mmWave Massive Massive Multiple-input Multiple-output Research Articles

Optimized CNN and adaptive RBFNN for channel estimation and hybrid precoding approaches for multi user millimeter wave massive MIMO

ABSTRACT The millimetre-wave (mmWave) communication satisfies the demand for high data rates due to the characteristic of wide bandwidth. Using massive multiple-input multiple-output (MIMO) technology, a significant propagation loss of mmWave communication is effectively compensated. However, it is challenging to provide a specialised radio frequency chain for each antenna due to the constrained physical area with closely spaced antennas and prohibitive power consumption in mmWave massive MIMO systems. This paper presents novel approaches for effective channel estimation and hybrid precoding in mmWave communication systems. To address the challenges of channel estimation, a convolutional neural network (CNN) is utilised, and network parameters are optimised using enhanced whale optimization algorithm (EWOA). The proposed CNN-based channel estimation method aims to accurately estimate the channel in mmWave systems with enhanced efficiency and reduced complexity. By training CNN using EWOA optimisation algorithm, the network parameters are fine-tuned to improve accuracy and generalisation capability of channel estimation process. Furthermore, hybrid precoding is achieved using adaptive radial-basis function neural networks (adaptive RBFNNs) which enables efficient precoding while minimising complexity. Moreover, the adaptive RBFNN approach determines the optimal precoding weights based on channel state information, resulting in a improved performance and a reduced computational overhead. The performance analysis is validated using the MATLAB/Simulink software and offers to provide effectual and reliable mmWave communication systems, facilitating the realisation of high-speed and high-capacity wireless networks.

Adaptable Hybrid Beamforming with Subset Optimization Algorithm for Multi-User Massive MIMO Systems.

The exploiting of hybrid beamforming (HBF) in massive multiple-input multiple-output (MIMO) systems can enhance the system's sum rate while reducing power consumption and hardware costs. However, designing an effective hybrid beamformer is challenging, and interference between multiple users can negatively impact system performance. In this paper, we develop a scheme called Subset Optimization Algorithm-Hybrid Beamforming (SOA-HBF) that is based on the subset optimization algorithm (SOA), which effectively reduces inter-user interference by dividing the users set into subsets while optimizing the hybrid beamformer to maximize system capacity. To validate the proposed scheme, we constructed a system model that incorporates an intelligent reflecting surface (IRS) to address obstacles between the base station (BS) and the users set, enabling efficient wireless communication. Simulation results indicate that the proposed scheme outperforms the baseline by approximately 8.1% to 59.1% under identical system settings. Furthermore, the proposed scheme was applied to a classical BS-users set link without obstacles; the results show its effectiveness in both mmWave massive MIMO and IRS-assisted fully connected hybrid beamforming systems.

Hybrid Beamforming for mm-Wave Massive MIMO Systems with Partially Connected RF Architecture

To satisfy the capacity requirements of future mobile systems, under-utilized millimeter wave frequencies can be efficiently exploited by employing massive multiple input-multiple output (MIMO) technology with highly directive beamforming. Hybrid analog-digital beamforming has been recognised as a promising approach for large-scale MIMO implementations with a reduced number of costly and power-hungry radio frequency (RF) chains. In comparison to fully connected architecture, hybrid beamforming (HBF) with partially connected RF architecture is particularly appealing for the practical implementation due to less complex RF power division and combining networks. In this paper, we first formulate single- and multi-user rate maximization problems as weighted minimum mean square error (WMMSE) and derive solutions for hybrid beamformers using alternating optimization. The algorithms are designed for the full-array- and sub-array-based processing strategies of partially connected HBF architecture. In addition, we propose lower complexity sub-array-based zero-forcing algorithms. The performance of the proposed algorithms is evaluated in two different channel models, a simple geometric model and a realistic statistical model. The performance results of the WMMSE HBF algorithms are meant to reveal the potential of partially connected HBF and serve as upper bounds for lower complexity methods. Numerical results imply that properly designed partially connected HBF has the potential to provide an good compromise between hardware complexity and system performance in comparison to fully digital beamforming.

