Per-antenna Power Research Articles

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.

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.

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.

Effects of Wall Reflection on the Per-Antenna Power Distribution of ZF-Precoded ULA for Indoor mmWave MU-MIMO Transmissions

Indoor access points (APs) with large-scale antenna arrays are commonly deployed in the vicinity of a wall, where wall reflection (WR) affects the indoor electromagnetic (EM) wave propagation. In this letter, we investigate the effects of WR on the per-antenna power distribution of a transmit uniform linear array (ULA) adopting a zero-forcing (ZF) precoder. A new channel model is constructed to characterise the impact of both the line-of-sight (LOS) path and the WR path on indoor millimetre wave (mmWave) multi-user (MU) multiple-input multiple-output (MIMO) downlink transmissions. Specifically for the dual user equipment (UE) scenario, the ZF precoding matrix is analytically obtained and verified through simulations. The effects of WR on the per-antenna power distribution of the ZF-precoded ULA, in terms of the normalised power distribution and maximum power ratio (MPR), are evaluated through the comparisons between our proposed channel model and the pure LOS channel model. Our analytical and numerical results reveal the impact of AP configurations (the number of antennas and the AP-wall distance), multi-user spatial distribution (the angle of departure (AoD) and length of the LOS path for each user), and wall parameters (permittivity and thickness) on the power distribution across the ZF-precoded ULA. It is found that the effects of WR will exacerbate the uneven power distribution across the ZF-precoded ULA.

Optimal power splitting for MIMO SWIPT relaying systems with direct link in IoT networks

Ultra-high reliability communications are greatly vital for massive user connections and network sensors such as Internet of Things (IoT) devices in the beyond 5th generation (B5G) communication networks. Simultaneous Wireless Information and Power Transfer (SWIPT) has evolved as an efficient strategy through prolonging the battery life by harvesting energy from radio-frequency (RF) signals. Moreover, cooperative relay sensors in IoT network can enhance the network coverage. In this paper, we investigate the multiple-input multiple-output (MIMO) SWIPT relaying systems with direct link, where the relay node splits the received RF signals into two power streams, one for information decoding (ID) and the other for energy harvesting (EH). Under per-antenna power constraints, the relay node forwards the ID signal to the destination. We propose a channel diagonalization scheme based on singular value decomposition (SVD) and eigenvalue decomposition (EVD) to design the precoding matrix of source and the amplifying matrix of relay respectively. Moreover, the closed-form expression of the optimal power splitting (PS) factor diagonal matrix is obtained to maximize the sum-rate of MIMO SWIPT relaying system. Finally, the efficiency of proposed precoding and PS factor design is verified by the presenting numerical results.

Computationally Efficient Constructive Interference Precoding for PSK Modulations Under Per-Antenna Power Constraint

This correspondence investigates computationally efficient constructive interference (CI)-based precoding for phase-shift-keying (PSK)-modulated multiuser multiple-input-single-output (MISO) systems. In contrast to the existing CI-based precoders which are designed exclusively under the sum power constraint, we focus on the design problem under the more challenging but realistic per-antenna power constraint (PAPC). We showed that both the strict and non-strict phase rotation CI-based precoders under PAPC can be efficiently realized under a unified new framework. Simulation results showed that the proposed CI-based precoders admit substantially lower complexity while achieving essentially the same error rate performance as their optimization-based counterparts.

Deep Learning Enabled Optimization of Downlink Beamforming Under Per-Antenna Power Constraints: Algorithms and Experimental Demonstration

This paper studies fast downlink beamforming algorithms using deep learning in multiuser multiple-input-single-output systems where each transmit antenna at the base station has its own power constraint. We focus on the signal-to-interference-plus-noise ratio (SINR) balancing problem which is quasi-convex but there is no efficient solution available. We first design a fast subgradient algorithm that can achieve near-optimal solution with reduced complexity. We then propose a deep neural network structure to learn the optimal beamforming based on convolutional networks and exploitation of the duality of the original problem. Two strategies of learning various dual variables are investigated with different accuracies, and the corresponding recovery of the original solution is facilitated by the subgradient algorithm. We also develop a generalization method of the proposed algorithms so that they can adapt to the varying number of users and antennas without re-training. We carry out intensive numerical simulations and testbed experiments to evaluate the performance of the proposed algorithms. Results show that the proposed algorithms achieve close to optimal solution in simulations with perfect channel information and outperform the alleged theoretically optimal solution in experiments, illustrating a better performance-complexity tradeoff than existing schemes.

