mmWave Multiple-input Multiple-output Research Articles

Enhanced channel estimation with atomic norm minimization and reconfigurable intelligent surfaces in mmWave MIMO systems

SummaryThe performance of millimeter‐wave (mmWave) multiple‐input multiple‐output (MIMO) systems has been significantly enhanced by the incorporation of dynamic reconfigurable intelligent surfaces (RIS). This paper proposes a novel dynamic channel estimation technique that combines dynamic atomic norm minimization with dynamic RIS to optimize RIS‐aided mmWave MIMO systems. Leveraging the dynamic nature of both atomic norm minimization and RIS, the proposed approach efficiently adapts to changing environmental conditions, providing robust and accurate channel estimation. By dynamically optimizing the RIS configuration, the system achieves improved spectral and energy efficiency, enabling high‐speed and reliable communication in challenging mmWave environments. Theoretical analysis and simulation results demonstrate the effectiveness of the proposed dynamic channel estimation technique, highlighting its potential for enhancing the performance of future wireless communication systems.

Development of a metasurface-based slot antenna for 5G MIMO applications with minimized cross-polarization and stable radiation patterns through mode manipulation

This paper presents an approach for designing metasurface antennas using the characteristic mode analysis method for 5G mm-wave multiple input–multiple output (MIMO) systems. The proposed metasurface antenna consists of a 3 × 3 array of modified patches with additional slits and stubs, which are fed by a coupling slot. This configuration reshapes surface currents and improves the radiation performance across a broad frequency range. The design offers significant advantages such as reduced antenna size, minimized influence of higher-order modes, and maintained low cross-polarization (XP) level. Experimental results demonstrate that the proposed metasurface-based slot antenna provides a bandwidth of 29.6% (23–31 GHz) with a return loss better than 10 dB. It achieves a peak gain of 9.43 dB and exhibits an XP level below − 26 dB and − 48 dB at φ=0∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi = 0^{ \\circ }$$\\end{document} and φ=90∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi = 90^{ \\circ }$$\\end{document} planes, respectively. The physical dimensions of the antenna are 0.9λ0 × 0.9λ0 × 0.08λ0, where λ0 is the free space wavelength at 27 GHz, resulting in an approximately 41% reduction compared to the conventional metasurface patch antenna. Moreover, the design proves to be well-suited for MIMO systems, enabling close placement of antenna elements without degrading their radiation patterns. The experimental results in 1 × 2 and 2 × 2 MIMO configurations represent that the isolation between antenna elements are better than 18 dB and 21 dB, respectively. The performance of the antennas remains stable in both configurations, effectively addressing concerns such as beam squint and eliminating the common issue of beam splitting observed in conventional metasurface MIMO antennas. Moreover, the envelope correlation coefficient value in both MIMO configurations is lower than 0.003. This significant advancement offers a promising solution for compact 5G mm-wave massive MIMO applications.

Design and Simulation of a High Performance 5G mm-Wave MIMO Antenna Array for Mobile Applications

This paper presents the design and simulation of an efficient multiple input multiple output (MIMO) antenna array for 5G millimeter-wave (mm-wave) mobile applications. With a dielectric constant of 2.2 and a loss tangent of 0.0009, the substrate employed is a Rogers RT5880 that is 0.254 mm thick. The 37 GHz frequency spectrum, reserved for millimeter-wave mobile applications for 5G, is covered by the proposed MIMO antenna arrays. The single antenna element has a gain of 6.44 dBi, which is increased to 7.89 dBi with a two-element array configuration and 10.88 dBi with a four-element array configuration. The proposed MIMO antenna array performance metrics—including reflection coefficient, VSWR, radiation efficiency, and gain—are seen and discovered to be below the accepted threshold. In the desired operating frequency band, it is noticed that more than 85% of the proposed MIMO antenna array's radiation efficiency is achieved. According to simulation findings, the proposed design may be potentially feasible for mobile applications using millimeter waves in the 5G network.

