Bayesian Channel Research Articles

EM-based parameter iterative approach for sparse Bayesian channel estimation of massive MIMO system

One of the main challenges for a massive multi-input multi-output (MIMO) system is to obtain accurate channel state information despite the increasing number of antennas at the base station. The Bayesian learning channel estimation methods have been developed to reconstruct the sparse channel. However, these existing methods depend heavily on the channel distribution. In this paper, based on sparse Bayesian method, an expectation maximization-based parameter iterative approach is proposed to estimate the massive MIMO channel with unknown channel distribution. Using the approximate sparse feature, the massive MIMO channel is modeled as a non-zero Gaussian mixture and the sparse Bayesian channel estimation is introduced. The channel marginal probability density function is expressed by using the general approximate message-passing algorithm. All of the required channel parameters are iteratively estimated by the EM method. Simulation results show that the proposed scheme enables evident performance in channel estimation accuracy with a lower complexity when channel distribution is unknown.

Efficient Bayesian compressed sensing-based channel estimation techniques for massive MIMO-OFDM systems

Efficient and highly accurate channel state information (CSI) at the base station (BS) is essential to achieve the potential benefits of massive multiple input multiple output (MIMO) systems. However, the achievable accuracy that is attainable is limited in practice due to the problem of pilot contamination. It has recently been shown that compressed sensing (CS) techniques can address the pilot contamination problem. However, CS-based channel estimation requires prior knowledge of channel sparsity to achieve optimum performance, also the conventional CS techniques show poor recovery performance for low signal to noise ratio (SNR). To overcome these shortages, in this paper, an efficient channel estimation approach is proposed for massive MIMO systems using Bayesian compressed sensing (BCS) based on prior knowledge of statistical information regarding channel sparsity. Furthermore, by utilizing the common sparsity feature inherent in the massive MIMO system channel, we extend the proposed Bayesian algorithm to a multi-task (MT) version, so the developed MT-BCS can obtain better performance results than the single task version. Several computer simulation based experiments are performed to confirm that the proposed methods can reconstruct the original channel coefficient more effectively when compared to the conventional channel estimator in terms of estimation accuracy.

A Multi-Agent Collaborative Model for Bayesian Opportunistic Channel Accessibility in Railway Cognitive Radio

A Multi-Agent Collaborative Model for Bayesian Opportunistic Channel Accessibility in Railway Cognitive Radio

A Message-Passing Receiver for OFDM-Based Self-Interference-Limited Networks

In this paper, we develop a reliable bandwidth-efficient solution for coherent reception in networks prone to self-interference. Our primary focus is on orthogonal-frequency-division-multiplexing (OFDM)-based amplify-and-forward (AF) two-way relaying, where each source node suffers from reradiation of its own signal. An important issue is the superposition of the desired and interfering signals, which makes the channel estimation task difficult, particularly for varying channel coefficients. To address this challenging problem, we introduce a factor graph model of the estimation and detection problem at hand. Exploiting the conditional independence between unknown variables in the factor graph, an efficient message-passing algorithm, which performs joint Bayesian channel estimation, self-interference mitigation, and decoding, is derived. Simulation results show that the performance of the proposed method is close to that given by perfect knowledge of the channel for the target and interfering signals, even with limited training overhead.

Joint interference mitigation approach using space‐time pilot design in large‐scale antenna systems

This study addresses the problem of interference mitigation in multi-cell time division duplex cellular networks with large-scale antennas. Network performance in such systems is hampered by pilot contamination effect, which results in the inter-cell interference. To mitigate the interference, the authors propose a space-time pilot design-based approach to jointly eliminate interference from both time domain and space domain. The authors’ space-time pilot design divides a cellular network into different groups which proceed channel estimation alternately in time. Moreover, a low-rate coordination assisted pilot assignment scheme is added into each cell group during its pilot phase. This pilot assignment scheme relies on the minimum mean square of the updated Bayesian channel estimation. It can make use of the second-order statistical information about the users' channel vectors within the same group to assign an identical pilot sequence to users that tend to interfere with each other at a lower level. On the basis of space-time pilot design, the base station can proceed the maximal ratio transmitting and maximal ratio combining. With rigorous theoretic proof, their joint approach is able to significantly decrease interference. Simulations verified its excellent performance promotion.

