Intelligent Reflecting Surface-Assisted Millimeter Wave Communications: Joint Active and Passive Precoding Design
Peilan Wang, Jun Fang, Xiaojun Yuan, Zhi Chen, Huiping Duan, Hongbin Li
备注：
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2020.3031657,IEEE Transactions on Vehicular Technology
Millimeter wave (MmWave) communications is capable of supporting multi-gigabit wireless access thanks to its abundant spectrum resource. However, the severe path loss and high directivity make it vulnerable to blockage events, which can be frequent in indoor and dense urban environments. To address this issue, in this paper, we introduce intelligent reflecting surface (IRS) as a new technology to provide effective reflected paths to enhance coverage of mmWave signals. In this framework, we study joint active and passive precoding design for IRS-assisted mmWave systems, where multiple IRSs are deployed to assist the data transmission from a base station (BS) to a single-antenna receiver. Our objective is to maximize the received signal power by jointly optimizing the transmit precoding vector at the BS and the phase shift parameters used by IRSs for passive beamforming. Although such an optimization problem is generally non-convex, we show that, by exploiting some important characteristics of mmWave channels, an optimal closed-form solution can be derived for the single IRS case and a near-optimal analytical solution can be obtained for the multi-IRS case. Our analysis reveals that the received signal power increases quadratically with the number of reflecting elements for both the single IRS and multi-IRS cases. Simulation results are included to verify the optimality and near-optimality of our proposed solutions. Results also show that IRSs can help create effective virtual LOS paths and thus substantially improve robustness against blockages in mmWave communications.
This paper investigates the use of a reconfigurable intelligent surface (RIS) to aid point-to-point multi-data-stream multiple-input multiple-output (MIMO) wireless communications. With practical finite alphabet input, the reflecting elements at the RIS and the precoder at the transmitter are alternatively optimized to minimize the symbol error rate (MSER). In the reflecting optimization with a fixed precoder, two reflecting design methods are developed, referred as eMSER-Reflecting and vMSER-Reflecting. In the optimization of the precoding matrix with a fixed reflecting pattern, the matrix op…
Intelligent reflecting surfaces (IRSs) have emerged as a revolutionary solution to enhance wireless communications by changing propagation environment in a cost-effective and hardware-efficient fashion. In addition, symbol-level precoding (SLP) has attracted considerable attention recently due to its advantages in converting multiuser interference (MUI) into useful signal energy. Therefore, it is of interest to investigate the employment of IRS in symbol-level precoding systems to exploit MUI in a more effective way by manipulating the multiuser channels. In this paper, we focus on joint symbo…
In this work, we propose an iterative scheme for computing a linear precoder that takes into account the impact of hardware impairments in the multiuser multiple-input single-output downlink. We particularly focus on the case when the transmitter is equipped with nonlinear power amplifiers. Using Bussgang's theorem, we formulate a lower bound on the achievable sum rate in the presence of hardware impairments, and maximize it using projected gradient ascent. We provide numerical examples that demonstrate the efficacy of the proposed distortion-aware scheme for precoding over a millimeter-wave~c…
Channel estimation and hybrid precoding are considered for multi-user millimeter wave massive multi-input multi-output system. A deep learning compressed sensing (DLCS) channel estimation scheme is proposed. The channel estimation neural network for the DLCS scheme is trained offline using simulated environments to predict the beamspace channel amplitude. Then the channel is reconstructed based on the obtained indices of dominant beamspace channel entries. A deep learning quantized phase (DLQP) hybrid precoder design method is developed after channel estimation. The training hybrid precoding n…
This paper investigates the hybrid precoding design for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems with finite-alphabet inputs. The precoding problem is a joint optimization of analog and digital precoders, and we treat it as a matrix factorization problem with power and constant modulus constraints. Our work presents three main contributions: First, we present a sufficient condition and a necessary condition for hybrid precoding schemes to realize unconstrained optimal precoders exactly when the number of data streams Ns satisfies Ns = minfrank(H);Nrfg, where H rep…
In this paper, we study the performance of cooperative millimeter wave (mmWave) networks with hybrid precoding architectures. Considering joint transmissions and BS silence strategy, we propose hybrid precoding algorithms which minimize the sum power consumption of the base stations (BSs), for both fully- and partially-connected hybrid precoding (FHP and PHP, respectively) schemes, for single-carrier and orthogonal frequency-division multiplexing systems. We reformulate the analog precoding part as an equal-gain transmission problem, which only depends on the channel information, and the digit…
Millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) has been regarded to be an emerging solution for the next generation of communications, in which hybrid analog and digital precoding is an important method for reducing the hardware complexity and energy consumption associated with mixed signal components. However, the fundamental limitations of the existing hybrid precoding schemes is that they have high computational complexity and fail to fully exploit the spatial information. To overcome these limitations, this paper proposes, a deep-learning-enabled mmWave massive MIMO…
This paper considers symbol-level precoding (SLP) for multiuser multi-input single-output (MISO) downlink transmission with the aid of intelligent reflecting surface (IRS). Specifically, by assuming one-bit transmitted signals at the base station (BS), which arises from the use of low-resolution DACs in the regime of massive transmit antennas, a joint design of one-bit SLP at the BS and the phase shifts at the IRS is proposed with a goal of minimizing the worst-case symbol error probability (SEP) of the users under the PSK modulation. This joint design problem is essentially a mixed integer no…
A major source of difficulty when operating with large arrays at mmWave frequencies is to estimate the wideband channel, since the use of hybrid architectures acts as a compression stage for the received signal. Moreover, the channel has to be tracked and the antenna arrays regularly reconfigured to obtain appropriate beamforming gains when a mobile setting is considered. In this paper, we focus on the problem of channel tracking for frequency-selective mmWave channels, and propose two novel channel tracking algorithms that leverage prior statistical information on the angles-of-arrival and an…
Intelligent reflecting surface (IRS) has emerged as a promising solution to enhance wireless information transmissions by adaptively controlling prorogation environment. Recently, the brand-new concept of utilizing IRS to implement a passive transmitter attracts researchers' attention since it potentially realizes low-complexity and hardware-efficient transmitters of multiple-input single/multiple-output (MISO/MIMO) systems. In this paper we investigate the problem of precoder design for a low-resolution IRS-based transmitter to implement multi-user MISO/MIMO wireless communications. Particula…
The high energy consumption of massive multi-input multi-out (MIMO) system has become a prominent problem in the millimeter wave(mm-Wave) communication scenario. The hybrid precoding technology greatly reduces the number of radio frequency(RF) chains by handing over part of the coding work to the phase shifting network, which can effectively improve energy efficiency. However, conventional hybrid precoding algorithms based on mathematical means often suffer from performance loss and high computational complexity. In this paper, a novel BP-neural-network-enabled hybrid precoding algorithm is pr…
Intelligent reflecting surfaces (IRS) have been proposed as a revolutionary technology owing to its capability of adaptively reconfiguring the propagation environment in a cost-effective and hardware-efficient fashion. While the application of IRS as a passive reflector to enhance the performance of wireless communications has been widely investigated in the literature, using IRS as a passive transmitter recently is emerging as a new concept and attracting steadily growing interest. In this paper, we propose two novel IRS-based passive information transmission systems using advanced symbol-lev…
Millimeter wave communication is eminently suitable for high-rate wireless systems, which may be beneficially amalgamated with intelligent reflecting surfaces (IRS), relying on beam-index modulation. Explicitly, we propose three different architectures based on IRSs for beam-index modulation in millimeter wave communication, which circumvent the line-of-sight blockage of millimeter wave frequencies. We conceive both the optimal maximum likelihood detector and a low-complexity compressed sensing detector for the proposed schemes. Finally, the schemes conceived are evaluated through extensive si…
Aiming at maximizing the achievable sum-rate of wideband multiuser mmWave massive MIMO systems, the hybrid precoding is studied. Since each computation of the achievable sum-rate can be performed only after the analog precoder and digital precoder are both determined, the maximization of the achievable sum-rate has intractable computational complexity. By introducing the interference free (IF) achievable sum-rate, the design of the analog and digital precoders can be decoupled. To avoid the beam conflict and maximize the IF achievable sum-rate, a Hungarian-based codeword selection algorithm is…
