Hybrid Beamforming Algorithm Research Articles

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

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

Transceiver Beamforming for Over-the-Air Computation in Massive MIMO Systems

This paper investigates the transmitter and receiver beamforming (TB and RB) for over-the-air computation (AirComp) in massive multiple-inputs and multiple-outputs (MIMO) systems. First, we propose a two-phase hybrid beamforming algorithm to design TB and hybrid RB. In the first phase, we adopt a projected gradient descent with momentum (PGDM) algorithm to search for the optimal fully-digital TB matrices. Compared with the benchmarks on the mean square error (MSE) performances, PGDM can achieve up to 5 dB gain in signal-to-noise ratio (SNR) with less algorithm execution time when fully-digital RB is assumed. In the second phase, we plug the TB matrices obtained in PGDM as well as the optimal baseband RB (BBRB) matrix into the MSE objective, and adopt gradient descent to search for the optimal radio-frequency RB (RFRB) matrix. Compared with the state-of-the-arts, the proposed two-phase algorithm reduces up to 30% of the algorithm execution time and 18% of the MSE. Second, we propose a statistical TB algorithm to reduce the communication overheads, in which TB completely depends on statistical channel state information (CSI) and thus does not rely on the feedback from the base station (BS). We prove that orthonormal matrices are asymptotically optimal for statistical TB when uncorrelated <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rayleigh</i> channels are assumed and the number of receiving antennas approaches to infinity. For correlated channels, experimental results show that the proposed statistical TB can achieve about 5 dB gain in SNR compared with orthonormal matrices in terms of the MSE performance. Third, a large scale system analysis is made in this paper. As the number of the receiving antennas approaches to infinity, asymptotically optimal choices for TB and RB are provided, and upper bounds of MSE are derived in terms of the number of clients and receiving antennas. For hybrid RB, an upper bound of the squared distance between the optimal hybrid RB and the optimal fully-digital RB is also derived.

Hybrid Beamforming in Sub-THz LoS MIMO Systems

In this study, we design a hybrid beamforming algorithm for sub-terahertz-band communications. We introduce a near-field propagation model for an indoor line-of-sight environment. A hybrid beamforming method for sparse arrays of subarray structures is proposed. Using MATLAB simulation results, we show that the proposed algorithm achieves high capacity.

RIS-Assisted Hybrid Beamforming and Connected User Vehicle Localization for Millimeter Wave MIMO Systems

A reconfigurable intelligent surface (RIS) is a type of metasurface that can dynamically control the reflection and transmission of electromagnetic waves, such as radio waves, by changing its physical properties. Recently, RISs have played an important role in intelligently reshaping wireless propagation environments to improve the received signal gain as well as spectral efficiency performance. In this paper, we consider a millimeter wave (mmWave) vehicle-to-vehicle (V2V) multiple-input multiple-output (MIMO) system in which, an RIS is deployed to aid downlink V2V data transmission. In particular, the line-of-sight path of the mmWave system is affected by blockages, resulting in higher signaling overhead. Thus, the system performance may suffer due to interruptions caused by static or mobile blockers, such as buildings, trees, vehicles, and pedestrians. In this paper, we propose an RIS-assisted hybrid beamforming scheme for blockage-aware mmWave V2V MIMO systems to increase communication service coverage. First, we propose a conjugate gradient and location-based hybrid beamforming (CG-LHB) algorithm to solve the user sub-rate maximization problem. We then propose a double-step iterative algorithm that utilizes an error covariance matrix splitting method to minimize the effect of location error on the passive beamforming. The proposed algorithms perform quite well when the channel uncertainty is smaller than 10%. Finally, the simulation results validate the proposed CG-LHB algorithm in terms of the RIS-assisted equivalent channel for mmWave V2V MIMO communications.

