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In this paper, we design receivers for filter bank multicarrier-based (FBMC-based) massive MIMO considering practical aspects such as channel estimation and equalization. In particular, we propose a spectrally efficient pilot structure and a channel estimation technique in the uplink to jointly estimate all the users’ channel impulse responses. We mathematically analyze our proposed channel estimator and find the statistics of the channel estimation errors. These statistics are incorporated into our proposed equalizers to deal with the imperfect channel state information (CSI) effect. We revisit the channel equalization problem for FBMC-based massive MIMO, address the shortcomings of the existing equalizers in the literature, and make them more applicable to practical scenarios. The proposed receiver in this paper consists of two stages. In the first stage, a linear combining of the received signals at the base station (BS) antennas provides a coarse channel equalization and removes any multiuser interference. In the second stage, a per subcarrier fractionally spaced equalizer (FSE) takes care of any residual distortion of the channel for the user of interest. We propose an FSE design based on the equivalent channel at the linear combiner output. This enables the applicability of our proposed technique to small and/or distributed antenna setups such as cell-free massive MIMO. Finally, the efficacy of the proposed techniques is corroborated through numerical analysis. [ABSTRACT FROM AUTHOR]

Millimeter wave (mmWave) frequency spectrum offers orders of magnitude greater spectrum to mitigate the severe spectrum shortage in conventional cellular bands. To overcome the high propagation loss in the mmWave band, massive multiple-input and multiple-output (MIMO) can be adopted at both transmitter and receiver to provide large beamforming gains. At the same time, hybrid architecture is applied to reduce the huge power consumption caused by devices operating at radio frequency (RF). However, because of the hybrid architecture and large number of antennas, it is hard to obtain the channel state information (CSI) which is crucial for obtaining desirable beamforming gains. Off-grid error and sparsity pattern (SP) estimation error are two main limiting factors of the performance of most existing compressive sensing (CS) based channel estimation (CE) algorithms. Off-grid error presents when the true angle does not lie on the discretized angle grid of mmWave channel in the spatial domain. In this paper, we first propose a fast Bayesian matching pursuit method with ‘virtual sparsity’ to improve the accuracy of SP estimation and name it as the improved Bayesian matching pursuit (IBMP). Then an enhanced algorithm, named off-grid IBMP (OG-IBMP), is developed to mitigate the off-grid problem, followed by a theoretical analysis of OG-IBMP. This method iteratively updates the selected grid points and updates the corresponding parameters based on the maximum a posteriori (MAP) criterion. Numerical simulations are performed to validate our theoretical analysis and evaluate the performance of the proposed method. Compared to other existing methods, the results show that our proposed OG-IBMP algorithm greatly reduces the off-grid error and significantly enhances the accuracy of the SP estimation with low computational complexity. [ABSTRACT FROM AUTHOR]

Reconfigurable intelligent surface (RIS) is a passive antenna array composed of a large number of reflecting elements. In a RIS-assisted communication system, it is a challenging task to acquire accurate channel state information (CSI). In this paper, we propose a semi-blind channel estimation method for a RIS-assisted massive multiple-input single-output (MISO) system. Assuming a Gaussian priori on the data symbols, an iterative expectation maximization (EM)-based algorithm is developed to obtain the maximum likelihood (ML) estimate of the cascaded RIS channel. Different from existing pilot-based methods, the proposed semi-blind channel estimation method exploits the data symbols for channel estimation enhancement and only a fraction of full-pilot signaling overhead is required. Simulation results verify that the proposed method achieves significant improvement in the accuracy of the channel estimation while it noticeably reduces the training pilot overhead. [ABSTRACT FROM AUTHOR]

Reconfigurable intelligent surfaces (RISs) and cell-free (CF) massive multiple-input multiple-output (MIMO) are two promising technologies for realizing beyond-fifth generation (5G) networks. In this paper, we study the uplink spectral efficiency (SE) of a practical spatially correlated RISs-aided CF massive MIMO system over Rician fading channels. Specifically, we derive the closed-form expression for characterizing the uplink SE of the system, which shows that increasing the number of RIS elements can improve the system performance. Moreover, the results unveil that the spatial correlation of RIS has a significant impact on the system while leading to the best performance gain at a half wavelength spacing. Finally, the accuracy of our analytical results are verified by Monte-Carlo simulations. [ABSTRACT FROM AUTHOR]

Intelligent reflecting surface (IRS)-enhanced wireless communication is one of the critical technologies of the sixth generation mobile communication, which has recently emerged as an innovative solution to the realization of intelligent transportation. It can meet the increasing demand for high-speed railway (HSR) communications services. In this paper, we consider a train-ground TDD wireless mobile communication paradigm to deploy two IRSs on the roadside and the train roof to assist the wireless transmission for the HSR communication system. To achieve the more significant performance gain, in the uplink transmission phase, we propose the practical channel estimation framework of the MIMO system aided by double IRSs to acquire reliable channel state information (CSI) of each channel. To facilitate the processing of the three-dimension tensor, we leverage the trilinearity of the parallel factor decomposition to decompose the received signal into a two-dimensional matrix. The Doppler frequency offset compensating scheme and channel tracking scheme based on Kalman-Filter are proposed to further decrease the pilot overheads. Then, in the downlink phase, a block coordinate descent (BCD) algorithm is proposed to handle the data rate maximization problem of double IRSs communication system with the estimated CSI. We reformulate the original problem and decouple the double IRSs phase optimization problem into two single IRS phase optimization non-convex problems under the unit-modulus constraint. The Majorization-Minimization (MM) algorithm is proposed to approximate the optimal solution of the two optimization subproblems. Simulation results corroborate the effectiveness of the proposed channel estimation and phase shifts optimization scheme. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a two-hop simultaneous wireless information and power transfer (SWIPT) amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay communication system with an energy-limited relay node. The relay node harvests energy based on the radio-frequency (RF) signal transmitted from the source node through the time-switching (TS) protocol and fully uses the harvested energy to precode and forward the information to the destination node. The non-linear energy harvesting models are considered at the relay node. With the consideration of the channel estimation error, the joint optimization of the TS factor, source and relay precoding matrices is proposed with robustness against the channel state information (CSI) mismatch to maximize the mutual information (MI) between the source and destination nodes. The optimal structure for the source and relay precoding matrices is derived to simplify the transceiver optimization problem. Numerical simulations show that the system performance provided by the proposed algorithms with robustness is better than the non-robust algorithm. [ABSTRACT FROM AUTHOR]