SEAttention-residual based channel estimation for mmWave massive MIMO systems in IoV scenarios

To improve the accuracy and efficiency of time-varying channels estimation algorithms for millimeter Wave (mmWave) massive Multiple-Input Multiple-Output (MIMO) systems in Internet of Vehicles (IoV) scenarios, the paper proposes a deep learning (DL) algorithm, Squeeze-and-Excitation Attention Residual Network (SEARNet), which integrates Squeeze-and-Excitation Attention (SEAttention) mechanism and residual module. Specifically, SEARNet considers the channel information as an image matrix, and embeds a SEAttention module in residual module to construct the SEAttention-Residual block. Through a data-driven approach, SEARNet can effectively extract key information from the channel matrix using the SEAttention mechanism, thereby reducing noise interference and estimating the channel in an accurate and efficient manner. The simulation results show that compared to two traditional and two DL channel estimation algorithms, the proposed SEARNet can achieve a maximum reduction in normalized mean square error (NMSE) of 97.66% and 84.49% at SNR of -10 dB, 78.18% at SNR of 5 dB, and 43.51% at SNR of 10 dB, respectively.

Quantum mechanics denoising based channel estimation algorithm for mmWave massive MIMO systems

Channel estimation of millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) is crucial for the application of wireless transmission. The signal system is susceptible to external noise, which reduces the accuracy of channel estimation. The denoising of the received signal is a research hotspot and challenge for channel estimation. Therefore, this paper proposes a quantum mechanics denoising-based channel estimation method. The proposed quantum mechanics denoising-based algorithm has the advantages of not relying on the original conditions, no grid error, and strong adaptive ability. The first part is that the received noisy signal is denoised. The conversion between the signal model of mmWave massive MIMO and the physical model of quantum mechanics needs to be solved. The received noisy signal is equivalent to the potential of the stationary Schrodinger equation. Then, the Hamiltonian matrix is constructed by the received signal and the corresponding eigenvalues and eigenvectors are calculated. The eigenvectors of the Hamiltonian matrix are related to the energy of Schrodinger equation, which are determined to the adaptive basis. In addition, the received signal is projected onto the adaptive basis to calculate the coefficients. The denoised received signal is reconstructed through the soft threshold processing of the coefficients. The second part is that channel estimation is performed on the denoised received signal using the l1/2-singular value decomposition (SVD)-based algorithm. The angle parameters are iteratively moved to the actual values by gradient descent. Besides, the initial values of the angles are obtained through the SVD preprocessing method. Simulation results show that the proposed quantum mechanics denoising-based method exhibits good estimation accuracy.

Cell-free ISAC massive MIMO systems with capacity-constrained fronthaul links

Integrated sensing and communication (ISAC), millimeter wave (mmWave) massive multiple-input multiple-output (MIMO), and cell-free networks are emerged as some of the most potential physical layer enablers for the future wireless communication networks. In this paper, we consider a cell-free ISAC mmWave massive MIMO system with hybrid analog and digital precoders while accounting for the impacts of capacity-constrained fronthaul links. In the system, the digital baseband processing is dictated at a geographical scale while the analog precoders are carried out at each transmit access point (AP). Based on the characteristics of the considered model, we formulate the optimization problem as a function of power allocation and fronthaul compression strategies. To address this problem, two block coordinate descend (BCD)-based methods are proposed to alternatively solve the three decomposed subproblems corresponding to the power allocation, the downlink and backward fronthaul compression strategies. Simulation results indicate that the proposed schemes can achieve 90% performance of the optimal full-search (FS) method with much lower computational complexity. In addition, there exists an optimal configuration of APs, UEs, and antennas for a cell-free ISAC system with capacity-constrained fronthaul links.

