Robust Bayesian learning approach for massive MIMO channel estimation

Hybrid analog and digital beamforming transceivers are instrumental in addressing the challenge of expensive hardware and high training overheads in the next generation millimeter-wave (mm-Wave) massive MIMO (multiple-input multiple-output) systems. However, lack of fully digital beamforming in hybrid architectures and short coherence times at mm-Wave impose additional constraints on the channel estimation. Prior works on addressing these challenges have focused largely on narrowband channels wherein optimization-based or greedy algorithms were employed to derive hybrid beamformers. In this paper, we introduce a deep learning (DL) approach for channel estimation and hybrid beamforming for frequency-selective, wideband mm-Wave systems. In particular, we consider a massive MIMO Orthogonal Frequency Division Multiplexing (MIMO-OFDM) system and propose three different DL frameworks comprising convolutional neural networks (CNNs), which accept the raw data of received signal as input and yield channel estimates and the hybrid beamformers at the output. We also introduce both offline and online prediction schemes. Numerical experiments demonstrate that, compared to the current state-of-the-art optimization and DL methods, our approach provides higher spectral efficiency, lesser computational cost and fewer number of pilot signals, and higher tolerance against the deviations in the received pilot data, corrupted channel matrix, and propagation environment.

In this letter, a novel robust two-dimensional nearfield millimeter-wave (MMW) image reconstruction algorithm is developed based on compressed sensing (CS) in the presence of impulsive measurement noise. To enable the sparse MMW image recovery, the CS algorithm usually employs the popular l 2 -norm as the data fidelity term and a combination of multiple sparsityinduced functions as the penalty term. The l 2 -norm is non-robust against impulsive noise since the Gaussian noise distribution assumption is not valid, and the presence of impulsive noise will severely degrade the robustness of the compressive MMW image recovery. To gain more robustness performance, a complex correntropy based data-fitting term, namely complex correntropic loss (CC-loss), is used to replace the l2-norm for the near-field MMW measurement contaminated by impulsive noise. In order to solve the corresponding minimization problem, an additive half quadratic method is used to transform the CC-loss term to its convex form, and then a parallel primal-dual process is used to guarantee the convergence of the proposed algorithm. In total, 150-GHz MMW experimental results show that the proposed algorithm can achieve accurate image reconstruction from compressive measurements under different impulsive noise levels.

Sparse angular reciprocity learning for massive MIMO channel estimation

In this paper, we study channel estimation for multiuser millimeter wave (mmWave) systems. Since most conventional channel estimation schemes rely entirely on pilot signals, such methods cannot accurately estimate mmWave channels with low signal-to-noise ratio (SNR). To address this challenge, a direction of arrival (DoA)-assisted channel estimation scheme exploiting the sparsity of mmWave channels is developed. The proposed scheme utilizes data symbols as well as the pilot signals to estimate DoA of effective paths, and the estimated DoA information is used to suppress the noise given that the number of effective path directions is much smaller than the number of antennas. Furthermore, it is shown that sparse Bayesian learning (SBL) approach is suitable for DoA estimation in mmWave communications scenarios where signals from different angles are highly correlated as a result of multipath propagation, and a low complexity SBL algorithm for this setup is derived. By utilizing data symbols and adopting the SBL approach, the proposed scheme can identify the directions of effective path even in low SNR regime, enabling accurate estimation of mmWave channels.

Massive multiple input multiple output (MIMO) transmission and coordinated multipoint transmission are candidate technologies for increasing data throughput in evolving 5G standards. Frequency division duplex (FDD) is likely to remain predominant in large parts of the spectrum below 6 GHz for future 5G systems. Therefore, it is important to estimate the downlink FDD channels from a very large number of antennas, while avoiding an excessive downlink reference signal overhead. We here propose and investigate a three part solution. First, massive MIMO downlinks use a fixed grid of beams. For each user, only a subset of beams will then be relevant, and require estimation. Second, sets of coded reference signal sequences, with cyclic patterns over time, are used. Third, each terminal estimates its most relevant channels. We here propose and compare a linear mean square estimation and a Kalman estimation. Both utilize frequency and antenna correlation, and the later also utilizes temporal correlation. In extensive simulations, this scheme provides channel estimates that lead to an insignificant beamforming performance degradation as compared to full channel knowledge. The cyclic pattern of coded reference signals is found to be important for reliable channel estimation, without having to adjust the reference signals to specific users.