Cell-free (CF) massive multiple-input multiple-output (mMIMO) is a promising candidate to support the requirements of the fifth-generation (5 G) and beyond networks. However, the capacity of the fronthaul network dramatically influences its performance. While wired fronthaul links can be seen as the optimal choice, they may not be practically feasible. Exploiting the enormous bandwidth available in the millimeter-Wave (mmWave) band to support the fronthaul links paves the way to achieve the full potential of CF mMIMO systems. In this paper, we investigate the uplink (UL) performance of CF mMIMO systems supported by mmWave-fronthaul networks. Using tools from stochastic geometry, we derive analytical expressions for both the distribution of the provided fronthaul capacity and the average UL data rates. We show that although increasing the density of blockages degrades the average UL data rates, increasing the density of CPUs can limit such effect. Moreover, the obtained results reveal that the network deployment should be adjusted according to the available fronthaul bandwidth and the density of blockages. In particular, for a given fronthaul bandwidth, increasing the density of APs beyond a certain limit would not achieve further improvement in the UL data rates. Besides, increasing the number of antennas per AP may even cause a degradation in the system performance. [ABSTRACT FROM AUTHOR]

Consider a base station (BS) relying on a massive antenna array, which transmits information to multiple vehicles of vehicular networks. In order to jointly consider both the communication resource consumption and the road-traffic efficiency, we define a metric given by the BS's downlink power normalized by the vehicular velocity. We refer to it as the Power to Velocity Ratio (PVR). The prime objective of this paper is to minimize either the maximum individual vehicle PVR or the entire system's PVR by optimizing the power allocation at the BS, while guaranteeing the information requirements of the vehicles both under the total transmit power constraint and driving velocity constraint. As for the individual vehicle PVR, a closed-form power allocation expression is derived by assuming that the transmit power constraint is non-restrictive. Based on this an optimal power allocation algorithm is proposed for arbitrary finite transmit power constraints. As for the system PVR, the non-convex problem formulated is first transformed into a convex problem and then the optimal solution is found by conceiving an efficient iterative algorithm. Our simulation results show that the proposed algorithms indeed succeed in achieving the optimal individual vehicle or system PVR. [ABSTRACT FROM AUTHOR]

In this paper, we propose a deep neural network (DNN) aided codebook based beamforming scheme for frequency-division-duplex (FDD) millimeter-Wave (mmWave) massive multiple-input multiple-output (MIMO) systems under multipath. Different from the time-division-duplex (TDD) systems, for FDD systems the reciprocity between the down-link (DL) and up-link (UL) channel state information (CSI) does not hold in general, requiring an extra CSI feedback stage. Based on the previous theoretical analysis and measurements, however, partial reciprocities, including the spatial directional angles and number of propagation paths, do exist for FDD mmWave systems. Given such partial reciprocities, we propose a beamforming scheme based on a predefined codebook. Furthermore, we consider the channels with multipath where multiple codewords can be selected for some mobile stations (MSs) to utilize more than one propagation paths, which improves the link reliability. We then propose the corresponding beamforming strategy that not only identifies the number of paths, but also reconstructs the individual single-path channels which are easier to deal with at the beamforming stage. To select the optimal codewords for these single-path channels with lower complexity, we then present a DNN-aided approach that predicts the optimal codewords. The integration of DNN resolves not only the issue of power leakage, but also angular ambiguity in the codebook. Simulation results demonstrate that the performance of the proposed DNN-aided approach is very close to that of an exhaustive search. [ABSTRACT FROM AUTHOR]

In the existing millimeter-wave (mmWave) wireless positioning systems, the method based on sparse Bayesian learning (SBL) uses the channel sparsity to estimate the parameters required for positioning, such as angle of arrival (AOA) and time delay, but most existing SBL solutions only consider the angle sparsity. In this paper, we consider the joint sparsity of the angle domain and time delay domain to propose an improved SBL algorithm by using a new two-dimensional adaptive grid refinement method in the SBL framework. This algorithm solves the grid mismatch problem caused by the fixed grid in the traditional SBL method, and reduces the algorithm complexity of the off-grid SBL (OGSBL) algorithm. We also obtain the Cramér-Rao bound (CRB) of AOA, time delay and position estimation based on the mmWave multipath signals to analyze the estimation errors. Simulation results show that the performance of the proposed algorithm is better than existing algorithms and can approach CRB. [ABSTRACT FROM AUTHOR]

In this paper, we study a beam tracking problem for millimeter wave (mmWave) channels in massive multiple-input and multiple-output communication systems. We formulate the beam tracking problem as a stochastic filtering problem by modeling the dynamic state equation and the observation equation. Then, given prior information of the channel, we propose an efficient grid-based Bayesian beam tracking algorithm by leveraging the sparsity of the mmWave channel. Our proposed algorithm examines neighboring transmit and receive beam pairs and exploits multiple observations on the angular domain representation in the sense of the Bayesian statistics. Numerical results show that the proposed Bayesian method with multiple observations outperforms conventional schemes in terms of both the beam tracking accuracy and computational complexity. [ABSTRACT FROM AUTHOR]

In this paper, we propose three new compressive sensing-based algorithms for channel estimation in millimeter wave hybrid MIMO systems over doubly (time and frequency) selective channels. Utilizing the basis expansion model (BEM) for effectively representing doubly selective channels, we first propose a BEM-based block orthogonal matching pursuit (BBOMP) algorithm, which can work with any training sequence structure. Next, we present the second algorithm to reduce the complexity of the BBOMP method by employing a special training sequence which results in a computationally efficient block sparse sensing matrix. Finally, in order to further decrease the computational complexity, we propose the third algorithm, where the channel estimation is split into two separate steps of tap detection and gain estimation. The proposed algorithms exploit the entire available training sequence to estimate all channel parameters, and can capture channel variations across the entire training frames without requiring a feedback channel. The Cramer-Rao lower bound and the computational complexity of the proposed algorithms are also addressed. Intensive computer simulations are conducted to evaluate the accuracy of the proposed approaches, showing that they can significantly improve the mean squared error performance compared with the state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

