Reduced Pilot Overhead Research Articles

Compressive Sensing-Based Channel Estimation for Uplink and Downlink Reconfigurable Intelligent Surface-Aided Millimeter Wave Massive MIMO Systems

This paper investigates single-user uplink and two-user downlink channel estimation in reconfigurable intelligent surface (RIS)-aided millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) wireless communication systems. Because of the difficulty associated with the estimation of channels in RIS-aided wireless communication systems, channel state information (CSI) is assumed to be known at the receiver in some previous works in the literature. By assuming that prior knowledge of the line-of-sight (LoS) channel between the RIS and the base station (BS) is known, two compressive sensing-based channel estimation schemes that are based on simultaneous orthogonal matching pursuit and structured matching pursuit (StrMP) algorithms are proposed for estimation of uplink channel between RIS and user equipment (UE), and joint estimations of downlink channels between BS and a UE, and between RIS and another UE, respectively. The proposed channel estimation schemes exploit the inherent common sparsity shared by the angular domain mmWave channels at different subcarriers. The superiority of one of the proposed channel estimation techniques, the StrMP-based channel estimation technique, with negligibly higher computational complexity cost compared with other channel estimators, is documented through extensive computer simulation. Specifically, with a reduced pilot overhead, the proposed StrMP-based channel estimation scheme exhibits better performance than other channel estimation schemes considered in this paper for signal-to-noise ratio (SNR) between 0 dB and 5 dB upward at different instances for both uplink and downlink scenarios, respectively. However, below these values of SNR the proposed StrMP-based channel estimation scheme will require higher pilot overhead to perform optimally.

Deep Learning–Based Channel Extrapolation and Multiuser Beamforming for RIS-aided Terahertz Massive MIMO Systems over Hybrid-Field Channels

The reconfigurable intelligent surface (RIS) is a promising technology for terahertz (THz) massive multiple-input multiple-output (MIMO) communication systems. However, acquiring high-dimensional channel state information (CSI) and realizing efficient active/passive beamforming for RIS are challenging owing to its cascaded channel structure and lack of signal processing units. To overcome these challenges, this study proposes a deep learning (DL)-based physical signal processing scheme for RIS-aided THz massive MIMO systems over hybrid far-near field channels wherein channel estimation with low pilot overhead and robust beamforming are implemented. Specifically, first, an end-to-end DL-based channel estimation framework that consists of pilot design, CSI feedback, subchannel estimation, and channel extrapolation is introduced. In this framework, only some RIS elements are first activated, a subsampling RIS channel is then estimated, and a DL-based extrapolation network is finally used to reconstruct the full-dimensional CSI. Next, to maximize the sum rate under imperfect CSI, a DL-based scheme is developed to simultaneously design hybrid active beamforming at the base station and passive beamforming at the RIS. Simulation results show that the proposed channel extrapolation scheme achieves better CSI reconstruction performance than conventional schemes while greatly reducing pilot overhead. Moreover, the proposed beamforming scheme outperforms conventional schemes in terms of robustness to imperfect CSI.

Innovative Approach of Spectral Efficiency Optimization over Various Pilot Reuse Factors

The Massive MIMO with TDD is breakthrough technology for spectral efficiency gains. The CSI is essential for spectral efficiency gains and CSI can be obtained by channel estimation methods. The channel estimation methods employ known pilot s sequences to estimate the channel before actual data transmission. However, the channel coherence is time and frequency limited, which reflects the trade-off between the resources available for pilots and those available for data in coherent block for transmission. The pilot sequences reuse in other cells can reduce pilot overhead, called pilot reuse. However potential interference is introduced, by pilot reuse, in the channel estimation phase, called pilot contamination. The aim is to determine optimum pilot reuse factor for better SE using low computational complexity estimation method. The sum averaged SE has been obtained for pilot reuse factor 1, 2, 4, 8 and 16 using MMSE, EW-MMSE and LS channel estimation methods. The obtained results reveals that the difference between values of SEs for f=1 to f=2 to f=4 is very low and performance difference between estimators decreases as pilot reuse factor increases, which allows to use LS estimator to get performance almost equal to MMSE with less computational complexity. Also, the pilot reuse factor f=4 found optimum among all for given constraint.