Millimeter-wave (mmWave) technology is one of the most promising candidates for future wireless communication systems as it can offer large underutilized bandwidths and eases the implementation of large antenna arrays which are required to help overcome the severe signal attenuation that occurs at these frequencies. To reduce the high cost and power consumption of a fully digital mmWave precoder and combiner, hybrid analog/digital designs based on analog phase shifters are often adopted. In this work we derive an iterative algorithm for the hybrid precoding and combining design for spatial mul…
We address the problem of analyzing and classifying in groups the downlink channel environment in a millimeter-wavelength cell, accounting for path loss, multipath fading, and User Equipment (UE) blocking, by employing a hybrid propagation and multipath fading model, thus using accurate inter-group interference modeling. The base station (BS) employs a large Uniform Planar Array (UPA) to facilitate massive Multiple-Input, Multiple-Output (MIMO) communications with high efficiency. UEs are equipped with a single antenna and are distributed uniformly within the cell. The key problem is analyzing…
In this paper, a framework of beamspace channel estimation in millimeter wave (mmWave) massive MIMO system is proposed. The framework includes the design of hybrid precoding and combining matrix as well as the search method for the largest entry of over-sampled beamspace receiving matrix. Then based on the framework, three channel estimation schemes including identity matrix approximation (IA)-based scheme, scattered zero off-diagonal (SZO)-based scheme and concentrated zero off-diagonal (CZO)-based scheme are proposed. These schemes together with the existing channel estimation schemes are co…
Hybrid analog/digital precoding in millimeter-wave (mmWave) multi-input multi-ouput (MIMO) systems is capable of achieving the near-optimal full-digital performance at reduced hardware cost and power consumption compared to its full-RF digital counterpart. However, having numerous phase shifters is still costly, especially when the phase shifters are of high resolution. In this paper, we propose a novel twin-resolution phase-shifter network for mmWave MIMO systems, which reduces the power consumption of an entirely high-resolution network, whilst mitigating the severe array gain reduction of a…
Recently, the use of intelligent reflecting surface (IRS) has gained considerable attention in wireless communications. By intelligently adjusting the passive reflection angle, IRS is able to assist the base station (BS) to extend the coverage and improve spectral efficiency. This paper considers a joint symbol-level precoding (SLP) and IRS reflecting design to minimize the symbol-error probability (SEP) of the intended users in an IRS-aided multiuser MISO downlink. We formulate the SEP minimization problems to pursue uniformly good performance for all users for both QAM and PSK constellations…
The millimeter wave is a promising technique for the next generation of mobile communication. The large antenna array is able to provide sufficient precoding gain to overcome the high pathloss at millimeter wave band. However, the accurate channel state information is the key for the precoding design. Unfortunately, the channel use overhead and complexity are two major challenges when estimating the channel with high-dimensional array. In this paper, we propose a two-stage approach which reduces the channel use overhead and the computational complexity. Specifically, in the first stage, we est…
Intelligent reflecting surface (IRS) is envisioned as a promising solution for controlling radio propagation environments in future wireless systems. In this paper, we propose a distributed intelligent reflecting surface (IRS) assisted multi-user millimeter wave (mmWave) system, where IRSs are exploited to enhance the mmWave signal coverage when direct links between base station and users are unavailable. First, a joint active and passive beamforming problem is established for weighted sum-rate maximization. Then, an alternating iterative algorithm with closed-form expressions is proposed to t…
In this paper, we derive the uplink achievable rate expression of intelligent reflecting surface (IRS)-aided millimeter-wave (mmWave) systems, taking into account the phase noise at IRS and the quantization error at base stations (BSs). We show that the performance is limited only by the resolution of analog-digital converters (ADCs) at BSs when the number of IRS reflectors grows without bound. On the other hand, if BSs have ideal ADCs, the performance loss caused by IRS phase noise is a constant. Finally, our results validate the feasibility of using low-precision hardware at the IRS when BSs…
This work investigates the effect of double intelligent reflecting surface (IRS) in improving the spectrum efficient of multi-user multiple-input multiple-output (MIMO) network operating in the millimeter wave (mmWave) band. Specifically, we aim to solve a weighted sum rate maximization problem by jointly optimizing the digital precoding at the transmitter and the analog phase shifters at the IRS, subject to the minimum achievable rate constraint. To facilitate the design of an efficient solution, we first reformulate the original problem into a tractable one by exploiting the majorization-min…
