Tracking Of Time-varying Channels Research Articles

Adaptive Data-Aided Time-Varying Channel Tracking for Massive MIMO Systems

Adaptive Data-Aided Time-Varying Channel Tracking for Massive MIMO Systems

EM-EKF fast time-varying channel estimation based on superimposed pilot for high mobility OFDM systems

The scarcity of wireless spectrum resources and high mobility have brought serious challenges to orthogonal frequency division multiplexing (OFDM) communication systems. To improve spectral efficiency and combat fast time-varying channel fading, this paper studies the OFDM system with high mobility based on superimposed pilots, and adopts a basis expansion model (BEM) to describe fast time-varying channels. An iterative channel estimation algorithm combining expectation–maximization (EM) and extended Kalman filtering (EKF) is proposed, which is called EM-EKF in this paper. It uses EM to calculate the parameter matrix, measured values and the covariance of the process noise of the unknown first-order time-varying autoregressive (TVAR) model to obtain the optimal estimation. To further enhance the system’s robustness for fast time-varying channel fading, EKF and smoothing algorithms are jointly used for time-varying channel tracking. The results show that compared with the existing representative channel estimation algorithms, the iterative EM-EKF algorithm proposed in this paper not only solves the problem of unknown prior information, but also significantly outperforms other non-iterative algorithms, and the performance of the proposed algorithm is similar to that of the iterative EKF algorithm, which is more suitable for the actual OFDM communication systems with high mobility.

Recent Progress on Novel DSP Techniques for Mode Division Multiplexing Systems: A Review

This paper provides an overview of latest progress on the novel advanced digital signal processing (DSP) techniques for long-haul mode division multiplexing (MDM) systems with high capacity. Space-division multiplexing (SDM) techniques have been developed for a period to increase the capacity of optical communication system by at least one order of magnitude through MDM techniques using few-mode fibers (FMFs) or multi-core multiplexing (MCM) using multi-core fibers (MCFs). The signals in MDM links are mainly impaired by the linear and nonlinear effects in FMFs, making DSP techniques become necessary to undo these impairments. In this paper, we not only review the advanced multiple-input multiple-output (MIMO) DSP techniques for compensating linear impairments in FMFs, but also enclose the state of the art of novel DSP techniques to deal with nonlinear effects. Firstly, we introduce the MIMO schemes for equalizing modal crosstalk and modal dispersion. Then, we focus on the fast tracking of time-varying (TV) channels in FMF links through frequency-domain (FD) recursive least square (RLS) algorithm. Besides, we also cover the mainstream DSP solutions for mode-dependent loss (MDL) and several possible methods to compensate nonlinearity in FMF. Moreover, artificial intelligence (AI) technologies are also discussed for its high nonlinearity tolerance and may bring a revolution in MDM systems on the process of channel equalization, link monitoring, etc. In the end, a brief conclusion and perspective will be provided.

Data Aided MSE-Optimal Time Varying Channel Tracking in Massive MIMO Systems

The temporal variations in the wireless propagation channel, referred to as channel aging, cause a mismatch between the estimated channel and the channel state at the time of data detection. This mismatch has been shown to severely impair the performance of massive MIMO systems. In this paper, we present data aided MSE-optimal channel tracking algorithms to decode the received symbols and update the channel estimates at the base station (BS) and the UEs. These algorithms combine ideas from Kalman filtering for channel tracking and deterministic equivalent analysis for symbol estimation. In the uplink case, we first develop a minimum mean squared error (MMSE) data estimator and the MSE-optimal channel predictor based on the Kalman filtering algorithm. We analytically show that the updated channel estimate obtained from the estimates of the data symbols leads to significantly larger signal to interference-plus-noise ratio (SINR), and hence achievable rate, compared to that obtained from the channel estimate based on pilot symbols. Following this, in the downlink case, we develop an algorithm to track the effective channel at the UEs and analyze its MSE, SINR and achievable rate performance. We show that tracking the effective downlink channel mitigates the effects of channel aging and leads to improved performance. However, since the beamforming matrices at the BS are not updated, downlink channel tracking is not as effective as uplink channel tracking. Finally, via Monte Carlo simulations, we validate our derived results, and demonstrate the gains achievable by tracking the time-varying channels in massive MIMO systems.

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.

Time Varying Channel Tracking With Spatial and Temporal BEM for Massive MIMO Systems

In this paper, we design a channel tracking method for massive multiple-input multiple-output systems under both time-varying and spatial-varying circumstances. By exploiting the characteristics of massive antenna array, a spatial-temporal basis expansion model is proposed to reduce the effective dimension of uplink/downlink channel, which decomposes channel state information into time-varying spatial information and gain information. We first model the user’s movement as the one-order unknown Markov process, whose parameters are blindly obtained by expectation and maximization learning. Then, the uplink time-varying spatial information can also be blindly tracked by unscented Kalman filter and Taylor series expansion of the steering vector, while the rest of uplink channel gain information can be trained by only a few pilot symbols. Due to physical angle reciprocity, the spatial information of the downlink channel can be immediately computed from the uplink counterpart, which greatly reduces the complexity of downlink channel tracking. Various numerical results are provided to demonstrate the effectiveness of the proposed method.

