Massive Massive Multiple-input Multiple-output Channel Estimation Research Articles

Sparse angular reciprocity learning for massive MIMO channel estimation

Sparse angular reciprocity refers to the fact that downlink and uplink channels share common sparsity in angular domain. This sophisticated sparsity can be exploited to improve the channel estimation performance for massive multiple-input multiple-output (MIMO) systems. All the existing sparse angular reciprocity methods solve the uplink channel estimation problem independently with an LS estimator in the first stage, and then assist the downlink channel estimation with the sparse angular reciprocity in the second stage. Such a two-stage scheme, as well as the prior LS estimator, will inevitably result in performance loss. To overcome the drawback, we consider the downlink and uplink channel estimation problems as a whole one, and present a new sparse angular reciprocity learning framework to leverage the sparse angular reciprocity. Since the framework provides a joint solution for the downlink and uplink channel estimation in the sense of Bayesian optimality, it is expected to yield higher channel estimation accuracy. Moreover, we devise an efficient variational Bayesian inference (VBI)-based algorithm to automatically decouple the uplink channel. The proposed method can further enhance the channel estimation performance as the prior LS estimator is avoided. Another advantage is that it can be applied to the underdetermined uplink channel estimation problem, where the number of uplink pilot symbols is less than the number of MUs. Simulation results verify the superiority of the proposed method.

Deep learning-based massive MIMO channel estimation with reduced feedback

The downlink channel state information (CSI) must be available on the base station (BS) side to take advantage of all the features of massive multiple-input multiple-output (MIMO) systems. The channel estimation in massive MIMO systems is a challenging task because of the huge pilot and feedback overhead due to the large size of antennas. In this paper, we have proposed a multi task deep network for the channel estimation with the aim of decreasing the pilot and feedback overhead. An encoder network is designed to compress the received signal and reduce the feedback overhead. Furthermore, a decoder network is developed to reconstruct the compressed feedback. The estimator network is suggested to provide the channel estimation from the reconstructed feedback. The performance of the presented scheme has been evaluated in various simulation scenarios. The results confirm that the proposed method is capable of estimating the channel more accurately than the contemporary works. Moreover, this method has reduced the feedback and pilot overhead to a great extent.

MpNet: Variable Depth Unfolded Neural Network for Massive MIMO Channel Estimation

Massive multiple-input multiple-output (MIMO) communication systems have a huge potential both in terms of data rate and energy efficiency, although channel estimation becomes challenging for a large number of antennas. Using a physical model allows to ease the problem by injecting a priori information based on the physics of propagation. However, such a model rests on simplifying assumptions and requires to know precisely the configuration of the system, which is unrealistic in practice. In this paper we present mpNet, an unfolded neural network specifically designed for massive MIMO channel estimation. It is trained online in an unsupervised way. Moreover, mpNet is computationally efficient and automatically adapts its depth to the signal-to-noise ratio (SNR). The method we propose adds flexibility to physical channel models by allowing a base station (BS) to automatically correct its channel estimation algorithm based on incoming data, without the need for a separate offline training phase. It is applied to realistic millimeter wave channels and shows great performance, achieving a channel estimation error almost as low as one would get with a perfectly calibrated system. It also allows incident detection and automatic correction, making the BS resilient and able to automatically adapt to changes in its environment.

Downlink channel estimation in FDD cell-free massive MIMO

In frequency-division duplexing (FDD) cell-free massive multiple-input multiple-output (MIMO) systems, an excessive channel estimation overhead is a critical issue that limits the system performance. In this paper, by exploiting the sparse channel characteristics of such a cell-free system, we apply compressive sensing to estimate the channel state information and solve the excessive pilot overhead problem. The proposed algorithm estimates several channel coefficients with significant gains in the power domain and ignores the approximately zero coefficients. Compared to minimum mean square error (MMSE) estimation with orthogonal pilots, the proposed method significantly reduces the pilot overhead in an FDD cell-free massive MIMO system. The access points (APs) that contribute low gains feature reduced energy consumption because the power coefficients corresponding to zero gains in the sparse channel are assigned zeros in the power control process. Therefore, to improve the energy efficiency, the ignored channel coefficients reduce the power overhead.