In this paper, we consider channel estimation for intelligent reflecting surface (IRS)-assisted millimeter wave (mmWave) systems, where an IRS is deployed to assist the data transmission from the base station (BS) to a user. It is shown that for the purpose of joint active and passive beamforming, the knowledge of a large-size cascade channel matrix needs to be acquired. To reduce the training overhead, the inherent sparsity in mmWave channels is exploited. By utilizing properties of Katri-Rao and Kronecker products, we find a sparse representation of the cascade channel and convert cascade ch…
Millimeter wave (mmWave) communication is expected to play an important role in next generation cellular networks, aiming to cope with the bandwidth shortage affecting conventional wireless carriers. Using side-information has been proposed as a potential approach to accelerate beam selection in mmWave massive MIMO (m-MIMO) communications. However, in practice, such information is not error-free, leading to performance degradation. In the multi-user case, a wrong beam choice might result in irreducible inter-user interference at the base station (BS) side. In this paper, we consider location-a…
Millimeter-wave (mmWave) multiple-input multiple-out (MIMO) systems relying on lens antenna arrays are capable of achieving a high antenna-gain at a considerably reduced number of radio frequency (RF) chains via beam selection. However, the traditional beam selection network suffers from significant performance loss in wideband systems due to the effect of beam squint. In this paper, we propose a phase shifter-aided beam selection network, which enables a single RF chain to support multiple focused-energy beams, for mitigating the beam squint in wideband mmWave MIMO systems. Based on this arch…
Millimeter wave (mmWave) communications are evolving as a promising technology to meet the ever increasing data rate requirements. However, high directivity and severe path loss make it vulnerable to blockages, which could be frequent in indoor or urban environments. To address this issue, intelligent reflecting surfaces (IRSs) are introduced to provide additional adjustable reflected paths. Most prior works assume that elements of IRSs have an infinite phase resolution, which is difficult to be realized in practical systems. In this paper, IRSs with low-resolution phase shifters are considere…
In this paper, we investigate the energy-efficient hybrid precoding design for integrated multicast-unicast millimeter wave (mmWave) system, where the simultaneous wireless information and power transform is considered at receivers. We adopt two sparse radio frequency chain antenna structures at the base station (BS), i.e., fully-connected and subarray structures, and design the codebook-based analog precoding according to the different structures. Then, we formulate a joint digital multicast, unicast precoding and power splitting ratio optimization problem to maximize the energy efficiency of…
Duzce University（杜兹切大学）；University of Hertfordshire（赫特福德大学）；University of Luxembourg（卢森堡大学）
In multi-user millimeter wave (mmWave) multiple-input-multiple-output (MIMO) systems, hybrid precoding is a crucial task to lower the complexity and cost while achieving a sufficient sum-rate. Previous works on hybrid precoding were usually based on optimization or greedy approaches. These methods either provide higher complexity or have sub-optimum performance. Moreover, the performance of these methods mostly relies on the quality of the channel data. In this work, we propose a deep learning (DL) framework to improve the performance and provide less computation time as compared to convention…
Intelligent reflecting surfaces (IRSs) constitute a disruptive wireless communication technique capable of creating a controllable propagation environment. In this paper, we propose to invoke an IRS at the cell boundary of multiple cells to assist the downlink transmission to cell-edge users, whilst mitigating the inter-cell interference, which is a crucial issue in multicell communication systems. We aim for maximizing the weighted sum rate (WSR) of all users through jointly optimizing the active precoding matrices at the base stations (BSs) and the phase shifts at the IRS subject to each BS'…
Hybrid analog-digital precoding is challenging for broadband millimeter-wave (mmWave) massive MIMO systems, since the analog precoder is frequency-flat but the mmWave channels are frequency-selective. In this paper, we propose a principal component analysis (PCA)-based broadband hybrid precoder/combiner design, where both the fully-connected array and partially-connected subarray (including the fixed and adaptive subarrays) are investigated. Specifically, we first design the hybrid precoder/combiner for fully-connected array and fixed subarray based on PCA, whereby a low-dimensional frequency-…
This paper proposes a novel neural network architecture, that we call an auto-precoder, and a deep-learning based approach that jointly senses the millimeter wave (mmWave) channel and designs the hybrid precoding matrices with only a few training pilots. More specifically, the proposed machine learning model leverages the prior observations of the channel to achieve two objectives. First, it optimizes the compressive channel sensing vectors based on the surrounding environment in an unsupervised manner to focus the sensing power on the most promising spatial directions. This is enabled by a no…