Time-Varying Channel Tracking for Amplify-and-Forward Relay Network in High Doppler Spread

Next generation wireless communication technologies such as wireless metropolitan area network, long-term evolution (LTE), and LTE advanced are designed to deploy cooperative relaying incorporated with orthogonal frequency division multiplexing system. In addition to the higher data rate, these technologies allow users to have a faster mobility than the previous standards. However, due to the fast movement, Doppler frequency causes the carrier frequency offset resulting in intercarrier interference. Modeling and estimating this type of channel play a vital role to fulfill the data rate requirement of the network. In this paper, we develop a high mobility channel estimation method for amplify-and-forward relay-based network. Specifically, we use basis expansion modeling (BEM) to capture the time variation of the channel. Using pilot symbols, the BEM coefficients are estimated by least square and linear minimum mean square error estimators to reconstruct the channel in both time and frequency domains. In addition to the estimators, Cramer–Rao lower bound has been derived as a benchmark of the estimation performance of the channel estimators. It has been shown that the time-domain channel estimation method is simpler and can approximate the channel more efficiently than frequency-domain estimation in very high Doppler spread scenario.

Time-varying Channel Tracking and Prediction Based on Complex-valued Back-propagation Neural Network

The Complex-valued Back-propagation Neural Network (CVBPNN) algorithm is applied for time-varying channel tracking and prediction in communication system and is verified in the communication simulation system. Firstly, the CVBPNN tracking model is constructed, the hidden layer and output layer of which have non-linear and linear activation function respectively, and the delayed CSI is looked as the supervised signal for the model training to acquire model parameters. Then the tracking parameters is transferred to the prediction neural network which has the same network architecture as the tracking neural network, and the network is used to forward prediction for the output of the tracking model. Simulation results show that the proposed algorithm has less prediction error, lower computational complexity and faster running speed.

An ICVBPNN Algorithm for Time-varying Channel Tracking and Prediction

An improved complex-valued back propagation neural network (ICVBPNN) algorithm is proposed in this paper. In allusion to the defect of gradient descent of traditional complex-valued back propagation network (CVBPNN) algorithm, additive momentum has been introduced. It is used for time-varying channel tracking and prediction in wireless communication system and better application results are acquired. Firstly, with the use of the learning ability of the neural network, the tracking training is started based on the obtained channel state information (CSI), thus the nonlinear channel model is constructed. Secondly, the unknown channel state information is predicted using the ICVBPNN trained model. The simulation results demonstrate that the proposed method has less estimated error, and can track the channel more accurately than the traditional CVBPNN and the Kalman Filter algorithm.

An ICVBPNN Algorithm for Time-varying Channel Tracking and Prediction

An ICVBPNN Algorithm for Time-varying Channel Tracking and Prediction

Real-time DSP and FPGA Implementation of Wiener LMS Based Multipath Channel Estimation in 3G CDMA Systems

This paper investigates real-time DSP and FPGA implementations of a low complexity technique for asynchronous multiuser delay acquisition and time varying channel tracking for multipath channels in WCDMA and cdma2000 systems. A multiuser-LMS-like structure along with smoothing/prediction filters to improve tracking quality is reviewed. We investigate an efficient implementation based on FFT/IFFT technique, under fixed-point data representation and computation constraint. The measured BER reveals that fixed-point implementation is feasible at possibly no performance degradation. Based on real time execution made on a fixed-point high performance DSP, the maximum number of users is 15 and 17 for the proposed method and correlator, respectively. Due to the inherent parallelism and regular data flow FPGA implementation is suggested wherein a maximum number of users more than 80 can be afforded in Xilinx Virtex? II Pro device.

Tracking of time-varying channels using two-step LMS-type adaptive algorithm

This paper presents a modified version of the two-step least-mean-square (LMS)-type adaptive algorithm motivated by the work of Gazor. We describe the nonstationary adaptation characteristics of this modified two-step LMS (MG-LMS) algorithm for the system identification problem. It ensures stable behavior during convergence as well as improved tracking performance in the smoothly time-varying environments. The estimated weight increment vector is used for the prediction of weight vector for the next iteration. The proposed modification includes the use of a control parameter to scale the estimated weight increment vector in addition to a smoothing parameter used in the two-step LMS (G-LMS) algorithm, which controls the initial oscillatory behavior of the algorithm. The analysis focuses on the effects of these parameters on the lag-misadjustment in the tracking process. The mathematical analysis for a nonstationary case, where the plant coefficients are assumed to follow a first-order Markov process, shows that the MG-LMS algorithm contributes less lag-misadjustment than the conventional LMS and G-LMS algorithms. Further, the stability criterion imposes upper bound on the value of the control parameter. These derived analytical results are verified and demonstrated with simulation examples, which clearly show that the lag-misadjustment reduces with increasing values of the smoothing and control parameters under permissible limits

