Per-antenna Power Constraints Research Articles

A Single-Loop Algorithm for Weighted Sum Rate Maximization in Multiuser MIMO Systems With Per-Antenna Power Constraints

This paper investigates the linear precoder design for multiuser multiple-input-multiple-output (MIMO) systems, in which the problem of maximizing weighted sum rate (WSR) subject to per-antenna power constraints (PAPC) is considered. This problem is hard to solve due to its nonconvexity and the existence of multiple quadratic constraints. Conventional methods to tackle this problem, such as the iterative weighted minimum mean squared error (WMMSE) algorithm, typically consist of two nested loops and thus suffer from high computational complexity. By leveraging the inherent separability of the PAPC constraint set, we propose a low-complexity single-loop algorithm for solving the WSR maximization problem under PAPC, in which each updating step is done efficiently with closed form. Theoretically, we prove the convergence of the proposed algorithm to stationary solutions. Then we extend the proposed algorithm to the multi-carrier scenario where the power constraints are shared over the subcarriers. Complexity analysis and numerical results show that the proposed single-loop algorithm maintains the same WSR performance as existing methods but dramatically reduces the computational complexity.

Complete Power Reallocation for MU-MISO Under Per-Antenna Power Constraint

This paper proposes a beamforming method under a per-antenna power constraint (PAPC). Although many beamformer designs with the PAPC need to solve complex optimization problems, the proposed complete power reallocation (CPR) method can generate beamformers with excellent performance only with linear operations. CPR is designed to have a simple structure, making it highly flexible and practical. In this paper, three CPR variations considering algorithm convergence speed, sum-rate maximization, and robustness to the channel uncertainty are developed. Simulation results verify that CPR and its variations satisfy their design criteria, and, hence, CPR can be readily utilized for various purposes.

Low-Complexity WSRMax Precoder Design Using the Dual Coordinate Ascent Method

We propose a low-complexity precoder design for weighted sum rate maximization (WSRMax) in multiuser multiple-input-multiple-output systems with per-antenna power constraints (PAPCs). The proposed design is based on the alternating optimization framework and a fast dual coordinate ascent method in the inner loop. Specifically, the original nonconvex WSRMax problem is first approximated as a sequence of convex quadratic optimization problems subject to PAPCs by adopting alternating optimization. Then, each convex quadratic problem is solved by a dual coordinate ascent method. The proposed dual coordinate ascent method includes no turning parameters, such as the step size in the projected gradient method, which offers both stability and fast convergence. Simulation results show that the dual coordinate ascent method converges faster than existing methods, which significantly improves the total computational efficiency of alternating optimization.

Rethinking WMMSE: Can Its Complexity Scale Linearly With the Number of BS Antennas?

Precoding design for maximizing weighted sum-rate (WSR) is a fundamental problem for downlink of massive multi-user multiple-input multiple-output (MU-MIMO) systems. It is well-known that this problem is generally NP-hard due to the presence of multi-user interference. The weighted minimum mean-square error (WMMSE) algorithm is a popular approach for WSR maximization. However, its computational complexity is cubic in the number of base station (BS) antennas, which is unaffordable when the BS is equipped with a large antenna array. In this paper, we consider the WSR maximization problem with either a sum-power constraint (SPC) or per-antenna power constraints (PAPCs). For the former, we prove that any nontrivial stationary point must have a low-dimensional subspace structure, and then propose a reduced-WMMSE (R-WMMSE) with linear complexity by exploiting the solution structure. For the latter, we propose a linear-complexity WMMSE approach, named PAPC-WMMSE, by using a novel recursive design of the algorithm. Both R-WMMSE and PAPC-WMMSE have simple closed-form updates and guaranteed convergence to stationary points. Simulation results verify the efficacy of the proposed designs, especially the much lower complexity as compared to the state-of-the-art approaches for massive MU-MIMO systems.

