Finite Resolution Phase Shifters Research Articles

Low complexity hybrid beamforming for downlink multi-user MIMO OFDM systems

Hybrid beamforming is critical for massive multiple input multiple output (MIMO) to achieve high spectral efficiency at reduced hardware cost. Existing hybrid beamforming schemes either design the analog beamforming and digital beamforming separately, or jointly optimize them through alternating optimization. Such strategies incur non-negligible performance degradation or huge computational complexity in optimization, which is especially evident with the partially connected architecture. In this work, we consider a general downlink multi-user MIMO orthogonal frequency division multiplexing (OFDM) system with the hybrid beamforming architecture, where finite-resolution phase shifters are adopted. We propose an efficient beamforming strategy on the sum rate maximization criterion. Rather than eliminating the interference entirely by digital beamforming, we optimize the analog beamforming by considering the interference at the same time. We consider a fixed digital beamforming structure to reduce the overall complexity. Given the fact of finite-resolution phase shifters, the analog beamforming is optimized over discrete phase values. Compared to existing hybrid beamforming designs, the proposed algorithm achieves much improved performance. By applying the average channel covariance to the analog beamforming design, the computational complexity of the proposed algorithm is further reduced. Meanwhile, the proposed algorithm is applicable to both fully and partially connected architectures.

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.

Joint Transceiver and Intelligent Reflecting Surface Design for mmWave Massive MIMO Systems

This article aims to maximize the spectral efficiency of an intelligent reflecting surface (IRS)-assisted hybrid millimeter-wave massive multiple-input–multiple-output system by jointly optimizing the hybrid precoding at the base station, hybrid combining at the user equipment, and reflecting beamforming at the IRS, where the reflecting beamforming and analog precoding/combining are implemented with finite-resolution phase shifters. This joint design problem can be decoupled into reflecting beamforming and hybrid precoding/combining design problems. However, such a decoupled approach experiences difficulties in solving the reflecting beamforming design problem. A known solution further reformulates the reflecting beamforming design problem into a more tractable problem addressed by a Riemannian manifold optimization (RMO)-based algorithm. However, the application of the RMO-based algorithm to solve the reformulated problem may lead to performance degradation given that the reformulated problem differs from the original one. Moreover, the RMO-based algorithm is tailored for the IRS with infinite-resolution phase shifters rather than practical finite-resolution phase shifters. Furthermore, the complexity of the RMO-based algorithm remains high. Therefore, we propose two coordinate descent method-based algorithms to tackle these issues. Simulation results demonstrate the effectiveness of the proposed algorithms compared with the state-of-the-art RMO-based algorithm.

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.

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.

Copula-Based Modeling of RIS-Assisted Communications: Outage Probability Analysis

Statistical characterization of the signal-to-noise ratio (SNR) of reconfigurable intelligent surface (RIS)-assisted communications in the presence of phase noise is an important open issue. In this letter, we exploit the concept of copula modeling to capture the non-standard dependence features that appear due to the presence of discrete phase noise. In particular, we consider the outage probability of RIS systems in Rayleigh fading channels and provide joint distributions to characterize the dependencies due to the use of finite resolution phase shifters at the RIS. Numerical assessments confirm the validity of closed-form expressions of the outage probability and motivate the use of bivariate copula for further RIS studies.

Beampattern Synthesis Using Quantized Phase Control via Multi-Point Iterative Gradient Descent

The finite resolution phase shifters pose significant challenges for the beampattern synthesis. In this letter, we propose a novel joint multi-point control and iterative gradient descent (MIGD) algorithm, which aims to minimize the performance losses caused by phase quantization and can be solved efficiently. The deviation caused by quantization is firstly minimized as objective function in optimization problem. Then, an explicit solution of weight vector is obtained by utilizing the iterative gradient descent method. To make sure that the beampattern can be synthesized to the desired one by the weight vector, a multi-point control method is combined during the iteration. Representative examples are presented to illustrate the effectiveness and superiority of the proposed algorithm.

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.

