Knowledge-Driven Channel Estimation for Asymmetrical Massive MIMO Systems

In this paper, we develop the channel estimation algorithm for a massive multiple input multiple output (MIMO) system using one-bit analog-to-digital converters (ADCs). Although, one-bit quantization significantly reduces the deployment cost and power consumption of the massive MIMO, the great distortion induced by one-bit quantization makes channel estimation more difficult. Therefore, a channel estimation method by executing a deep neural network (DNN) over multiple signal segments is proposed for the uplink of one-bit massive MIMO. The average of the DNN’s outputs throughout all the segments is the final channel estimate for a transmission block. In order to improve the estimation accuracy without increasing the length of pilot, the data symbols got based on the initial channel estimates are used as the other part of pilots to refine the estimation result. Moreover, a sliding window based pilot segment method is adopted to increase the number of signal segments with a same pilot length. The simulation results show that the proposed scheme outperforms least squares (LS) and Bussgang linear minimum mean squared error (BLMMSE) channel estimators in the whole signal-to-noise-ratio (SNR) region.

Channel estimation is one of the foremost challenges for realizing practical millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. To circumvent this problem, deep convolutional neural networks (CNNs) have been recently employed to achieve impressive success. However, current deep CNNs based channel estimators are only suitable to a small range of signal-to-noise ratios (SNRs). Unlike the existing works, the modified convolutional blind denoising network (CBDNet) is proposed to improve the robustness for noisy channel by adopting noise level estimation subnetwork, non-blind denosing subnetwork, and asymmetric joint loss functions for blind channel estimation. Furthermore, the CBDNet can adjust the estimated noise level map to interactively reduce the noise in the channel matrix. Numerical results demonstrate that the proposed CBDNet-based channel estimator can outperform the traditional channel estimators, traditional compressive sensing techniques and deep CNNs in terms of the normalized mean squared error. In addition, the CBDNet can be used over a large range of SNRs, which hugely reduce the cost of offline training.

Accurate beamspace channel estimation is critical in wideband millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) communication systems. However, the beam squint effect caused by the increase in bandwidth and array dimension can bring additional challenges to the wideband channel estimation. In this study, we propose a wideband channel estimation scheme based on compressed sensing to solve the beam squint effect in broadband mmWave massive MIMO systems. First, the channel estimation problem is transformed into a beamspace direction estimation problem by exploiting the special frequency-dependent sparse structure of a broadband beamspace channel. Then, we propose a beam-band function-based orthogonal matching pursuit algorithm, in which a beam-band function is constructed and used to capture the power of each path component to estimate the spatial direction. In addition, the support of each path component at different sub-carriers is estimated to reduce the influence of the beam squint effect. Moreover, the support is estimated adaptively to improve the estimation accuracy further. Simulation results demonstrate that the proposed scheme reduces the pilot overhead under the beam squint effect and improve the estimation accuracy significantly.

Channel estimation and beamforming play critical roles in frequency-division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems. However, these two modules have been treated as two stand-alone components, which makes it difficult to achieve a global system optimality. In this paper, we propose a deep learning-based approach that directly optimizes the beamformers at the base station according to the received uplink pilots, thereby, bypassing the explicit channel estimation. Different from the existing fully data-driven approach where all the modules are replaced by deep neural networks (DNNs), a neural calibration method is proposed to improve the scalability of the end-to-end design. In particular, the backbone of conventional time-efficient algorithms, i.e., the least-squares (LS) channel estimator and the zero-forcing (ZF) beamformer, is preserved and DNNs are leveraged to calibrate their inputs for better performance. The permutation equivariance property of the formulated resource allocation problem is then identified to design a low-complexity neural network architecture. Simulation results will show the superiority of the proposed neural calibration method over benchmark schemes in terms of both the spectral efficiency and scalability in large-scale wireless networks.

User-segregation based channel estimation in the MIMO system

In time division duplexing (TDD) millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, downlink channel state information (CSI) can be obtained from uplink channel estimation thanks to channel reciprocity. However, under high-mobility scenarios, frequent uplink channel estimation is needed due to channel aging. Additionally, large amounts of antennas and subcarriers result in high-dimensional CSI matrices, aggravating pilot training overhead. To address this, we propose a three-domain (3D) channel extrapolation framework across spatial, frequency, and temporal domains. First, considering the effectiveness of traditional knowledge-driven channel estimation methods and the marginal effects of pilots in the spatial and frequency domains, a knowledge-and-data driven spatial-frequency channel extrapolation network (KDD-SFCEN) is proposed for uplink channel estimation via joint spatial-frequency channel extrapolation to reduce spatial-frequency domain pilot overhead. Then, leveraging channel reciprocity and temporal dependencies, we propose a temporal uplink-downlink channel extrapolation network (TUDCEN) powered by generative artificial intelligence for slot-level channel extrapolation, aiming to reduce the tremendous temporal domain pilot overhead caused by high mobility. Numerical results demonstrate the superiority of the proposed framework in significantly reducing the pilot training overhead by 16 times and improving the system’s spectral efficiency under high-mobility scenarios compared with state-of-the-art channel estimation/extrapolation methods.

The huge pilot overhead required for channel estimation is one of the key issues for massive multiple-input multiple-output (MIMO) systems. Existing compressed sensing and deep learning methods generally implement pilot compression under the assumption of the huge number of antennas and strict channel sparsity, while the channel estimation performance decreases sharply under quasi-sparse channel environment. Motivated by the powerful learning ability of deep learning for extracting the major characteristics of the target, we propose approximate message passing (AMP) algorithm-based multi-stage training optimization architecture to solve the above problem, where the whole system is considered as a deep neural network (DNN). In the first stage, the optimized sensing matrix of the AMP algorithm is learned by training to match the quasi-sparse channel. In the second stage, we optimize the linear coefficients and nonlinear shrinkage parameters of AMP to further improve the performance. In the third stage, all parameters are jointly optimized by training to make the whole system optimal. Numerical simulation results show that the proposed architecture can achieve high precision channel estimation under the premise of reducing pilot overhead effectively.