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.

Spectrum Allocation and User Scheduling Based on Combinatorial Multi-Armed Bandit for 5G Massive MIMO.

As a key 5G technology, massive multiple-input multiple-output (MIMO) can effectively improve system capacity and reduce latency. This paper proposes a user scheduling and spectrum allocation method based on combinatorial multi-armed bandit (CMAB) for a massive MIMO system. Compared with traditional methods, the proposed CMAB-based method can avoid channel estimation for all users, significantly reduce pilot overhead, and improve spectral efficiency. Specifically, the proposed method is a two-stage method; in the first stage, we transform the user scheduling problem into a CMAB problem, with each user being referred to as a base arm and the energy of the channel being considered a reward. A linear upper confidence bound (UCB) arm selection algorithm is proposed. It is proved that the proposed user scheduling algorithm experiences logarithmic regret over time. In the second stage, by grouping the statistical channel state information (CSI), such that the statistical CSI of the users in the angular domain in different groups is approximately orthogonal, we are able to select one user in each group and allocate a subcarrier to the selected users, so that the channels of users on each subcarrier are approximately orthogonal, which can reduce the inter-user interference and improve the spectral efficiency. The simulation results validate that the proposed method has a high spectral efficiency.

Joint Pilot Spacing and Power Optimization Scheme for Nonstationary Wireless Channel: A Deep Reinforcement Learning Approach

Pilot-assisted channel estimation techniques are essential for wireless communication systems. Most studies focus on the estimation algorithms and interpolation techniques. However, the design of pilot pattern is often neglected. In this letter, we propose a joint pilot spacing and power optimization scheme based on deep reinforcement learning (DRL) to address the mismatch problem of pilot configuration for nonstationary wireless channel. First, we model the adaptive pilot design decision-making process as a Markov Decision Process (MDP) to reduce pilot overhead and power loss. Then a deep Q-network (DQN) based learning algorithm is proposed to optimize the spacing and power of pilots so as to maximize estimation performance while reducing system cost. Simulation results show that the performance of the proposed approach is better than conventional pilot configuration algorithms. Moreover, we analyze the key factors that affect the performance of the proposed scheme.

Integrated Sensing and Communication With mmWave Massive MIMO: A Compressed Sampling Perspective

Integrated sensing and communication (ISAC) has opened up numerous game-changing opportunities for realizing future wireless systems. In this paper, we propose an ISAC processing framework relying on millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. Specifically, we provide a compressed sampling (CS) perspective to facilitate ISAC processing, which can not only recover the high-dimensional channel state information or/and radar imaging information, but also significantly reduce pilot overhead. First, an energy-efficient widely spaced array (WSA) architecture is tailored for the radar receiver, which enhances the angular resolution of radar sensing at the cost of angular ambiguity. Then, we propose an ISAC frame structure for time-varying ISAC systems considering different timescales. The pilot waveforms are judiciously designed by taking into account both CS theories and hardware constraints induced by hybrid beamforming (HBF) architecture. Next, we design the dedicated dictionary for WSA that serves as a building block for formulating the ISAC processing as sparse signal recovery problems. The orthogonal matching pursuit with support refinement (OMP-SR) algorithm is proposed to effectively solve the problems in the existence of the angular ambiguity. We also provide a framework for estimating the Doppler frequencies during payload data transmission to guarantee communication performances. Simulation results demonstrate the good performances of both communications and radar sensing under the proposed ISAC framework.