Simultaneous Learning and Inferencing of DNN-Based mmWave Massive MIMO Channel Estimation in IoT Systems With Unknown Nonlinear Distortion

In this article, we propose an online training framework for deep neural network (DNN)-based mmWave massive multiple-input multiple-output (MIMO) channel estimation (CE) in Internet-of-Things (IoT) systems with nonlinear amplifier distortions. The DNN-based channel estimator is trained online in the IoT device based on real-time received pilot measurements from the base station (BS) without knowledge of the true channels, and can simultaneously generate CE in real time. To realize this, we first propose three axioms for a legitimate online loss function under known nonlinearity, based on which we develop a channel model-free online training algorithm with convergence analysis. For unknown nonlinearity, we propose a two-stage DNN structure with nonlinear modules, for which the DNN-based CE and nonlinear functions can be jointly trained online based on real-time received pilots. Simulation results show that the proposed solution achieves better CE accuracy than traditional compressive sensing (CS) algorithms while enjoying a much faster computational efficiency. In addition, the proposed method is robust to various nonlinear channel model mismatches and is able to track the change of the nonlinear channel model.

Massive MIMO Channel Estimation With Low-Resolution Spatial Sigma-Delta ADCs

We consider channel estimation for an uplink massive multiple-input multiple-output (MIMO) system where the base station (BS) uses an array with low-resolution (1-2 bit) analog-to-digital converters and a spatial Sigma-Delta ( ΣΔ) architecture to shape the quantization noise away from users in some angular sector. We develop a linear minimum mean squared error (LMMSE) channel estimator based on the Bussgang decomposition that reformulates the nonlinear quantizer model using an equivalent linear model plus quantization noise. We also analyze the uplink achievable rate with maximal ratio combining (MRC), zero-forcing (ZF) and LMMSE receivers and provide a lower bound for the achievable rate with the MRC receiver. Numerical results show superior channel estimation and sum spectral efficiency performance using the ΣΔ architecture compared to conventional 1- or 2-bit quantized massive MIMO systems.

Bayesian Channel Estimation in Multi-User Massive MIMO With Extremely Large Antenna Array

We investigate wideband uplink channel estimation for a multi-user (MU) multiple-input single-output (MISO) OFDM system, in which the base station (BS) is equipped with an extremely large antenna array (ELAA). The existing compressive sensing massive multiple-input multiple-output (MIMO) channel estimation approach with a traditional sparsity promoting prior model becomes invalid in the ELAA scenario due to the spatial non-stationary effects caused by the spherical wavefront and visibility region (VR) issue. We therefore propose a new structured prior with the Hidden Markov Model (HMM) to promote the structured sparsity of the spatial non-stationary ELAA channel. Based on this, a Bayesian inference problem on the posterior of the ELAA channel coefficients is formulated. In addition, we propose the turbo orthogonal approximate message passing (Turbo-OAMP) algorithm to achieve a low-complexity channel estimation. Comprehensive simulations verify that the proposed algorithm has supreme performance under spatial non-stationary ELAA channels compared to various state-of-the-art baselines.

Lower Performance Bound for Beamspace Channel Estimation in Massive MIMO

In this letter, we present a lower performance bound for discrete Fourier transform (DFT)-based beamspace channel estimation (CE) in 64 antennas Massive Multiple-Input Multiple-Output (MIMO) receiver. The beamspace CE is implemented after antennas digital signal transformation to a priori estimated DFT sub-space resulting in less complexity. To estimate the performance, we calculate noise power after the beamspace CE unit by decomposing an ideal channel response into separate taps and transforming them into the beam domain. Then the minimum mean squared error (MMSE) method is employed with taps to estimate the CE error power. An artificial CE is calculated as a sum of the ideal beamspace channel and additive Gaussian noise with the same error power. The artificial CE is utilized in the MIMO detector and decoder to achieve performance bound. Simulation results are presented for the non-line-of-sight model of the 5G QuaDRiGa 2.0 channel.

