Low-resolution Phase Shifters Research Articles

Machine learning-inspired hybrid precoding with low-resolution phase shifters for intelligent reflecting surface (IRS) massive MIMO systems with limited RF chains

Machine learning-inspired hybrid precoding with low-resolution phase shifters for intelligent reflecting surface (IRS) massive MIMO systems with limited RF chains

Angle-Based Multicast Analog Beamforming With Low Resolution Phase Shifters for LEO Satellite Communications

Angle-Based Multicast Analog Beamforming With Low Resolution Phase Shifters for LEO Satellite Communications

Secure RIS-Assisted Hybrid Beamforming Design with Low-Resolution Phase Shifters

Secure RIS-Assisted Hybrid Beamforming Design with Low-Resolution Phase Shifters

Hybrid Beamforming for Wideband Terahertz Massive MIMO Communications with Low-Resolution Phase Shifters and True-Time-Delay

Hybrid Beamforming for Wideband Terahertz Massive MIMO Communications with Low-Resolution Phase Shifters and True-Time-Delay

QoS-Guaranteed Hybrid Beamforming Design for Multi-User Systems With Finite-Resolution Phase Shifters

Massive multiple input multiple output (MIMO) technology is a key enabler of the next generation wireless communications. The partially-connected hybrid beamforming architecture is attractive in massive MIMO systems for its reduced cost, power consumption, and hardware complexity. On the other hand, the specific analog beamforming structure and finite-resolution in phase shifters complicate the beamforming design. In this paper, we study the hybrid beamforming design for the partially-connected architecture, where users can have multiple antennas and different requirements on quality of service (QoS). A transmit power minimization problem is formulated. The beamforming design needs to be aligned to discrete phase values due to the practical limitations. Such problem is non-convex and is hard to solve. We propose an effective algorithm for this problem. In particular, the penalty-based method is used to decouple the variables. The original problem is decomposed into several sub-problems. The block prox-linear method is applied to solve the sub-problems alternatively with convergence guarantee. We show the effectiveness and robustness of our proposed algorithm via simulations. Our proposed algorithm with low resolution phase shifters achieves better performance with lower transmit power than existing methods.

Energy Efficient Beamforming for Small Cell Systems: A distributed Learning and Multicell Coordination Approach

The integration of small cell architecture and edge intelligence is expected to make high-grade mobile connectivity accessible and thus provide smart and efficient services for various aspects of urban life. It is well known that small cell architecture will cause high inter-cell interference since the adjacent cells share the same frequency band. One of the most promising techniques to mitigate inter-cell interference is beamforming, however, how to coordinate the beamformers in a multicell dynamic network to reach a global optimum is an extremely challenging problem. In this paper, we consider analog beamforming with low-resolution phase shifters, and propose a distributed learning and multicell coordination based energy efficient beamforming approach for multiple-input and single-output (MISO) small cell system. The goal is to maximize the energy efficiency (EE) of the whole system by jointly optimizing the beamformer and transmit power. We perform extensive simulations in both static and dynamic scenarios, and validate the performance of the proposed approach by comparing with baseline and existing schemes. The simulation results demonstrate that the proposed approach outperforms the baseline and existing schemes with an significant improvement in terms of EE for both static and dynamic network settings.

Machine Learning-Inspired Hybrid Precoding for HAP Massive MIMO Systems with Limited RF Chains

