Channel Temporal Correlation Research Articles

Interleaved Training for Massive MIMO Downlink via Exploring Channel Temporal Correlation

Interleaved Training for Massive MIMO Downlink via Exploring Channel Temporal Correlation

Temporal Correlation Characteristics of Air-to-Ground Wireless Channel With UAV Wobble

Air-to-ground (A2G) communication based on Unmanned aerial vehicle (UAV) is an important part of the future communication system. In this paper, an A2G channel model with UAV three-dimensional (3D) wobbles (pitch, roll, and yaw) based on the geometry-based stochastic model (GBSM) is proposed. On this basis, the UAV’s internal vibration is modeled as a sinusoidal random process, and the UAV wobble caused by the atmospheric flow is modeled as the uniform distribution random process. We derive the channel temporal correlation function (CF) with UAV 3D wobbles, analyze the variation of the temporal CF with different carrier frequencies, and amplitudes of the wobble angles. It is found that, even if the UAV wobbles slightly, the channel temporal correlation will be significantly affected. Numerical results show that the channel CF will decrease rapidly with the increase of the amplitudes of wobble angles and the carrier frequency. Therefore, the coherence time of millimeter wave (mmWave) band is significantly less than that of sub-6 GHz band. The consistency of simulation results and measurement results in published papers ensures the availability of the proposed model. For the MUAVs scenario, when the distance between different UAVs is much greater than the wavelength, the A2G channels between different UAVs and user equipment (UE) on the ground are not correlated to each other, and the temporal auto-correlation function (ACF) of each UAV is the same as that of the SUAV scenario. This work contributes to the theoretical exploration and system design of A2G communication based on UAV.

Impact of Channel Aging on Dual-Function Radar-Communication Systems: Performance Analysis and Resource Allocation

In conventional dual-function radar-communication (DFRC) systems, the radar and communication channels are routinely estimated at fixed time intervals based on their worst-case operation scenarios. Such situation-agnostic repeated estimations cause significant training overhead and dramatically degrade the system performance, especially for applications with dynamic sensing/communication demands and limited radio resources. In this paper, we leverage the channel aging characteristics to reduce training overhead and to design a situation-dependent channel re-estimation interval optimization-based resource allocation in a multi-target tracking DFRC system. Specifically, we exploit the channel temporal correlation to predict radar and communication channels for reducing the need for training preamble retransmission. Then, we characterize the channel aging effects on the Cramer-Rao lower bounds (CRLBs) for radar tracking performance analysis and achievable rates with maximum ratio transmission (MRT) and zero-forcing (ZF) transmit beamforming for communication performance analysis. In particular, the aged CRLBs and achievable rates are derived as closed-form expressions with respect to the channel aging time, bandwidth, and power. Based on the analyzed results, we optimize these factors to maximize the average total aged achievable rate subject to individual target tracking precision demand, communication rate requirement, and other practical constraints. Since the formulated problem belongs to a non-convex problem, we develop an efficient one-dimensional search based optimization algorithm to obtain its suboptimal solutions. Finally, simulation results are presented to validate the correctness of the derived theoretical results and the effectiveness of the proposed allocation scheme.

Channel temporal correlation-based optimization method for imperfect underwater acoustic channel state information

The rapid time variations and large channel estimation errors in underwater acoustic (UWA) channels mean that transmitters for adaptive resource allocation quickly become outdated and provide inaccurate channel state information (CSI). This results in poor resource allocation efficiency. To address this issue, this paper proposes an optimization approach for imperfect CSI based on a Gauss–Markov model and the per-subcarrier channel temporal correlation (PSCTC) factor. The proposed scheme is applicable to downlink UWA orthogonal frequency division multiple access systems. The proposed PSCTC factors are measured, and their long-term stability is verified using data recorded in real-world sea tests. Simulation and experimental results show that the optimized CSI effectively mitigates the effects of the temporal variability of UWA channels. It demonstrates that the resource allocation scheme using optimized CSI achieves a higher effective throughput and a lower bit error rate than both imperfect CSI and the CSI predicted by the recursive least-squares (RLS) algorithm.