Channel estimation for reconfigurable intelligent surface-assisted mmWave based on Re‘nyi entropy function

This study focuses on channel estimation for reconfigurable intelligent surface (RIS)-assisted mmWave systems, in which the RIS is used to facilitate base-to-user data transfer. For beamforming to work with active and passive elements, a large-size cascade channel matrix should always be known. Low training costs are achieved by using the mmWave channels’ inherent sparsity. The research provides a unique compressive sensing-based channel estimation approach for reducing pilot overhead issues to a minimum. The proposed technique estimates channel data signals in a downlink for RIS-assisted mmWave systems. The mmWave systems often have a sparse distribution of signal sources due to the spatial correlations of the domains. This distribution pattern makes it possible to use compressive sensing methods to resolve the channel estimation issue. In order to decrease the pilot overhead, which is necessary to predict the channel, the proposed method extends the Re‘nyi entropy function as the sparsity-promoting regularizer. In contrast to conventional compressive sensing techniques, which necessitate an initial knowledge of the signal’s sparsity level, the presented method employs sparsity adaptive matching pursuit (SAMP) techniques to gradually determine the signal’s sparsity level. Furthermore, it introduces a threshold parameter based on the signal’s energy level to eliminate the sparsity level requirement. Extensive simulations show that the presented channel estimation approach surpasses the traditional OMP-based channel estimation methods in terms of normalized mean square error performance. In addition, the computational cost of channel estimation is lowered. Based on the simulations, our approach can estimate the channel well while reducing training overhead by a large amount.

Multi-Stage Training Optimization for Pilot Compression and Channel Estimation in Massive MIMO Systems Under Quasi-Sparse Channel Environment

The huge pilot overhead required for channel estimation is one of the key issues for massive multiple-input multiple-output (MIMO) systems. Existing compressed sensing and deep learning methods generally implement pilot compression under the assumption of the huge number of antennas and strict channel sparsity, while the channel estimation performance decreases sharply under quasi-sparse channel environment. Motivated by the powerful learning ability of deep learning for extracting the major characteristics of the target, we propose approximate message passing (AMP) algorithm-based multi-stage training optimization architecture to solve the above problem, where the whole system is considered as a deep neural network (DNN). In the first stage, the optimized sensing matrix of the AMP algorithm is learned by training to match the quasi-sparse channel. In the second stage, we optimize the linear coefficients and nonlinear shrinkage parameters of AMP to further improve the performance. In the third stage, all parameters are jointly optimized by training to make the whole system optimal. Numerical simulation results show that the proposed architecture can achieve high precision channel estimation under the premise of reducing pilot overhead effectively.

Channel Estimation for RIS-Aided Multi-User mmWave Systems With Uniform Planar Arrays

In this paper, we adopt a three-stage based uplink channel estimation protocol with reduced pilot overhead for an reconfigurable intelligent surface (RIS)-aided multi-user (MU) millimeter wave (mmWave) communication system, in which both the base station (BS) and the RIS are equipped with a uniform planar array (UPA). Specifically, in Stage I, the channel state information (CSI) of a typical user is estimated. To address the power leakage issue for the common angles-of-arrival (AoAs) estimation in this stage, we develop a low-complexity one-dimensional search method. In Stage II, a re-parameterized common BS-RIS channel is constructed with the estimated information from Stage I to estimate other users’ CSI. In Stage III, only the rapidly varying channel gains need to re-estimated. Furthermore, the proposed method can be extended to multi-antenna UPA-type users, by decomposing the estimation of a multi-antenna channel with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$J$ </tex-math></inline-formula> scatterers into estimating <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$J$ </tex-math></inline-formula> single-scatterer channels for a virtual single-antenna user. An orthogonal matching pursuit (OMP)-based method is proposed to estimate the angles-of-departure (AoDs) at the users. Simulation results demonstrate that the proposed algorithm significantly achieves high channel estimation accuracy, which approaches the genie-aided upper bound in the high signal-to-noise ratio (SNR) regime.