In this paper, a generalized uplink cell-free massive multiple-input multiple-output (mMIMO) system with hardware imperfections is investigated. Specifically, the hardware impairments consist of multiplicative phase drifts, additive distortion, and amplified thermal noise. Leveraging on a generic hardware impairment model, closed-form expressions for the channel estimation and achievable rate are presented. Based on these tractable results, we explore the uplink achievable rate surrounding the key design parameters, i.e., the channel estimation error, the number of antenna arrays, the local oscillator (LO) setup, and the variance of phase drifts. Aside from this, we also design a power optimization algorithm to maximize the sum-rate under variant channel use. The weighted minimum mean square error (MMSE) methodology is introduced to iteratively determine the solution in closed form. Numerical simulations validate the analytical analyses and examine the effectiveness of the proposed power control algorithm. [ABSTRACT FROM AUTHOR]

Multiple remote antenna units (RAUs) cooperate to serve a certain user in cell-free distributed massive multiple-input multiple-output (MIMO) systems. Due to the different distances between each RAU and the user, asynchronous reception effects will occur. This paper studies the impacts of asynchronous reception effects on cell-free distributed massive MIMO systems. We first derive the minimum-mean-square error (MMSE) channel estimation under the asynchronous reception effects. Given the estimated channel state information, we derive the closed-form expressions of the user achievable rates with maximum ratio transmission (MRT) and regularized zero-forcing (RZF) precoders, which are further used to analyze the impacts of asynchronous reception effects. The accuracy of the closed-form expressions are verified. Simulation results demonstrate that asynchronous reception effects cause a non-negligible drop on the system spectral efficiency. Moreover, the performance degradation is proportional to the subcarrier sequence number and even more serious with the increasing of signal-to-noise ratio (SNR) or the number of antennas per RAU. [ABSTRACT FROM AUTHOR]

For large-scale antenna array multiple-input multiple-output (MIMO) systems, a typical solution often put forward for uplink detection consists in applying low-complexity linear receivers such as zero-forcing (ZF) and minimum mean-square error (MMSE) combiners. In this paper, the performance of uplink MMSE detection has been analyzed in the context of a multi-cell multiuser MIMO system. An approximate expression for the signal-to-interference-plus-noise ratio (SINR) is proposed, which is in simple form and becomes exact in the low SNR regime. This approximate SINR applies to systems where the base station (BS) has the statistical information of the out-of-cell interfering signals, and systems where the BS ignores the presence of such interfering signals. This approximate SINR is tight for arbitrary user powers, arbitrary number of antennas at the base station, and arbitrary channel correlation matrix associated with any particular user. Approximate expressions for capacity and bit-error rate/symbol-error rate have also been derived. Particularly, it can be proven that, when the MMSE receiver ignores the presence of out-of-cell interfering signals, the performance gap between ZF and MMSE vanishes in the high SNR regime. [ABSTRACT FROM AUTHOR]

This paper considers the secure transmission in a cell-free massive MIMO system with imperfect radio frequency (RF) chains and low-resolution analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) at both access points (APs) and legitimate users, where an active eavesdropper attempts to wiretap the confidential data. The Gaussian RF impairment model (GRFIM) and additive quantization noise model (AQNM) are used to evaluate the impacts of the RF impairments and low resolution ADCs/DACs, respectively. The analytical results of the linear minimum mean square error (MMSE) channel estimation show that there is nonzero floor on the estimation error with respect to the RF impairments, ADC/DAC precision and the pilot power of the eavesdropper which is different from the conventional case with perfect transceiver. Then, a tractable closed-form expression for the ergodic secrecy rate is obtained with respect to key system parameters, such as the antenna number per AP, the AP number, user number, quality factors of the ADC/DAC and the RF chain, pilot signal power of the eavesdropper, etc. Moreover, a compensation algorithm between the imperfect RF components and the inexpensive coarse ADCs/DACs is also presented. Finally, numerical results are provided to illustrate the efficiency of the achieved expressions and the devised algorithm, and show the effects of RF impairments and low resolution ADC/DAC on the secrecy performance. [ABSTRACT FROM AUTHOR]

Hybrid precoding is used in millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems instead of full digital precoding to reduce the cost and power consumption. Conventional hybrid precoding however requires complex channel estimation before beamforming. In this paper, we propose a low complexity low-cost channel estimation-free deep direct beamforming method composed of two basic steps-beam impulse and beamforming for time division duplex (TDD). This method is built upon randomized singular value decomposition (RSVD) and can directly complete the process of beamforming. Furthermore, a realistic dataset of mmWave channel-DeepMIMO is adopted to evaluate and determine the practicability of this method. The simulation results demonstrate that the proposed deep direct beamforming achieves high performance while its complexity and power consumption are very low. Compared with other methods without perfect channel status information (CSI), the proposed method costs less and requires lower computational resources while achieves higher spectral efficiency. Furthermore, the RSVD can be easily combined with conventional beamforming methods hence the proposed method is easily extendable to other applications. [ABSTRACT FROM AUTHOR]

This paper proposes a flexible pilot assignment method to jointly optimize the uplink and downlink data transmission in multi-cell Massive multiple input multiple output (MIMO) systems with correlated Rayleigh fading channels. By utilizing a closed-form expression of the ergodic spectral efficiency (SE) achieved with maximum ratio processing, we formulate an optimization problem for maximizing the minimum weighted sum of the uplink and downlink SEs subject to the transmit powers and pilot assignment sets. This combinatiorial optimization problem is solved by two sequential algorithms: a heuristic pilot assignment is first proposed to obtain a good pilot reuse set and the data power control is then implemented. Numerical results manifest that the proposed algorithm converges fast to a better minimum sum SE per user than the algorithms in previous works. [ABSTRACT FROM AUTHOR]