Hybrid Beamforming Design for OFDM Dual-Function Radar-Communication System

Dual-function radar-communication (DFRC) systems with Orthogonal Frequency Division Multiplexing (OFDM) make efficient use of spectrum, while maintaining reliable robustness against multipath fading for communication and improved estimation accuracy for radar. Nevertheless, it would be costly to use a fully digital beamforming architecture, where each antenna is equipped with a radio frequency (RF) chain. This motivates us to consider hybrid beamforming for OFDM-DFRC system in this work. More specifically, the analog beamformer for the whole bandwidth and digital beamformer for each subcarrier are simultaneously designed, by jointly optimizing the spectral efficiency (SE) of communication and spatial spectrum matching error (SSME) of radar. To tackle the resulting optimization problem, a consensus alternating direction method of multipliers (consensus-ADMM) approach is devised. Further, in a practical sense, we consider the issue of hybrid transmit beamforming design with finite-resolution phase shifters, to facilitate economical implementation of the analog beamformer. Numerical simulations are provided to demonstrate the effectiveness of the proposed schemes.

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 Analog-Digital Precoder Design for Securing Cognitive Millimeter Wave Networks

Millimeter wave (mmWave) communications and cognitive radio technologies constitute key technologies of improving the spectral efficiency of communications. Hence, we conceive a hybrid secure precoder for enhancing the physical layer security of a cognitive mmWave wiretap channel, where a secondary transmitter broadcasts confidential information signals to multiple secondary users under the interference temperature constraint of the primary user (PU). The optimization problem is formulated as jointly optimizing the analog and digital precoder for maximizing the minimum secrecy rate of all the secondary users under practical constraints. In particular, our design satisfies the constraint on the maximum interference power received by multiple PUs, as well as the secondary users’ minimum quality-of-service (Qos), and the unit-modulus constraint on the analog precoder. Due to the non-convexity of the resultant objective function and owing to the coupling between the analog and digital precoder, the optimization problem formulated is nonconvex and nonlinear, hence it is very challenging to solve directly. Hence, we first transform it into a tractable form, and develop a penalty dual decomposition (PDD) based iterative algorithm to locate its Karush-Kuhn-Tucker (KKT) solution. Finally, we generalize the proposed PDD algorithm to a secure hybrid precoder design relying on practical finite-resolution phase shifters and show that the proposed PDD algorithm can be straightforwardly adapted to handle the scenario, where each PU is equipped with multiple antennas and the CSI of multiple eavesdroppers (Eves) is imperfectly known. Our simulation results validate the efficiency of the proposed iterative algorithm.

Secure Directional Modulation With Few-Bit Phase Shifters: Optimal and Iterative-Closed-Form Designs

In this paper, directional modulation (DM) is investigated to enhance physical layer security. Practical transmitter designs are exploited under imperfect channel state information (CSI) and hardware constraints, such as finite-resolution phase shifters (PSs) and per-antenna power budget. Tailored for the practical issues in realizing DM, a series of practical scenarios are investigated. Starting from the scenario where eavesdroppers (Eve)s' information is completely unknown, corresponding designs are proposed to optimize legitimate users (LU)s' receiving performance while randomizing the Eves' received signal. When the Eves' CSI is imperfectly known, in the second scenario, the Eves' receiving performance is further deteriorated by imposing destructive interference to the Eves. For each scenario, three algorithms are proposed under hardware constraints and imperfect CSI, i.e., one direct-mapping algorithm suitable for high/moderate number of bits in PSs, one heuristic algorithm with improved receiving performance at the cost of complexity, and one iterative-closed-form algorithm with enhanced practicality of symbol-level based DM. Simulation demonstrates that the algorithms achieve lower symbol error rate (SER) at the LUs while significantly deteriorating the Eves' SER, leading to an improved secrecy throughput over the benchmarks.