Additive asynchronous and cyclostationary impulsive noise limits\ncommunication performance in OFDM powerline communication (PLC) systems.\nConventional OFDM receivers assume additive white Gaussian noise and hence\nexperience degradation in communication performance in impulsive noise.\nAlternate designs assume a parametric statistical model of impulsive noise and\nuse the model parameters in mitigating impulsive noise. These receivers require\noverhead in training and parameter estimation, and degrade due to model and\nparameter mismatch, especially in highly dynamic environments. In this paper,\nwe model impulsive noise as a sparse vector in the time domain without any\nother assumptions, and apply sparse Bayesian learning methods for estimation\nand mitigation without training. We propose three iterative algorithms with\ndifferent complexity vs. performance trade-offs: (1) we utilize the noise\nprojection onto null and pilot tones to estimate and subtract the noise\nimpulses; (2) we add the information in the data tones to perform joint noise\nestimation and OFDM detection; (3) we embed our algorithm into a decision\nfeedback structure to further enhance the performance of coded systems. When\ncompared to conventional OFDM PLC receivers, the proposed receivers achieve SNR\ngains of up to 9 dB in coded and 10 dB in uncoded systems in the presence of\nimpulsive noise.\n

Chapter 6 - Channel estimation for mmWave massive MIMO systems

The impulsive noise and the time-varying channel are two major detrimental factors which greatly constrain the performance of underwater acoustic communications (UACs). Utilizing the joint sparsity of the impulsive noise and the channel impulse response, the paper proposes the generalized approximate message passing (GAMP)-based sparse Bayesian learning (SBL) frameworks for joint impulsive noise mitigation and channel estimation and tracking for orthogonal frequency division multiplexing (OFDM) UACs. Firstly, the SBL framework for the joint estimation is employed. To reduce the computational complexity, the GAMP is introduced into the expectation-maximization (EM) algorithm, and a low-complexity GAMP based SBL framework is formulated without performance degradation. To further estimate and track the impulsive noise and channel state information in the slow time-varying scenarios, we propose a novel GAMP-based temporal SBL framework. The factor graph and GAMP are used to achieve the approximated estimation for the posterior statistics of both the channel state information and the impulsive noise. The algorithm formulates the message passing scheduling for the EM algorithm to solve the joint multiple sparse signal recovery problem. Simulations and sea-trial results demonstrate that the proposed algorithms significantly improve the performance in terms of the mean square error of channel estimation, impulsive noise estimation, bit error rate and computational complexity compared with their corresponding SBL-based counterparts.

Channel state information (CSI) at the base station (BS) is crucial to achieve beamforming and multiplexing gains in multiple-input multiple-output (MIMO) systems. State-of-the-art limited feedback schemes require feedback overhead that scales linearly with the number of BS antennas, which is prohibitive for 5G massive MIMO. This paper proposes novel limited feedback algorithms that lift this burden by exploiting the inherent sparsity in double-directional MIMO channel representation using overcomplete dictionaries. These dictionaries are associated with angle of arrival and angle of departure that specifically account for antenna directivity patterns at both ends of the link. The proposed algorithms achieve satisfactory channel estimation accuracy using a small number of feedback bits, even when the number of transmit antennas at the BS is large-making them ideal for 5G massive MIMO. Judicious simulations reveal that they outperform a number of popular feedback schemes and underscore the importance of using angle dictionaries matching the given antenna directivity patterns, as opposed to uniform dictionaries. The proposed algorithms are lightweight in terms of computation, especially on the user equipment side, making them ideal for actual deployment in 5G systems.

Hardware problems are the most detrimental issues to channel estimates in wireless communication systems. Because of the enormous number of antennas at the base station (BS) in cellular massive multiple-input multiple-output (MIMO) systems and because one radio frequency (RF) chain per antenna is required, hardware impairments in such systems will be quite severe. Many research publications have used a quality-cost tradeoff to adjust for RF unit hardware issues. In this study, we have taken a different approach by reducing the error floor caused by impairments in the predicted channels. Here are two steps to remedy the problem. In phase 1, a single active user channel in a single cell was calculated statistically rather than parametrically. In phase 2, a convex optimization approach was used to regularize the estimated channel in phase 1 to reduce error and provide a robust channel estimate. The results of our proposed procedure are measured by the normalized minimum mean squared error (NMSE) versus a range from the effective signal-to-noise ratio, and it shows a significant reduction (nearly one order of magnitude) in the error floor as compared with the conventional one, especially at high signal-to-noise ratio (SNR) in the range of (20 dB-30 dB). Simulation results were extracted in MATLAB R2020a.