Secure downlink transmission in massive multiple-input multiple-output (MIMO) systems has sparked great research enthusiasm. However, the secrecy of uplink transmission is equally important although relatively less attention has been dedicated to. In this paper, we show that a multi-antenna eavesdropper could potentially reduce the secrecy rate of legitimate communications severely through channel estimation in the training phase and coherent detection in the payload data transmission phase. To safeguard uplink transmission, an artificial noise (AN)-assisted scheme is proposed. Specifically, the optimization problem that aims to optimize the power allocation between AN and data symbols in the sense of maximizing the secrecy rate is formulated. We investigate optimal power allocation strategies for two distinct cases. That is, the base station and the eavesdropper know the channel state information to the users, and the opposite case. In each case, we further consider whether the accurate position of the eavesdropper is known to the users. Due to the complexity of the cost function, a closed-form solution is intractable. As a result, the bisection method is employed to obtain the numerical results. The impacts of the non-idealities, including the channel estimation error and the uncertainty of eavesdropper's position, on the power allocation strategy are discussed. Finally, extensive simulations are carried out to validate our proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper studies the channel estimation performance in massive multiple-input multiple-output (MIMO) systems with Ricean fading through considering the relative channel estimation error (RCEE) metric. The closed-form expressions of the probability distribution function (PDF) and cumulative distribution function of RCEE are derived, according to which the PDFs of RCEE with Rayleigh fading and pure line-of-sight (LoS) propagation are obtained as special cases. Through analyzing RCEE, it notes that as the number of base-station antennas M becomes unbounded, RCEE approaches a given constant. Moreover, the asymptotic analysis proves that, in high M-regime, the increasing rate of the RCEE scales in the order of √M for Rayleigh fading and pure LoS propagation, while the scaling order with general Ricean fading is capped by √M. All the above mentioned results are verified through Monte-Carlo simulations. [ABSTRACT FROM AUTHOR]

Pilot contamination resulting from pilot reuse seriously restricts the communication performance of the cell-free massive multiple-input multiple-output (MIMO) networks. To deal with this problem, an efficient pilot assignment scheme using a weighted graphic framework is proposed in this correspondence paper. Specifically, a novel metric is first introduced for capturing the severity of potential mutual pilot contamination in cell-free topology. On this basis, the weighted pilot contamination graph is constructed to depict the dynamic interference relationship corresponding to the network. Then, the pilot assignment optimization is mapped to the Max k-Cut problem, and a heuristic algorithm is exploited to realize pilot decontamination. Numerical simulation results reveal the superior performance of the proposed scheme, which is capable of achieving a significant improvement in throughput with low complexity. [ABSTRACT FROM AUTHOR]

This paper investigates the downlink (DL) rate of multicell massive multiuser multiple-input and multiple-output systems over Ricean fading channels that takes into account channel estimation errors. To acquire channel state information at all users, beamforming training (BT) is examined. Considering both maximum-ratio transmission (MRT) and zero forcing, this paper derives closed-form expressions on the lower bound of the achievable rates for two cases, with or without BT. With the obtained expressions, Bernoulli's inequality is invoked to find the ranges for the length of DL pilots such that the sum spectral efficiency of the scheme with BT is superior to that of the scheme without BT, and vice versa. Various power scaling laws concerning DL data and pilot transmit powers and uplink pilot transmit power are analyzed. Numerical results corroborate the accuracy of the closed-form expressions. In particular, the results show that employing BT with MRT processing is only preferred in environments having a high signal-to-noise ratio, low mobility, and small Ricean $K$ -factors. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the average transmit power of non-orthogonal multiple access (NOMA) systems with requirements on the user signal-to-interference-plus-noise-ratios (SINRs), and propose new transmission schemes and user clustering algorithms to reduce the average transmit power. First, for systems with a multi-antenna base station (BS) and a single cluster of two single-antenna users, the average transmit power with SINR constraints is analyzed for channel-alignment-based NOMA and multi-user beamforming with matched filter (MF) beamformers. Properties of the average transmit power are obtained with respect to the alignment threshold and the BS antenna number. It is shown that using either scheme alone without the alignment consideration leads to unbounded average transmit power. With the observation that the two schemes have distinct preferred regions of channel alignment, hybrid transmissions of NOMA and multi-user beamforming are proposed for power saving and outage avoidance. Further, for systems with more than two users, clustering algorithms are developed to group users into multiple two-user clusters with respect to the minimization of the total transmit power for NOMA and hybrid schemes. Simulation results are provided to validate our theoretical results. In addition, the proposed transmission schemes and clustering algorithms are shown to achieve significant saving in the average transmit power. [ABSTRACT FROM AUTHOR]

Intelligent reflecting surfaces (IRSs) can improve the wireless link between the transmitter and receiver by configuring the propagation environments of the system. In order to achieve intelligence of the configuration, the channel state information is required. In this paper, we study the downlink channel estimation problem in an IRS-aided frequency division duplexing (FDD) multiple-input multiple-output (MIMO) system. We propose a two-phase training scheme such that the direct channel (non-IRS channel) and the cascaded channel (IRS-aided channel) can be tracked by two Kalman filters separately. The pilots transmitted by the base station (BS) and the reflective coefficients at the IRS are then jointly optimized to improve the channel estimation accuracy. Since the formulated problem is non-convex, the optimal solution is not straightforward. A lower bound of the objective function is derived to serve as the baseline for evaluating the performance of a certain pilot and reflective coefficients design. In two special cases, namely the direct channel dominant scenario and the cascaded channel dominant scenario, we find that the optimal pilots and the optimal reflective coefficient matrix can be approximated by some columns of the discrete Fourier transform (DFT) matrices as the number of antennas at the BS and the number of reflective elements at the IRS get larger. We further propose a codebook-based low-complexity design for a general scenario which can significantly reduce the control overhead of the IRS and cut the computational burden. Numerical results are provided to verify the efficiency of the proposed channel estimation method. [ABSTRACT FROM AUTHOR]

The use of low-resolution analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) is recognized as a practical technique to reduce power consumption and hardware cost for massive multiple-input and multiple-output (MIMO) systems. In this context, by leveraging on the additive quantization noise model (AQNM), this paper investigates the performance of massive MIMO relay systems with a variable-resolution ADC/DAC-based architecture, where each ADC and DAC use arbitrary bits for quantization. To be specific, we first derive the closed-form expression of achievable rate over spatially correlated Rayleigh fading channels by using perfect channel state information (CSI), maximal ratio combining (MRC), and maximal ratio transmission (MRT). Afterwards, we extend the work to the case of imperfect CSI. The analytical expressions reveal some insights of key parameters, i.e., spatial channel correlation, large-scale fading coefficients, estimate errors, and the resolution of ADCs/DACs. Finally, simulation results validate our theoretical analyses and confirm that the achievable rate reduces as the spatial correlation rises. Besides, we provide the condition under which coarse DACs (ADCs) and receive spatial correlation (transmit spatial correlation) dominate the loss of achievable rate. Moreover, provided that the total number of quantization bits is constant, we find that the achievable rate is optimal over spatially correlated channels when all ADC and DAC adopt the same quantization bits from the perspective of statistic. [ABSTRACT FROM AUTHOR]