Energy efficiency (EE) is the main target of wireless communication nowadays. In this paper, we investigate hybrid precoding (HP) and massive multiple-input multiple-output (MIMO) systems for a high-altitude platform (HAP). The HAP is an emerging solution operating in the stratosphere at an amplitude of up to 20–40 km to provide communication facilities that can achieve the best features of both terrestrial and satellite systems. The existing hybrid beamforming solution on a HAP requires a large number of high-resolution phase shifters (PSs) to realize analog beamforming and radio frequency (RF) chains associated with each antenna and achieve better performance. This leads to enormous power consumption, high costs, and high hardware complexity. To address such issues, one possible solution that has to be tweaked is to minimize the number of PSs and RFs or reduce their power consumption. This study proposes an HP sub-connected low-resolution bit PSs to address these challenges while lowering overall power consumption and achieving EE. To significantly reduce the RF chain in a massive MIMO system, HP is a suitable solution. This study further examined adaptive cross-entropy (ACE), a machine learning-based optimization that optimizes the achievable sum rate and energy efficiency in the Rician fading channel for HAP massive MIMO systems. ACE randomly generates several candidate solutions according to the probability distribution (PD) of the elements in HP. According to their sum rate, it adaptively weights these candidates’ HP and improves the PD in HP systems by minimizing the cross-entropy. Furthermore, this work suggests energy consumption analysis performance evaluation to unveil the fact that the proposed technique based on a sub-connected low-bit PS architecture can achieve near-optimum EE and sum rates compared with the previously reported methods.

Full-Duplex mmWave MIMO With Finite-Resolution Phase Shifters

Enabling simultaneous transmission and reception on the same carrier frequency, i.e., full-duplex (FD) communication, critically requires that the self-interference (SI) be sufficiently suppressed. We investigate the design of precoders and combiners for an FD millimeter wave point-to-point bidirectional link, where dense antenna arrays provide an opportunity for SI suppression via beamforming cancellation. In practice the precoders and combiners are usually implemented in a hybrid digital/analog fashion with a reduced number of radio frequency (RF) chains, and it becomes necessary to overcome a number of limitations imposed by this structure. We focus on a hybrid architecture with a phase shifter-based fully-connected analog stage, assuming finite-resolution phase shifters. To avoid analog-to-digital converter saturation at the receiver, the proposed design aims at cancelling SI at the analog combiner output. Although accurate SI suppression is difficult with low-resolution phase shifters, our design is able to provide reasonable performance, significantly improving upon previous approaches, and allowing to efficiently exploit the availability of RF chains to partially compensate for coarse phase quantization effects.

Data-Driven Deep Learning Based Hybrid Beamforming for Aerial Massive MIMO-OFDM Systems With Implicit CSI

In an aerial hybrid massive multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM) system, how to design a spectral-efficient broadband multi-user hybrid beamforming with a limited pilot and feedback overhead is challenging. To this end, by modeling the key transmission modules as an end-to-end (E2E) neural network, this paper proposes a data-driven deep learning (DL)-based unified hybrid beamforming framework for both the time division duplex (TDD) and frequency division duplex (FDD) systems with implicit channel state information (CSI). For TDD systems, the proposed DL-based approach jointly models the uplink pilot combining and downlink hybrid beamforming modules as an E2E neural network. While for FDD systems, we jointly model the downlink pilot transmission, uplink CSI feedback, and downlink hybrid beamforming modules as an E2E neural network. Different from conventional approaches separately processing different modules, the proposed solution simultaneously optimizes all modules with the sum rate as the optimization object. Therefore, by perceiving the inherent property of air-to-ground massive MIMO-OFDM channel samples, the DL-based E2E neural network can establish the mapping function from the channel to the beamformer, so that the explicit channel reconstruction can be avoided with reduced pilot and feedback overhead. Besides, practical low-resolution phase shifters (PSs) introduce the quantization constraint, leading to the intractable gradient backpropagation when training the neural network. To mitigate the performance loss caused by the phase quantization error, we adopt the transfer learning strategy to further fine-tune the E2E neural network based on a pre-trained network that assumes the ideal infinite-resolution PSs. Numerical results show that our DL-based schemes have considerable advantages over state-of-the-art schemes.