Iterative Channel Estimation and Turbo Equalization for Multiple-Input Multiple-Output Underwater Acoustic Communications

This article investigates a robust receiver scheme for a single carrier, multiple-input–multiple-output (MIMO) underwater acoustic (UWA) communications, which uses the sparse Bayesian learning algorithm for iterative channel estimation embedded in Turbo equalization (TEQ). We derive a block-wise sparse Bayesian learning framework modeling the spatial correlation of the MIMO UWA channels, where a more robust expectation–maximization algorithm is proposed for updating the joint estimates of channel impulse response, residual noise, and channel covariance matrix. By exploiting the spatially correlated sparsity of MIMO UWA channels and the second-order a priori channel statistics from the training sequence, the proposed Bayesian channel estimator enjoys not only relatively low complexity but also more stable control of the hyperparameters that determine the channel sparsity and recovery accuracy. Moreover, this article proposes a low complexity space-time soft decision feedback equalizer (ST-SDFE) with successive soft interference cancellation. Evaluated by the undersea 2008 Surface Processes and Acoustic Communications Experiment, the improved sparse Bayesian learning channel estimation algorithm outperforms the conventional Bayesian algorithms in terms of the robustness and complexity, while enjoying better estimation accuracy than the orthogonal matching pursuit and the improved proportionate normalized least mean squares algorithms. We have also verified that the proposed ST-SDFE TEQ significantly outperforms the low-complexity minimum mean square error TEQ in terms of the bit error rate and error propagation.

Low-Complexity Polynomial Channel Estimation in Large-Scale MIMO With Arbitrary Statistics

This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as massive MIMO, where there are hundreds of antennas at one side of the link. Motivated by the fact that computational complexity is one of the main challenges in such systems, a set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced for arbitrary channel and interference statistics. While the conventional minimum mean square error (MMSE) estimator has cubic complexity in the dimension of the covariance matrices, due to an inversion operation, our proposed estimators significantly reduce this to square complexity by approximating the inverse by a L-degree matrix polynomial. The coefficients of the polynomial are optimized to minimize the mean square error (MSE) of the estimate. We show numerically that near-optimal MSEs are achieved with low polynomial degrees. We also derive the exact computational complexity of the proposed estimators, in terms of the floating-point operations (FLOPs), by which we prove that the proposed estimators outperform the conventional estimators in large-scale MIMO systems of practical dimensions while providing a reasonable MSEs. Moreover, we show that L needs not scale with the system dimensions to maintain a certain normalized MSE. By analyzing different interference scenarios, we observe that the relative MSE loss of using the low-complexity PEACH estimators is smaller in realistic scenarios with pilot contamination. On the other hand, PEACH estimators are not well suited for noise-limited scenarios with high pilot power; therefore, we also introduce the low-complexity diagonalized estimator that performs well in this regime. Finally, we ...

Modification of CFCM in The Presence of Heavy AWGN for Bayesian Blind Channel Equalizer

In this paper, the modification of conditional Fuzzy C-Means (CFCM) aimed at estimation of unknown desired channel states is accomplished for Bayesian blind channel equalizer under the presence of heavy additive Gaussian noise (AWGN). For the modification of CFCM to search the optimal channel states of a heavy noise-corrupted communication channel, a Gaussian weighted partition matrix, along with the Bayesian likelihood fitness function and the conditional constraint of ordinary CFCM, is developed and exploited. In the experiments, binary signals are generated at random and transmitted through both types of linear and nonlinear channels which are corrupted with various degrees of AWGN, and the modified CFCM estimates the channel states of those unknown channels. The simulation results, including the comparison with the previously developed algorithm exploiting the ordinary CFCM, demonstrate the effectiveness of proposed modification in terms of accuracy and speed, especially under the presence of heavy AWGN. Therefore, the proposed modification can possibly constitute a search algorithm of optimal channel states for Bayesian blind channel equalizer in severe noise-corrupted communication environments.

On Bayesian Channel Estimation and FFT-Based Symbol Detection in MIMO Underwater Acoustic Communications

Reliable channel estimation and effective interference cancellation are essential for enhancing the performance of multiple-input-multiple-output (MIMO) underwater acoustic communication (UAC) systems. In this paper, an efficient user-parameter-free Bayesian approach, referred to as sparse learning via iterative minimization (SLIM), is presented. SLIM provides good channel estimation performance along with reduced computational complexity compared to iterative adaptive approach (IAA). Moreover, RELAX-BLAST, which is a linear minimum mean-squared error (MMSE)-based symbol detection scheme, is implemented efficiently by making use of the conjugate gradient (CG) method and diagonalization properties of circulant matrices. The proposed algorithm requires only simple fast Fourier transform (FFT) operations and facilitates parallel implementations. These MIMO UAC techniques are evaluated using both simulated and in-water experimental examples. The 2008 Surface Processes and Acoustic Communications Experiment (SPACE08) experimental results show that the proposed MIMO UAC schemes can enjoy almost error-free performance even under severe ocean environments.

Bayesian channel estimation for K-distributed fading models.

