes.

Joint pilot design and beamforming optimization in massive MIMO surveillance systems

This paper proposes a novel joint channel estimation and beamforming scheme for the massive multiple-input-multiple-output (MIMO) frequency-division duplexing (FDD) wireless legitimate surveillance system. With the proposed scheme, the monitor with the full duplex capability realizes the proactive eavesdropping of the suspicious link by leveraging the pilot attack approach. Specifically, exploiting the effective eavesdropping rate and the mean square error as performance metrics and setting a total power budget at the training and transmission phases, while guaranteeing the information from suspicious source can be successfully decode, joint pilot design, power allocation and beamforming strategy are formulated as optimization problems for the two objective functions: MSE and effective eavesdropping rate. A closed-form expression of the optimal pilot with the limited length can be obtained via the channel correlation. The optimal power problem at the training phase can be solved by a simple bisection method. Then, based on the obtained imperfect estimated channel, the jamming beamforming at monitor optimization algorithm is proposed by utilizing the convex Semidefinite Programming approach to maximize the effective eavesdropping rate. Numerical results show that the proposed joint pilot design, power allocation and beamforming optimization scheme can improve the surveillance performance of the legitimate monitor as compared to the existing passive eavesdropping and jamming-assisted eavesdropping.

Joint Precoding and Pre-Equalization for Faster-Than-Nyquist Transmission Over Multipath Fading Channels

Faster-than-Nyquist signaling (FTNS) has emerged as a promising technique to increase communication capacity in bandwidth-limited channels. However, the presence of FTN-induced inter-symbol interference (FTN-ISI) in the received observations, is detrimental to channel estimation (CE) and data detection in terms of computational complexity and performance. This paper copes with these problems by incorporating linear pre-equalization (LPE) and composite precoding formed by linear spectral precoding and Tomlinson-Harashima precoding (THP), into the FTNS. Specifically, LPE completely pre-equalizes the FTN-ISI, while spectral precoding resolves the LPE-caused signal spectral broadening by introducing proper artificial ISI, which is pre-equalized by THP. Channel-induced ISI, as the only ISI component in the observations, is estimated and equalized using the classical frequency-domain low-complexity schemes. We show that there are four advantages of the LPE-aided CE over the CE designed for the FTN transmissions without FTN-ISI pre-equalization, namely lower pilot overhead, simpler yet optimal pilot sequence design, lower mean-squared error of CE, and more robust against the FTN-ISI. Simulation results show that our scheme improves the performance of CE and detection, compared to existing FTN frequency-domain CE and equalization schemes.

Deep Compressed Sensing-Based Cascaded Channel Estimation for RIS-Aided Communication Systems

To reduce the pilot overhead of cascaded channel estimation for RIS-aided Massive MIMO communication system, we proposed a deep compressed sensing-based channel estimation scheme, where U-shaped network (U-Net), an encoder-decoder with skip connection, is used to recover the high-dimensional cascaded channel matrix from limited pilot overhead. The skip connections between encoder and decoder can fuse features of different scales and semantic by concatenating the feature map, which enhance the reconstruction performance of cascaded channel. To further improve the feature extraction ability of U-Net, we design a ResU-Net architecture with stacked residual units to increase the depth of network. Simulation results show the channel estimation of ResU-Net is more accurate than conventional algorithm and other network model. Meanwhile, ResU-Net has good generalization and robustness for different pilot lengths and phase quantization errors.

Multi-Task Learning-Based Channel Estimation for RIS Assisted Multi-User Communication Systems

In this letter, we propose a multi-task learning (MTL)-based joint channel estimation scheme for reconfigurable intelligent surface (RIS) assisted millimeter-wave communication system, where the direct channel (DC) and cascaded channel (CC) are estimated at the same coherence time by learning the feature of shared pilots. Since the dimension of CC is much larger than the DC, we design a learnable joint loss function based on homoscedastic task uncertainty to balance the training of two subtasks. Meanwhile, the residual shrinkage blocks are introduced into the multi-task network architecture to release the noise effect. Simulation results show that the estimation accuracy of MTL with less pilot overhead outperforms conventional channel estimation scheme, and significantly reduces training overhead compared with the single-task network.

Time-Domain Channel Estimation Scheme for OFDM over Fast Fading Channels

In high-mobility scenarios, the time variation of mobile radio channels leads to a loss of orthogonality among subcarriers in orthogonal frequency division multiplexing (OFDM) systems, resulting in intercarrier interference (ICI) and performance deterioration. Conventional channel estimation schemes are usually based on pilot tones, which are distributed in each OFDM symbol to estimate the channel variation. Hence, the channel estimator itself suffers from ICI. In this study, a new estimation scheme, which does not suffer from ICI, is proposed to estimate the channel variation within OFDM symbols. The main idea is to zero-pad (ZP) the OFDM symbol in the time domain. Then, in the middle of the ZP interval, an impulse signal is inserted as a pilot sample, which is used to estimate the channel at the pilot signal in the OFDM symbol. Finally, a linear model is used to estimate the channel variation over an OFDM symbol. Additionally, we derive the mean squared error (MSE) of the proposed estimation technique under the constraint that the channel varies linearly within OFDM symbols. Simulation results show that our scheme can achieve a substantial improvement in the bit error rate (BER) performance of OFDM, in spite of the OFDM symbol length being increased. Moreover, in many cases, the new scheme can achieve the same BER performance as the perfect knowledge of channel state information (CSI). Theoretical analysis and numerical simulations show that our scheme achieves excellent performance with much lower computational complexity.

Channel estimation via GAMP for millimeter wave hybrid massive MIMO systems

Abstract In this paper, we study the channel estimation problem for the millimeter wave (mm-wave) hybrid massive multiple-input multiple-output (MIMO) system. Based on the sparsity exhibited by the mm-wave channel in the angular domain, we select a portion of the beams that contribute to the communication process from the beamspace. Then, only the channel coefficients in the selected beamspace need to be estimated. The channel estimation problem is converted into a sparse signal reconstruction problem and solved by employing the generalized approximate message passing (GAMP) algorithm with Laplace distribution. The scale parameter of distribution is designed by analyzing the variance of the partial channel coefficients. Because only the partial channel coefficients need to be estimated, the computational complexity of the proposed GAMP approach is much lower than other methods. Simulation results show that the proposed channel estimation scheme exhibits significant advantages both in terms of estimation accuracy and spectral efficiency.

Analysis and Design for Pilot Power Allocation and Placement in OFDM Based Integrated Radar and Communication in Automobile Systems

In this paper, we consider the orthogonal frequency division modulation (OFDM) based integrated radar-communication (Rad-Com) for automobile systems operating in millimeter wave band with imperfect time-frequency synchronization for communications. Since different pilot power allocation and placement strategies can result in different performance, we investigate the power allocation and placement design for the Rad-Com system. We analyze the effect of power allocation and pilot placement on the system performance. Based on the analysis, we provide, along with a channel estimation scheme, the pilot power allocation and placement designs that can optimize the radar and communication performance, respectively. Moreover, the tradeoff between radar and communication performance is discussed and a tradeoff design is presented. We conduct simulations to validate our analysis and evaluate the proposed designs. Results show that our analysis is valid and insightful and the proposed designs are effective.