Robust Multi-Beam Secure mmWave Wireless Communication for Hybrid Wiretapping Systems

In this paper, we consider the physical layer (PHY) security problem for hybrid wiretapping wireless systems in millimeter wave transmission, where active eavesdroppers (AEs) and passive eavesdroppers (PEs) coexist to intercept the confidential messages and emit jamming signals. To achieve secure and reliable transmission, we propose an artificial noise (AN)-aided robust multi-beam array transceiver scheme. Leveraging beamforming, we aim to minimize transmit power by jointly designing the information and AN beamforming, while satisfying valid reception for legitimate users (LUs), per-antenna power constraints for transmitter, as well as all interception power constraints for eavesdroppers (Eves). In particular, the interception power formulation is taken into account for protecting the information against hybrid Eves with imperfect AE channel state information (CSI) and no PE CSI. In light of the intractability of the problem, we reformulate the considered problem by replacing non-convex constraints with tractable forms. Afterwards, a two-stage algorithm is developed to obtain the optimal solution. Additionally, we design the received beamforming weights by means of minimum variance distortionless response, such that the jamming caused by AEs can be effectively suppressed. Simulation results demonstrate the superiority of our proposed scheme in terms of energy efficiency and security.

A Framework for Hardware Impairments-Aware Multi-Antenna Transceiver Design in IoT Systems via Majorization–Minimization

In view of the nonideality of communication links in the Internet of Things (IoT) originating from transceiver hardware impairments, in this article, we introduce a general framework for hardware impairments-aware multiantenna transceiver design, which considers different availabilities of CSI at the transmitter (CSIT) and the receiver (CSIR). The well-known Kronecker model is applied to characterize stochastic channel state information (CSI) errors. For each case, we aim to minimize the (average) total mean square error (MSE) of all data streams subject to the practical per-antenna power constraints. To address the nonconvexity of the formulated problem, we propose an efficient majorization–minimization (MM)-based iterative algorithm to transform the original problem into a series of convex subproblems with semiclosed-form optimal solutions. For low-complexity implementation, we also develop an alternative scheme for directly finding a high-quality suboptimal solution by considering both worst case hardware impairments and worst case CSI errors. In particular, since an explicit expression of the average total MSE for the perfect CSIR and imperfect CSIT case is hard to derive, we instead optimize its effective upper and lower bounds. The prospective applications of our work in the two currently popular multiple-input–multiple-output (MIMO) IoT scenarios are then discussed. Furthermore, we fundamentally reveal the MSE floor effect caused by both hardware distortion and CSI imperfection in the high-SNR regime. Numerical results illustrate the excellent average total MSE and average bit error rate (BER) performance of our proposed algorithms over the adopted benchmark schemes.

QoS-Aware Precoder Optimization for Radar Sensing and Multiuser Communications Under Per-Antenna Power Constraints

In this work, we concentrate on designing the precoder for the multiple-input multiple-output (MIMO) dual functional radar-communication (DFRC) system, where the dual-functional waveform is designed for performing multiuser downlink transmission and radar sensing simultaneously. Specifically, considering the signal-independent interference and signal-dependent clutter, we investigate the optimization of transmit precoding for maximizing the sensing signal-to-interference-plus-noise ratio (SINR) at the radar receiver under the constraint of the minimum SINR received at multiple communication users and per-antenna power budget. The formulated problem is challenging to solve due to the nonconovex objective function and nonconvex per-antenna power constraint. In particular, for the signal-independent interference case, we propose a distance-majorization induced algorithm to approximate the nonconvex problem as a sequence of convex problems whose optima can be obtained in closed form. Subsequently, our complexity analysis shows that our proposed algorithm has a much lower computational complexity than the widely-adopted semidefinite relaxation (SDR)-based algorithm. For the signal-dependent clutter case, we employ the fractional programming to transform the nonconvex problem into a sequence of subproblems, and then we propose a distance-majorization based algorithm to obtain the solution of each subproblem in closed form. Finally, simulation results confirm the performance superiority of our proposed algorithms when compared with the SDR-based approach. In conclusion, the novelty of this work is to propose an efficient algorithm for handling the typical problem in designing the DFRC precoder, which achieves better performance with a much lower complexity than the state-of-the-art algorithm.