Phased Array System Toolbox Pack Overview for New Course «5G Smart Antennas Technologies»

In the field of smart antenna technologies, approaches based on simulation modeling in special Matlab software, including the Phased Array System Toolbox extension package, deserve special attention. This package provides the implementation of algorithms and methods for modeling antenna arrays (AA) and beamforming (BF) systems in various applications, including radio communication, radar and radio navigation systems. Using the capabilities of this extension package, you can analyze the performance of active and passive AAs of various geometric configurations, including complex AAs formed from composite arrays of elements. The simulation models built with this expansion package allow the formation and processing of signals using models and methods of beamforming, when working on transmission and reception. For LTE and 5G NR mobile networks, satellite systems and WLANs, the PAST extension package allows modeling multipath AAs, including those operating in the adaptive BF mode. The extension package includes models of digital and hybrid BF algorithms that operate as part of massive MIMO spatial signal processing systems in the mmWave. Simulation capabilities in the extension package include, but are not limited to, reproducing fading conditions in a multipath radio channel and evaluating their impact on communication systems with an AP; algorithms and methods for determining signal direction of arrival (DOA). In this paper, we review the coordinate systems used in the PAST extension package. Subject of study. The article is devoted to an overview of the PAST extension package for use in the new 5G Smart Antenna Technologies training course. Method. The study of the possibilities of the PAST extension package is carried out by the simulation. Main results. The result of this work is an overview of the coordinate systems in basic software tools of the PAST extension package for use in the new course "5G Smart Antenna Technologies". Practical significance. This review introduces the capabilities of the PAST extension package and is the foundation of methodological support in the implementation of algorithms and methods for modeling antenna arrays and beamforming systems within the framework of the new training course “5G Smart Antenna Technologies”.

On the Secrecy Design of STAR-RIS Assisted Uplink NOMA Networks

This paper investigates the secure transmission in a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted uplink non-orthogonal multiple access system, where the legitimate users send confidential signals to the base station by exploiting STAR-RIS to reconfigure the electromagnetic propagation environment proactively. Depending on the availability of the eavesdropping channel state information (CSI), both the full CSI and statistical CSI of the eavesdropper are considered. For the full eavesdropping CSI scenario, we adopt the adaptive-rate wiretap code scheme with the aim of maximizing minimum secrecy capacity subject to the successive interference cancellation decoding order constraints. To proceed, we propose an alternating hybrid beamforming (AHB) algorithm to jointly optimize the receive beamforming, transmit power, and reflection/transmission coefficients. While for the statistical eavesdropping CSI scenario, the constant-rate wiretap code scheme is employed to minimize the maximum secrecy outage probability (SOP) subject to the quality-of-service requirements of legitimate users. Then, we derive the exact SOP expression under the constant-rate coding strategy and develop an extended AHB algorithm for the joint secrecy beamforming design. Simulation results demonstrate the effectiveness of the proposed scheme. Moreover, some useful guidance about the quantification of phase shift/amplitude and the deployment of STAR-RIS is provided.

Latency Minimization for mmWave D2D Mobile Edge Computing Systems: Joint Task Allocation and Hybrid Beamforming Design

Mobile edge computing (MEC) and millimeter wave (mmWave) communications are capable of significantly reducing the network's delay and enhancing its capacity. In this paper we investigate a mmWave and device-to-device (D2D) assisted MEC system, in which user A carries out some computational tasks and shares the results with user B with the aid of a base station (BS). We assume partial offloading model and the task can be partitioned into two portions: the first part is computed locally at user A, while the second part is transmitted to the BS and computed by the MEC server. The computational results are then sent to user B through a D2D link and via the link from the BS to user B, respectively. To support computation offloading, both the users and the BS are equipped with multiple antennas and employ analog and digital (A/D) hybrid beamforming. Moreover, we propose a novel two-timescale joint hybrid beamforming and task allocation algorithm to reduce the system latency whilst cut down the required signaling overhead. Specifically, the high-dimensional analog beamforming matrices are updated in a frame-based manner based on the channel state information (CSI) samples, where each frame consists of a number of time slots, while the low-dimensional digital beamforming matrices and the offloading ratio are optimized more frequently relied on the low-dimensional effective channel matrices in each time slot. A stochastic successive convex approximation (SSCA) based algorithm is developed to design the long-term analog beamforming matrices. As for the short-term variables, the digital beamforming matrices are optimized relying on the innovative penalty-concave convex procedure (penalty-CCCP) for handling the mmWave non-linear transmit power constraint, and the offloading ratio can be obtained via the derived closed-form solution. Simulation results verify the effectiveness of the proposed algorithm by comparing the benchmarks.