This paper investigates the hybrid precoding design in millimeter-wave (mmWave) systems with a fully-adaptive-connected precoding structure, where a switch-controlled connection is deployed between every antenna and every radio frequency (RF) chain. To maximally enhance the energy efficiency (EE) of hybrid precoding under this structure, the joint optimization of switch-controlled connections and the hybrid precoders is formulated as a large-scale mixed-integer non-convex problem with high-dimensional power constraints. To efficiently solve such a challenging problem, we first decouple it into…
Hybrid beamforming is key to achieving energy-efficient 5G wireless networks equipped with massive amount of antennas. Low-resolution data converters bring yet another degree of freedom to energy efficiency for the state-of-the-art 5G transceivers. In this work, we consider the design of hybrid precoders for massive multiple-input multiple-output (MIMO) channels in millimeter-wave (mmWave) spectrum along with one-bit digital-to-analog converters (DACs) and finite-quantized phase shifters. In particular, we propose an alternating-optimization-based precoder design which recursively computes the…
Low-cost passive intelligent reflecting surfaces (IRSs) have recently been envisioned as a revolutionary technology capable of reconfiguring the wireless propagation environment through carefully tuning reflection elements. This paper proposes deploying an IRS to cover the dead zone of cellular multiuser full-duplex (FD) two-way communication links while suppressing user-side self-interference (SI) and co-channel interference (CI). Based on information exchanged by the base station (BS) and all users, this approach can potentially double the spectral efficiency. To ensure network fairness, we …
Hybrid precoding is a cost-effective approach to support directional transmissions for millimeter-wave (mm-wave) communications, but its precoder design is highly complicated. In this paper, we propose a new hybrid precoder implementation, namely the double phase shifter (DPS) implementation, which enables highly tractable hybrid precoder design. Efficient algorithms are then developed for two popular hybrid precoder structures, i.e., the fully- and partially-connected structures. For the fully-connected one, the RF-only precoding and hybrid precoding problems are formulated as a least absolut…
In this paper, a downlink intelligent reflecting surface (IRS) enhanced millimeter-wave (mmWave) non-orthogonal multiple access (NOMA) system is considered. A joint optimization problem over active beamforming, passive beamforming and power allocation is formulated. Due to the highly coupled variables, the formulated optimization problem is non-convex. To solve this problem, an alternative optimization and successive convex approximation based iterative algorithm is proposed. Numerical results illustrate that: 1) the proposed scheme offers significant sum-rate gains, which confirms the effecti…
We consider the problem of spatial channel covariance matrix (CCM) estimation for intelligent reflecting surface (IRS)-assisted millimeter wave (mmWave) communication systems. Spatial CCM is essential for two-timescale beamforming in IRS-assisted systems; however, estimating the spatial CCM is challenging due to the passive nature of reflecting elements and the large size of the CCM resulting from massive reflecting elements of the IRS. In this paper, we propose a CCM estimation method by exploiting the low-rankness as well as the positive semi-definite (PSD) 3-level Toeplitz structure of the …
Hybrid precoding has been recognized as a promising technology to combat the path loss of millimeter wave signals in massive multiple-input multiple-output (MIMO) systems. However, due to the joint optimization of the digital and analog precoding matrices as well as extra constraints for the analog part, the hybrid precoding design is still a tough issue in current research. In this paper, we adopt the thought of clustering in unsupervised learning and provide design schemes for fully-connected hybrid precoding (FHP) and adaptively-connected hybrid precoding (AHP) in multi-user massive MIMO sy…
In this letter, we focus on the hybrid precoding (HP) design for the reconfigurable intelligent surface (RIS) aided multi-user (MU) millimeter wave (mmWave) communication systems. Specifically, we aim to minimize the mean-squared-error (MSE) between the received symbols and the transmitted symbols by jointly optimizing the analog-digital HP at the base-station (BS) and the phase shifts (PSs) at the RIS, where the non-convex element-wise constant-modulus constraints for the analog precoding and the PSs are tackled by resorting to the gradient-projection (GP) method. We analytically prove the co…