Robust Downlink Precoding for LEO Satellite Systems With Per-Antenna Power Constraints

Downlink precoding has been widely accepted as a crucial technique in low-earth-orbit (LEO) satellite communications due to its advantages in improving the space division multiplexing capability and enhancing spectrum efficiency. Because of the strong spatial directivity in the satellite channels, the downlink precoder can be efficiently designed based on the angle of departure (AoD)-based channel state information (CSI). However, acquiring perfect AoD-based CSI is challenging due to the angle estimation error and attitude jitter of the LEO satellites. In light of this, this paper investigates the precoder design for the LEO satellite downlinks with imperfect AoD-based CSI. For robust design, we treat the angle deviations of each user as random variables, which are supposed to exhibit a particular distribution, then integrate them within a certain range to achieve the robustness of the proposed downlink precoder against the angle mismatch. Instead of using the sum-power constraint on the transmit antennas, we adopt a more realistic per-antenna power constraint (PAPC). Accordingly, we formulate the problem to maximize the ergodic sum rate of the system. By leveraging the corresponding Lagrangian formulation and identifying the optimal precoder structure as the solution to a generalized eigenvalue problem, an iterative algorithm for the robust precoder design is derived. To reduce the computational complexity, a low-complexity version of the proposed algorithm is implemented based on deep learning techniques to meet the high demand for real-time applications in LEO satellite systems. Simulation results verify the effectiveness of the proposed precoding approach.

Rate-Splitting Multiple Access for 6G—Part II: Interplay With Integrated Sensing and Communications

This letter is the second part of a three-part tutorial focusing on rate-splitting multiple access (RSMA) for 6G. As Part II of the tutorial, this letter addresses the interplay between RSMA and integrated radar sensing and communications (ISAC). In particular, we introduce a general RSMA-assisted ISAC architecture, where the ISAC platform has a dual capability to simultaneously communicate with downlink users and probe detection signals to a moving target. Then, the metrics of radar sensing and communications are respectively introduced, followed by a RSMA-assisted ISAC waveform design example which jointly minimizes the Cramér-Rao bound (CRB) of target estimation and maximizes the minimum fairness rate (MFR) amongst communication users subject to the per-antenna power constraint. The superiority of RSMA-assisted ISAC is verified through simulation results in both terrestrial and satellite scenarios. RSMA is demonstrated to be a powerful multiple access and interference management strategy for ISAC, and provides a better communication-sensing trade-off compared with the conventional benchmark strategies. Consequently, RSMA is a promising technology for next generation multiple access (NGMA) and future networks such as 6G and beyond.

On the MIMO Capacity With Joint Sum and Per-Antenna Power Constraints: A New Efficient Numerical Method

We propose a semi-closed-form solution to the problem of computing the capacity and optimal signaling for a Gaussian MIMO channel under a joint sum power constraint (SPC) and per-antenna power constraint (PAPC). Existing efficient solutions to this fundamental problem are only applicable to some special cases: multiple-input single-output (MISO) systems, or full column rank MIMO channels with sufficiently high transmit power, or full-rank optimal signaling. For the general case, we present an efficient numerical method to solve the considered problem which does not make any assumptions on the rank of the channel matrix or the maximum transmit power. To achieve this, the considered problem is transformed into an equivalent minimax problem. We then exploit the special structure of the minimax problem to derive a closed-form solution based on a concave-convex procedure (CCP)-like algorithm. Extensive simulation results show that our proposed algorithm outperforms the existing solutions in terms of complexity and generality.

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.

Rate-Splitting Multiple Access for Multigateway Multibeam Satellite Systems With Feeder Link Interference

This paper studies the precoder design problem of achieving max-min fairness (MMF) amongst users in multigateway multibeam satellite communication systems with feeder link interference. We propose a beamforming strategy based on a newly introduced transmission scheme known as rate-splitting multiple access (RSMA). RSMA relies on multi-antenna rate-splitting at the transmitter and successive interference cancellation (SIC) at the receivers, such that the intended message for a user is split into a common part and a private part and the interference is partially decoded and partially treated as noise. In this paper, we formulate the MMF problem subject to per-antenna power constraints at the satellite for the system with imperfect channel state information at the transmitter (CSIT). We also consider the case of two-stage precoding which is assisted by on- board processing (OBP) at the satellite. Numerical results obtained through simulations for RSMA and the conventional linear precoding method are compared. When RSMA is used, MMF rate gain is promised and this gain increases when OBP is used. RSMA is proven to be promising for multigateway multibeam satellite systems whereby there are various practical challenges such as feeder link interference, CSIT uncertainty, per-antenna power constraints, uneven user distribution per beam and frame-based processing.