MGGAN-Based Hybrid Beamforming Design for Massive MIMO Systems Against Rank-Deficient Channels

The design of hybrid beamforming (HBF) is one of the key issues in millimeter wave (mmWave) and terahertz (THz) massive multi-input multi-output (MIMO) communications. In particular, only rank-deficient channel state information (CSI) can be acquired in hybrid MIMO architecture, which enhances design challenges. However, this practical problem of rank-deficient channels has been avoided by most of the existing studies on HBF. In this letter, we propose a new deep learning (DL) network model called Multi-Generator Generative Adversarial Network (MGGAN) to accomplish the design of HBF against rank-deficient channels. Specifically, MGGAN includes three generators for recovering the rank-deficient channels, achieving the analog and the digital beamforming matrices, respectively. In addition, a spectrum efficiency (SE) module is introduced to take system SE as the optimization goal of the network. Simulation results show the superiority of our proposed MGGAN model in SE performance over several DL network architectures and classical HBF algorithms. Moreover, it is more robust against the rank-deficiency of hybrid architecture MIMO channels.

Hybrid beamforming for millimeter-wave massive MIMO heterogeneous networks

In this paper, we investigate the hybrid beamforming designs in millimeter wave (mmWave) massive MIMO relaying heterogeneous networks (HetNet), where small cells are overlaid onto the service area of a macrocell. The deployment of HetNet and utilization of the adequate bandwidth in the mmWave band are capable of addressing the explosive growth of data rates in next-generation wireless networks. However, the severe path loss and attenuation in the mmWave band and complex interference in HetNet should be addressed. For the macrocell, we propose a minimum mean squared error (MMSE)-based alternative iterative hybrid analog/digital beamforming algorithm for the downlink multi-user mmWave relaying system. With the constant modulus constraints and the higher-order polynomial function, we reformulate the optimization problem as three convex quadratic subproblems, and the coupling approximate optimal precoders and combiners are jointly obtained by the proposed alternative iterative algorithm. For the picocells, we propose a hybrid beamforming algorithm for downlink mmWave massive MIMO system. An alternative iterative optimization algorithm based on manifold optimization is developed to approximate the optimal beamforming designs. The baseband digital beamforming scheme is investigated by leveraging the mean square error (MSE) criteria for macrocell users and picocell users to manage cross-tier and inter-user interference. Simulation results demonstrate the obvious advantages of the proposed hybrid beamforming algorithms in terms of achievable sum-rate for various setting scenarios.

Mixed-Timescale Deep-Unfolding for Joint Channel Estimation and Hybrid Beamforming

In massive multiple-input multiple-output (MIMO) systems, hybrid analog-digital beamforming is an essential technique for exploiting the potential array gain without using a dedicated radio frequency chain for each antenna. However, due to the large number of antennas, the conventional channel estimation and hybrid beamforming algorithms generally require high computational complexity and signaling overhead. In this work, we propose an end-to-end deep-unfolding neural network (NN) joint channel estimation and hybrid beamforming (JCEHB) algorithm to maximize the system sum rate in time-division duplex (TDD) massive MIMO. Specifically, the recursive least-squares (RLS) algorithm and stochastic successive convex approximation (SSCA) algorithm are unfolded for channel estimation and hybrid beamforming, respectively. In order to reduce the signaling overhead, we consider a mixed-timescale hybrid beamforming scheme, where the analog beamforming matrices are optimized based on the channel state information (CSI) statistics offline, while the digital beamforming matrices are designed at each time slot based on the estimated low-dimensional equivalent CSI matrices. We jointly train the analog beamformers together with the trainable parameters of the RLS and SSCA induced deep-unfolding NNs based on the CSI statistics offline. During data transmission, we estimate the low-dimensional equivalent CSI by the RLS induced deep-unfolding NN and update the digital beamformers. In addition, we propose a mixed-timescale deep-unfolding NN where the analog beamformers are optimized online, and extend the framework to frequency-division duplex (FDD) systems where channel feedback is considered. Simulation results show that the proposed algorithm can significantly outperform conventional algorithms with reduced computational complexity and signaling overhead.