Triple-Structured Compressive Sensing-Based Channel Estimation for RIS-Aided MU-MIMO Systems

Reconfigurable intelligent surface (RIS) has been recognized as a potential technology for 5G beyond and attracted tremendous research attention. However, channel estimation for RIS-aided systems is still a critical challenge due to the excessive amount of parameters in the cascaded channel. The existing compressive sensing (CS)-based RIS estimation schemes only adopt incomplete sparsity, which induces redundant pilot consumption. In this paper, we analyze and exploit the specific triple-structured sparsity of the cascaded channel, i.e., the common column sparsity, structured row sparsity after offset compensation and the common offsets among all users. Furthermore, a novel on-grid Multi-user Triple-Structured-Compressive-Sensing simultaneous orthogonal matching pursuit (MTSCS-SOMP) algorithm along with an enhanced super-resolution (gridless) generalized iterative reweighted (MTSCS-IR) scheme are successively proposed. The former is practical and can be easily employed with low computational complexity, and the latter is further proposed to handle the severe power leakage problem encountered in mmWave channel estimations. Besides, we extend the sparsity property and algorithms from uniform linear array (ULA) configuration to uniform planar array (UPA), by transforming cascaded channel from matrix to tensor. Simulation results show that our approaches can significantly reduce pilot overhead over 50% and achieve enhanced performance on estimation accuracy.

Deep Learning-Based Nonstationary Channel Prediction in Tactical Vehicle-to-Vehicle Communication Environments

In this paper, we focus on the vehicle-to-vehicle dynamic channel in tactical communication environments, which shows time-varying and nonstationary characteristics due to the fast mobility, directional antennas, and harsh terrain. These situations present great challenges for the channel state information (CSI) acquisition. To obtain an accurate CSI and reduce pilot overhead, we propose a CSI predictor based on the long short-term memory (LSTM) network. As an improved recurrent neural network (RNN), LSTM units have an excellent learning result on both long- and short-term inputs by adding the gating mechanism. Using the outdated sampling CSI sequence as input data of LSTM units enables the predictor to extract complex data characteristics and capture the temporal law of the nonstationary channel. Simulation results are demonstrated to verify that the LSTM-based predictor has better performance than conventional algorithms in IEEE 802.11p standard. Additionally, the key factors that affect the performance of the proposed predictor are further analyzed.

Two-Stage Channel Estimation for Semi-Passive RIS-Assisted Millimeter Wave Systems

In a reconfigurable intelligent surface (RIS) assisted millimeter Wave (mmWave) communication system, the channel coefficient increases exponentially with the number of RIS elements which results in expensive pilot overhead. Most previous works have proposed some channel estimation algorithms for the estimation accuracy of cascaded channels, which have improved the estimation accuracy, but the pilot overhead is discouraging in the estimation process. To improve the channel estimation accuracy with reduced pilot overhead, we propose a two-stage channel estimation protocol by exploiting semi-passive elements and the coherent time difference of the channel, where the quasi-static channel between the base stations (BS) and RIS is estimated at the RIS, and the user (UE)-RIS time-varying channel is estimated at the BS. In the first stage, we formulate the BS-RIS channel estimation as a mathematical optimization problem by an iterative weighting method and then propose a gradient descent (GD)-based algorithm to solve it. In the second stage, we first transform the received the UE-RIS signal model into an equivalent parallel factor (PARAFAC) tensor model and estimate the UE-RIS channel by the least-squares (LS) algorithm. The simulation results show that the proposed method has better estimation accuracy than the LS, compression sensing (CS) and minimum mean square error (MMSE) methods with less pilot overhead, and the spectral efficiency is improved by at least 10.5% compared to the other three methods.