Proportionally Fair Robust Beamforming for Multicast Multibeam Satellite Systems

We study the proportionally fair beamforming design for the downlink channel of multibeam satellite systems. Due to the channel phase uncertainty caused by oscillators and the long round trip delay, the beamforming design needs to be robust to the imperfect channel state information (CSI). We formulate an optimization problem with outage probability and per-antenna power constraints to maximize the weighted sum utility of the signal-to-interference-plus-noise (SINR) threshold to realize proportional fairness. The optimization problem is non-convex and we transformed it into the convex form through accurate approximation. We solve the optimization problem via a proposed sub-optimal algorithm. The simulation result shows that the proposed algorithm can converge within 30 iterations when the number of beams is 9. Furthermore, the proposed beamforming scheme obtains a 10% average performance gain in weighted sum utility over the robust max-min schemes in different levels of phase uncertainty.

Practical Hybrid Beamforming for Millimeter Wave Massive MIMO Full Duplex With Limited Dynamic Range

Full Duplex (FD) radio has emerged as a promising solution to increase the data rates by up to a factor of two via simultaneous transmission and reception in the same frequency band. This paper studies a novel hybrid beamforming (HYBF) design to maximize the weighted sum-rate (WSR) in a single-cell millimeter wave (mmWave) massive multiple-input-multiple-output (mMIMO) FD system. Motivated by practical considerations, we assume that the multi-antenna users and hybrid FD base station (BS) suffer from the limited dynamic range (LDR) noise due to non-ideal hardware and an impairment aware HYBF approach is adopted by integrating the traditional LDR noise model in the mmWave band. In contrast to the conventional HYBF schemes, our design also considers the joint sum-power and the practical per-antenna power constraints. A novel interference, self-interference (SI) and LDR noise aware optimal power allocation scheme for the uplink (UL) users and FD BS is also presented to satisfy the joint constraints. The maximum achievable gain of a multi-user (MU) mmWave FD system over a fully digital half duplex (HD) system with different LDR noise levels and numbers of the radio-frequency (RF) chains is investigated. Simulation results show that our design outperforms the HD system with only a few RF chains at any LDR noise level. The advantage of having amplitude control at the analog stage is also examined, and additional gain for the mmWave FD system becomes evident when the number of RF chains at the hybrid FD BS is small.

Wideband Precoding for MIMO-OFDM Systems With Per-Antenna Power Constraints

This letter describes a wideband precoding design for multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems under per-antenna power constraints, wherein all subcarriers share one wideband precoder. With new insight into the objective function, we first reformulate the precoding designing as a stochastic optimization problem. Then, an algorithm based on the free probability theory is proposed to solve the stochastic optimization problem; consequently, a wideband precoder is obtained, with a computational complexity nearly equivalent to that required for a single narrowband precoder. The effectiveness of this wideband precoder is validated through simulations.

Intelligent Reflecting Surface Aided NOMA for Millimeter-Wave Massive MIMO With Lens Antenna Array

In this paper, we propose a downlink intelligent reflecting surface (IRS) aided non-orthogonal multiple access (NOMA) for millimeter-wave (mmWave) massive MIMO with lens antenna array, i.e., IRS-aided mmWave beamspace NOMA, where the single-antenna users without direct-link but connected to the base station (BS) with the aid of the IRS are grouped as one NOMA group. Considering the power leakage problem in beamspace channel and the per-antenna power constraint, we propose two multi-beam selection strategies for the BS-IRS link under two channel models, i.e., 2-dimension (2D) channel model and 3-dimension (3D) channel model, respectively, where two corresponding RF chain configuration strategies are designed, respectively. Then, we formulate and solve the optimization problem for maximizing the weighted sum rate by jointly optimizing the active beamforming at the BS and the passive beamforming at the IRS, where we propose the alternating optimization (AO) method to solve the above joint optimization problem. Especially, different from the stochastic method, based on the beam-splitting technique, we propose the method to initialize the feasible solution for the proposed AO method, where the conditional transmit power minimization problem is formulated and solved. Through simulations, the weighted sum rate performance of the proposed IRS-aided mmWave beamspace NOMA is verified.