Channel reconstruction for mmWave Massive MIMO systems based on Channel Path Map

For the needs of high data rate and massive device access in current fifth-generation (5G) mobile communication networks and future sixth-generation (6G) mobile communication networks, Millimeter-Wave (mmWave) Massive Multiple-Input Multiple-Output (MIMO) is a crucial technical support. However, the conventional pilot based channel estimation methods are exceedingly time-consuming and substantially degrade system performance when the number of users or antennas is high. This paper proposes a Path Clustering based Channel Reconstruction (PCCR) scheme for channel reconstruction in order to solve this issue. By leveraging channel information (such as angle of arrival, angle of departure, and path gain) at a number of geographical locations that are recorded in the Channel Path Map (CPM), we aim to reconstruct the mmWave channel of any locations of interests. To be specific, the CPM is used to extract the neighborhood propagation path data, and an autonomous determination algorithm is used to find the number of path clusters at the location of interest. The recorded propagation path information is processed by the Equivalent Base Station (EBS) scheme, and the path clustering is accomplished by using the AGglomerative NESting (AGENS) algorithm. In each path cluster, Inverse Distance Weighted (IDW) algorithm is developed to forecast the path information at the user location. With all path information at user location are forecast, the channel can be reconstructed. The anticipated overhead is substantially lower than that of conventional methods because the computational cost of the procedure only depends on the total number of paths at the nearby locations. Ray-tracing based simulations are carried out to demonstrate the performance of the proposed algorithm. The results show that, when applied to a CPM with a spatial location precision of 5 m, the Normalized Mean Squared Error (NMSE) of the proposed algorithm is nearly identical to that of Linear Minimum Mean Square Error (LMMSE) estimation. The actual achievable date rate can match the needs of upcoming wireless communications and is superior over the conventional LMMSE.

Learned-SBL-GAMP based hybrid precoders/combiners in millimeter wave massive MIMO systems.

In Millimeter-Wave (mm-Wave) massive Multiple-Input Multiple-Output (MIMO) systems, hybrid precoders/combiners must be designed to improve antenna gain and reduce hardware complexity. Sparse Bayesian learning via Expectation Maximization (SBL-EM) algorithm is not practically feasible for high signal dimensions because estimating sparse signals and designing optimal hybrid precoders/combiners using SBL-EM still provide high computational complexity for higher signal dimensions. To overcome the issues of high computational complexity along with making it suitable for larger data sets, in this paper, we propose Learned-Sparse Bayesian Learning with Generalized Approximate Message Passing algorithm (L-SBL-GAMP) algorithm for designing optimal hybrid precoders/combiners suitable for mmWave Massive MIMO systems. The L-SBL-GAMP algorithm is an extension of the SBL-GAMP algorithm that incorporates a Deep Neural Network (DNN) to improve the system performance. Based on the nature of the training data, the L-SBL-GAMP can design the optimal Hybrid precoders/combiners, which enhances the spectral efficiency of mmWave massive MIMO systems. The proposed L-SBL-GAMP algorithm reduces the iterations, training overhead, and computational complexity compared to the SBL-EM algorithm. The simulation results unveil that the proposed L-SBL-GAMP provides higher achievable rates, better accuracy, and low computational complexity compared to the existing algorithm, such as Orthogonal Matching Pursuit (OMP), Simultaneous Orthogonal Matching Pursuit (SOMP), SBL-EM and SBL-GAMP for mmWave massive MIMO architectures.

Interference Alignment in Channel Estimation Using Hybrid Deep Neural Network with Multi-user Propagation Model for 5G in MM Wave Massive MIMO

Massive Multiple Input Multiple Output (MIMO) technologies, as well as higher frequencies utilization, such as MilliMeter Wave (MM Wave) frequencies, should be utilized in the 5G wireless network. This massive transmission will require a higher frequency band and in cellular massive MIMO, frequencies re-use leads to interference in channel estimation. Interference Alignment (IA) is a transmission strategy of the channel with higher capacities of signal-to-noise ratio. This interference needs to be aligned before the transmission of signal, so this research proposes a novel technique in IA by hybridization of deep learning techniques for Heterogeneous Networks (HetNets). The aim of this work is to develop a new interference alignment scheme based on multi-user with a neural network which can be efficient in mitigation of interference of the networks. The model that is proposed properly exploits the interference alignment concept by developing a multi-user group of small cells assisted by various BSs in the heterogeneous networks for MM Wave. The paper focuses on channel estimation by IA for a 5G network that transmits MMWave using neural networks. The neural network is utilized for learning the mapping functions between the received mmWave channels with negligible overhead. Here Hybrid Deep Neural Network is used with Multi-User Propagation (HDNN-MUP) model for IA and demonstrates a practical upper bound for MIMO array sizes that balance throughput and estimation overhead. The experimental analysis is done by utilizing the parameters namely Signal-to-noise ratio (SNR), Bit Error Rate (BER), computational time, energy efficiency, and spectral efficiency.