In large scale multiple-input multiple-output (MIMO) systems (or massive MIMO systems), hybrid beamforming is a promising technique due to its versatile tradeoff between implementation cost (including hardware cost and power consumption) and system performance. In this paper, we investigate the downlink millimeter wave (mmWave) multi-user massive MIMO system and propose an interference cancellation (IC) framework on hybrid beamforming design. Based on the proposed framework, three successive interference cancellation (SIC) aided hybrid beamforming algorithms are proposed to deal with inter-user and intra-user interference. Specifically, for the first proposed algorithm, we use zero-forcing (ZF) to cancel inter-user interference and use SIC to cancel intra-user interference. For the second one, SIC is used to cancel inter-user interference and ZF is used to cancel intra-user interference. Both inter-user interference and intra-user interference are suppressed by SIC in the third algorithm. Furthermore, the optimal detection order of data streams is derived according to the post-detection signal-to-interference-plus-noise ratio (SINR). Numerical results show that the proposed SIC-aided hybrid beamforming algorithms outperforms the existing approaches in terms of spectral efficiency (SE) at the cost of computational complexity for the SIC procedure. Moreover, the results indicate that the proposed algorithms can achieve good SE performance with 2-bit finite resolution phase shifters and channel estimation error. [ABSTRACT FROM AUTHOR]

Channel estimation is crucial to beamforming techniques in directional millimetre wave (mmWave) communications, which is generally designed based on channel state information static. However, due to the Doppler effect caused by the mobility of users, such as unmanned aerial vehicles, high-speed trains and autonomous vehicles, the mmWave channel is changing rapidly. Spatial channel covariance, defined by long-term statistic information of channels, is a promising solution to reduce channel estimation frequency and can be used to design hybrid precoders. In this paper, we first proposed a highly mobile hybrid mmWave multi-user (MU) multiple input multiple output (MIMO) system based on transition probabilities which can represent moving action of the MU. Secondly, we investigate compressive sensing based spatial channel covariance estimation based on the proposed dynamic system. We then propose a dynamic covariance forward-backward pursuit (DCFBP) algorithm which introduces forward and backward mechanisms to reconstruct the Hermitian sparse covariance matrix. We further explore the constructed MU sensing matrix quality for conventional sparse Bayesian learning (SBL) framework. The updated sparse Bayesian learning (Updated-SBL) algorithm is developed to reduce the total squared coherence of a constructed sensing matrix with updated receive precoder. Numerical analysis demonstrates the proposed DCFBP method outperforms the benchmark methods. The total squared coherence of the proposed Updated-SBL algorithm is dramatically reduced. and the superiority of this algorithm is validated compared with other benchmark methods with comparable computation complexity. [ABSTRACT FROM AUTHOR]

We consider the recently proposed extra-large scale massive multiple-input multiple-output (XL-MIMO) systems, with some hundreds of antennas serving a smaller number of users. Since the array length is of the same order as the distance to the users, the long-term fading coefficients of a given user vary with the different antennas at the base station (BS). Thus, the signal transmitted by some antennas might reach the user with much more power than that transmitted by some others. From a green perspective, it is not effective to simultaneously activate hundreds or even thousands of antennas, since the power-hungry radio frequency (RF) chains of the active antennas increase significantly the total energy consumption. Besides, a larger number of selected antennas increases the power required by linear processing, such as precoding matrix computation, and short-term channel estimation. In this paper, we propose four antenna selection (AS) approaches to be deployed in XL-MIMO systems aiming at maximizing the total energy efficiency (EE). Besides, employing some simplifying assumptions, we derive a closed-form analytical expression for the EE of the XL-MIMO system, and propose a straightforward iterative method to determine the optimal number of selected antennas able to maximize it. The proposed AS schemes are based solely on long-term fading parameters, thus, the selected antennas set remains valid for a relatively large time/frequency intervals. Comparing the results, we find that the genetic-algorithm based AS scheme usually achieves the best EE performance, although our proposed highest normalized received power AS scheme also achieves very promising EE performance in a simple and straightforward way. [ABSTRACT FROM AUTHOR]

Discriminatory channel estimation (DCE) based on two-way training can effectively enhance physical layer security in multiple-input multiple-output (MIMO) systems. In this paper, considering an active eavesdropping scenario where the eavesdropper (Eve) can adaptively switch between passive eavesdropping, and active jamming modes, we propose a new DCE-based secure transmission scheme with cooperative jamming, and artificial noise (AN) insertion in massive MIMO decode-and-forward (DF) relay systems. To characterize the performance of the proposed scheme, firstly, the closed-form expressions for normalized mean squared error (NMSE) of legitimate channels, and wiretap channels are derived. Then, according to the NMSE obtained during channel estimation phase, we design different secure transmission schemes, and derive the approximative expressions of average security rate with respect to the behavior of active Eve, including malicious jamming, and passive eavesdropping, respectively. Finally, the power allocation at source, and relay is jointly optimized to minimize the average signal to interference plus noise ratio (SINR) at the Eve while ensuring that of the legitimate receivers to be large than a threshold for the quality-of-service (QoS) requirement. Numerical results show that the proposed DCE-based secure transmission scheme can effectively discriminate the CSI between legitimate receivers, and Eve even in the presence of an active Eve, and therefore achieve a better security performance than that without DCE. [ABSTRACT FROM AUTHOR]