TDoA positioning with data-driven LoS inference in mmWave MIMO communications

Location awareness is an essential feature to support various mobile services, and cooperative positioning with channel state information (CSI) in millimeter wave multiple-input multiple-output (MIMO) networks is promising. Meanwhile, strong non-line of sight (NLoS) effects in outdoor scenarios severely reduce the model-based localization accuracy, and existing fingerprint-based methods have a critical requirement for labeled data and lack scalability. To overcome these shortcomings, we propose a hybrid data-and-model driven cooperative localization scheme using uplink wideband MIMO CSI at multiple base stations (BS) as measurements. First, we design a data-driven line of sight (LoS) inference module, realized by a transformer with an attention mechanism, to estimate the statistics of LoS arrival times. Each BS is equipped with a module, and the counterpart LoS inferences are simultaneously and distributedly performed. Second, we locate the mobile user by a model-driven approximate maximum likelihood time difference of arrival algorithm with the estimated statistics. Experiment results in urban scenarios show that the proposed localization scheme is extensible and also robust to varying number of channel paths and combination of BS measurements. Considering a small training dataset, the proposed scheme significantly outperforms the data- and model-driven baselines in NLoS scenarios, in terms of positioning accuracy.

Design of High-Gain and Low-Mutual-Coupling Multiple-Input–Multiple-Output Antennas Based on PRS for 28 GHz Applications

In this paper, a high-gain and low-mutual-coupling four-port Multiple Input Multiple Output (MIMO) antenna based on a Partially Reflective Surface (PRS) for 28 GHz applications is proposed. The antenna radiator is a circular-shaped patch with a circular slot and a pair of vias to secure a wide bandwidth ranging from 24.29 GHz to 28.45 GHz (15.77%). The targeted band has been allocated for several countries such as Korea, Europe, the United States, China, and Japan. The optimized antenna offers a peak gain of 8.77 dBi at 24.29 GHz with a gain of 6.78 dBi. A novel PRS is designed and loaded on the antenna for broadband and high-gain characteristics. With the PRS, the antenna offers a wide bandwidth from 23.67 GHz to 29 GHz (21%), and the gain is improved up to 11.4 dBi, showing an overall increase of about 3 dBi. A 2 × 2 MIMO system is designed using the single-element antenna, which offers a bandwidth of 23.5 to 29 GHz (20%), and a maximum gain of 11.4 dBi. The MIMO antenna also exhibits a low mutual coupling of −35 dB along with a low Envelope Correlation Coefficient and Channel Capacity Loss, making it a suitable candidate for future compact-sized mmWave MIMO systems.

Hybrid mmWave MIMO Systems Under Hardware Impairments and Beam Squint: Channel Model and Dictionary Learning-Aided Configuration

Low overhead channel estimation based on compressive sensing (CS) has been widely investigated for hybrid wideband millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems. The channel sparsifying dictionaries used in prior work are built from ideal array response vectors evaluated on discrete angles of arrival/departure. In addition, these dictionaries are assumed to be the same for all subcarriers, without considering the impacts of hardware impairments and beam squint. In this manuscript, we derive a general channel and signal model that explicitly incorporates the impacts of hardware impairments, practical pulse shaping functions, and beam squint, overcoming the limitations of mmWave MIMO channel and signal models commonly used in previous work. Then, we propose a dictionary learning (DL) algorithm to obtain the sparsifying dictionaries embedding hardware impairments, by considering the effect of beam squint without introducing it into the learning process. We also design a novel CS channel estimation algorithm under beam squint and hardware impairments, where the channel structures at different subcarriers are exploited to enable channel parameter estimation with low complexity and high accuracy. Numerical results demonstrate the effectiveness of the proposed DL and channel estimation strategy when applied to realistic mmWave channels.

A Four Element mm-Wave MIMO Antenna System with Wide-Band and High Isolation Characteristics for 5G Applications.