Current underwater acoustic channel estimation techniques generally apply linear MMSE estimation. This approach is optimal in a mean square error sense under the assumption that the impulse response fluctuations are well characterized by Gaussian statistics, leading to a Rayleigh distributed envelope. However, field data suggest that the envelope statistics of the channel are better modeled by the K-distribution. MAP and MMSE estimators for a scalar channel tap have been derived assuming K-distributed fading models. The MAP estimator for a vector of K-distributed channel taps has also been derived. The implementation of these estimators on simulated data demonstrates an improvement in performance over linear MMSE estimation. [Work supported by the ONR Grant No. N00014-05-10085 and NSF Grant No. OCE-0519903.]

On the effect of receiver estimation error upon channel mutual information

Our goal in this paper is to study the effect of the receiver structure upon the achievable data rates. We consider transmission of linearly precoded data symbols over a frequency selective block fading multiple input multiple output (MIMO) wireless channel. To encompass a number of transmission schemes, we study this problem utilizing affine precoding, which is a unified model of linearly precoded data symbols with superimposed training. We focus on Bayesian receivers that estimate both the unknown fading coefficients and the data symbols. The receiver may adopt either of the following strategies to retrieve the data symbols: strategy (i) the receiver obtains joint Bayesian channel and symbol estimates, strategy, (ii) the receiver obtains a Bayesian channel estimate initially and the channel measurement is utilized to estimate the data symbols. For both strategies, we provide lower bounds on the mutual information between the data symbols and their corresponding estimates, and we relate these bounds to the symbol Cramer-Rao bound (CRB) matrices. In contrast to strategy (ii), for strategy (i) the lower bound does not depend on either the channel estimate or the covariance of the channel estimation error. For strategy (ii) we show that asymptotically (as the size of the transmission block grows) there is no loss of information after the maximum a posteriori (MAP) estimate of Gaussian symbols. We also provide guidelines to design affine precoders that maximize the derived lower bounds under the total average transmit power constraint.

A Decision-Theoretic Approach to Summarising Posterior Information in a Sample of step Functions

An important task in analysing time series of the current passed by a single ion channel is the restoration of the true signal from the noisy recording. Hodgson [1] devised a reversible jump Markov chain Monte Carlo (MCMC) algorithm to implement fully Bayesian single channel analysis. Noiseless ion channel signals are typically modelled as step functions with a discrete number of levels. As the number of steps is unknown, the joint posterior distribution under the Bayesian paradigm exhibits variable dimensionality, necessitating the use of reversible jump MCMC (Green [2]). This paper addresses the task of summarising posterior knowledge about the step function representing the noiseless channel signal, using Bayesian decision theory and the ideas of Rue [3]. We compute Bayes estimates of the true step function under a selection of loss functions from the same family.

Bayesian channel equalisation and robust features for speech recognition

The use of a speech recognition system with telephone channel environments, or different microphones, requires channel equalisation. In speech recognition, the speech model provides a bank of statistical information that can be used in the channel identification and equalisation process. The authors consider HMM-based channel equalisation, and present results demonstrating that substantial improvement can be obtained through the equalisation process. An alternative method, for speech recognition, is to use a feature set which is more robust to channel distortion. Channel distortions result in an amplitude tilt of the speech cepstrum, and therefore differential cepstral features provide a measure of immunity to channel distortions. In particular the cepstral–time feature matrix, in addition to providing a framework for representing speech dynamics, can be made robust to channel distortions. The authors present results demonstrating that a major advantage of cepstral–time matrices is their channel insensitive character.

A Modified Bayesian Algorithm with Decision Feedback for Blind Adaptive Equalization

Abstract A new blind equalization algorithm is presented that incorporates a Bayesian channel estimator and a decision-feedback (DF) adaptive filter. The Bayesian algorithm operates as a preprocessor on the received signal to provide an initial estimate of the channel coefficients. It is an approximate maximum a posteriori (MAP) sequence estimator that generates reliable estimates of the transmitted symbols. These decisions are then filtered by an adaptive decision-feed back algorithm in order to further reduce the intersymbol interference. The new algorithm is more robust to catastrophic error propagation than the standard decision-feedback equalizer (DFE), with only a modest increase in the computational complexity.

Bayesian/decision-feedback algorithm for blind adaptive equalization

A new blind equalization algorithm is presented that incorporates a Bayesian channel estimator and a decision-feedback (DF) adaptive filter. The Bayesian algorithm operates as a preprocessor on the received signal to provide an initial estimate of the channel coefficients. It is an approximate maximum <i>a posteriori</i> (MAP) sequence estimator that generates reliable estimates of the transmitted symbols. These decisions are then filtered by an adaptive decision-feedback algorithm to further reduce the intersymbol interference. The new algorithm is more robustto catastrophic error propagation thanthe standard decision-feedback equalizer (DFE), with only a modest increase in the computational complexity.