Impact of Subcarrier Allocation and User Mobility on the Uplink Performance of Multiuser Massive MIMO-OFDM Systems

This paper considers the uplink performance of a multi-user massive multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) system with mobile users. Mobility brings two major problems to a MIMO-OFDM system: inter carrier interference (ICI) and channel aging. In practice, it is common to allot multiple contiguous subcarriers to a user as well as schedule multiple users on each subcarrier. Motivated by this, we consider a general subcarrier allocation scheme and derive expressions for the ICI power, uplink signal to interference plus noise ratio and the achievable uplink sum-rate, taking into account the ICI and the multi-user interference due to channel aging. We show that the system incurs a near-constant ICI power that depends linearly on the ratio of the number of users per subcarrier to the number of subcarriers per user, nearly independently of how the UEs distribute their power across the subcarriers. Further, we exploit the coherence bandwidth of the channel to reduce the length of the pilot sequences required for uplink channel estimation. We consider both zero-forcing and maximal-ratio combining at the receiver and compare the respective sum-rate performances. In either case, the proposed subcarrier allocation scheme leads to significantly higher sum-rates compared to previous work, owing to the near-constant ICI property as well as the reduced pilot overhead.

Distributed Machine Learning Based Downlink Channel Estimation for RIS Assisted Wireless Communications

The downlink channel estimation requires a huge pilot overhead in the reconfigurable intelligent surface (RIS) assisted communication system. By exploiting the powerful learning ability of the neural network, the machine learning (ML) technique can be used to estimate the high-dimensional channel from a few received pilot signals at the user. However, since the training dataset collected by the single user only contains the information of part of the channel scenarios of a cell, the neural network trained by the single user is not able to work when the user moves from one channel scenario to another. To solve this challenge, we propose to leverage the distributed machine learning (DML) technique to enable the reliable downlink channel estimation. Specifically, we firstly build a downlink channel estimation neural network shared by all users, which can be collaboratively trained by the BS and the users with the help of the DML technique. Then, we further propose a hierarchical neural network architecture to improve the channel estimation accuracy, which can extract different channel features for different channel scenarios. Simulation results show that compared with the neural network trained by the single user, the proposed DML based neural networks can achieve better estimation performance with the reduced pilot overhead for all users from different scenarios.

Improved Pilot Designs for Enhancing Connectivity in Multicarrier Massive MIMO Systems

This letter proposes improved pilot designs to enhance the connectivity of multicarrier massive MIMO systems. Exploiting the fact that orthogonal frequency-division multiplexing (OFDM) training symbols end with zero samples, the proposed pilot designs reduce pilot overhead by truncating the zero samples and/or intentionally using them for a guard interval without affecting the channel estimation quality. The proposed designs allow a massive MIMO system either to serve more users with a fixed amount of training time, or requires less training time for a fixed number of users. Numerical results obtained for a cell-free massive MIMO system (as an application use case) demonstrate significant improvements in connectivity and spectral efficiency by the proposed designs over the conventional designs.

Millidegree-Level Direction-of-Arrival Estimation and Tracking for Terahertz Ultra-Massive MIMO Systems

Terahertz (0.1-10 THz) wireless communications are expected to meet 100+ Gbps data rates for 6G communications. Being able to combat the distance limitation with reduced hardware complexity, ultra-massive multiple-input multiple-output (UM-MIMO) systems with hybrid dynamic array-of-subarrays (DAoSA) beamforming are a promising technology for THz wireless communications. However, fundamental challenges in THz DAoSA systems include millidegree-level three-dimensional direction-of-arrival (DoA) estimation and millisecond-level beam tracking with reduced pilot overhead. To address these challenges, an off-grid subspace-based DAoSA-MUSIC and a deep convolutional neural network (DCNN) methods are proposed for DoA estimation. Furthermore, by exploiting the temporal correlations of the channel variation, an augmented DAoSA-MUSIC-T and a convolutional long short-term memory (ConvLSTM) solutions are further developed to realize DoA tracking. Extensive simulations and comparisons on the proposed subspace- and deep-learning-based algorithms are conducted. Results show that both DAoSA-MUSIC and DCNN achieve super-resolution DoA estimation and outperform existing solutions, while DCNN performs better than DAoSA-MUSIC at a high signal-to-noise ratio. Moreover, DAoSA-MUSIC-T and ConvLSTM can capture fleeting DoA variation with an accuracy of 0.1° within milliseconds, and reduce 50% pilot overhead. Compared to DAoSA-MUSIC-T, ConvLSTM can tolerate large angle variation and remain robust over a long duration.