In this article, we propose a light weight, low profile Multiple Input Multiple Output (MIMO) antenna system for compact 5th Generation (5G) mmwave devices. Using a RO5880 substrate that is incredibly thin, the suggested antenna is made up of circular rings stacked vertically and horizontally on top of one another. The single element antenna board has dimensions of 12 × 12 × 0.254 mm3 while the size of the radiating element is 6 × 2 × 0.254 mm3 (0.56λ0 × 0.19λ0 × 0.02λ0). The proposed antenna showed dual band characteristics. The first resonance showed a bandwidth of 10 GHz with a starting frequency of 23 GHz to an ending frequency point of 33 GHz followed by a second resonance bandwidth of 3.25 GHz ranging from 37.75 to 41 GHz, respectively. The proposed antenna is transformed into a four element Linear array system with size of 48 × 12 × 0.254 mm3 (4.48λ0 × 1.12λ0 × 0.02λ0). The isolation levels at both resonance bands were noted to be >20 dB which shows high levels of isolation among radiating elements. The MIMO parameters such as Envelope Correlation Co-efficient (ECC), Mean Effective Gain (MEG) and Diversity Gain (DG) were derived and were found to be in satisfactory limits. The proposed MIMO system model is fabricated and through validation and testing of the prototype, the results were found to be in good agreement with simulations.

Pilot spoofing detection for massive MIMO mmWave communication systems with a cooperative relay

In massive millimeter-wave (mmWave) multiple-input–multiple-output (MIMO) systems, eavesdroppers may transmit the identical pilot sequences as legitimate users to manipulate channel estimation in pilot phase and afterwards intercept the transmitted information in data transmission stage, constituting a severe attack for secure communications. In this paper, for a three-terminal massive mmWave MIMO system with a cooperative relay, the achievable secrecy rate under the presence of a pilot spoofing attack is investigated, and then an accurate detection scheme is proposed. Specifically, in the first slot of the uplink pilot stage, the full-duplex relay sends pilot sequence to the base station simultaneously when it receives the transmitted pilot signal from the user, through which the CSI from the relay to the base station is obtained. In the second slot, after the received pilot signal has been forwarded from the cooperative relay, the equivalent CSI from the base station to the user is obtained, and the joint CSI from the user/attacker to the relay is derived, based on which the likelihood ratio method is exploited to detect the potential pilot spoofing attack. Finally, numerical simulation is presented to show the performance of the proposed scheme in terms of miss detection and false detection events.

Compressive Beam and Channel Tracking With Reconfigurable Hybrid Beamforming in mmWave MIMO OFDM Systems

An efficient beam and channel acquisition and tracking scheme is developed under a reconfigurable hybrid beamforming (R-HBF) architecture for wideband millimeter wave (mmWave) multiple input multiple output (MIMO) systems. Under such an R-HBF, a hierarchical multi-resolution beam scanning and space-frequency compressive sensing method is proposed to achieve fast beam and channel acquisitions in mmWave MIMO orthogonal frequency division multiplexing (OFDM) systems. With the initial frequency-domain beam space channel estimates, Kalman-based algorithms are further developed to track the transmit and receive beamforming directions and the channel coefficients of the sparse propagation paths in mmWave mobile channels. Simulations show that the proposed method can greatly reduce the beam training time, and that the channel capacity evaluated with the estimated channels is only 2 dB inferior to the one with ideal channels. Moreover, the beam selection error rates are less than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> in typical urban mmWave mobile channels and traveling speeds even if the transmit power is only 10 dBm.

Direct Conversion of Hybrid Precoding and Combining From Full Array Architecture to Subarray Architecture for mmWave MIMO Systems

