mmWave Multiple-input Multiple-output Systems Research Articles

Joint Power Allocation and Hybrid Beamforming for Cell-Free mmWave Multiple-Input Multiple-Output with Statistical Channel State Information.

Cell-free millimeter wave (mmWave) multiple-input multiple-output (MIMO) can effectively overcome the shadow fading effect and provide macro gain to boost the throughput of communication networks. Nevertheless, the majority of the existing studies have overlooked the user-centric characteristics and practical fronthaul capacity limitations. To solve these practical problems, we introduce a resource allocation scheme using statistical channel state information (CSI) for uplink user-centric cell-free mmWave MIMO system. The hybrid beamforming (HBF) architecture is deployed at each access point (AP), while the central processing unit (CPU) only combines the received signals by the large-scale fading decoding (LSFD) method. We further frame the issue of maximizing sum-rate subject to the fronthaul capacity constraint and minimum rate constraint. Based on the alternating optimization (AO) and fractional programming method, we present an algorithm aimed at optimizing the users' transmit power for the power allocation (PA) subproblem. Then, an algorithm relying on the majorization-minimization (MM) method is given for the HBF subproblem, which jointly optimizes the HBF and the LSFD coefficients.

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 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.

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.

Intelligent channel estimation in millimeter wave massive MIMO communication system using hybrid deep learning with heuristic improvement

SummaryThe major goal of millimeter wave (mmWave) multiple‐input multiple‐output (MIMO) systems is to get effective channel state information (CSI). Most of the recent works use nuclear norm theory for recovering the low‐rank scheme of channels. Some suboptimal solutions to the rank minimization problem can occur while addressing the nuclear norm‐based convex problem, which degrades the accuracy of channel estimation. Some works recover the channel with the assumption of the mmWave channel using an over‐complete dictionary. On the other hand, the accuracy of available CSI may openly influence the efficiency of mmWave communications. The main intention of this paper is to develop an enhanced channel estimation model with an optimized hybrid deep learning model. Here, the integration of deep neural network (DNN) and long short‐term memory (LSTM) form the hybrid deep learning model termed optimized D‐LSTM, which is modified by the opposition searched exploration‐based Harris hawks optimization (OE‐HHO). The input to the proposed hybrid deep learning is taken as the correlation among the received signal vectors and the measurement matrix for predicting the beam space channel amplitude. Finally, the successful channel estimation is observed by deep hybrid learning by the experimental outcomes, which also demonstrate that the proposed channel estimation model overwhelms the conventional models in terms of Normalized Mean‐Squared Error (NMSE) and spectral efficiency. The experimental results show that the designed OE‐HHO method obtains 9.2%, 8.9%, 8.65%, and 0.47% progressed than DA, DHOA, GWO, and HHO, respectively. Therefore, higher efficiency is observed by OE‐HHO based mmWave MIMO communication system.

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 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.

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.

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.

Intelligent Reflecting Surface Assisted mmWave Communication Using Mixed Timescale Channel State Information

A key challenge for millimeter wave (mmWave) multiple-input multiple-output (MIMO) communication is that the signals at mmWave band are highly susceptible to blockage. To address this challenge, we introduce intelligent reflecting surface (IRS) to increase coverage area and improve communication performance. This paper considers a joint design of hybrid precoders at the base station and the passive precoder at the IRS to maximize the average spectral efficiency in an IRS-assisted mmWave MIMO system by exploiting the mixed timescale channel state information (CSI). Specifically, the hybrid precoders are designed according to the instantaneous CSI of the overall channel, while the IRS reflection coefficient matrix is optimized using the statistical CSI of all links. However, such a design problem is challenging to solve due to the non-convexity and the mixed timescale. This work proposes efficient algorithms to design jointly the hybrid precoders and the IRS reflection coefficient matrix where the update of the IRS reflection coefficient matrix is independent of the hybrid precoders. Simulation results demonstrate the effectiveness of the proposed algorithms. More interestingly, the results also show that adding low-cost reflector elements at the IRS can reduce the number of required high-cost radio frequency chains.

Online machine learning-based physical layer authentication for MmWave MIMO systems

Transmitter authentication is significantly critical to secure millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems. By utilizing the mmWave MIMO channel and carrier frequency offset (CFO), this paper proposes a novel online machine learning-based physical layer authentication scheme to validate transmitter identities. In particular, with the help of the Gaussian kernel method and representer theorem, we formulate the physical layer authentication model as a binary classification model. Based on the developed classification model and a constructed convex objective function, we then design an online algorithm to achieve updating authentication parameters, and thus establish a novel online machine learning-based physical layer authentication scheme. Based on the developed authentication model and theories of statistical hypothesis testing, we statistically derive the analytical expressions for false alarm and detection rates for the proposed authentication scheme. Finally, we carry out extensive experiments to verify the authentication performance in terms of the false alarm and detection rates. In addition, we investigate the related authentication efficiency issues (e.g., convergence process) and the capability of resisting against spoofing attacks in mmWave MIMO systems.

