Analog Beamforming Research Articles

Mutual Information Maximizing Wideband Multi-User (wMU) mmWave Massive MIMO

To enable next-generation mmWave cellular, it is vital to design high-performance precoding schemes for wideband multi-user (wMU) mmWave massive MIMO (mMIMO). As existing approaches are mostly ad-hoc, thereby lacking performance guarantee, we will tailor an enhanced transceiver design explicitly for wMU mmWave mMIMO, with the goal of maximizing mutual information (MI). The proposed scheme follows the prevalent hybrid block diagonalization (HBD-)based framework that is well-known for balancing the transmitter-end processing flexibility and the user-end detection complexity. In this paper, we for the first time prove that HBD is optimal in the sense of MI. In terms of the transceiver design, we start by decoupling the hybrid processing into a two-stage analog and digital processing, and then derive the MI bounds associated with HBD. By optimizing the tight MI bound, excellent HBD transceivers are devised for both the multi-aperture structure (MAS) and the multi-beam structure (MBS). The proposed HBD technique does not rely on substantial computational complexity, striking channel sparsity, or high-resolution analog beamformers, and can achieve a superb MI performance even with inferior hardware configurations.

Hybrid Beamforming for Massive MIMO Over-the-Air Computation

Over-the-air computation (AirComp) has been recognized as a promising technique in Internet-of-Things (IoT) networks for fast data aggregation from a large number of wireless devices. However, the computation accuracy of AirComp highly depends on the devices with the worst channels condition, which degrades severely when the number of devices becomes large. To address this issue, we exploit the massive multiple-input multiple-output (MIMO) with hybrid beamforming, in order to enhance the computational accuracy of AirComp in a cost-effective manner. In particular, we consider the scenario with a large number of multi-antenna devices simultaneously sending data to an access point (AP) equipped with massive antennas for functional computation over the air. Under this setup, we jointly optimize the transmit digital beamforming at the wireless devices and the receive hybrid beamforming at the AP, with the objective of minimizing the computational mean-squared error (MSE) subject to the individual transmit power constraints at the wireless devices. To solve the non-convex hybrid beamforming design optimization problem, we propose an alternating-optimization-based approach, in which the transmit digital beamforming and the receive analog and digital beamforming are optimized in an alternating manner. In particular, we propose two computationally efficient algorithms to handle the challenging receive analog beamforming problem, by exploiting the techniques of successive convex approximation (SCA) and coordinate descent (CD), respectively. It is shown that for the special case with a fully-digital receiver at the AP, the achieved MSE of the massive MIMO AirComp system is inversely proportional to the number of receive antennas. Furthermore, numerical results show that the proposed hybrid beamforming design substantially enhances the computation MSE performance as compared to other benchmark schemes, while the SCA-based algorithm performs closely to the performance upper bound achieved by the fully-digital beamforming.

Accurate Statistical Model of Radiation Patterns in Analog Beamforming Including Random Error, Quantization Error, and Mutual Coupling

Analog beamforming technology is being used to overcome various technical drawbacks of mm-wave wireless communications systems. However, the errors caused by circuit implementations, quantized control, and imperfect isolation between antenna elements result in radiation pattern (RP) distortion and performance deterioration. In particular, the quantization error and mutual coupling cause the active reflection coefficient (ARC) of each antenna element to vary with respect to the main beam direction, resulting in statistical behavior changes depending on steering angles. In this article, we derive the statistical behavior of RPs with all those dominant errors taken into account. The analysis reveals that Beckmann distribution offers the exact solution for the cumulative distribution of the sidelobe level (SLL), which is very consistent with a Monte Carlo simulation including the ARC. In addition, the Rician distribution reflecting the three errors exhibits overall good accuracy, with inherent deviation from the Monte Carlo simulation results at certain steering angles due to the approximation of uncorrelated RPs and identical variances that are not valid in real antenna arrays. Our analysis also indicates that, to define the maximum probability of exceeding a certain SLL, the variance and correlation should be considered along with the mean of the RPs.