Cellular Communications Over Unlicensed mmWave Bands With Hybrid Beamforming

In this paper, we study the cellular communications over unlicensed millimeter-wave (mmWave) bands to satisfy the extra-high transmission rate demands. To guarantee the harmonious coexistence of cellular and WiGig users over 60 GHz bands, we design a frame structure for the unlicensed mmWave spectrum sharing to reduce the interference caused by cellular data transmission to WiGig networks. By joint frequency and spatial resource allocation, an iterative channel allocation and hybrid beamforming algorithm is designed to maximize the sum rate of all cellular users while minimizing the interference to WiGig networks. Simulation results show that our proposed scheme outperforms the SVD-based hybrid beamforming method. The fairness between the cellular and the WiGig users is achieved by setting an optimal transmit power of the gNB for unlicensed mmWave spectrum sharing. The influence of the beamwidth and beam direction of the gNB is evaluated in terms of the system performances of both the unlicensed cellular users and WiGig users.

Hybrid Beamforming for MISO System via Convolutional Neural Network

Hybrid beamforming (HBF) is a promising approach to obtain a better balance between hardware complexity and system performance in massive MIMO communication systems. However, the HBF optimization problem is a challenging task due to its nonconvex property in terms of design complexity and spectral efficiency (SE) performance. In this work, a low-complexity convolutional neural network (CNN)-based HBF algorithm is proposed to solve the SE maximization problem under the constant modulus constraint and transmit power constraint in a multiple-input single-output (MISO) system. The proposed CNN framework uses multiple convolutional blocks to extract more channel features. Considering that the solutions for the HBF are hard to obtain, we derive an unsupervised learning mechanism to avoid any labeled data when training the constructed CNN. We discuss the performance of the proposed algorithm in terms of both the generalization ability for multiple CSIs and the specific solving ability for an individual CSI, respectively. Simulations show its advantages in both SE and complexity over other related algorithms.

Massive MIMO Indoor Transmissions at 38 and 65 GHz Applying Novel HBF Techniques for 5G.

The 5G Infrastructure Public Private Partnership (5GPPP) has recently published a white paper about 5G service indoors, since up to now, it had mainly focused on the outdoors. In an indoor environment, the requirements are different since the propagation mechanism differs from other scenarios. Furthermore, previous works have shown that space frequency block code (SFBC) techniques applied to multiple antennas improve performance compared to single-input single-output (SISO) systems. This paper presents an experimental study in an indoor environment regarding the performance of a massive multiple-input multiple-output (mMIMO) millimeter-wave (mmWave) system based on the 5G New Radio (NR) standard in two frequency bands. In a first step, the 38 and 65 GHz bands are compared by applying a low-complexity hybrid beamforming (HBF) algorithm. In a second step, the throughput and the maximum achievable distance are studied using a new algorithm that combines the SFBC technique and HBF. Results show, at 38 GHz with HBF and aggregated bandwidths (4 × 100 MHz), a maximum throughput of 4.30 Gbit/s up to 4.1 m. At 65 GHz, the SFBC + HBF algorithm improves the communication distance by 1.34, 1.61, or 1.75 m for bandwidths of 100, 200, or 400 MHz, respectively.