Hybrid precoding and combining for millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems with subarray (SA) architecture is a promising technology for 6G because of their low complexity, cost, and power consumption compared to the full array (FA) architecture. This paper proposes an iterative algorithm for designing hybrid precoding and combining for the SA architecture. It is called direct conversion of iterative hybrid precoding and combining from FA to SA (DCIFS). The proposed algorithm involves an iterative process that begins by designing a hybrid precoding and combining matrix for the FA structure and then converts it into an SA matrix by setting certain entries to zero while achieving better performance. It does not depend on the antenna array geometry, unlike other techniques such as the orthogonal matching pursuit (OMP) hybrid precoding and combining approach. We investigate the proposed algorithm with two scenarios. In the first scenario, we use the proposed DCIFS scheme only at the base station (BS) and the iterative FA hybrid scheme at the mobile station (MS), whereas in the second, we use the proposed DCIFS scheme at both the BS and the MS. Simulation results demonstrate that the proposed design approach achieves a spectral efficiency comparable to that of the FA hybrid design counterpart, especially for a large system, while maintaining low complexity. For example, when SNR= 0 dB and the number of transmitted streams ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N_s</i> ) = 2, the proposed algorithm provides about 1.5 bps/Hz spectral efficiency gain compared to the OMP hybrid design for the first scenario. Moreover, when the number of iterations is low and the number of BS antenna and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N_s</i> is high, the proposed approach outperforms the conventional SA hybrid design in terms of spectral efficiency with the same hardware complexity.

Hybrid Analog-Digital Transceiver Design for RIS-Assisted mmWave MIMO Communications

Reconfigurable intelligent surface (RIS) is a cost-effective solution to support millimeter wave (mmWave) communications suffering from severe blockage. In this letter, we aim to maximize the spectral efficiency (SE) of the RIS-assisted mmWave multiple-input multiple-output (MIMO) system by jointly optimizing the hybrid transceiver and passive RIS under the nonconvex unit-modulus constraints. It is revealed that the considered system is equivalent to a conventional mmWave system with a Kronecker-structured hybrid transmit antenna array. Using this fact, we firstly propose to jointly design the RIS and hybrid transceiver based on the idea of unitary matching. Motivated by the asymptotic orthogonality of array steering vectors for very large systems, a low-complexity two-stage scheme is also developed by simply choosing the transmit/receive array steering vectors associated with the first several largest path gains as the analog precoder/combiner. Numerical results further demonstrate the superior performance of the proposed schemes in terms of the achievable SEs and average run time.

Utilizing Multi-Dimensional MmWave MIMO Channel Features for Location Verification

In this paper, we address the problem of authenticating transmitters in millimeter-wave (mmWave) multiple-input multiple-output (MIMO) communication systems, and propose a location verification scheme based on multi-dimensional mmWave MIMO channel features. In particular, we first examine the mmWave MIMO channel features in terms of azimuth angle of arrival (AAoA), elevation angle of arrival (EAoA), and path gain, and then extract these fine-grained channel features through the maximum-likelihood (ML) estimation method. Based on the extracted feature parameters, authentication validation is cast in the framework of hypothesis testing theory. We also derive the analytical expressions for the typical false alarm and detection rates by using the likelihood ratio test and thus the statistical performance is analytically established. Finally, extensive numerical results are provided to demonstrate the performance of the proposed authentication scheme.

Hybrid Beamforming Design for Self-Interference Cancellation in Full-Duplex Millimeter-Wave MIMO Systems with Dynamic Subarrays.

Full-duplex (FD) millimeter-wave (mmWave) multiple-input multiple-output (MIMO) communication is a promising solution for the extremely high-throughput requirements in future cellular systems. The hybrid beamforming structure is preferable for its low hardware complexity and low power consumption with acceptable performance. In this paper, we introduce the hardware efficient dynamic subarrays to the FD mmWave MIMO systems and propose an effective hybrid beamforming design to cancel the self-interference (SI) in the considered system. First, assuming no SI, we obtain the optimal fully digital beamformers and combiners via the singular value decomposition of the uplink and downlink channels and the water-filling power allocation. Then, based on the obtained fully digital solutions, we get the dynamic analog solutions and digital solutions using the Kuhn-Munkres algorithm-aided dynamic hybrid beamforming design. Finally, we resort to the null space projection method to cancel the SI by projecting the obtained digital beamformer at the base station onto the null space of the equivalent SI channel. We further analyze the computational complexity of the proposed method. Numerical results demonstrate the superiority of the FD mmWave MIMO systems with the dynamic subarrays using the proposed method compared to the systems with the fixed subarrays and the half-duplex mmWave communications. When the number of RF chains is 6 and the signal-to-noise ratio is 10 dB, the proposed design outperforms the FD mmWave MIMO systems with fixed subarrays and the half-duplex mmWave communications, respectively, by 22.4% and 47.9% in spectral efficiency and 19.9% and 101% in energy efficiency.