Efficient Beamforming Training and Channel Estimation for Millimeter Wave OFDM Systems

We study the problem of downlink beamforming training and channel estimation for millimeter wave (mmWave) OFDM systems, where a hybrid analog and digital beamforming structure is employed at the transmitter (i.e., base station) and an omni-directional antenna or an antenna array is used at the receiver (i.e., user). To efficiently probe the channel, we form multiple directional beams simultaneously at the transmitter and steer them towards different directions. The objective is to devise the beam training sequence and develop an efficient algorithm to estimate the channel. By exploiting the sparse scattering nature of mmWave channels, the above problem is formulated as one of sparse encoding and signal recovery, which involves finding a sparse sensing matrix to compress the sparse channel and an efficient channel estimation algorithm to recover the sparse channel from compressive measurements. In this article, we propose a sparse bipartite graph code-based algorithm, where a set of bipartite graphs are employed to encode the sparse channel and a simple decoding procedure that relies on the presence of a No-Multiton-graph (NM-graph) is used to reconstruct the sparse channel. Theoretical analysis shows that our proposed method can help achieve a substantial training overhead reduction. Simulations are provided to show the effectiveness of the proposed algorithm and its performance advantage over compressed sensing-based methods.

Dual-Polarized Two-Dimensional Multibeam Antenna Array With Hybrid Beamforming and its Planarization

A feeding network crossing method is proposed to form an N $\times $ N dual-polarized two-dimensional multibeam antenna array (2D-MBAA) with analog-digital hybrid beamforming, which solves the problem of needing additional connection structure between the dual-polarized antenna array and analog feeding network for large-scale antenna arrays. The main design work is focused on the analog-beamformer (ABF) and two structures are proposed. One is vertical-crossed (VC) ABF and the other is parallel-crossed (PC) ABF, and the latter is a more complex design in exchange for a significantly reduced profile. As a verification, a $4\times 4$ dual-polarized 2D-MBAA with PC-ABF has been fabricated and tested. It is operated at 3.45GHz with a bandwidth of about 10%, and it can realize a scanning angle of ±45°.

Hybrid Beamforming for Sum Rate Maximization in Wideband Multi-User MIMO Relay Systems

Hybrid precoding has a great potential to achieve near-optimal performance with few radio-frequency (RF) chains in comparison to the number of antennas. This paper proposes a novel hybrid beamforming solution for sum rate maximization in a wideband multi-user multi-input multi-output (MU-MIMO) relay system. The problem at hand is non-convex and hence mathematically intractable due to the constant modulus constraints associated with the analog beamforming design at communicating nodes shared by all sub-carriers. Furthermore, relaying in MU-MIMO systems under frequency-selective channels is also a challenging task as it requires complicated signal processing. To address this problem, source analog beamformer, relay RF combiner and phase-only processing component at each destination are obtained by deriving the common RF processing matrix which enables beamforming gain over all sub-carriers. This process involves reconstruction loss minimization for designing the required analog beamforming vectors having ability to maximize end-to-end signal-to-interference plus noise ratio (SINR). The relay analog precoder is designed by maximizing the received power at each destination through gain maximization of the equivalent baseband channel over the allocated frequency spectrum. To reduce the computational complexity of the iterative approach used to find the relay RF precoding matrix, the closed form expression is derived for achieving the desired objective. Finally, digital baseband processing components are obtained from the equivalent baseband channels by suppressing the interference among transmitted signals indirectly. Simulation results for different system configurations reveal that the proposed algorithm can achieve near-optimal performance.