Beam Selection for Cell-Free Millimeter-Wave Massive MIMO Systems: A Matching-Theoretic Approach

In this letter, we consider beam selection in cell-free millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. To address the beam selection of all access points in the network for cell-free operation, a beam selection problem that maximizes the minimum of spectral efficiencies of all user equipments is formulated. We propose an extended deferred acceptance algorithm for beam selection based on the matching theory. Additionally, we propose two intuitive beam selection algorithms. System-level simulation results demonstrate the advantage of the proposed matching theory-based beam selection method in terms of spectral efficiency for cell-free mmWave massive MIMO systems.

Tensor-Based Joint Beamforming with Ultrasonic and RIS-Assisted Dual-Hop Hybrid FSO mmWave Massive MIMO of V2X

Reconfigurable intelligent surface (RIS)-assisted millimeter-wave (mmWave) communication systems relying on hybrid beamforming structures are capable of achieving high spectral efficiency at a low hardware complexity and with low power consumption. Tensor-based joint beamforming with low-cost ultrasonic and RIS-assisted Dual-Hop Hybrid free space optical (FSO) mm Wave massive Multiple Input Multiple Output (MIMO) of vehicle-to-everything (V2X) is proposed. To address the occlusion problem for high-speed mobility of the vehicle, an RIS-assisted mixed FSO-MIMO V2X system is proposed. The low-cost ultrasonic array signal model is developed to solve the accurate direction-of-arrival (DOA) estimation. The ultrasonic-assisted RIS phase shift matrix based on subspace self-organizing iterations is designed to track the beam direction between RIS and vehicle. Specifically, the associated bandwidth-efficiency maximization problem is transformed into a series of subproblems, where the subarray of phase shifters and RIS elements is jointly optimized to maximize each subarray’s rate. The vehicle motion state is transformed into a two-dimensional model for prior distribution to calculate the particle weights of the RIS phase. Multi-vehicle Tucker tensor decomposition is used to describe the high-dimensional beam space. We conceive a multi-vehicle joint optimization method for designing the hybrid beamforming matrix of the base station (BS) and the passive beamforming matrix of the RIS. A cascaded channel decomposition method based on Singular Value Decomposition (SVD) is used to obtain the combined matrix beamforming of BS and vehicle. Our simulation results demonstrate the superiority of the proposed method compared to its traditional counterparts.

Spatial attention and quantization-based contrastive learning framework for mmWave massive MIMO beam training

Deep learning (DL)-based beam training schemes have been exploited to improve spectral efficiency with fast optimal beam selection for millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. To achieve high prediction accuracy, these DL models rely on training with a tremendous amount of labeled environmental measurements, such as mmWave channel state information (CSI). However, demanding a large volume of ground truth labels for beam training is inefficient and infeasible due to the high labeling cost and the requirement for expertise in practical mmWave massive MIMO systems. Meanwhile, a complex environment incurs critical performance degradation in the continuous output of beam training. In this paper, we propose a novel contrastive learning framework, named self-enhanced quantized phase-based transformer network (SE-QPTNet), for reliable beam training with only a small fraction of the labeled CSI dataset. We first develop a quantized phase-based transformer network (QPTNet) with a hierarchical structure to explore the essential features from frequency and spatial views and quantize the environmental components with a latent beam codebook to achieve robust representation. Next, we design the SE-QPTNet including self-enhanced pre-training and supervised beam training. SE-QPTNet pre-trains by the contrastive information of the target user and others with the unlabeled CSI, and then, it is utilized as the initialization to fine-tune with a reduced volume of labeled CSI. Finally, the experimental results show that the proposed framework improves beam prediction accuracy and data rates with 5% labeled data compared to existing solutions. Our proposed framework further enhances flexibility and breaks the limitation of the quantity of label information for practical beam training.