Hybrid Beamforming and Data Stream Allocation Algorithms for Power Minimization in Multi-User Massive MIMO-OFDM Systems

A hybrid beamforming structure is suggested as one of the solutions to reduce implementation costs and energy consumption in millimeter-wave massive multiple-input, multiple-output (MIMO) systems. In this study, an optimization problem of resource allocation was formulated to minimize the total system transmission power on downlink under a certain quality-of-service (QoS), such as bit/block error rates and data rates for each user, and the solution was proposed therein. Our proposed stream incremental algorithm can dynamically adjust the number of data streams for each user according to the channel state information. Precoding and combining schemes need to be developed to solve the formulated problem and also are proposed in this paper to be paired up with the stream incremental algorithm. Our proposed algorithms consider the practical modulation and coding scheme for transmission in various data stream allocation and beamforming designs. The proposed algorithms provide beamforming solutions for millimeter-wave massive MIMO systems, which achieve comparable performance to that of a fully digital block-diagonalization (BD) algorithm with a lower implementation cost and outperform those of modified existing hybrid beamforming algorithms. Simulation results demonstrate the efficacy of the proposed schemes by allocating the different numbers of data streams for each user according to the channel state information. The simulation results verified that the proposed method can achieve a good trade-off between complexity and performance on comparison with the modified existing schemes and the full digital solutions.

User Association and Hybrid Beamforming Designs for Cooperative mmWave MIMO Systems

Hybrid analog and digital beamforming has emerged as a key enabling technology for millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) communication systems since it can balance the trade-off between system performance and hardware efficiency. Owing to the strong ability of central control, cooperative networks show great potential to enhance the spectral efficiency of mmWave communications. In this paper, we consider cooperative mmWave MIMO systems and propose user association and hybrid beamforming design algorithms for three typical hybrid beamforming architectures. The central processing unit (CPU) of the cooperative networks first matches the service pairs of base stations (BSs) and users. Then, an iterative hybrid beamforming design algorithm is proposed to maximize the weighted achievable sum-rate performance of the mmWave MIMO system with fully connected hybrid beamforming architecture. Moreover, a heuristic analog beamforming design algorithm is introduced for the fixed subarray hybrid beamforming architecture. In an effort to further exploit multiple-antenna diversities, we also consider the dynamic subarray architecture and propose a novel antenna design algorithm for the analog beamforming design. Simulation results illustrate that the proposed hybrid beamforming algorithms achieve a significant performance improvement than other existing approaches and the dynamic subarray architecture has great advantages of improving the energy efficiency (EE) performance.

Partially-Connected Hybrid Beamforming for Spectral Efficiency Maximization via a Weighted MMSE Equivalence

Hybrid beamforming (HBF) is an attractive technology for practical massive multiple-input and multiple-output (MIMO) millimeter wave (mmWave) systems. Compared with the fully-connected HBF architecture, the partially-connected one can further reduce the hardware cost and power consumption. However, the special block diagonal structure of its analog beamforming matrix brings additional design challenges. In this paper, we develop effective HBF algorithms for spectral efficiency maximization (SEM) in wideband mmWave massive MIMO systems with the partially-connected architecture. One main contribution is that we prove the equivalence of the SEM problem and a weighted mean square error minimization (WMMSE) problem, which leads to a convenient algorithmic approach to directly tackle the SEM problem. Specifically, we decompose the equivalent WMMSE problem into the hybrid precoding and hybrid combining subproblems, for which both the optimal digital precoder and combiner have closed-form solutions. For the more challenging analog precoder and combiner, we propose an element iteration based algorithm and a manifold optimization based algorithm. Finally, the hybrid precoder and combiner are alternatively updated. The overall HBF algorithms are proved to monotonously increase the spectral efficiency and converge. Furthermore, we also propose modified algorithms with reduced computational complexity and finite-resolution phase shifters. Simulation results demonstrate that the proposed HBF algorithms achieve significant performance gains over conventional algorithms.