A new approach of channel estimation for multiantenna systems is put forward in this paper, which can be adopted in high-mobility situations such as high speed trains. The channel impulse response is abstracted as three domains to improve the modeling accuracy. Both the time-domain preamble and the frequency-domain pilot are adopted in the orthogonal frequency division multiplexing (OFDM) frame. First, the training in time domain is exploited to obtain the partial common support of the channel. Then, the pilot location optimized by the genetic algorithm is employed to build the framework of structured compressive sensing and recover the channel. A novel compressive recovery algorithm called adaptive support-aware block orthogonal matching pursuit for multiple input multiple output-OFDM systems is proposed to solve the problem. It is manifested in the simulation that the scheme in this paper outperforms the traditional ones in both recovery probability, mean square error, and bit error rate over the doubly selective channel with low computational complexity. [ABSTRACT FROM AUTHOR]

This correspondence paper studies the impact of nonidentically distributed channel estimation error on performance of a scheduled space-time block coding with mean-value power allocation in cognitive-radio multiple-input multiple-output system. Using the derived probability density function, the exact closed-form expressions of the proposed system for outage probability, ergodic capacity, and symbol-error rate (SER) with both $\rm M$ -ary quadrature amplitude modulation and phase shift keying modulation are derived. Using asymptotic analysis, this paper quantifies the diversity order for both outage probability and SER in the presence of nonidentically distributed error. From the analysis results, this paper shows that the diversity order is enhanced by the multiuser diversity as the number of user terminals increases regardless of outage probability and SER, while the spatial diversity is eliminated. [ABSTRACT FROM AUTHOR]

This paper investigates the performance analysis of dual selection (i.e., combining user selection and transmit antenna selection) with maximal ratio combining (MRC) over nonidentical imperfect channel estimation in a multiple-input multiple-output system. This paper derives the exact and approximate cumulative density function and probability density function (PDF) for the dual selection with MRC over nonidentical imperfect channel estimation. Using the distribution, the exact and approximate closed-form expressions of the outage probability are derived with quantification of diversity order. Further, this paper derived the exact ergodic capacity and approximate outage capacity of the the dual selection via Gaussian and Gamma approximations. The numerical results show that the capacity of the dual selection with MRC is enhanced by the number of receive antennas as well as the number of user terminals and sum of channel correlation coefficients, while the order of the receive spatial diversity for outage probability is eliminated by the nonidentical channel estimation error. [ABSTRACT FROM AUTHOR]

The quasi-static assumption of channels becomes invalid in a number of emerging applications of massive multiple-input multiple-output (MIMO) systems with high base station (BS)/user mobility, such as high speed train and unmanned aerial vehicle communications. In these situations, the time variation of channels shortens the channel coherence time and decreases the efficiency of traditional channel estimation schemes significantly. This paper focuses on the time-varying channel estimation problem in massive MIMO systems, where the mobility of BS/user is assumed to be high. The sparse property of the time-varying massive MIMO channels is analyzed, which reveals that the angular domain channels exhibit two kinds of spatial-temporal sparse (STS) structures, namely the temporal-common sparse structure and spatial-clustered sparse structure. By exploiting the STS structures, a novel structured variational Bayesian inference (VBI) framework is formulated to make a robust channel estimation during the training phase. A data-aided channel predication scheme is further proposed to combat the time variation of the channels during the data transmission phase without increasing the pilot consumption. The simulation results demonstrate the superiority of the proposed scheme in the time-varying scenarios with different BS/user mobilities. [ABSTRACT FROM AUTHOR]

This paper investigates pilot design and allocation in multi-cell massive multiple-input multiple-output systems with two-tier receiving. As the length of pilot is limited, the pilots cannot be orthogonal and cause interference. The sum rate as well as the signal-to-interference-plus-noise ratio (SINR) of the system are firstly analyzed. The sum rate upper bound and the asymptotic SINR are derived. The analysis shows that the pilot correlation and the spatial correlation jointly affect the sum rate. Based on this observation, the discrete Fourier transform vectors are employed in designing pilots with various correlation values. Then, with the channel correlation information and the designed pilots, the pilots are allocated to the cells in a greedy way with the object of maximizing the sum rate upper bound. Moreover, the sum rate analysis, the pilot design, and the pilot allocation are extended to the scenario with grouped correlations. Simulation results show that the proposed pilot design and allocation performs better than other pilots and the derived upper bound is effective. [ABSTRACT FROM AUTHOR]

Data transmission over the millimeter wave (mmWave) in fifth-generation wireless networks aims to support very high speed wireless communications. A substantial increase in spectrum efficiency for mmWave transmission can be achieved by using advanced hybrid analog-digital precoding, for which accurate channel state information (CSI) is the key. Rather than estimating the entire channel matrix, it is now well-understood that directly estimating subspace information, which contains fewer parameters, does have enough information to design transceivers. However, the large channel use overhead and associated computational complexity in the existing channel subspace estimation techniques are major obstacles to deploy the subspace approach for channel estimation. In this paper, we propose a sequential two-stage subspace estimation method that can resolve the overhead issues and provide accurate subspace information. Utilizing a sequential method enables us to avoid manipulating the entire high-dimensional training signal, which greatly reduces the computational complexity. Specifically, in the first stage, the proposed method samples the columns of channel matrix to estimate its column subspace. Then, based on the obtained column subspace, it optimizes the training signals to estimate the row subspace. For a channel with $N_r$ receive antennas and $N_t$ transmit antennas, our analysis shows that the proposed technique only requires $\mathcal {O}(N_t)$ channel uses, while providing a guarantee of subspace estimation accuracy. By theoretical analysis, it is shown that the similarity between the estimated subspace and the true subspace is linearly related to the signal-to-noise ratio (SNR), i.e., $\mathcal {O}(\text{SNR})$ , at high SNR, while quadratically related to the SNR, i.e., $\mathcal {O}(\text{SNR}^2)$ , at low SNR. Simulation results show that the proposed sequential subspace method can provide improved subspace accuracy, normalized mean squared error, and spectrum efficiency over existing methods. [ABSTRACT FROM AUTHOR]

Different from the existing works, in this paper we investigate the pilot allocation in multi-cell massive multiple-input multiple-output (MIMO) systems, aiming to maximize the spectral efficiency (SE) subject to the constraint that the number of user equipments (UEs) satisfying the quality of service (QoS) is maximized. Since the considered bilevel optimization problem that is tough to handle, we resort to the greedy algorithms with low computational complexity. We propose a QoS constrained (QC) pilot allocation scheme, which sequentially allocates the pilot sequence having large interference power to the UE with small signal power so that the number of UEs satisfying QoS can be maximized and then the SE can also be maximized. Simulation results show that the propose QC scheme outperforms the conventional scheme and smart pilot allocation (SPA) scheme. [ABSTRACT FROM AUTHOR]