Vector Modulator-Based Analog Beamforming Using the Least Euclidean Distance Criterion

In traditional multiple-input multiple-output (MIMO) receivers, radio frequency (RF) front-ends are exposed to interference as no analog spatial filtering is employed before the digital beamforming stage. Therefore the RF front-end is power-hungry, and analog to digital converters require a high dynamic range. In this paper, we consider an analog beamforming system in case of narrowband signals to cancel interference early in the analog domain, thus reducing the required ADC resolution. In contrast to existing analog beamformers with only phase shifts, our proposed design employs vector modulators where the coefficients can be selected from a set of weights with variable phases and amplitudes. We also propose an efficient and fast Euclidean distance algorithm to determine the analog beamformer coefficients while being suitable for realistic scenarios. Finally, an expression is introduced to estimate the interference rejection achieved by employing the proposed algorithm and a vector modulator in the RF domain. The introduced algorithm leads to considerable improvement in computational complexity by slightly sacrificing interference rejection.

An Efficient Interference-Aware Constrained Massive MIMO Beamforming for mm-Wave JSDM

Low-complexity beamformer design with practical constraints is an attractive research area for hybrid analog/digital systems in mm-wave massive multiple-input multiple-output (MIMO). This paper investigates interference-aware pre-beamformer (analog beamformer) design for joint spatial division and multiplexing (JSDM) which is a user-grouping based two-stage beamforming method. Single-carrier frequency domain equalization (SC-FDE) is employed in uplink frequency-selective channels. First, unconstrained slowly changing statistical analog beamformer of each group, namely, generalized eigenbeamformer (GEB) which has strong interference suppression capability is designed by maximizing the mutual information in reduced dimension. Then, constant-modulus constrained approximations of unconstrained beamformer are obtained by utilizing alternating minimization algorithms for fully connected arrays and fixed subarrays. In addition, a dynamic subarray algorithm is proposed where the connections between radio frequency (RF) chains and antennas are changed with changing channel statistics. Convergence of the proposed alternating minimization-based algorithms is provided along with their complexity analysis. It is observed that the additional complexity of proposed algorithms is insignificant for the overall system design. Although most of the interference is suppressed with the help of proposed constrained beamformers, there may be some residual interference after analog beamforming stage. Thus, minimum mean square error (MMSE) criterion based iterative block decision feedback equalization (IB-DFE) method, which takes the residual interference in reduced dimension into account, is promoted for digital beamforming stage. Simulation results verify the superiority of the proposed interference-aware constrained design over existing approaches in terms of beampattern, spectral efficiency, outage capacity, bit-error rate (BER), and channel estimation accuracy.

Hybrid Beamforming Optimization for DOA Estimation Based on the CRB Analysis

Direction-of-arrival (DOA) estimation is one of the most demanding tasks for the millimeter wave (mmWave) communication of massive multiple-input multiple-output (MIMO) systems with the hybrid beamforming (HBF) architecture. In this paper, we focus on the optimization of the HBF matrix for receiving pilots to enhance the DOA estimation performance. Motivated by the fact that many existing DOA estimation algorithms can achieve the Cram\'{e}r-Rao bound (CRB), we formulate the HBF optimization problem aiming at minimizing the CRB with the prior knowledge of the rough DOA range. Then, to tackle the problem with intractable non-convex constraint introduced by the analog beamformers, we propose an efficient manifold optimization (MO) based algorithm. Simulation results demonstrate the significant improvement of the proposed CRB-MO algorithm over the conventional random HBF algorithm, and provide insights for the HBF design in the beam training stage for practical applications.

Research on 5G‐Oriented Wireless Sensor Array of Millimeter Hybrid Beam Sensing Terminal