Joint User Association and Hybrid Beamforming Designs for Cell-Free mmWave MIMO Communications

Cell-free millimeter-wave (mmWave) multiple-input multiple-output (MIMO) communications have been proposed as promising enablers for the next generation wireless networks. In this paper, we study the user association and hybrid beamforming in cell-free mmWave systems without full channel state information (CSI) acquisition. We consider a cloud radio access network (C-RAN), where multiple remote radio heads (RRHs) are distributed to communicate with users via analog beamforming, and connected to a centralized baseband unit (BBU) through fronthaul links which executes digital beamforming. We aim to jointly design user association, hybrid beamforming, and fronthaul compression with the aid of uplink training. A train-and-design framework is developed to achieve this goal. In particular, we first propose a two-stage uplink training approach to assist RRH-level design, during which the analog beamforming and user association are obtained. After that, digital beamforming and fronthaul compression are optimized at BBU based on the training results. Two performance metrics are considered in this paper, i.e. weighted sum-rate maximization and max-min fairness. Simulation results demonstrate the effectiveness of the proposed train-and-design framework for both sum-rate maximization and max-min fairness performance metrics. It is shown that the proposed algorithms can achieve comparable performance to the full-digital beamformer.

Mobility and Routing based Channel Estimation for Hybrid Millimeter-Wave MIMO WSNs

Recently, technological developments have enhanced, the use of Millimeter-wave (mm-Wave) Multiple Input Multiple Output (MIMO) system in various communication applications and wireless sensor networks as channel estimation efficiency can be immensely improved with the help of this technological developments in Millimeter-wave MIMO system and wireless sensor network as well. Moreover, they can improve quality of communication services to a great extent. However, cell interference in Millimeter-wave (mm-Wave) MIMO system can produce a massive impact on spectral efficiency. Therefore, a Routing Enabled Channel Estimation (RECE) technique is presented in this article to minimize interference between cells. The proposed Channel Estimation technique improves channel capacity as well as spectral efficiency. Moreover, Normalized Mean Square Error (NMSE) is minimized heavily using proposed RECE technique. Here, main aim of this article is to reduce cell interference and channel estimation inside a cell by using route selection, beam selection, and spatial frequency estimation. Here, different scenarios and parameters are considered to evaluate performance efficiency of proposed RECE technique in terms of spectral efficiency, NMSE and SNR and compared against varied traditional channel estimation techniques. Moreover, it is clearly evident from performance results that the proposed channel estimation technique performs better than the other two methods.

Particle Swarm Optimization–Long Short-Term Memory based Channel Estimation with Hybrid Beam Forming Power Transfer in WSN-IoT Applications

Non-Orthogonal Multiple Access (NOMA) helps to overcome various difficulties in future technology wireless communications. NOMA, when utilized with millimeter wave multiple-input multiple-output (MIMO) systems, channel estimation becomes extremely difficult. For reaping the benefits of the NOMA and mm-Wave combination, effective channel estimation is required. In this paper, we propose an enhanced particle swarm optimization based long short-term memory estimator network (PSOLSTMEstNet), which is a neural network model that can be employed to forecast the bandwidth required in the mm-Wave MIMO network. The prime advantage of the LSTM is that it has the capability of dynamically adapting to the functioning pattern of fluctuating channel state. The LSTM stage with adaptive coding and modulation enhances the BER.PSO algorithm is employed to optimize input weights of LSTM network. The modified algorithm splits the power by channel condition of every single user. Participants will be first sorted into distinct groups depending upon respective channel conditions, using a hybrid beamforming approach. The network characteristics are fine-estimated using PSO-LSTMEstNet after a rough approximation of channels parameters derived from the received data.