OFDM-based Wideband Hybrid Beamformer for mmWave Massive MIMO Multiuser 5G Systems

Employing massive antennas array at the user terminals can be feasible by using millimeter wave (mmWave) transmission which significantly reduce the antennas array size. The implementation of massive multiple input multiple output (MIMO) at the user terminals facilitates accurate beamforming. In this paper, a modified orthogonal matching pursuit (OMP) algorithm is used to design a wideband hybrid combiner based on the sparse structure of mmWave channel and orthogonal frequency-division multiplexing (OFDM). Based on OFDM, the wideband channel considered as multiple narrowband channels so a modified narrowband hybrid combiner can be implemented for each subcarrier channel in a manner where the RF combiner is the same for all subcarriers, whilst the baseband combiner is obtained for each subcarrier. For the multiuser 5G system, a wideband hybrid precoder based on the block diagonalization (BD) method is used at the base station (BS) to cancel the interference at each user due to the other users. The performance of this hybrid beamformers (precoder/combiner) are tested for different scenarios of base station antennas number, numbers of users’ antennas, and number of users.

Deep Learning-Based Channel Estimation for Wideband Hybrid MmWave Massive MIMO

Hybrid analog-digital (HAD) architecture is widely adopted in practical millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems to reduce hardware cost and energy consumption. However, channel estimation in the context of HAD is challenging due to only limited radio frequency (RF) chains at transceivers. Although various compressive sensing (CS) algorithms have been developed to solve this problem by exploiting inherent channel sparsity and sparsity structures, practical effects, such as power leakage and beam squint, can still make the real channel features deviate from the assumed models and result in performance degradation. Besides, the high complexity of CS algorithms caused by a large number of iterations hinders their applications in practice. To tackle these issues, we develop a deep learning (DL)-based channel estimation approach where the sparse Bayesian learning (SBL) algorithm is unfolded into a deep neural network (DNN). In each SBL layer, Gaussian variance parameters of the sparse angular domain channel are updated by a tailored DNN, which is able to capture complicated channel sparsity structures in various domains effectively and efficiently. The measurement matrix is jointly optimized for performance improvement. Then, the proposed approach is extended to the multi-block case where channel correlation in time is further exploited to adaptively predict the measurement matrix and facilitate the update of variance parameters. Simulation results show that the proposed approaches outperform existing approaches in terms of both performance and complexity.

Two-Stage Channel Estimation Using Convolutional Neural Networks for IRS-Assisted mmWave Systems

Intelligent reflecting surface (IRS) is expected to be an essential component of next-generation wireless communication networks due to its potential to provide similar or higher array gain with lower hardware cost and energy consumption compared with massive multiple-input--multiple-output (MIMO) technology. However, channel estimation in IRS-assisted communication systems is more challenging than that in conventional systems. In this article, we propose a two-stage channel estimation approach using deep learning in millimeter-wave (mmWave) communication systems with a hybrid passive/active IRS structure. In the first stage, the sparsity of the mmWave massive MIMO channel in the angular domain is exploited to estimate the amplitude of the sparse channel through a convolutional neural network. In this way, the indices of the nonzero entries of the sparse channel can be simultaneously obtained. In the second stage, the channel is reconstructed by solving a least squares problem with the acquired indices. The simulation results show that the proposed channel estimation scheme could achieve better performance with manageable complexity over the existing solutions.

Covert Millimeter Wave Communications Based on Beam Sweeping

The combination of millimeter wave (mmWave) and covert communications can ensure high security for some specific circumstances. Instead of considering the covertness only in the data transmission (DT) phase for mmWave massive MIMO systems, the covertness in both the beam alignment (BA) phase and the DT phase is investigated. As a common beam training method for mmWave massive multiple-input multiple-output (MIMO), beam sweeping is adopted to obtain the optimal beam pair in the BA phase. Aiming at maximizing the average effective achievable covert rate in the DT phase, a two-stage power optimization scheme is proposed subject to the covertness and power constraints in both the BA and the DT phases. Specifically, by introducing a covertness allocation factor, closed-form expressions of the transmit power in both phases are derived according to the likelihood function of the received signal. Simulation results demonstrate that the average covert rate of MIMO is larger than that of multiple-input single-output (MISO) although the BA success rate of the former is lower than that of the latter.