Hybrid beamforming design for mmWave OFDM distributed antenna systems

This paper presents a hybrid beamforming design for millimeter-wave (mmWave) orthogonal frequency division multiplexing (OFDM) distributed antenna systems (DASs). First, we derive a downlink signal transmission model that considers the delay spread differences (DSDs) caused by the distributed nature of the network. We then propose a cooperative wideband hybrid beamforming method under the transmitting power constraints of each remote access unit. In a simulation study, the proposed method performed comparably to fully-digital beamforming, even when operated with practical finite-resolution phase shifters. We further confirm that the DSDs are the dominant cause of performance degradation in mmWave OFDM DASs.

Practical Hybrid Beamforming With Finite-Resolution Phase Shifters for Reconfigurable Intelligent Surface Based Multi-User Communications

In this paper, we study the reconfigurable intelligent surface (RIS) based downlink multi-user system where a multi-antenna base station (BS) sends signals to various users assisted by the RIS reflecting the incident signals of the BS towards the users. Unlike most existing works, we consider the practical case where only the large-scale fading gain is required at the BS and a limited number of phase shifts can be realized by the finite-sized RIS. To maximize the sum rate, we propose a hybrid beamforming scheme where the continuous digital beamforming and discrete RIS-based analog beamforming are performed at the BS and the RIS, respectively. An iterative algorithm is designed for beamforming and theoretical analysis is provided to evaluate how the size of RIS influences the achievable rate. Simulation results show that the RIS-based system can achieve a good sum-rate performance by setting a reasonable size of RIS and a small number of discrete phase shifts.

Alternating Optimization Based Hybrid Precoding Strategies for Millimeter Wave MIMO Systems

In millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems, the hybrid beamforming architecture has been put forward to reduce the high hardware cost and power consumption, which are resulted from the tremendous requirements of dedicated radio frequency (RF) chains. In this paper, we propose several strategies to design analog and digital precoders for a point-to-point (P2P) hybrid MIMO system. Aiming at minimizing the Euclidean distance between the optimal digital precoder and hybrid precoder, we decouple this matrix factorization problem into a nonconvex quadratically constrained quadratic programming (QCQP) problem and an unit-modulus least-squares (ULS) problem, which can be solved by the presented three alternating optimization algorithms. Simulation and analysis results indicate that the proposed semidefinite relaxation based alternating optimization (SDR-AO) algorithm can approach near-optimal spectral efficiency performance compared with previous algorithms in the literature, but shows extremely high computational complexity. The alternating direction method of multipliers based alternating optimization (ADMM-AO) algorithm is preferred in the case that the number of transmit antennas is much larger than that of receive antennas or the amount of data streams is small. Moreover, when equal number of RF chains and data streams are employed, the analytical constant modulus factorization based alternating optimization (ACMF-AO) algorithm is a better choice. Finally, the proposed algorithms can also be well applied in finite resolution phase shifters (PSs) of the analog component and are extended to wideband mmWave systems.

Power-Efficient Beam Designs for Millimeter Wave Communication Systems

The use of the millimeter wave (mmwave) spectrum for next generation mobile communication systems has gained significant attention recently. Large antenna arrays along with beamforming techniques are required to combat the large path-loss at mmwave frequencies. However, the existing beam designs often cause a large peak to average power ratio, and thus require power-inefficient power amplifiers (PAs). In this paper, we propose power-efficient beam design methods that facilitate the use of power-efficient PAs. Specifically, we design digital and hybrid analog-digital mmwave beams that possess a per-antenna constant envelope (PACE) and thus are highly power-efficient. Meanwhile, we also minimize the ripples in the mainlobe and sidelobe of the beams and consider both infinite and finite resolution phase shifters. To this end, we first propose an efficient feasible point search method to provide a feasible solution for the considered difficult beam design problem. Then, a novel hybrid analog-digital mapping algorithm is developed to map a designed digital beam to a hybrid analog-digital beam. To achieve better performance, we propose an improved hybrid analog-digital beam design method employing further optimization based on the feasible point. The proposed method is applicable to both infinite-resolution and finite-resolution phase shifters. Comprehensive simulation results are provided to demonstrate the effectiveness and superiority of the proposed beam designs.