One of the challenges of modulation techniques used in Fifth-Generation (5G) is their robustness in noisy environment. Conventional Orthogonal Frequency Division Multiplexing (OFDM) cannot be considered as a 5G waveform in its original form because of its certain limitations, such as performance degradation by impulsive noise (IN) and high peak to average power ratio (PAPR). Numerous modulation schemes proposed for 5G communications are able to overcome these drawbacks. Generalised Frequency Division Multiplexing (GFDM) is one of them. This paper analyses the performance of GFDM in presence of Additive White Gaussian Noise (AWGN), IN and Narrow Band Interference (NBI). It is found that GFDM is able to perform better than OFDM and Vector Orthogonal Frequency Division Multiplexing (VOFDM) in presence of noises, which can potentially be present in 5G applications. Simulation results show that GFDM achieve lower PAPR and Symbol Error Rate (SER) and an average of 10.73 dB and 4.73 dB gain in Signal to Noise Ratio (SNR) in presence of IN and combined IN and NBI respectively, as compared to OFDM and VOFDM.

Massive multiple-input multiple-output (MIMO) enables reliability in low latency communication systems. This paper proposes a channel estimation scheme in orthogonal time frequency space (OTFS) massive MIMO systems, where the inherent channel cluster structure in Doppler-angle domain is considered. In our proposed scheme, a local Beta process (LBP) is utilized to characterize a two-dimensional (2-D) structure in Doppler-angle domain. The uplink channel estimation problem is modelled as a sparse channel reconstruction problem, and it is solved by estimating channel parameters (i.e., Doppler, angle and delay) with sparse Bayesian learning (SBL). Thus, downlink channel estimation can be performed with the help of these parameters. Finally, simulation results verify that the proposed algorithm can not only achieve ideal performance of channel estimation, but also have robust adaptation to variable Doppler.

This paper studies the estimation of fast fading channel in the presence of impulse noise. The fast fading channel in a wireless communications system is typically modeled as an autoregressive (AR) process. The least-squares algorithm and Kalman filter have been previously proposed for estimating the AR parameters and the channel impulse response respectively using a training sequence. The performance of these algorithms, however, is very sensitive to impulse noise. In this paper, a robust Kalman filter and a robust recursive least M-estimate algorithm are employed to jointly estimate the channel impulse response and the AR parameters of fast fading channel under impulse noise. Simulation showed that the proposed algorithms are much less sensitive to impulse noise than the conventional algorithms.

Accurate channel-estimation algorithms are critical for enhancing the throughput of wireless communication systems, including millimetre wave (mmWave) multiple-input multiple-output (MIMO) systems, where precise channel knowledge enables reliable signal detection and beamforming. In practical wireless environments, impulsive non-Gaussian noise with unknown statistics often occurs due to electromagnetic interference and harsh propagation conditions, significantly degrading estimation accuracy and overall system performance. In this context, the maximum correntropy criterion (MCC) has emerged as an attractive solution for robust channel estimation that outperforms state-of-the-art algorithms. However, the MCC-based algorithm’s performance is sensitive to the tuning of hyperparameters, which is challenging in the presence of non-Gaussian noise, such as impulsive noise (IN). Furthermore, a recent genre of kernel width sampling methods makes MCC hyperparameter-free and allows for asymptotic convergence to the squared-error performance of MCC with the ideal kernel width. To ensure their practical applicability, convergence analysis is essential to theoretically guarantee stability and performance under various IN scenarios. This study presents convergence analysis of hyperparameter-free MCC-based channel estimation for mmWave MIMO systems considering various IN scenarios. To validate the theoretical analysis, simulations are conducted on practical mmWave MIMO system models. Simulation results closely match the analytical findings, which confirms the accuracy and effectiveness of the analysis we here present.

Accurate channel state information is the foundation of the receiver design for power line communication (PLC) system. However, the presence of impulsive noise makes the problem more complex. As traditional impulsive noise mitigation methods are based on the assumption that the channel state information is known in advance, which limits their applications. In this paper, by exploiting the parametric sparsity, we propose a joint channel and impulsive noise estimation scheme based on compressed sensing theory for narrowband PLC systems. Observing the strong coherence of measurements matrix, we adopt the sparse Bayesian learning (SBL) to solve the compressed sensing problem. Simulation results verify our proposed algorithm has smaller mean square error and bit error rate.