Joint Power Allocation and Hybrid Beamforming for Downlink mmWave-NOMA Systems

This paper investigates the application of nonorthogonal multiple access (NOMA) in millimeter-Wave (mmWave) communications to address resource allocation issues for multiuser downlink transmission. Inspired by the K-means clustering algorithm, a NOMA user grouping policy is first employed in accordance with the channel correlation between users. The first-stage decoding order for each NOMA group is then determined by merely utilizing the users’ channel gain to formulate a joint power allocation and hybrid beamforming optimization problem. Specifically, we use signal-to-leakage-plus-noise ratio (SLNR) as the performance index of the optimization problem to reduce the computational complexity, because it can decouple the design of the beamforming and power allocation issues so they can be executed iteratively. Under given beamforming matrix, the power allocation issue is expressed as a quadratic programming (QP) problem, and then transformed into a convex problem by introducing an auxiliary-positive real variable to solve through the Lagrange multiplier method. On the contrary, the beamforming optimization problem is non-convex and very difficult to solve due to the constant modulus constraints in the hybrid architecture. However, the optimum solution of the ideal full-digital beamforming can be acquired primarily by generalized eigenvalue decomposition (GED). In this condition, two hybrid beamforming algorithms are proposed, in which normalized phase matching and equal gain transmission are performed respectively in the analog domain. On this basis, a second-stage decoding order can be employed according to the effective channel gain of users to perform successive interference cancellation (SIC) successfully. Numerical results show that the proposed joint power allocation and hybrid beamforming algorithms are superior to the classical mmWave-NOMA and orthogonal multiple access (OMA) schemes not only in lower implementation complexity, but also in better spectrum efficiency and energy efficiency performance.

Interference Cancellation Aided Hybrid Beamforming for mmWave Multi-User Massive MIMO Systems

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

Hybrid beamforming in Multiuser mmWave Massive MIMO System

Conventional MIMO systems typically use full digital processing for optimal performance while it requires an independent radio frequency (RF) chain for each antenna, which is not feasible for large-scale antenna arrays due to the high cost, high-power consumption and high complexity of RF chain components in high frequencies. Fortunately, in recent years, the Hybrid beamforming has been proposed as an efficient and auspicious technique for the practical implementation of millimeter-Wave (mmWave) multiple-input multiple-output (MIMO) wireless systems. In this paper we propose a novel HBF (Hybrid beamforming) algorithm and simulate the sum rate of the proposed approach, then compare it with other algorithms in the sum rates. Specifically, the HBF algorithm as well as the maximizing minimum phase difference algorithm are based on the MMSE (Minimum Mean Square Error). For the full-digital beamforming and the beam steering, the ZF (zero forcing) criterion is employed. Simulations demonstrate that the performance of the proposed algorithm is similar to the full digital algorithm, and its robustness is confirmed by comparisons with other existing algorithms under the same channel model.

Efficient Hybrid Beamforming Design in mmWave Massive MU-MIMO DF Relay Systems With the Mixed-Structure

In this paper, we consider the decode-and-forward (DF) relay system in millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems, and propose a hybrid beamforming design method for the mixed structure, which contains the fully-connected and sub-connected structures. To satisfy constant-modulus and block-diagonalization (BD) constraints, the analog beamforming is designed by the idea of sorted successive interference cancellation (SSIC). More specifically, the proposed method first sorts the capacities of different analog sub-channels in descending order, and then designs the analog beamforming serially according to the order of the capacities. To efficiently mitigate the inner-user and inter-user interference, we propose a modified baseband BD technology to reduce the information loss in digital beamforming design, thereby improving the system capacity. In addition, the proposed hybrid beamforming algorithm is designed by considering both uniform linear arrays (ULAs) and uniform planar arrays (UPAs). Simulation results demonstrate that the proposed hybrid beamforming design scheme can obtain good performance in terms of the achievable sum-rate and power efficiency in ULAs and UPAs.