Switch-and-inverter based adaptive subarrays for hybrid mmWave multi-user MIMO systems

ABSTRACT The hybrid precoding design is considered for a millimeter-wave (mmWave) multi-user (MU) multiple-input multiple-output (MIMO) downlink communication system. A small quantity of more energy-efficient switches and inverters (SIs) are being substituted for a large amount of high-resolution phase shifters (PSs) in the analog precoder of the mmWave MIMO system. This SI-based hybrid precoding architecture reduces significantly both the hardware complexity and energy consumption and thus enhances substantially the transmission energy efficiency (EE). On the basis of the achievable sum-rate (ASR) maximization, the SI-based overlapped subarray (OSA) hybrid precoding is exploited. Compared with the traditional SI-based sub-connected (SC) array configurations, the greater the overlapping antenna elements, the better the transmission ASR performance, and the nearer the fully PS-based precoding configuration. Finally, the SI-based hybrid precoding is equipped with the Gram–Schmidt orthogonalization (GSO) based dynamic subarray mapping and antenna selection (AS) mechanism to improve further the EE measure while maintaining excellent ASR performance.

Hybrid Precoding for mmWave MIMO Systems With Overlapped Subarray Architecture

Traditional precoding is incompatible with millimetre wave (mmWave) multiple input multiple output (MIMO) systems due to hardware costs and power consumption. As a result, hybrid precoding is being considered as a promising technology for balancing hardware complexity and system performance. This paper proposes a hybrid precoding technique for overlapped subarrays (OSA) architecture in mmWave MIMO systems. It exploits the OSA’s structure to decompose the hybrid precoding problem into a series of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L_tN_s</i> /2 subproblems and then solves them iteratively, where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L_t</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N_s</i> are the numbers of RF chains and transmitted data streams, respectively. First, the proposed scheme determines the analog and digital precoding submatrices of each OSA iteratively and then constructs the analog and digital precoding matrices of the whole OSA architecture. The digital precoding submatrix of each OSA is determined from each vector in the OSA submatrix. The results show that the proposed hybrid precoding for the OSA architecture outperforms the successive interference cancellation (SIC)-based hybrid precoding for non-overlapped SA (NOSA) and provides performance close to the fully-connected (FC) spatially sparse hybrid precoding, despite requiring less hardware and computational complexities.

Efficient Security Architecture for Physical Layer in mmWave Communication Systems

Employing mmWave is a good way to achieve the data demands for the new and future generations of communication systems. In order to decrease power consumption and complexity of hardware, hybrid precoding is implemented for mmWave systems with large scale antenna. Lack of secure communication paths in mmWave multiple-input multiple-output (MIMO) systems leads to attack and degrade the system efficiency. For secure communications, this paper proposes a deep and secure hybrid precoder and decoder design for mmWave MIMO systems to maximize the secrecy rate. Lack of secure communication paths being eavesdropped by Eves is illustrated and the scatterer sharing channel model is assumed. The proposed algorithm consists of two convolutional neural networks for calculating the secure RF analog precoder, and then obtains the digital precoder that can further improve the security. In addition, singular value decomposition technique based physical layer security is implemented to determine digital precoders. Results showed that the secrecy performance improvement of the proposed algorithm in comparison to the benchmark algorithms and algorithms based on optimization methods.

Low-Complexity Hybrid Precoding for Subarray Architecture mmWave MIMO Systems

Hybrid precoding for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems has attracted much attention in recent years for subarray architecture compared to array architecture because of its low cost and low power consumption. This is due to the small number of required phase shifters in the subarray architecture. In this paper, we investigate the issue of hybrid precoding for the subarray architecture in narrowband mmWave MIMO systems. First, we derive the spectral efficiency of the subarray architecture with hybrid precoding and discuss the problem formulation. Then, we propose two low-complexity hybrid precoding algorithms for the subarray architecture for narrowband mmWave MIMO systems. In the first algorithm, the hybrid precoding matrix is divided into subarrays submatrices and each subarray submatrix is then divided into vectors. The analog precoding of each subarray is determined from the first vector of the subarray submatrix, which is then used to determine the elements of the digital precoder from all vectors in the subarray submatrix (vector by vector) using a simple maximum ratio combining (MRC) method. The proposed algorithm is called vector-by-vector (VBV) hybrid precoding. Finally, to further enhance the system performance, the proposed VBV precoding in the first algorithm is also combined with an iterative solution, and the resulting algorithm is called iterative VBV precoder. Simulation results verify that the proposed precoding algorithms outperform that of the successive interference cancellation-based subarray precoding and has a performance that is close to that obtained by the fully-connected spatially sparse precoding in various system settings, with lower complexity.