Overcoming the Channel Estimation Barrier in Massive MIMO Communication via Deep Learning

A new wave of wireless services, including virtual reality, autonomous driving and Internet of Things, is driving the design of new generations of wireless systems to deliver ultra-high data rates, massive numbers of connections and ultra-low latency. Massive multiple-input multiple-output (MIMO) is one of the critical underlying technologies that allow future wireless networks to meet these service needs. This article discusses the application of deep learning (DL) for massive MIMO channel estimation in wireless networks by integrating the underlying characteristics of channels in future high-speed cellular deployment. We develop important insights derived from the physical radio frequency (RF) channel properties and present a comprehensive overview on the application of DL for accurately estimating channel state information (CSI) with low overhead. We provide examples of successful DL application in CSI estimation for massive MIMO wireless systems and highlight several promising directions for future research.

Enhanced Channel Estimation in Massive MIMO via Coordinated Pilot Design

Pilot contamination is a limiting factor in multicell massive multiple-input multiple-output (MIMO) systems because it can severely impair channel estimation. Prior works have suggested coordinating pilot design across cells in order to reduce the channel estimation error caused by pilot contamination. In this paper, we propose a method for coordinated pilot design using fractional programming to minimize the weighted mean squared-error (MSE) in channel estimation. In particular, we apply the recently proposed quadratic transform to the MSE expression which allows the effect of pilot contamination to be decoupled. The resulting problem reformulation enables the pilots to be optimized in closed form if they can be designed arbitrarily. When the pilots are restricted to a given set of orthogonal sequences, pilot optimization reduces to an assignment problem which can be solved by weighted bipartite matching. Furthermore, we consider the max-min fairness of data rates with orthogonal pilots and obtain an extension of the proposed method to correlated Rayleigh fading. Finally, simulations demonstrate the advantage of the proposed (orthogonal and nonorthogonal) pilot designs as compared with state-of-the-art methods in combating pilot contamination.

Uplink-Aided High Mobility Downlink Channel Estimation Over Massive MIMO-OTFS System

Although it is often used in the orthogonal frequency division multiplexing (OFDM) systems, application of massive multiple-input multiple-output (MIMO) over the orthogonal time frequency space (OTFS) modulation could suffer from enormous training overhead in high mobility scenarios. In this paper, we propose one uplink-aided high mobility downlink channel estimation scheme for the massive MIMO-OTFS networks. Specifically, we firstly formulate the time domain massive MIMO-OTFS signal model along the uplink and adopt the expectation maximization based variational Bayesian (EM-VB) framework to recover the uplink channel parameters including the angle, the delay, the Doppler frequency, and the channel gain for each physical scattering path. Correspondingly, with the help of the fast Bayesian inference, one low complex approach is constructed to overcome the bottleneck of the EM-VB. Then, we fully exploit the angle, delay and Doppler reciprocity between the uplink and the downlink and reconstruct the angles, the delays, and the Doppler frequencies for the downlink massive channels at the base station. Furthermore, we examine the downlink massive MIMO channel estimation over the delay-Doppler-angle domain. The channel dispersion of the OTFS over the delay-Doppler domain is carefully analyzed and is utilized to associate one given path with one specific delay-Doppler grid if different paths of any user have distinguished delay-Doppler signatures. Moreover, when all the paths of any user could be perfectly separated over the angle domain, we design the effective path scheduling algorithm to map different users' data into the orthogonal delay-Doppler-angle domain resource and achieve the parallel and low complex downlink 3D channel estimation. For the general case, we adopt the least square estimator with reduced dimension to capture the downlink delay-Doppler-angle channels. Various numerical examples are presented to confirm the validity and robustness of the proposed scheme.