With the rapid development of information technology, facing the problems and new challenges brought by mobile Internet and Internet of things technology, as one of the key technologies of 5G, millimeter‐wave mobile communication (28/38/60/70 GHz) which can realize gigabit (GB/s, or even higher) data transmission rate has also attracted extensive attention of wireless researchers all over the world, it has quickly become a research hotspot in the field of wireless communication. In the millimeter‐wave massive MIMO downlink wireless sensor system, a block diagonal beamforming algorithm based on the approximate inverse of Neumann series is improved to obtain complete digital beamforming. Then, when designing hybrid beamforming, channel estimation and high‐dimensional singular value decomposition are required for traditional analog and digital hybrid beamforming. A low complexity hybrid beamforming scheme is designed. An improved gradient projection algorithm is proposed in the design of analog beamforming, which can solve the problem of high computational complexity and less damage to guarantee and rate. Simulation results show that the hybrid beam terminal of the sensor reduces the number of RF links required for full digital beamforming and is as close to the spectral efficiency performance of full digital beamforming as possible. The results show that the performance of the designed hybrid beamforming scheme can still be close to that of the pure digital beamforming scheme without involving channel estimation and SVD decomposition.

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.

Joint Trajectory and Hybrid Beamforming Design for Multi Antenna UAV Enabled Network

In this paper, we investigate the transmission design in a multi antenna unmanned aerial vehicle (UAV)-enabled network, where the flight trajectory and hybrid digital and analog beamforming (BF) of the UAV are jointly designed, for both the fully-connected structure and sub-connected structure. Our goal is to maximize the weighted sum rate for multiply ground users, subject to the transmit power and trajectory constraints. Due to the non-convex property of the formulated problem, we propose to linearize the objective by using a newly Lagrangian dual transform. Then, an alternating optimization (AO) method is proposed, where the digital BF can be obtained by utilizing the bisection search method, while the analog BF and the flight trajectory are handled by the alternating direction of multipliers method (ADMM) algorithm. Finally, simulation results verify the performance of the proposed algorithm.

Hybrid Analog and Digital Beamforming Design for Channel Estimation in Correlated Massive MIMO Systems

In this paper, we study the channel estimation problem in correlated massive multiple-input-multiple-output (MIMO) systems with a reduced number of radio-frequency (RF) chains. Importantly, other than the knowledge of channel correlation matrices, we make no assumption as to the structure of the channel. To address the limitation in the number of RF chains, we employ hybrid beamforming, comprising a low dimensional digital beamformer followed by an analog beamformer implemented using phase shifters. Since there is no dedicated RF chain per transmitter/receiver antenna, the conventional channel estimation techniques for fully-digital systems are impractical. By exploiting the fact that the channel entries are uncorrelated in its eigen-domain, we seek to estimate the channel entries in this domain. Due to the limited number of RF chains, channel estimation is typically performed in multiple time slots. Under a total energy budget, we aim to design the hybrid transmit beamformer (precoder) and the receive beamformer (combiner) in each training time slot, in order to estimate the channel using the minimum mean squared error criterion. To this end, we choose the precoder and combiner in each time slot such that they are aligned to transmitter and receiver eigen-directions, respectively. Further, we derive a water-filling-type expression for the optimal energy allocation at each time slot. This expression illustrates that, with a low training energy budget, only significant components of the channel need to be estimated. In contrast, with a large training energy budget, the energy is almost equally distributed among all eigen-directions. Simulation results show that the proposed channel estimation scheme can efficiently estimate correlated massive MIMO channels within a few training time slots.

Channel Estimation and Hybrid Precoding for Millimeter Wave Communications: A Deep Learning-Based Approach

Hybrid analog and digital beamforming (HBF) has been regarded as a key technology for future millimeter wave (mmWave) communication systems due to its ability to obtain a good trade-off between achievable beamforming gain and hardware cost. In this paper, we investigate the channel estimation and hybrid precoding for mmWave MIMO systems with deep learning. We adopt the hierarchical codebook based algorithm for channel estimation as it requires limited number of pilot transmissions, and enhance its performance by proposing a new codebook design algorithm based on manifold optimization (MO). With the estimated channel state information (CSI) as the input, we develop a robust HBF network (HBF-Net) by applying convolutional layers and attention mechanism, which can be trained to generate a robust HBF matrix targeting at spectral efficiency maximization with imperfect CSI. To further improve the performance, we propose a joint channel estimation and HBF optimization network (CE-HBF-Net). Considering that the adaptively selected HBF vectors in the hierarchical codebook based channel estimation are different for different channel realizations, we skillfully propose an index assign-and-input method to efficiently feed such information to the CE-HBF-Net to reduce the network input dimensions and make the network trainable. Furthermore, we propose a signal self-attention mechanism to enable the CE-HBF-Net to intelligently assign larger weight coefficients to those signals that contribute more to channel estimation. Simulation results show that the well-designed HBF-Net and CE-HBF-Net outperform the conventional HBF algorithms with imperfect channel and exhibit robustness to mismatches between offline training and online deployment stages.