Channel estimation based on superimposed pilot and weighted averaging

Channel estimation based on superimposed pilot (SP) is a challenge in orthogonal frequency division multiplexing (OFDM) systems. To reduce the pilot data interference in the SP and estimate the channel state information accurately, a weighted averaging (WA) channel estimation method based on the superimposed pilot is proposed in this paper. At the transmitter, two signals with data symbols and pilot symbols superimposed at different subcarriers are transmitted. At the receiver, the elimination scheme is proposed to remove the pilot data interference. Based on the temporal correlation of wireless channels, the WA method is used to reduce the interference caused by additive white Gaussian noise in the channel. Simulation results verify that the proposed method can be applied to different channel scenarios. It has better normalized mean square error and bit error rate performance than other existing methods, and the superimposed pilot can improve the throughput of wireless communication systems.

Performance analysis of reconfigurable intelligent surface assisted systems under channel aging

Reconfigurable intelligent surfaces (RISs) have attracted significant attention due to their capability in customizing wireless communication environments to improve system performance. In this study, we investigate the performance of an RIS-assisted multi-user multiple-input single-output wireless communication system, considering the impact of channel aging caused by users' relative movements. In particular, first, we propose a model incorporating the joint effects of channel aging and channel estimation errors to investigate the performance of the RIS-assisted system. Then, we derive novel closed-form expressions for characterizing the sum spectral efficiency with zero-forcing precoding. From our analysis, we unveil that an increase in the temporal channel correlation coefficient, the number of base station antennas, and the received power at the users could help improve system performance. Furthermore, increasing the number of reflecting elements <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> of the RIS generally yields a good system performance, but with a diminishing return when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> is sufficiently large. Finally, simulation results are presented to validate the accuracy of the analytical results.

Sparse Channel Estimation via Hierarchical Hybrid Message Passing for Massive MIMO-OFDM Systems

In this paper, we investigate a sparse channel estimation problem for broadband massive multiple-input-multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. We propose a hidden Markov model to capture the structured sparsity and temporal dependency characteristic of massive MIMO-OFDM channels in the angle-delay domain, and this probability model exhibits extensive adaptability to different realistic propagation scenarios. Then we solve the channel estimation problem based on a novel optimization framework named constrained Bethe free energy (BFE) minimization, which is valid for a generic statistical model. Under this systematic theoretical framework, a hierarchical hybrid message passing (HHMP) algorithm is proposed to track dynamic channel parameters recursively. The proposed method can adaptively learn the sparse structure and temporal correlation of multiuser channels without requiring the knowledge of hidden Markov channel parameters. Numerical simulations demonstrate that the proposed HHMP algorithm can accurately estimate angle-delay domain channels with reduced iteration times and pilot overhead.

A Hybrid Pilot Beamforming and Channel Tracking Scheme for Massive MIMO Systems

In massive MIMO systems, the effective channel state information (CSI) is an essential prerequisite for the beamforming (BF) design. While there is a handful of previously proposed compressive sensing (CS)-based channel estimation algorithms in the literature, the large BF gain provided by the massive MIMO array has not been fully exploited in the channel estimation stage. In order to obtain higher BF gain and better estimation performance with less pilot overhead, we study the joint design of the transmitting and receiving hybrid pilot BF as well as the associated channel tracking scheme. Specifically, a Markov prior is used to model the temporal correlation in massive MIMO channels over different time slots. Then, the hybrid pilot BF is optimized by maximizing the mutual information between the channel measurements and the corresponding downlink sparse channels with the Markov prior. Following, we derive an efficient channel tracking algorithm called Turbo Bayesian Inference (Turbo-BI) to solve the resulting CS problem and generate the channel prior information required to calculate the mutual information for the optimization of hybrid pilot BF in the next time slot. The proposed Turbo-BI can exploit both the sparsity and the temporal correlation of massive MIMO channels to enhance the estimation performance. Finally, simulations show that our proposed algorithm can achieve significant gain over the existing state-of-the-art baselines.