Tracking of time-varying mobile radio channels. II. A case study

For pt.I see ibid., vol.49, p.2207-17 (2001). Low-complexity Wiener LMS (WLMS) adaptation algorithms, of use for channel estimation, have been derived in Lindbom et al. (2001). They are here evaluated on the fast fading radio channels encountered in IS-136 TDMA systems, with the aim of clarifying several issues: How much can channel estimation performance be improved with these tools, as compared to LMS adaptation? When can an improved tracking MSE be expected to result in a meaningful reduction of the bit error rate? Will optimal prediction of future channel estimates significantly improve the equalization? Can one single tracker with fixed gain be used for all encountered Doppler frequencies and SNRs, or must a more elaborate scheme be adopted? These questions are here investigated both analytically and by simulation. An exact analytical expression for the tracking MSE on two-tap FIR channels is presented and utilized. With this tool, the MSE performance and robustness of WLMS algorithms based on different statistical models can be investigated. A simulation study then compares the uncoded bit error rate of detectors, where channel trackers are used in decision directed mode in conjunction with Viterbi algorithms. A Viterbi detector combined with WLMS, based on second order autoregressive fading models possibly combined with integration, provides good performance and robustness at a reasonable complexity.

Tracking of time-varying mobile radio channels .1. The Wiener LMS algorithm

Adaptation algorithms with constant gains are designed for tracking smoothly time-varying parameters of linear regression models, in particular channel models occurring in mobile radio communications. In a companion paper, an application to channel tracking in the IS-136 TDMA system is discussed. The proposed algorithms are based on two key concepts. First, the design is transformed into a Wiener filtering problem. Second, the parameters are modeled as correlated ARIMA processes with known dynamics. This leads to a new framework for systematic and optimal design of simple adaptation laws based on prior information. The algorithms can be realized as Wiener filters, called learning filters, or as "LMS/Newton" updates complemented by filters that provide predictions or smoothing estimates. The simplest algorithm, named the Wiener LMS, is presented. All parameters are here assumed governed by the same dynamics and the covariance matrix of the regressors is assumed known. The computational complexity is of the same order of magnitude as that of LMS for regressors which are either white or have autoregressive statistics. The tracking performance is, however, substantially improved.

Adaptive maximum likelihood algorithms for the blind tracking of time-varying multipath channels

Transmissions through multipath channels suffer from Rayleigh fading and intersymbol interference. This can be overcome by sending a (known) training sequence and identifying the channel (active identification). However, in a non-stationary context, the channel model has to be updated by periodically sending the training sequence, thus reducing the transmission rate. We address herein the problem of blind identification, which does not require such a sequence and allows a higher transmission rate. We have first proposed a two-stage algorithm (see Reference 2) for the blind identification of multipath channel. We investigate here the maximum-likelihood approach for the blind estimation of channel parameters. In order to track non-stationary channels, we have derived an adaptive (Kalman) algorithm which directly estimates the entire set of characteristic parameters. An original adaptive estimation of the noise model has been proposed for this investigation. Furthermore, the proposed method can easily cope with a model including Doppler shift, which is not directly possible with more common methods. Monte-Carlo simulations confirm the expected results and demonstrate the performance. © 1998 John Wiley & Sons, Ltd.

Optimal tracking of time-varying channels: a frequency domain approach for known and new algorithms

In this paper, we developed a systematic frequency domain approach to analyze adaptive tracking algorithms for fast time-varying channels. The analysis is performed with the help of two new concepts, a tracking filter and a tracking error filter, which are used to calculate the mean square identification error (MSIE). First, we analyze existing algorithms, the least mean squares (LMS) algorithm, the exponential windowed recursive least squares (EW-RLS) algorithm and the rectangular windowed recursive least squares (RW-RLS) algorithm. The equivalence of the three algorithms is demonstrated by employing the frequency domain method. A unified expression for the MSIE of all three algorithms is derived. Secondly, we use the frequency domain analysis method to develop an optimal windowed recursive least squares (OW-RLS) algorithm. We derive the expression for the MSIE of an arbitrary windowed RLS algorithm and optimize the window shape to minimize the MSIE. Compared with an exponential window having an optimized forgetting factor, an optimal window results in a significant improvement in the h MSIE. Thirdly, we propose two types of robust windows, the average robust window and the minimax robust window. The RLS algorithms designed with these windows have near-optimal performance, but do not require detailed statistics of the channel.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>