Integrated Sensing and Communication With mmWave Massive MIMO: A Compressed Sampling Perspective

Integrated sensing and communication (ISAC) has opened up numerous game-changing opportunities for realizing future wireless systems. In this paper, we propose an ISAC processing framework relying on millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. Specifically, we provide a compressed sampling (CS) perspective to facilitate ISAC processing, which can not only recover the high-dimensional channel state information or/and radar imaging information, but also significantly reduce pilot overhead. First, an energy-efficient widely spaced array (WSA) architecture is tailored for the radar receiver, which enhances the angular resolution of radar sensing at the cost of angular ambiguity. Then, we propose an ISAC frame structure for time-varying ISAC systems considering different timescales. The pilot waveforms are judiciously designed by taking into account both CS theories and hardware constraints induced by hybrid beamforming (HBF) architecture. Next, we design the dedicated dictionary for WSA that serves as a building block for formulating the ISAC processing as sparse signal recovery problems. The orthogonal matching pursuit with support refinement (OMP-SR) algorithm is proposed to effectively solve the problems in the existence of the angular ambiguity. We also provide a framework for estimating the Doppler frequencies during payload data transmission to guarantee communication performances. Simulation results demonstrate the good performances of both communications and radar sensing under the proposed ISAC framework.

Covert Communication for Spatially Sparse mmWave Massive MIMO Channels

Covert communication, also known as communication with low probability of detection, aims to provide reliable communication for legal users and prevent any other user from detecting the occurrence of legal communication. Motivated by the strong need of security links of the next generation communication systems, we study covert communication with millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) hybrid beamforming. Consistent with existing studies on covert communication, we use the Kullback-Leibler (KL) divergence and the total variation (TV) distance as the covertness measure. Under both covertness measures, for block fading channels, we derive the covert transmission rate with and without artificial noise. These results are obtained by optimizing the transmit power and the jamming power to satisfy the covertness constraints and to maximize the transmission rate. Specifically, when artificial noise is allowed, we show that there exists an optimal jamming power to achieve the covert transmission rate given the transmit signal power. Furthermore, we propose a metric to measure the inherent sparsity of the mmWave massive MIMO channel in the spatial domain, and study its effect on the covertness measures and the corresponding covert transmission rates. Our results provide insights and benchmarks for the design of practical covert communication systems with mmWave massive MIMO.

An enhanced beamspace channel estimation algorithm for wideband millimeter-wave massive MIMO systems

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.

Clustered Sparse Bayesian Learning Based Channel Estimation for Millimeter-Wave Massive MIMO Systems

In this article, we present two clustered sparse Bayesian learning (Cluster-SBL) channel estimation algorithms for millimeter-wave (mmWave) massive multiple-input-multiple-output (MIMO) systems. Different from prior literature, channel path correlations at both the transmitter and the receiver are considered and exploited for estimation performance enhancement. Specifically, we first propose a Kronecker product-based multivariate Gaussian (KP-Gaussian) prior model for mmWave massive MIMO channels, which captures not only sparsity but also the widely existing clustering channel property in mmWave communications. Then, a channel approximation method is derived and leveraged to overcome the challenge caused by channel priors' uncertainty due to the varying propagation environments and improve the robustness of the channel estimation algorithm against channel sparsity. After that, the Cluster-SBL channel estimation algorithm, which is developed based on the expectation maximization (EM) framework and has superior estimation accuracy and high robustness, is proposed. Moreover, to reduce the computation complexity in the channel estimation for practical applications, we also propose an efficient Cluster-SBL (eCluster-SBL) channel estimation algorithm. It is highly beneficial to mmWave massive MIMO systems, especially when the angular resolution is relatively high. Numerical results reveal that, compared with the existing compressed sensing-based and Bayesian criterion-based algorithms, the proposed two channel estimation algorithms exhibit the better performance from both the aspect of estimation accuracy and the aspect of robustness.