Combination of temporal‐channels correlation information and bilinear feature for action recognition

In this study, the authors focus on improving the spatio–temporal representation ability of three‐dimensional (3D) convolutional neural networks (CNNs) in the video domain. They observe two unfavourable issues: (i) the convolutional filters only dedicate to learning local representation along input channels. Also they treat channel‐wise features equally, without emphasising the important features; (ii) traditional global average pooling layer only captures first‐order statistics, ignoring finer detail features useful for classification. To mitigate these problems, they proposed two modules to boost 3D CNNs’ performance, which are temporal‐channel correlation (TCC) and bilinear pooling module. The TCC module can capture the information of inter‐channel correlations over the temporal domain. Moreover, the TCC module generates channel‐wise dependencies, which can adaptively re‐weight the channel‐wise features. Therefore, the network can focus on learning important features. With regards to the bilinear pooling module, it can capture more complex second‐order statistics in deep features and generate a second‐order classification vector. We can get more accurate classification results by combining the first‐order and second‐order classification vector. Extensive experiments show that adding our proposed modules to I3D network could consistently improve the performance and outperform the state‐of‐the‐art methods. The code and models are available at https://github.com/caijh33/I3D_TCC_Bilinear.

Time-Varying Downlink Channel Tracking for Quantized Massive MIMO Networks

This paper proposes a Bayesian downlink channel estimation framework for time-varying massive MIMO networks. In particular, the quantization effects at the receiver are considered. In order to fully exploit the sparsity and time correlations of channels, we formulate the time-varying massive MIMO channel as the simultaneously sparse signal model. Then, we propose a sparse Bayesian learning (SBL) framework to estimate the model parameters of the sparse virtual channel. The expectation maximization (EM) algorithm is employed to reduce complexity. Specifically, the factor graph and the general approximate message passing (GAMP) algorithms are used to compute the desired posterior statistics in the expectation step, so that high-dimensional integrals over the marginal distributions can be avoided. The non-zero supporting vector of the virtual channel is then obtained from channel statistics by a k-means clustering algorithm. After that, the reduced dimensional GAMP-based scheme is designed to make the full use of the channel temporal correlation so as to enhance the virtual channel tracking accuracy. Finally, the efficacy of the proposed framework is demonstrated through simulations.

Machine Learning-Based Channel Prediction in Massive MIMO With Channel Aging

To support the ever increasing number of devices in massive multiple-input multiple-output (mMIMO) systems, an excessive amount of overhead is required for conventional orthogonal pilot-based channel estimation schemes. To circumvent this fundamental constraint, we design a machine learning (ML)-based time-division duplex scheme in which channel state information (CSI) can be obtained by leveraging the temporal channel correlation. The presence of the temporal channel correlation is due to the stationarity of the propagation environment across time. The proposed ML-based predictors involve a pattern extraction implemented via a convolutional neural network, and a CSI predictor realized by an autoregressive (AR) predictor or an autoregressive network with exogenous inputs recurrent neural network. Closed-form expressions for the user uplink and downlink achievable spectral efficiency and average per-user throughput are provided for the ML-based time division duplex schemes. Our numerical results demonstrate that the proposed ML-based predictors can remarkably improve the prediction quality for both low and high mobility scenarios, and offer great performance gains on the per-user achievable throughput.

A Novel CSI Feedback Approach for Massive MIMO Using LSTM-Attention CNN

In this paper, a novel mechanism is studied to improve the performance of the channel state information (CSI) feedback in massive multiple-input multiple-output (MIMO) systems. The proposed mechanism encompasses convolutional neural network (CNN)-based CSI compression and reconstruction structure. In this structure, the long-short term memory (LSTM) is adopted to learn temporal correlation of channels, and then, an attention mechanism is developed to perceive local information and automatically weight feature information. In addition, the CNN framework is further adjusted to reduce the number of training parameters and accelerate CSI recovery. The CNN structure with optimal training parameters can be achieved via offline iterative training and learning based on various training datasets. Comparative experimental studies demonstrate the effectiveness of the proposed approach that the trained CNN can obtain the higher feedback accuracy and better system performance in massive MIMO CSI online feedback reconstruction. Moreover, the proposed scheme in the less parameters-based neural network owns a higher performance with lower computational complexity compared to the conventional algorithms.