Reconfigurable Intelligent Surface Aided Constant-Envelope Wireless Power Transfer

By reconfiguring the propagation environment of electromagnetic waves artificially, reconfigurable intelligent surfaces (RISs) have been regarded as a promising and revolutionary hardware technology to improve the energy and spectrum efficiency of wireless networks. In this paper, we study a RIS aided multiuser multiple-input multiple-output (MIMO) wireless power transfer (WPT) system, where the transmitter is equipped with a constant-envelope analog beamformer. First, we maximize the total received power of the users by jointly optimizing the beamformer at transmitter and the phase-shifts at the RIS, and propose two alternating optimization based suboptimal solutions by leveraging the semidefinite relaxation (SDR) and the successive convex approximation (SCA) techniques respectively. Then, considering the user fairness, we formulate another problem to maximize the total received power subject to the users’ individual minimum received power constraints. A low complexity iterative algorithm based on both alternating direction method of multipliers (ADMM) and SCA techniques is proposed to solve this problem. In the case of multiple users, we further analyze the asymptotic performance as the number of RIS elements approaches infinity, and bound the performance loss caused by RIS phase quantization. Numerical results show the correctness of the analysis results and the effectiveness of the proposed algorithms.

5G K-SimSys for Open/Modular/Flexible System-Level Simulation: Overview and its Application to Evaluation of 5G Massive MIMO

5G K-SimSys is a system-level simulator which has been designed and implemented to provide an open platform and a tractable testbed for evaluating the system-level performance of 5G standard. In this paper, we present its design overview with the overall modular structure, including the functionality of the flexible modules. Meanwhile, massive multi-input multi-output (MIMO) is a key technology for improving the spectral efficiency of 5G systems. While massive MIMO has been standardized in 3GPP Rel-13 (LTE-Advanced Pro), the next generation of massive MIMO standard is now available in Rel-16, a.k.a New Radio (NR) interface, with further improvement by introducing more antenna elements over the higher frequency band. In particular, the beam-based air interface for above 6 GHz band involves various antenna configurations and feedback schemes, requiring a more complex testbed for system-level performance evaluation. This paper examines the multi-antenna technologies in 3GPP NR specification to develop its system-level model in 5G K-SimSys in order to test the factors affecting performance in the corresponding environments through various embodiments. In the simulation results, the baseline performance for massive MIMO in NR is evaluated by changing the number of antenna ports and the number of spatial multiplexing layers in different experimental environments. Particularly, the effect of vertical beamforming on interference is evaluated for Full Dimension MIMO (FD-MIMO). In order to demonstrate that 5G K-SimSys is an easy-to-design simulator that facilitates modification and reconfiguration, owing to its modularized and customized structure, we consider the proposed bandwise analog beamforming (BAB) scheme. The modular and flexible structure immediately allows implementation of virtual modules for bandwise analog beamforming by reusing the elementary modules as hierarchically designed simulator objects.