Hybrid Beamforming for Intelligent Reflecting Surface Aided Millimeter Wave MIMO Systems

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 architectures. We first exploit the sparse-scattering structure and large dimension of mmWave channels to develop the joint design of IRS reflection matrix and hybrid beamformer for narrowband MIMO systems. Then, we generalize the proposed joint design to broadband MIMO systems with orthogonal frequency division multiplexing (OFDM) modulation by leveraging the angular sparsity of frequency-selective mmWave channels. Simulation results demonstrate that the proposed joint designs can significantly enhance the spectral efficiency of the systems of interest and achieve superior performance over the existing designs.

Resisting Malicious Eavesdropping: Physical Layer Security of mmWave MIMO Communications in Presence of Random Blockage

Millimeter wave (Mmwave) communication can realize high rate service for the upcoming Internet of Things (IoT) networks. Although directional multiantenna gains can help enhance security, randomly distributed eavesdroppers can still intercept confidential messages by residing in both the main-lobe and side-lobe areas of the beam signal. Considering the unique propagation features of mmWave, this article explores the potential of physical layer security in mmWave multiple-input–multiple-output (MIMO) systems. We propose an artificial noise (AN)-aided capacity threshold on–off secure transmission scheme to resist the eavesdropping threat. Taking into account the influence of mmWave channel characteristics, random blockage, and multiantenna gains, we first derive the closed-form expressions of transmission probability (TP) and secrecy outage probability (SOP) in a noncolluding eavesdropping scenario. Then, the lower bound of SOP with AN and closed-form expression of SOP without AN is derived in a colluding eavesdropping scenario. Theoretical analysis evaluates the impacts of various system parameters on secrecy performance and verifies the effects of AN interference on inhibiting side-lobe eavesdropping. Simulation results validate the theoretical results and indicate that the combination of capacity threshold on–off transmission scheme, AN interference, and multiantenna directional gains can effectively reduce the security threats of mmWave MIMO systems. Besides, the optimal power allocation ratio of AN in noncolluding scenarios is demonstrated and its rule is summarized, which depends on whether legitimate communication links are in blockage.

Joint RF Precoding and Beam Selection Design for Uplink mmWave Beamspace MIMO Systems

Phase-only radio frequency (RF) precoding and lens antenna array-based beam selection are two promising low-hardware-cost technologies for millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems. This letter aims to jointly design users’ RF precoders and base station’s beam selection network to maximize the uplink sum rate (SR) of mmWave MIMO systems. For the sake of tackling the formulated mixed-integer optimization problem, a fractional programming-based iterative algorithm is developed via capitalizing on the Riemannian gradient (RG)-based and penalty-based methods. In addition, a low-complexity algorithm is proposed at the expense of a slight SR performance loss, which combines the stepwise refinement-based beam selection scheme with the RG approach. The convergence of the proposed algorithms are discussed and their effectiveness is illustrated by numerical results.

Hybrid Beamforming Designs for Frequency-Selective mmWave MIMO Systems With Per-RF Chain or Per-Antenna Power Constraints

Configuring precoders and combiners is a major challenge to deploy practical multiple-input multiple-output (MIMO) millimeter wave (mmWave) communication systems with large antenna arrays. Most prior work addresses the problem focusing on a total transmit power constraint. In practical transmitters, however, power amplifiers must operate within their linear range, so that a power constraint applies to each one of the input signals to these devices. Therefore, precoder and combiner designs should incorporate per-antenna or per-radio frequency (RF) chain transmit power constraints. We focus on such problem for frequency-selective channels with multicarrier modulation, and assuming hybrid analog/digital architectures based on fully connected analog blocks implemented with finite-resolution phase shifters. We first derive an all-digital solution which aims to maximize spectral efficiency. Then, we develop hybrid precoders and combiners by approximately matching the corresponding all-digital matrices while still enforcing the power constraints. Numerical results show that the proposed all-digital design performs close to the upper bound given by the standard waterfilling-based solution with a total power constraint. Additionally, the hybrid designs exhibit a moderate loss even when low-resolution phase shifters are considered.