User Location Tracking in Massive MIMO Systems via Dynamic Variational Bayesian Inference

Accurate user location tracking is the key to enable location-based services and assist communications in 5 G networks. The massive multiple-input multiple-output (MIMO) technology employed in 5 G networks could potentially provide accurate user localization due to increased spectral efficiency and high directivity. In this paper, we propose an efficient user location tracking algorithm in massive MIMO systems. Firstly, we propose a temporal Markov group-sparse (TMGS) model based on a grid reference to capture the probabilistic temporal correlation and group sparsity of the massive MIMO channels jointly. Then we propose a dynamic variational Bayesian inference (D-VBI) algorithm to handle the TMGS priors under ill-conditioned measurement matrix in the location tracking problem. The proposed D-VBI can jointly recover the user's coarse location in the grid reference and refine the off-grid points to automatically learn the user's exact location to high accuracy. Moreover, the TMGS-based D-VBI algorithm can provide prior information about the user's next location and the possible arriving directions of the future channels to the consecutive time slot to improve the location tracking accuracy. Finally, we verify the superior performance of the proposed location tracking algorithm by extensive simulations.

A channel state information updating method based on the first-order Gauss Markov model under time-varying underwater acoustic channel

Because of the time-varying characteristic and the large propagation delay in underwater acoustic (UWA) channel, adaptive resource allocation in UWA orthogonal frequency-division multiplexing access (OFDMA) system cannot be performed with the assumption of perfect channel state information (CSI) at the transmitter. Therefore, this paper focuses on the imperfect CSI and proposes a CSI updating method to reduce the impact of imperfect CSI on the performance of resource allocation under time-varying UWA channel. First, we analyze the channel estimation error of OFDM system under time-varying UWA channel and define the per-subcarrier channel temporal correlation (PSCTC). Finally, a CSI updating method based on the first-order Gauss-Markov model (GM-CSI) is proposed for optimizing CSI feedback in the UWA channel with large propagation delay, where the channel estimation error and PSCTC factor are considered as two influencing factors in this model. Simulation results show that the GM-CSI can effectively mitigate the effect of time on CSI effectiveness, and the resource allocation by using GM-CSI has higher effective throughput and lower BER than that of imperfect CSI.

Power Control and Frequency Band Selection Policies for Underlay MIMO Cognitive Radio

We study power control and frequency band selection policies for multi-band underlay MIMO cognitive radio with the objective of maximizing the rate of a secondary user (SU) link while limiting the interference leakage toward primary users (PUs) below a threshold. The goal of the SU in each policy is to select one frequency band in each time slot and determine the transmit power. To limit the interference toward PU in time-varying channels, we propose fixed and dynamic transmit power control schemes which depend on PU traffic and the temporal correlation of channels between the SU and the PU. We study the performance of frequency band selection policies that use fixed or dynamic power control. We show that dynamic frequency band selection policies, e.g., policies based on multi-armed bandit framework, wherein SU selects a different frequency band in each slot, result in higher interference toward PU as compared to the fixed band policy wherein SU stays on one band. We also provide an expression for the gap between the rate achieved by SU under a clairvoyant policy and the fixed band policy. It is observed that this gap reduces with increased temporal correlation and with increased number of SU antennas.

Throughput Enhancement Based on Optimized Regularized Particle Filter for H-CRAN

The fifth-generation technology is emerging with various real-time applications that demand high data rate. The number of connected devices is expected to increase. However, spectral and energy resources are limited. Therefore, it is challenging to meet users satisfaction. Thus, the necessity for a structure that can sustain real-time performance of wireless communication systems is pressing. This paper presents an efficient radio resource allocation scheme using regularized particle filter with optimized kernel size and kernel bandwidth, and Monte Carlo Markov chain move step based on metropolis algorithm is used to estimate next state of channel. Channel state is calculated from the temporal channel correlation using maximum likelihood estimation. Throughput for the next user state is predicted using posterior probability with normalized weights. The main aim of this paper is to observe the user throughput. The problem is modeled as throughput maximization subject to channel state. The optimization problem is formulated as a non convex optimization and solved using branch and bound method. It has been shown in the simulation results that the average throughput is increased by ${\text{5.94}\%}{\text{--52.98}\%}$ compared to sequential importance sampling with resampling (SISR) method. Therefore, the RPF scheme has proved to be efficient by its remarkable increase in user throughput compared to the SISR particle filter algorithm.