Training Beam Design for Channel Estimation in Hybrid mmWave MIMO Systems

Training beam design for channel estimation with infinite-resolution and low-resolution phase shifters (PSs) in hybrid analog-digital milimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems is considered in this paper. By exploiting the sparsity of mmWave channels, the optimization of the sensing matrices (corresponding to training beams) is formulated according to the compressive sensing (CS) theory. Under the condition of infinite-resolution PSs, we propose relevant algorithms to construct the sensing matrix, where the theory of convex optimization and the gradient descent in Riemannian manifold is used to design the digital and analog part, respectively. Furthermore, a block-wise alternating hybrid analog-digital algorithm is proposed to tackle the design of training beams with low-resolution PSs, where the performance degeneration caused by non-convex constant modulus and discrete phase constraints is effectively compensated to some extent thanks to the iterations among blocks. Finally, the orthogonal matching pursuit (OMP) based estimator is adopted for achieving an effective recovery of the sparse mmWave channel. Simulation results demonstrate the performance advantages of proposed algorithms compared with some existing schemes.

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.

Uplink millimeter-wave multi-cell multi-user massive multi-input multi-output systems

In this paper, we delve into the maximized spectral efficiency (SE) of millimeter-wave (mmWave) multicell multiuser massive MIMO Systems for uplink transmission with low-resolution phase shifters (LRPSs). Millimeter-wave massive multiple-input multiple-output (mMIMO) is an important technology for upcoming cellular networks which will provide higher bandwidth and throughput than current wireless systems and networks. LRPSs are commonly used to minimize power consumption, maximize spectral efficiency and diminish the complexity of hybrid precoder and combiner. In this paper, we consider a hybrid analog-digital precoder and combiner design with LRPSs for mmWave multi-cell multiuser mMIMO systems for uplink transmission to spectral efficiency in terms of iterations. The proposed technique outperforms when compared to traditional optimization approaches concerning spectral efficiency and bit error rate (BER). We show through simulation results that our designs with LRPSs outperform standard iteration procedures.

Location-Based Hybrid Precoding Schemes and QoS-Aware Power Allocation for Radar-Aided UAV–UGV Cooperative Systems

Unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) complement each other, promising a variety of benefits for unmanned cooperative systems. When infrastructures for communication are unavailable, such as disaster relief and patrol mission in sparsely populated areas, UGVs can be controlled to go to the esignated areas with the aid of a UAV. Specifically, the UAV hovers over the UGVs, sending commands to the UGVs and obtaining location information from the UGVs. In this paper, we consider integrating millimeter wave communication and UAV–UGV cooperative system. For high mobile unmanned cooperation systems, we develop two joint radar-aided hybrid precoding schemes, which are suitable for a fully connected (FC) hybrid precoding structure and partially connected (PC) hybrid precoding, respectively. Specifically, an effective hybrid precoding scheme is first proposed by using location information to jointly design hybrid precoding and power allocation. Moreover, we also derive the radar parameter estimation problem Cramér-Rao lower bound (CRLB). In order to ensure the minimum quality-of-service (QoS) of UGVs, we propose a QoS-aware power allocation scheme based on the difference-of-two-convex-function (D.C.) programming. Finally, a heuristic hybrid precoding design algorithm, where the analog precoding matrix is usually implemented by low-resolution phase shifters (PSs), is proposed based on antenna dynamic grouping and radar parameter acquisition, with the aim of maximizing the sum-rate of the UAV–UGV cooperative systems. Extensive computer simulation results indicated the validity of the proposed radar-aided location-based hybrid precoding schemes in the UAV–UGV heterogeneous cooperative system.

Codebook-Based Hybrid Beamforming Using Combined Phase Shifters of High and Low Resolutions

The hybrid beamforming architecture where a combination of analog and digital precoders is employed has attracted much attention recently for its flexible trade-off between power consumption and performance. A codebook-based beamforming scheme is generally considered as a more practical solution rather than the adaptive beamforming schemes due to the large number of antennas. However, the constant amplitude constraint brought by the phase shifters (PSs) in the analog precoder always makes the codebook design problem a tricky and complicated one. In this work, we consider a novel combined PS (CPS) architecture where one high-resolution PS is connected to each RF chain in parallel with low-resolution PSs to each antenna. The corresponding codebook design aiming for ideal flat beam gains is then proposed for the CPS architecture. Simulation results reveal that the proposed scheme achieves a good trade-off between performance and energy efficiency compared with conventional single PS (SPS) and the recently proposed double PS (DPS) architecture.