In intelligent transportation systems (ITSs), the communication between the base station (BS) and the vehicles can form a virtual multiple-input multiple-out put (VMIMO) vehicle communication system. This paper addresses the issue of channel estimation in a virtual MIMO system that simultaneously adopt a smart antenna (SA). First, based on quaternion theory, a novel algorithm named quaternion noncircular MUSIC (QNC-MUSIC) is proposed, and direction of arrival (DOA) estimation is achieved for circular and noncircular signals. Then, a dimension reduction procedure is performed for the parameter search by employing the partial derivative of the spectrum function with respect to the noncircular phase; thus, a novel dimensional reduction noncircular MUSIC (DRNC-MUSIC) algorithm with a low computational complexity is proposed for DOA and polarization estimation of circular signals and noncircular signals. Finally, numerical examples are provided to demonstrate the parameter estimation performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new beam allocation strategy aiming to maximize the average successful tracking probability (ASTP) of a single user time-varying millimeter-wave MIMO system. In contrast to most existing works that employ one transmitting-receiving (Tx-Rx) beam pair once only, we investigate a more general framework, where the Tx-Rx beam pairs are allowed to be used repeatedly in each beam training period to improve the received signal powers in specific directions. In the case of orthogonal Tx-Rx beam pairs, a power-based estimator is employed to track the time-varying AoA and AoD of the channel, and the resulting training beam pair sequence design problem is formulated as an integer nonlinear programming (I-NLP) problem. By dividing the feasible region into a set of subregions, the formulated I-NLP is decomposed into a series of concave sub I-NLPs, which can be solved by recursively invoking a nonlinear branch-and-bound algorithm. To reduce the computational cost, we relax the integer constraints of each sub I-NLP and obtain a low-complexity solution via solving the Karush-Kuhn-Tucker conditions of their relaxed problems. For the case when the Tx-Rx beam pairs are overlapped in the angular space, we estimate the updated AoA and AoD via an orthogonal matching pursuit (OMP) algorithm. Moreover, since no explicit expression for the ASTP exists for the OMP-based estimator, we derive a closed-form lower bound of the ASTP, based on which a favorable beam pair allocation strategy can be obtained. Numerical results demonstrate the superiority of the proposed beam allocation strategy over existing benchmarks. [ABSTRACT FROM AUTHOR]

In this paper, we study the performance of large-scale MIMO network where the base station has a large number of antennas and performs semi-blind channel estimation. We show that one can increase the number of antennas at the user side without increasing the overhead imposed by the channel estimation linearly with the number of user antennas. Specifically, we propose a simple data-aided channel estimation scheme which exploits the quasi-orthogonality of the channel vectors and takes advantage of the conventional pilot-aided channel estimation performed for the first antenna at each user. Two schemes are then analyzed using the extra antenna(s) at the users: data-multiplexing and interference alignment. We obtain achievable rates for the proposed uplink multi-cell MIMO system in both schemes. The rate bounds are tight and the system performance is also analyzed in terms of the outage probability to study the effect of the data length used for channel estimation scheme. [ABSTRACT FROM AUTHOR]

This paper addresses the channel estimation issue for millimeter wave (mmWave) massive MIMO systems with lens antenna array. Firstly, we formulate the channel estimation problem into the framework of sparse signal recovery. The formulation takes into account of the energy focusing property of the lens antenna array as well as the mutipath sparsity in mmWave MIMO channels. Then we develop an expectation maximization (EM) based algorithm to learn the parameters in the formulation, thereby fulfilling the channel estimation. Finally, we conduct simulations to verify the advantages of the proposed scheme over the state-of-the-art counterparts. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In multi-user multiple-input–multiple-output (MU-MIMO) systems that employ pilot-symbol aided channel estimation, the pilot-to-data power ratio (PDPR) has a large impact on the system performance. In this paper, we consider the problem of setting the PDPR in multi-cell MU-MIMO systems in the presence of channel estimation errors, intercell interference and pilot contamination. To analyze and address this problem, we first develop a model of the multi-cell MU-MIMO system and derive a closed-form expression for the mean squared error of the uplink received data symbols. Building on this result, we then propose two decentralized PDPR-setting algorithms based on game theoretic approaches that are applicable in multi-cell systems. We find that both algorithms converge to a Nash equilibrium and provide performance improvements over systems that do not properly set the PDPR, while they maintain different levels of fairness. [ABSTRACT FROM AUTHOR]

Massive multiple-input multiple-output (MIMO) systems consist of a large number of antennas and radio frequency (RF) chains, which cause enormous circuit power consumption at the RF front ends. Since high-resolution analog-to-digital converters are the main contributor in the RF circuit power consumption, one-bit massive MIMO is considered as one of the potential solutions. The channel state information (CSI) acquisition in the presence of pilot contamination is a challenging task in such systems. In this paper, we present an iterative semi-blind-based channel estimation scheme for pilot contaminated one-bit multi-cell multi-user massive MIMO systems, which comprise of two stages: initialization and iteration. The initial channel estimate uses pilots in the initialization stage, which is further refined in the iteration stage with the help of both pilot and a few data symbols. We derive lower bounds on the uplink achievable rate with both perfect and imperfect CSI availability at the base station. Through simulations, we show that the proposed estimator achieves a considerable improvement in mean square error, bit-error-rate, power efficiency, and spectral efficiency from one-bit pilot-aided estimators at the cost of a nominal increase in computational complexity. Moreover, the proposed scheme in one-bit system achieves almost the same spectral efficiency as that of a pilot-aided estimator in an infinite-resolution-based massive MIMO system for lower values of signal-to-noise-ratio (SNR). [ABSTRACT FROM AUTHOR]