Robust massive MIMO channel estimation for 5G networks using compressive sensing technique

The pilot overhead provides fundamental limits on the performance of massive multiple-input multiple-output (MIMO) systems. This is because the performance of such systems is based on the failure of the presentation of accurate channel state information (CSI). Based on the theory of compressive sensing, this paper presents a novel channel estimation technique as the mean of minimizing the problems associated with pilot overhead. The proposed technique is based on the combination of the compressive sampling matching and sparsity adaptive matching pursuit techniques. The sources of the signals in MIMO systems are sparsely distributed in terms of spatial correlations. This distribution pattern enables then use of compressive sampling techniques to solve the channel estimation problem in MIMO systems. Simulation results demonstrate that the proposed channel estimation outperforms the conventional compressive sensing (CS)-based channel estimation algorithms in terms of the normalized mean square error (NMSE) performance at high signal-to-noise ratios (SNRs). Furthermore, it reduces the computational complexity of the channel estimation compared to conventional methods. In addition to the achieved performance gain in terms of NMSE, the presented method significantly reduces pilot overhead compared to conventional channel estimation techniques.

Compressed sensing channel estimation in massive MIMO

Massive multiple-input-multiple-output (MIMO) emerges as a promising technology to meet the ever growing demand on a large volume of data transmission in an energy efficient manner in the upcoming fifth generation networks. This explores an integrated system model of improved wireless channel estimation (CE) and its consequent effect on image reconstruction, both done in compressed sensing (CS) framework. A massive MIMO channel exhibits sparse nature and has been modelled as a CS problem. Two CS-MIMO-CE algorithms, discrete cosine transform-based stagewise orthogonal matching pursuit and improved stagewise orthogonal matching pursuit (iStOMP), are suggested here. Low density parity check codes are also integrated to serve three-fold purposes, as a pilot signal, sensing matrix, and error control code, while Daubechies transform offers a sparse representation of the MIMO channel and transmitted image. The proposed iStOMP MIMO-CE algorithm offers ~ 6 dB gain in CE over the existing works and gain in 2 dB on image visual quality at 75% CS measurements.

Real-Valued Sparse Bayesian Learning Approach for Massive MIMO Channel Estimation

This letter describes a real-valued sparse Bayesian learning (SBL) approach for massive multiple-input multipleoutput (MIMO) downlink channel estimation. The main idea of the approach is to introduce a certain unitary transformation into pilots, so as to convert complex-valued channel recovery problems into real ones. Due to exploiting the real-valued structure of the data matrices, the new approach brings a significant decrease in computational complexity, as well as a good noise suppression. Simulation results demonstrate that the new method can reduce the computation load and improve the channel estimation performance simultaneously.

Learning the Structured Sparsity: 3-D Massive MIMO Channel Estimation and Adaptive Spatial Interpolation

This paper addresses the channel estimation problem for three-dimensional (3-D) massive multiple-input multiple-output (MIMO) systems, where the base station (BS) is equipped with a two-dimensional uniform planar array (UPA) to serve a number of user equipments (UEs). To implement with low hardware complexity, the number of available radio-frequency (RF) chains at BS is constrained to be much smaller than the number of antennas. The theoretical analysis of sparse property for 3-D massive MIMO channel reveals that there exists two kinds of sparse structures in beam-domain channel vector, namely the common sparsity structure among sub-arrays of UPA and block sparsity structure per sub-array. Based on this property, a novel structured sparse Bayesian learning framework is proposed to estimate the channel between BS and UE reliably. Moreover, an adaptive spatial interpolation scheme is proposed to further reduce the number of required RF chains at BS while maintaining the estimation performance. The simulation results show that the proposed scheme provides stable estimation performance for a variety of scenarios with different numbers of RF chains, transmit signal-to-noise ratios, Rician factors, and angular spreads, and outperforms the reference schemes significantly.