Lattice-Based mmWave Hybrid Beamforming

Conventional hybrid precoding and combining based transceivers require a large number of high-resolution radio frequency (RF) phase shifters (PSs), which impose prohibitive hardware costs and power consumption. To address the above issue, both partially connected RF PSs and low-resolution PSs have been proposed. However, the performance limits of these low-cost designs have not been investigated theoretically. Furthermore, there is room for improvement in their spectral efficiency. To fill this knowledge gap, we derive the mean square error performance discrepancy between an optimal precoder/combiner and the hybrid analog-digital precoder/combiner under the constraint of 1-bit PSs relying on lattice theory. Then, by observing that this performance gap can be reduced by deactivating parts of the PSs whilst improving both the spectral and energy efficiency, we develop an adaptive RF PS connection network. To resolve the associated hybrid precoding and combining problems, we appropriately adapt Babai's algorithm from the lattice decoding literature. Our simulation results demonstrate the superiority of the proposed scheme both in terms of its spectral and energy efficiency.

Discrete Phase Shifters-Based Hybrid Precoding for Full-Duplex mmWave Relaying Systems

This paper considers the hybrid precoding design with quantized phase shifters (PSs) for full-duplex millimeter-wave relaying systems, in which the relay node is equipped with PSs of different resolution levels. The joint optimization of relay hybrid precoding and discrete PSs is a high-dimensional non-convex problem with both higher-order polynomial and modulus constraints. To solve this challenging problem, the optimization function under the imperfect channel state information (CSI) is reformulated into a low-complexity norm-minimization form equation. Then, a relaxed algorithm based on the alternating direction method of multipliers and quantization steps is proposed to obtain the coupling approximate solutions for the above optimized equation. And the optimality of analytical solutions is guaranteed based on the imposed termination criterion and necessary conditions. Furthermore, given the requirement of arbitrary quantization, the trade-off between spectral efficiency (SE) and energy efficiency (EE) is investigated under the imperfect CSI. Numerical results verify that the hybrid precoding with low-resolution PSs can achieve excellent SE close to the full-resolution one but with a considerably lighter burden of energy consumption. Moreover, the transmission power plays a positive role in compensating quantization loss, but the excessive value will bring the reduction of EE.

Energy-Efficient MU-Massive-MIMO Hybrid Precoder Design: Low-Resolution Phase Shifters and Digital-to-Analog Converters for 2D Antenna Array Structures

This paper investigates a multi-user massive multiple-input multiple-output (MU-mMIMO) hybrid precoding (HP) scheme using low-resolution phase shifters (PSs) and digital-to-analog converters (DACs). The proposed HP approach involves two stages: RF beamforming based on the slowly time-varying channel second-order correlation matrix, and baseband MU precoding based on the instantaneous effective baseband channel to mitigate MU-interference by a regularized zero-forcing (RZF) technique. We consider three HP design architectures: (i) HP using full-resolution PSs and DACs, with a baseband transfer block for constant-modulus RF beamformer, (ii) HP using $b$ -bit PSs and full-resolution DACs, with an orthogonal matching pursuit (OMP) based algorithm that can approach the optimal unconstrained RF beamformer, and (iii) HP using $b$ -bit PSs and $q$ -bit DACs, taking into account also DAC quantization noise. Illustrative results show that the proposed HP schemes with low-resolution PSs can approach the sum-rate of full-resolution PSs by using only 2-bit PSs, while offering higher energy efficiency. Furthermore, a study of sum-rate results for various PS and DAC quantization levels reveals that HP can achieve near-optimal performance with only 2-bit PSs and 5-bit DACs. Moreover, a comparison of the different array configurations, namely, uniform linear array (ULA), uniform circular array (UCA), uniform rectangular array (URA), and concentric circular array (CCA), indicates that URA and CCA outperform UCA and ULA in terms of spectral and energy efficiencies.