Ambient backscatter, an emerging green communication technology, has aroused great interest from both academia and industry. One open problem for ambient backscatter communication (AmBC) systems is channel estimation for a massive-antenna reader. In this paper, we focus on a channel estimation problem in AmBC systems with a uniform linear array at the reader consisting of large number of antennas. We first design a two-step method to jointly estimate channel gains and direction of arrivals (DoAs), and then refine the estimates through angular rotation. Additionally, Cramér–Rao lower bounds are derived for both the modulus of the channel gain and the DoA estimates. Simulations are then provided to validate the analysis, and to show the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we investigate secure communication in a massive multiple-input multiple-output (MIMO) system with multiple users and multiple eavesdroppers (Eve) under both pilot spoofing attack (PSA) and uplink jamming. Specifically, Eve impairs the normal channel estimation by sending identical pilot sequences with the legitimate users. Based on the impaired channel estimation, the base station adopts linear processing schemes for uplink data reception, which is jammed by Eve, and downlink confidential information transmission. We first evaluate the impact of the PSA on the achievable rate with linear processing, and then propose a double channel training based scheme to combat PSA. By using the channel estimation difference in two training phases, the presence of the PSA can be detected and accurate legitimate channel estimation can be obtained by removing the effect of Eve's channel. Furthermore, we analyze the channel estimation errors and derive a closed-form expression of the minimum mean square error precoding scheme to maximize the minimum achievable secrecy rate, which outperforms the conventional linear precoding counterparts. [ABSTRACT FROM AUTHOR]

This paper introduces a hybrid pilot-aided channel estimation technique for mitigating the effect of pilot contamination for the uplink of multi-cell multiuser massive MIMO systems. The proposed hybrid pilot is designed such that it enjoys the complementary advantages between time-multiplexed (TM) pilot and time-superimposed (TS) pilot and, thereby, allows superior solution to the conventional pilot schemes. We mathematically characterize the impact of hybrid pilot on the massive MIMO uplink by deriving a closed-form approximation for the uplink achievable rate. In the large-number-of-antennas regime, we obtain the asymptotically optimal solution for the hybrid pilot by jointly designing the TM pilot and the TS pilot. It is shown that either TM pilot or TS pilot has the advantages for large frame-size and limited frame-size transmission, respectively, while the hybrid pilot scheme can offer a superior performance to that employing either TM pilot or TS pilot. Numerical results demonstrate the effectiveness of the proposed design. [ABSTRACT FROM AUTHOR]

In massive multiple-input and multiple-output (M-MIMO) systems, one of the key challenges in the implementation is the large-scale matrix inversion operation, as widely used in channel estimation, equalization, detection, and decoding procedures. Traditionally, to handle this complexity issue, several low-complexity matrix inversion approximation methods have been proposed, including the classic Cholesky decomposition and the Neumann series expansion (NSE). However, the conventional approaches failed to exploit neither the special structure of channel matrices nor the critical issues in the hardware implementation, which results in poorer throughput performance and longer processing delay. In this paper, by targeting at the correlated M-MIMO systems, we propose a modified NSE based on tridiagonal matrix inversion approximation (TMA) to accommodate the complexity as well as the performance issue in the conventional hardware implementation, and analyze the corresponding approximation errors. Meanwhile, we investigate the very-large-scale integration implementation for the proposed detection algorithm based on a Xilinx Virtex-7 XC7VX690T FPGA platform. It is shown that for correlated massive MIMO systems, it can achieve near minimum mean square error performance and 630 Mb/s throughput. Compared with other benchmark systems, the proposed pipelined TMA detector can get high throughput-to-hardware ratio. Finally, we also propose a fast iteration structure for further research. [ABSTRACT FROM AUTHOR]

This paper investigates the energy efficient downlink transmission in distributed massive multiple-input–multiple-output systems, where massive antennas are clustered on geographically distributed remote radio heads (RRH). A closed form of the ergodic achievable rate is derived for a specific RRH-user association and imperfect channel state information to assist the formulation of its system energy efficiency (EE). By assuming minimum user achievable rate requirements and a practical power consumption model including both the transmit power and the antenna circuit power, an optimization problem is formulated to maximize the system EE with respect to the power allocation, the antennas activation, and the RRH-user association in a combinatorial manner. The formulated problem is a mixed-integer nonlinear programming problem, which is NP-hard and usually has no feasible solution. To solve it, an efficient algorithm is proposed by utilizing hierarchical decomposition technique and iterative successive convex approximation. The feasibility as well as the effectiveness of the proposed algorithm are analyzed and proved through analysis and intensive computer simulations. Results show that the system EE can be greatly improved by the proposed scheme. [ABSTRACT FROM AUTHOR]

Orthogonal time frequency space (OTFS) modulation was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) in delay–Doppler channels. In order to detect OTFS modulated data, the channel impulse response needs to be known at the receiver. In this paper, we propose embedded pilot-aided channel estimation schemes for OTFS. In each OTFS frame, we arrange pilot, guard, and data symbols in the delay–Doppler plane to suitably avoid interference between pilot and data symbols at the receiver. We develop such symbol arrangements for OTFS over multipath channels with integer and fractional Doppler shifts, respectively. At the receiver, channel estimation is performed based on a threshold method and the estimated channel information is used for data detection via a message passing algorithm. Thanks to our specific embedded symbol arrangements, both channel estimation and data detection are performed within the same OTFS frame with minimum overhead. We compare through simulations the error performance of OTFS using the proposed channel estimation and OTFS with ideally known channel information and observe only a marginal performance loss. We also demonstrate that the proposed channel estimation in OTFS significantly outperforms OFDM with known channel information. Finally, we present extensions of the proposed schemes to multiple-input multiple-output (MIMO) and multi-user uplink/downlink. [ABSTRACT FROM AUTHOR]

Channel estimation is of great challenge for millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems. The underlying reason can be attributed to two facts. One is the huge dimension of MIMO channel matrix, since mmWave systems typically employ large antenna arrays at both the transmitter and receiver to realize sufficient link margin. The other fact is the limited number of radio-frequency chains available for transmitter/receiver array, due to the power and cost limitations. This paper proposes a two-stage accurate channel estimation scheme for mmWave MIMO. Initially, we utilize sparse Bayesian learning to obtain a coarse channel estimate. Then we refine the channel estimate by iteratively maximizing the likelihood function of channel parameters. It is shown through simulations that the proposed scheme significantly outperforms the counterparts, and can achieve accurate channel estimation performance. [ABSTRACT FROM AUTHOR]