Federated Online Deep Learning for CSIT and CSIR Estimation of FDD Multi-User Massive MIMO Systems

In this paper, we propose a federated online training framework for deep neural network (DNN)-based channel estimation (CE) in frequency-division duplexing (FDD) multi-user massive multiple-input multiple-output (MU-MIMO) systems. The proposed DNN consists of two stages, where Stage-I explores the partial common sparsity structure among the users, while Stage-II estimates the channel state information (CSI) with reduced pilot overhead leveraging the common support information provided by Stage-I. To realize online training, we first propose three axioms for a legitimate online loss function, based on which we develop the federated online training algorithm with convergence analysis. The proposed two-tier DNN is trained online at the base station (BS) based on real-time pilot measurements distributively fed back from the users without the need of true channel labels, and the estimates for the CSI at the transmitter (CSIT) can be simultaneously generated in real-time. Meanwhile, the weights of Stage-II can be broadcasted to the users for real-time estimation of the CSI at the receiver (CSIR) at each user. Simulation shows that the proposed solution achieves higher CE performance than traditional compressive sensing (CS)-based algorithms while enjoying much faster computation. The solution is also robust to the channel model mismatches induced by the change of propagation environment, and is able to track the time-varying channel model.

Sparse, Group-Sparse, and Online Bayesian Learning Aided Channel Estimation for Doubly-Selective mmWave Hybrid MIMO OFDM Systems

Sparse, group-sparse and online channel estimation is conceived for millimeter wave (mmWave) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. We exploit the angular sparsity of the mmWave channel impulse response (CIR) to achieve improved estimation performance. First a sparse Bayesian learning (SBL)-based technique is developed for the estimation of each individual subcarrier's quasi-static channel, which leads to an improved performance versus complexity trade-off in comparison to conventional channel estimation. Then a novel group-sparse Bayesian learning (G-SBL) scheme is conceived for reducing the channel estimation mean square error (MSE). The salient aspect of our G-SBL technique is that it exploits the frequency-domain (FD) correlation of the channel's frequency response (CFR), while transmitting pilots on only a few subcarriers, thus it has a reduced pilot overhead. A low complexity (LC) version of G-SBL, termed LCG-SBL, is also developed that reduces the computational cost of the G-SBL significantly. Subsequently, an online G-SBL (O-SBL) variant is designed for the estimation of doubly-selective mmWave MIMO OFDM channels, which has low processing delay and exploits temporal correlation as well. This is followed by the design of a hybrid transmit precoder and receive combiner, which can operate directly on the estimated beamspace domain CFRs, together with a limited channel state information (CSI) feedback. Our simulation results confirms the accuracy of the analysis.

Group Successive Interference Cancellation Assisted Semi-Blind Channel Estimation in Multi-Cell Massive MIMO-NOMA Systems

Both non-orthogonal multiple access (NOMA) and massive multiple-input multiple-output (MIMO) are the promising techniques to satisfy the foreseeable massive connectivity requirements. In this letter, a novel semi-blind channel estimation method is proposed for multi-cell massive MIMO-NOMA systems, in which a group successive interference cancellation (GSIC) assisted method is developed to mitigate pilot contamination. Specifically, the users in each cell are divided into multiple groups and the same pilot sets are reused by the different groups in order to reduce pilot overhead. Besides, by following the NOMA principle, a GSIC assisted method is proposed to eliminate inter-group pilot contamination. In simulations, it is shown that the proposed channel estimation method is capable of reducing the overlapping probability of different groups as the number of receiving antennas increases. In addition, the proposed scheme outperforms the conventional channel estimation methods in terms of normalized mean square error (NMSE) performance.