Joint Resource Allocation for Linear Precoding in Downlink Massive MIMO Systems

We study joint proportional-fair (PF) resource allocation (RA), including user selection, linear precoding design, power optimization, and modulation and coding scheme selection, in a single-cell downlink massive MIMO (m-MIMO) system over consecutive time-slots when taking per-antenna power constraints (PAPCs) into account. We formulate the general PF joint RA optimization problem as a weighted sum-rate maximization problem at each time-slot and develop a solution technique to obtain a quasi-optimal feasible solution via the introduction of auxiliary variables and a carefully chosen approximation of the spectral-efficiency function. To obtain results for larger settings (i.e., larger number of antennas and users), we propose an approximation to the general problem that yields quasi-optimal feasible solutions. Moreover, we consider state-of-the-art linear precoding techniques and propose a general heuristic RA scheme that takes PAPCs into account. Numerical results show that PAPCs have significant impact on performance even for a very large number of antennas, and that the best existing linear precoding technique, RZFT (regularized zero-forcing transmission) performs very well when RA is performed carefully as long as the PAPCs are not tight. However, RZFT is far from optimal under tight PAPCs, which highlights the need for practical PAPC-aware precoding techniques in this regime.

Supporting IoT With Rate-Splitting Multiple Access in Satellite and Aerial-Integrated Networks

To satisfy the explosive access demands of Internet-of-Things (IoT) devices, various kinds of multiple access techniques have received much attention. In this article, we investigate the multicast communication of a satellite and aerial-integrated network (SAIN) with rate-splitting multiple access (RSMA), where both satellite and unmanned aerial vehicle (UAV) components are controlled by network management center and operate in the same frequency band. Considering a content delivery scenario, the UAV subnetwork adopts the RSMA to support massive access of IoT devices (IoTDs) and achieve desired performances of interference suppression, spectral efficiency, and hardware complexity. We first formulate an optimization problem to maximize the sum rate of the considered system subject to the signal-interference-plus-noise-ratio requirements of IoTDs and per-antenna power constraints at the UAV and satellite. To solve this nonconvex optimization problem, we exploit the sequential convex approximation and the first-order Taylor expansion to convert the original optimization problem into a solvable one with the rank-one constraint, and then propose an iterative penalty function-based algorithm to solve it. Finally, simulation results verify that the proposed method can effectively suppress the mutual interference and improve the system sum rate compared to the benchmark schemes.

Multi-Group Multicast Beamforming by Superiorized Projections Onto Convex Sets

In this paper, we propose an iterative algorithm to address the nonconvex multi-group multicast beamforming problem with quality-of-service constraints and per-antenna power constraints. We formulate a convex relaxation of the problem as a semidefinite program in a real Hilbert space, which allows us to approximate a point in the feasible set by iteratively applying a bounded perturbation resilient fixed-point mapping. Inspired by the superiorization methodology, we use this mapping as a basic algorithm, and we add in each iteration a small perturbation with the intent to reduce the objective value and the distance to nonconvex rank-constraint sets. We prove that the sequence of perturbations is bounded, so the algorithm is guaranteed to converge to a feasible point of the relaxed semidefinite program. Simulations show that the proposed approach outperforms existing algorithms in terms of both computation time and approximation gap in many cases.

MISO NOMA downlink beamforming optimization with per-antenna power constraints

Consider a multiuser downlink beamforming optimization problem for the non-orthogonal multiple access (NOMA) transmission in a multiple-input single-output (MISO) system with a general number of users. The total transmission power minimization problem is formulated subject to both quality-of-service (QoS) constraints under the NOMA principal and per-antenna power constraints, which are more realistic since each antenna has its own power amplifier and is limited individually by the linearity of the power amplifier. The problem is a nonconvex quadratically constrained quadratic program, and the conventional semidefinite program (SDP) relaxation is not tight. In order to tackle the non-convex problem, we construct second-order cone program (SOCP) approximation for each signal-to-interference-plus-noise ratio (SINR) constraint and form an iterative algorithm, in which a sequence of SOCPs are solved. The optimal values of SOCPs in the sequence are proved to be non-increasing, and converging to a locally optimal value. In particular, we show that the SDP relaxation is tight for two-user case if one of the SINR constraints is strict (non-binding) at the optimality. Detailed simulation results are presented to demonstrate the performance gains of the NOMA downlink beamforming with per-antenna power constraints through the proposed algorithm, which is compared with some state-of-the-art methods.