Robust Bayesian learning approach for massive MIMO channel estimation

This paper addresses the problem of massive multiple-input multiple-output (MIMO) channel estimation in the presence of impulsive noise. In the literature, a sparse Bayesian learning (SBL) approach for outlier-resistant direction-of-arrival (DOA) estimation can be tailored to handle this problem. However, it suffers from two major shortcomings: first, it takes the impulsive noise as a part of the unknown signal-of-interest, which brings a high computational complexity due to the larger size of the problem; and second, the assumption that both the signal-of-interest and the impulsive noise have a common sparsity level is not always valid, which could cause a performance loss. To deal with these shortcomings, we resort to the variational Bayesian inference (VBI) methodology to separate effects from the signal-of-interest and the impulsive noise. Then, we introduce an improved two-stage hierarchical prior to enforce sparsity while guarantee a denser impulsive noise over the signal-of-interest simultaneously. Due to adopting the VBI separation and the new sparsity prior, our method can bring a considerable computational complexity reduction and achieve better channel estimation accuracy. Simulation results reveal substantial performance improvement over the existing methods.

Massive MIMO Channel Estimation Over the mmWave Systems Through Parameters Learning

In this letter, we formulate an off-grid channel model to characterize spatial sample mismatching in the discrete Fourier transform (DFT) based massive multiple-input-multiple-output (MIMO) channel estimation over the millimeter-wave (mmWave) band. Then, we decompose the off-grid mmWave massive MIMO channel estimation into the learning of model parameters and virtual channel estimation. Specifically, an expectation maximization (EM) based sparse Bayesian learning framework is first developed to learn the model parameters, such as bias parameters and spatial signatures, with unknown noise. With the learned model parameters, we resort to the linear minimum mean square error method to estimate the instantaneous virtual channel with less pilot overhead. Finally, we corroborate the validity of the proposed method through numerical simulations.

Non-Uniform Burst-Sparsity Learning for Massive MIMO Channel Estimation

We address the downlink channel estimation problem for massive multiple-input multiple-output (MIMO) systems in this paper, where the inherit burst-sparsity structure is exploited to improve the channel estimation performance. In the literature, the commonly used burst-sparsity model assumes a uniform burst-sparse structure in which all bursts have similar sizes. However, such assumption is oversimplified to hold in practice. Outliers deviated from such uniform burst structures can significantly degrade the accuracy of the existing burst-sparsity models, which may result in a reduced recovery performance. To capture a more general burst-sparsity structure in practice, we propose a novel non-uniform burst-sparsity model and introduce an improved pattern-coupled prior to account for more realistic non-uniform burst structures. A generic sparse Bayesian learning based framework to exploit the non-uniform burst-sparsity and to enhance massive MIMO channel estimation performance is then developed. We further prove that our solution converges to a stationary point of the associated optimization problem, and our framework includes the state-of-the-art pattern-coupled method as a special case. Simulation results verify the robust performance of the devised method.

Low-Overhead Cyclic Reference Signals for Channel Estimation in FDD Massive MIMO

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.

Multicell multiuser massive MIMO channel estimation and MPSK signal block detection applying two-dimensional compressed sensing

For the uplink multicell massive multiple-input multiple-output (MIMO) block fading systems, a two-dimensional smoothed l0 channel estimation method (2D-SL0-CE) with the aid of virtual channel representation is firstly exploited in this paper, which can jointly estimate the desired multiuser channels of the target cell and the interference links from neighbor cells without inducing pilot contamination. Then, a 2D-SL0 signal detection method (2D-SL0-SD) with the aid of sparse decomposing and the modified 2D sl0 recovery algorithm is proposed, which can jointly decode M-ary phase-shift keying (MPSK) signal block for whole desired users. Moreover, an improved 2D-SL0-SD is also proposed to remove multiuser interference of neighbor cells in high SNR scenario. Simulation results show that the 2D-SL0-CE method can remove performance floor induced by pilot contamination and need less pilot overhead than the conventional least square (LS) method. When detecting QPSK signal blocks at 12 dB SNR, the 2D-SL0-SD method with perfect channel state information (CSI) can obtain 10−2 BER. Moreover, in the case of 8PSK signals, the 2D-SL0-SD joining with the 2D-SL0-CE can obtain 10−2 BER at 20 dB SNR.