Deep-unfolding neural networks (NNs) have received great attention since they achieve satisfactory performance with relatively low complexity. Typically, these deep-unfolding NNs are restricted to a fixed-depth for all inputs. However, the optimal number of layers required for convergence changes with different inputs. In this paper, we first develop a framework of deep deterministic policy gradient (DDPG)-driven deep-unfolding with adaptive depth for different inputs, where the trainable parameters of deep-unfolding NN are learned by DDPG, rather than updated by the stochastic gradient descent algorithm directly. Specifically, the optimization variables, trainable parameters, and architecture of deep-unfolding NN are designed as the state, action, and state transition of DDPG, respectively. Then, this framework is employed to deal with the channel estimation problem in massive multiple-input multiple-output systems. Specifically, first of all we formulate the channel estimation problem with an off-grid basis and develop a sparse Bayesian learning (SBL)-based algorithm to solve it. Secondly, the SBL-based algorithm is unfolded into a layer-wise structure with a set of introduced trainable parameters. Thirdly, the proposed DDPG-driven deep-unfolding framework is employed to solve this channel estimation problem based on the unfolded structure of the SBL-based algorithm. To realize adaptive depth, we design the halting score to indicate when to stop, which is a function of the channel reconstruction error. Furthermore, the proposed framework is extended to realize the adaptive depth of the general deep neural networks (DNNs). Simulation results show that the proposed algorithm outperforms the conventional optimization algorithms and DNNs with fixed depth with much reduced number of layers.

Chapter 6 - Channel estimation for mmWave massive MIMO systems

Massive multiple-input multiple-output (MIMO) communication is a promising technology for increasing spectral efficiency in wireless networks. Two of the main challenges massive MIMO systems face are degraded channel estimation accuracy due to pilot contamination and increase in computational load and hardware complexity due to the massive number of antennas. In this paper, we focus on the problem of channel estimation in massive MIMO systems, while addressing these two challenges: We jointly design the pilot sequences to mitigate the effect of pilot contamination and propose an analog combiner which maps the high number of sensors to a low number of RF chains, thus reducing the computational and hardware cost. We consider a statistical model in which the channel covariance obeys a Kronecker structure, and treat two special cases, corresponding to fully- and partially-separable correlations. We prove that under these models, the analog combiner design can be performed independently of the pilot sequences. Given the resulting combiner, we derive a closed-form expression for the optimal pilot sequences in the fully-separable case and suggest a greedy sum of ratio traces maximization (GSRTM) method for designing sub-optimal pilots in the partially-separable scenario. We demonstrate via simulations that our pilot design framework achieves lower mean squared error than the common pilot allocation framework previously considered for pilot contamination mitigation.

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.

This letter presents the first work introducing a deep learning (DL) framework for channel estimation in large intelligent surface (LIS) assisted massive MIMO (multiple-input multiple-output) systems. A twin convolutional neural network (CNN) architecture is designed and it is fed with the received pilot signals to estimate both direct and cascaded channels. In a multi-user scenario, each user has access to the CNN to estimate its own channel. The performance of the proposed DL approach is evaluated and compared with state-of-the-art DL-based techniques and its superior performance is demonstrated.

Channel estimation is crucial in millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, especially with a few training sequences. To solve the problem of uplink channel estimation in mmWave massive MIMO systems, a PARAFAC-based algorithm is proposed for joint estimation of multiuser channels. The orthogonal frequency divisional multiplexing (OFDM) technique is exploited to combat the frequency selective fading channels. In this paper, the received signal at the base station (BS) is formulated as a third-order parallel factor (PARAFAC) tensor, and then a low-complexity algorithm is designed for fast estimation of the factor matrices related to channel parameters, thus leading to joint estimation of multiuser channel parameters via one-dimensional search. Moreover, the Cramér–Rao Bound (CRB) results for multiuser channel parameters are derived for evaluation. Theorical analysis and numerical results reveal that the algorithm performs well with a few training sequences. Compared with existing algorithms, the proposed algorithm has clear advantages both in estimation accuracy and computational complexity.

With the large number of antennas and subcarriers the overhead due to pilot transmission for channel estimation can be prohibitive in wideband massive multiple-input multiple-output (MIMO) systems. This can degrade the overall spectral efficiency significantly, and as a result, curtail the potential benefits of massive MIMO. In this paper, we propose a neural network (NN)-based joint pilot design and downlink channel estimation scheme for frequency division duplex (FDD) MIMO orthogonal frequency division multiplex (OFDM) systems. The proposed NN architecture uses fully connected layers for frequency-aware pilot design, and outperforms linear minimum mean square error (LMMSE) estimation by exploiting inherent correlations in MIMO channel matrices utilizing convolutional NN layers. Our proposed NN architecture uses a non-local attention module to learn longer range correlations in the channel matrix to further improve the channel estimation performance.We also propose an effective pilot reduction technique by gradually pruning less significant neurons from the dense NN layers during training. This constitutes a novel application of NN pruning to reduce the pilot transmission overhead. Our pruning-based pilot reduction technique reduces the overhead by allocating pilots across subcarriers non-uniformly and exploiting the inter-frequency and inter-antenna correlations in the channel matrix efficiently through convolutional layers and attention module.

Sparse angular reciprocity learning for massive MIMO channel estimation