Energy Efficient Analog Beamformer Design for mmWave Multicast Transmission

Millimeter wave (mmWave) communication is considered as a key enabling technology for 5G cellular networks because abundant spectrum in mmWave bands can provide multi-gigabit communication service. Analog beamforming architecture, which employs energy-efficient phase shifters (PSs) instead of energy-hungry radio frequency (RF) components, has emerged as a promising solution to overcome severe propagation loss of mmWave channels. On the other hand, multicast communication is another efficient approach to address the dramatic traffic demand by utilizing the broadcast nature of the wireless medium. This paper investigates energy efficient analog beamforming in mmWave single-group multicast communication systems. We focus on max–min fair (MMF) problem and aim to design the analog beamformer to maximize the minimum signal-to-noise ratio (SNR) over all users subject to a transmit power constraint. The analog beamformer design with infinite and finite resolution PSs are both studied. While the constraints of PSs make the problem intractable, we propose an alternative low-complexity algorithm, which iteratively determines each element of analog beamformer. Furthermore, we also investigate the asymptotically optimal beamformer designs and provide asymptotic performance analysis for large-scale mmWave multicasting systems. Extensive simulation results illustrate the effectiveness of the proposed analog beamforming designs in mmWave multicast systems. Besides, numerical results also demonstrate that the asymptotic performance of the proposed scheme is close to the optimal case.

Hybrid Beamforming for Millimeter Wave Massive Multiuser MIMO Systems Using Regularized Channel Diagonalization

This letter presents a novel hybrid analog-digital beamforming design for massive multiuser MIMO downlink transmission in sparse millimeter wave channels. The proposed hybrid regularized channel diagolnalization (HRCD) scheme combines analog (RF) phase-only beamforming with linear digital (baseband) precoding based on regularized channel diagonalization. Being a hybrid beamforming design utilizing simple non-iterative processing, HRCD provides a low complexity solution that is capable of outperforming several other hybrid schemes including those based on block diagonalization, as shown through simulations. Furthermore, it is also shown that the performance remains strong even with the use of finite-resolution phase shifters.

Low-Complexity Constant Envelope Precoding Using Finite Resolution Phase Shifters for Multiuser MIMO Systems With Large Antenna Arrays

The present study considers a constant envelope (CE) precoding design problem in massive multiuser multiple-input multiple-output systems, where CE precoding is implemented with a network of finite resolution phase shifters (PSs). Mathematically, such CE precoding design problem can be formulated as a discrete optimization problem whose optimal solution can be obtained through an exhaustive search. Unfortunately, an exhaustive search involves exponential complexity with numerous base station antennas ( $M$ ) and bits in PS resolution. We resolve the aforementioned concern by using a low-complexity algorithm developed from the iterative gradient descent (IGD) based algorithmic framework. However, unlike conventional IGD-based solvers, finite resolution PSs are considered directly in the optimization procedure of the proposed algorithm to improve performance. In addition, the proposed algorithm is roughly $M/2$ times less complex than the conventional IGD algorithm at each iteration. The simulation results reveal that the proposed algorithm has nearly the same performance as that of the unquantized version of the state-of-the-art IGD algorithm.

Hybrid Beamforming With Discrete Phase Shifters for Millimeter-Wave Massive MIMO Systems

Hybrid digital and analog beamforming design has been the focus of considerable interest in the context of millimeter-wave massive multiple-input multiple-output systems because such a design can provide a flexible compromise between hardware complexity and system performance. However, most existing hybrid beamforming designs usually assume that infinite resolution phase shifters (PSs) are available to produce analog beamformers. In a practical sense, the employment of such shifters with arbitrary phase is infeasible or, at least, is expensive because of hardware limitations. We propose an iterative hybrid transceiver design algorithm, where PSs can only supply discrete phase adjustments, to facilitate low-cost implementation of the analog beamformers via finite resolution PSs while maximizing spectral efficiency. Simulation results reveal that the performance of the proposed algorithm with low-resolution PSs is close to that of the state-of-the-art algorithm with infinite resolution PSs.