Downlink Channel Estimation in Massive Multiple-Input Multiple-Output with Correlated Sparsity by Overcomplete Dictionary and Bayesian Inference

We exploited the temporal correlation of channels in the angular domain for the downlink channel estimation in a massive multiple-input multiple-output (MIMO) system. Based on the slow time-varying channel supports in the angular domain, we combined the channel support information of the downlink angular channel in the previous timeslot into the channel estimation in the current timeslot. A downlink channel estimation method based on variational Bayesian inference (VBI) and overcomplete dictionary was proposed, in which the support prior information of the previous timeslot was merged into the VBI for the channel estimation in the current timeslot. Meanwhile the VBI was discussed for a complex value in our system model, and the structural sparsity was utilized in the Bayesian inference. The Bayesian Cramér–Rao bound for the channel estimation mean square error (MSE) was also given out. Compared with other algorithms, the proposed algorithm with overcomplete dictionary achieved a better performance in terms of channel estimation MSE in simulations.

Exploiting Dynamic Sparsity for Downlink FDD-Massive MIMO Channel Tracking

Accurate channel tracking with a small pilot overhead is vital for real-time massive multiple-input and multiple-output (MIMO) communication over a dynamic channel. Recently, compressive sensing has been applied to reduce the pilot overheads by exploiting the spatial and/or temporal correlation of massive MIMO channels. However, most existing channel estimation and tracking algorithms are based on oversimplified channel models with restrictive assumptions, and thus perform poorly under realistic channels. In this paper, we consider downlink frequency-division duplexing-massive MIMO system operating with limited scattering around the base station and flat fading channel is considered. We propose a two-dimensional Markov Model (2D-MM) to capture the 2-D dynamic sparsity (i.e., structured sparsity in the spatial domain and probabilistic temporal dependency of channel in the temporal domain) of massive MIMO channels. The 2D-MM has the flexibility to model different propagation environments in practice. We derive an effective message passing algorithm called dynamic turbo orthogonal approximate message passing (D-TOAMP) to recursively track a dynamic massive MIMO channel with a 2D-MM prior. The proposed D-TOAMP algorithm does not require knowledge of the 2D-MM channel parameters, which could be automatically learned through the expectation maximization framework. Extensive simulations show that the proposed D-TOAMP can achieve significant gains over the existing algorithms under realistic channels.

Nonlinear Hybrid Precoding for Coordinated Multi-Cell Massive MIMO Systems

This paper examines nonlinear hybrid precoding with minimum mean square error (MMSE)-vector perturbation (VP) for multi-cell massive multiple-input multiple-output (MIMO) systems. Two-timescale channel state information (CSI) is assumed, which consists of short-term noisy observations of the RF-precoded MIMO channel, and perfect knowledge of the long-term channel temporal and spatial correlation. By exploiting the low-dimensional effective CSI, we propose to estimate the instantaneous realization of the high-dimensional CSI via Kalman filtering. The CSI estimate is then utilized for RF precoding in consideration of centralized and distributed MMSE-VP at baseband. By abstracting the effect of nonlinear baseband precoding, RF precoding is separately formulated as a solution to balance the error performance of signal detection with the accuracy of channel tracking. To solve such nonconvex problems, we develop Cayley transformation-based gradient descent algorithms. Numerical results demonstrate the benefits of incorporating CSI tracking into hybrid precoding from its superior bit error rate to other transmit spatial correlation-based baselines, and its improved resilience to the channel estimation errors over the fully digital counterpart.

Sparse Bayesian Learning for the Time-Varying Massive MIMO Channels: Acquisition and Tracking

The low-rank property of the channel covariances can be adopted to reduce the overhead of the channel training in massive MIMO systems. In this paper, with the help of the virtual channel representation, we apply such property to both time-division duplex and frequency-division duplex systems, where the time-varying channel scenarios are considered. First, we formulate the dynamic massive MIMO channel as one sparse signal model. Then, an expectation maximization-based sparse Bayesian learning framework is developed to learn the model parameters of the sparse virtual channel. Specifically, the Kalman filter (KF) and the Rauch–Tung–Striebel smoother are utilized to track the model parameters of the uplink (UL) spatial sparse channel in the expectation step. During the maximization step, a fixed-point theorem-based algorithm and a low-complex searching method are constructed to recover the temporal varying characteristics and the spatial signatures, respectively. With the angle reciprocity, we recover the downlink (DL) model parameters from the UL ones. After that, the KF with the reduced dimension is adopt to fully exploit the channel temporal correlations to enhance the DL/UL virtual channel tracking accuracy. A monitoring scheme is also designed to detect the change of model parameters and trigger the relearning process. Finally, we demonstrate the efficacy of the proposed schemes through the numerical simulations.