Beamforming Optimization for Intelligent Reflecting Surface-Aided MISO Communication Systems

This article considers an intelligent reflecting surface (IRS)-assisted point-to-point multiple-input single-output communication system. An IRS implemented by configurable phase shifters is used to assist the transmission from an access point (AP) equipped with multiple antennas to a user having a single antenna. We aim to jointly optimize the transmit beamforming at the AP and the reflect beamforming at the IRS to maximize the spectral efficiency of the system. The considered joint optimization problem can be decoupled into the transmit and reflect beamforming design problems by applying the maximum-ratio transmission strategy. The former has a closed-form expression, whereas the latter requires solving a nonconvex optimization problem. A known solution based on manifold optimization (MO) is proposed to solve the reflect beamforming design problem. Although the MO-based algorithm achieves higher spectral efficiency than the conventional semidefinite relaxation approach, it incurs high time complexity. On this basis, we address this issue by proposing a computationally efficient gradient projection (GP)-based algorithm for the reflect beamforming design problem. When low-resolution (e.g., 1–2 bits) phase shifters are adopted, we leverage an innovative probability learning technique on the basis of the cross-entropy (CE) framework to alleviate the performance loss caused by the use of low-resolution phase shifters. Simulation results demonstrate that the proposed GP-based algorithm nearly obtains the same spectral efficiency as the state-of-the-art MO-based algorithm at a low complexity. However, the running time is significantly reduced. When low-resolution phase shifters are employed, the proposed CE-based algorithm outperforms the test algorithms in terms of spectral and energy efficiency in various system configurations.

Transceiver Design for Simultaneous Wireless Information and Power Multicast in Multi-User mmWave MIMO System

Millimetre wave (mmWave) has a range of merits for both wireless information and power transfer, such as high-bandwidth for high-throughput, massive antennas for efficient signal transmission, highly directional beams for overcoming channel attenuations and high degree of freedom for signal processing. Therefore, we investigate transceiver design in a multi-user mmWave MIMO system for simultaneous wireless information and power multicast (SWIPM). First of all, we obtain the asymptotically optimal solution include full-digital solutions for the transmitter and information users (IUs) as well as analog solutions for energy users (EUs) in the mmWave MIMO aided transceivers. It maximizes information multicast spectral efficiency of IUs, while satisfying individual wireless charging requirement of EUs. Then, based on this asymptotically optimal solution, hybrid beamformer at a transmitter and signal combiners at IUs are jointly designed with the same objective, when considering low hardware complexity (e.g. limited number of RF chains and low-resolution phase shifters). A low-complexity algorithm is developed for solving the resultant constraint max-min problem. Additionally, we also demonstrate a practical multi-antenna aided receiver architecture of EUs by considering practical non-linear energy harvesters. Numerical results validate the advantage of our joint transceiver design for SWIPM.

Energy-Efficient Analog Combiner Design Using Low-Resolution Phase Shifters and Antenna Selection for mmWave D2D Communications

This study investigates the use of an analog combiner comprising low -resolution phase shifters (PSs) to suppress interference from other devices and improve the received signal power of interest in millimeter-wave device-to-device networks simultaneously. Unlike typical analog combining architectures with PS numbers equaling the number of receiver antennas, the number of PSs in this study is less than that of receiver antennas; this feature saves on equipment costs and improves power efficiency. We jointly optimize the receiver antenna selection and analog combiner design with low-resolution PSs to maximize the spectral efficiency of the resultant device. Because the formulated joint optimization problem is non-convex, we propose a probabilistic evolutionary optimization algorithm with an explicit expression for learning the tilting parameters of the designed sampling distribution. Simulation results demonstrate the excellent performance of the proposed algorithm compared with the semidefinite relaxation approach in terms of spectral and energy efficiency.