An intelligent reflecting surface (IRS)-assisted millimeter-wave (mmWave) massive multiple input multiple output (MIMO) system with transmit antenna selection (TAS) using orthogonal space-time block codes (OSTBC) scheme is proposed in this paper. This system combines TAS and IRS with hybrid analog-digital beamforming (HBF) for 60 GHz mmWave communications in order to exploit the benefits of TAS, OSTBC, analog beamforming (ABF), and transmit digital precoding techniques. The proposed system, however, benefits from the transmit diversity gain of OSTBC scheme as well as from the signal-to-noise r…
Dynamic subarray achieves a compromise between sum rate and hardware complexity for millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems in which antenna elements are dynamically partitioned to radio frequency (RF) chain according to the channel state information.} However, multi-user hybrid precoding for the dynamic subarray is intractable to solve as the antenna partitioning would result in the user unfairness and multi-user interference (MUI). In this paper, a novel multi-user hybrid precoding framework is proposed for the dynamic subarray architecture. Different f…
Massive multi-user multiple-input multiple-output (MU-MIMO) wireless systems operating at millimeter-wave (mmWave) frequencies enable simultaneous wideband data transmission to a large number of users. In order to reduce the complexity of MU precoding in all-digital basestation architectures, we propose a two-stage precoding architecture that first performs precoding using a sparse matrix in the beamspace domain, followed by an inverse fast Fourier transform that converts the result to the antenna domain. The sparse precoding matrix requires a small number of multipliers and enables regular ha…
Intelligent reflecting surfaces (IRSs) are regarded as promising enablers for future millimeter wave (mmWave) wireless communication, due to their ability to create favorable line-of-sight (LoS) propagation environments. In this paper, we investigate channel estimation in downlink IRS-assisted mmWave multiple-input multiple-output (MIMO) systems. By leveraging the sparsity of mmWave channels, we formulate the channel estimation problem as a fixed-rank constrained non-convex optimization problem. To tackle the non-convexity, an efficient algorithm is proposed by capitalizing on alternating mini…
Intelligent reflecting surface (IRS) is a promising technology for enhancing wireless communication systems. It adaptively configures massive passive reflecting elements to control wireless channel in a desirable way. Due to hardware characteristics and deploying environments, an IRS may be subject to reflecting element blockages and failures, and hence developing diagnostic techniques is of great significance to system monitoring and maintenance. In this paper, we develop diagnostic techniques for IRS systems to locate faulty reflecting elements and retrieve failure parameters. Three cases of…
Energy efficiency (EE) optimization of millimeter wave (mm-Wave) massive multiple-input multiple-output (MIMO) systems is emerging as an important challenge for the fifth generation (5G) mobile communication systems. However, the power of radio frequency (RF) chains increases sharply due to the high carrier frequency in mm-Wave massive MIMO systems. To overcome this issue, a new energy efficiency optimization solution is proposed based on the structure of the generalized spatial modulation (GSM) and sub-connected hybrid precoding (HP). Moreover, the computation power of mm-Wave massive MIMO sy…
We propose a new scheme for the robust estimation of the millimeter wave (mmWave) channel. Our approach is based on a sparse formulation of the channel estimation problem coupled with a frame theoretic representation of the sensing dictionary. To clarify, under this approach, the combined effect of transmit precoders and receive beamformers is modeled by a single frame, whose design is optimized to improve the accuracy of the sparse reconstruction problem to which the channel estimation problem is ultimately reduced. The optimized sensing dictionary frame is then decomposed via a Kronecker dec…
As communication systems that employ millimeter wave (mmWave) frequency bands must use large antenna arrays to overcome the severe propagation loss of mmWave signals, hybrid beamforming has been considered as an integral component of mmWave communications. Recently, intelligent reflecting surface (IRS) has been proposed as an innovative technology that can significantly improve the performance of mmWave communication systems through the use of low-cost passive reflecting elements. In this paper, we study IRS-aided mmWave multiple-input multiple-output (MIMO) systems with hybrid beamforming arc…
Millimeter wave multiple-input multiple-output (MIMO) communication systems must operate over sparse wireless links and will require large antenna arrays to provide high throughput. To achieve sufficient array gains, these systems must learn and adapt to the channel state conditions. However, conventional MIMO channel estimation can not be directly extended to millimeter wave due to the constraints on cost-effective millimeter wave operation imposed on the number of available RF chains. Sparse subspace scanning techniques that search for the best subspace sample from the sounded subspace sampl…