Noncooperative Sub-6GHz Reconfigurable Antenna DoA Estimation to Aid mmWave Analog Beamforming: Algorithm and Measurements

Envisioned analog beamforming, high-gain, phased antenna array systems operating at millimeter-wave (mmWave) frequencies require a fast beam selection process for practical implementation in mobile units in a changing propagation environment. This paper proposes a novel direction of arrival (DoA) estimation technique using a single RF chain reconfigurable Alford loop antenna at sub-6GHz frequencies to facilitate a rapid optimal beam selection process at mmWave frequencies. Measurement-based DoA estimation, demonstration of reduced beam scanning overhead at mmWave frequencies, and design of a software-defined-radio (SDR)-based testbed for evaluating the proposed integrated system are addressed.

Power Minimization for Massive MIMO Over-the-Air Computation With Two-Timescale Hybrid Beamforming

This letter studies the massive multiple-input multiple-output (MIMO) analog uncoded over-the-air computation (AirComp), which is a promising solution in Internet-of-Things (IoT) networks for fusion centers (FCs) to compute functions of data distributed in a large number of wireless devices (WDs). To avoid the heavy overhead of the perfect real-time channel state information (CSI) estimation, we develop a two-timescale hybrid beamforming (THB) scheme in AirComp. Under this setup, we aim to minimize the transmit power over time, while ensuring a minimum required computation distortion in terms of the mean-squared error (MSE). We propose a constrained stochastic successive convex approximation (CSSCA) based algorithm to solve the formulated stochastic non-convex optimization problem for the THB design. Specifically, the short-timescale receive digital beamforming matrix at the FC is optimized at each time slot based on the real-time effective low-dimensional CSI matrices by a sum-minimization-mean-squared-error (sum-MMSE) receiver, which can better deal with the signal misalignment. By contrast, the long-timescale transmit beamforming matrix at WDs and the receive analog beamforming matrix at the FC are designed based on the available channel statistics and updated in a frame-based manner, where a frame contains a fixed number of time slots. Numerical results show that the proposed THB design algorithm achieves similar transmit power performance as that achieved by the design when the perfect real-time CSI is available.

AoD-based localization with cots millimeter-wave devices

Radio frequency-based localization techniques have undergone rapid development in recent years. However, existing localization systems on commercial Wi-Fi devices are either impractical or inaccurate. The newly emerging WiGig devices use millimeter-wave signals to communicate. As they have much more antennas than Wi-Fi devices, and they also have a higher angular resolution. However, because of cost limitations, commercial WiGig devices use analog beamforming, and the channel response of each antenna is unavailable. In this work, we propose WiGLoc a system for WiGig devices that provides accurate localization. To achieve this goal, we model the RSS of the antenna array, from which the CSIs of individual antennas are recovered. Then, the antenna array is calibrated, and the array geometry is obtained. WiGLocestimates AoDs from WiGig APs to the target with antenna CSIs and array geometry to localize the target. Experimental results show that the average 3D tracking and 2D localization errors of WiGLocare only 6 and 27 cm, respectively; whereas those of the state-of-the-art beamforming approach are 11 and 44 cm, respectively.

Joint Beamwidth and Power Optimization in MmWave Hybrid Beamforming-NOMA Systems

The use of directional transmission in millimeter-Wave (mmWave) frequencies results in limited channel coherence time. In this paper, we take the limited channel coherence time into account for non-orthogonal multiple access (NOMA) in mmWave hybrid beamforming systems. Due to the limited coherence time, the beamwidth of the hybrid beamformer affects the beam-training time, which in turn directly impacts the data transmission rate. To investigate this trade-off, we utilize a combined beam-training algorithm. Then, we formulate a sum-rate expression which considers the channel coherence time and beam-training time as well as users' power and other system parameters. Further, a joint power and beamwidth optimization problem is solved by iterating between the power allocation and the beamwidth optimization. When allocating the power, we use the log-exponential reformulation and the sequential parametric convex approximation (SPCA) methods to solve the non-convex problem. Since beamwidth optimization involves too many variables, we propose an algorithm which iterates between clusters of users. Numerical results show that the optimized mmWave hybrid beamforming-NOMA system can achieve much higher sum-rates compared to NOMA with analog beamforming and traditional multiple access techniques.