On Range Sidelobe Reduction for Dual-Functional Radar-Communication Waveforms

In this letter, we propose a novel waveform design for multi-input multi-output (MIMO) dual-functional radar-communication systems by taking the range sidelobe control into consideration. In particular, we focus on optimizing the weighted summation of communication and radar metrics under per-antenna power budget. While the formulated optimization problem is non-convex, we develop a first-order descent algorithm by exploiting the manifold structure of its feasible region, which finds a near-optimal solution within a low computational overhead. Numerical results show that the proposed waveform design outperforms the conventional techniques by improving the communication rate while reducing the range sidelobe level.

Energy Efficient Beamforming Schemes for Satellite-Aerial-Terrestrial Networks

In this paper, we investigate energy efficient transmission for a satellite-aerial-terrestrial network (SATN), where a multi-antenna unmanned aerial vehicle (UAV) is employed as a relay to assist the satellite signal delivery. By considering total power constraint (TPC) or per-antenna power constraint (PPC) at the UAV, we first formulate an optimization problem to maximize the energy efficiency of the SATN, which is defined as ratio of the ergodic capacity to the total power consumption for communication at UAV. Then, by jointly exploiting array signal processing with the Dinkelbach's method, two new beamforming (BF) schemes, namely, TPC-BF and PPC-BF are proposed to solve the non-convex energy efficiency maximization problem. The main advantage of our method is that only angular information-based channel state information is used to obtain BF weight vectors so that a low implementation complexity is achieved. Furthermore, by assuming that the satellite-UAV link undergoes correlated Shadowed-Rician fading while the UAV-terminal link experiences correlated Rician fading, closed-form expressions for the statistics of the equivalent output signal-to-noise ratio are derived and, thus energy efficiency for the considered SATN with BF schemes is analytically presented. Finally, simulation results corroborate the derived expressions and confirm the effectiveness of the proposed BF schemes.

Per-Antenna Power Constrained Transceiver Design for MIMO Multisource and Multidestination Amplify-and-Forward Relay Systems

This study addresses the transceiver design method for multiple-input multiple-output multisource multidestination amplify-and-forward relay systems. The source, relay, and destination filters are designed to minimize the sum mean-squared-error under the per-antenna power constraints at the source and relay nodes. The joint optimization is challenging due to its non-convexity and multiple power constraints. To resolve these difficulties, we propose a source and relay filter design method and present an alternating algorithm that is based on the block-coordinate descent method. Specifically, by introducing transmit-centric modified MSEs and reformulating the problem, the non-convex problem is transformed into tractable forms with multiple power constraints. The multiple power constraints are then adjusted by semidefinite programming of the source filters and a 1-D line search method for the relay transceiver. Simulation results demonstrate the effectiveness of the proposed schemes under the per-antenna power constraints that are compared with the conventional method under the sum power constraints.

MIMO Radar Waveform Optimization in Clutter Under General Power Constraints

In this paper, we investigate a novel framework on the waveform optimization for multiple-input multiple-output (MIMO) radar systems under assumptions of statistical information of scattering matrices and colored noise. Different from most of traditional designs under total power constraint, in our framework, a general power constraint named as multiple weighted power constraints is provided, which includes total power constraint, per-antenna power constraints as its special cases. In the framework, the transmit and receive correlations of parameter matrix to estimate and the spatial and time correlations of noise matrix are all taken into account. Moreover, the signal-dependent interference is also taken into account, which can be considered as a self-interference noise. Based on the available statistics of scattering matrices and colored noise, two kinds of estimation schemes are proposed in this paper, which can realize different trade-offs between complexity and performance. Finally, some numerical results are given to demonstrate the performance advantages of the proposed radar waveform designs.

On the Optimal Two-Antenna Static Beamforming With Per-Antenna Power Constraints

This letter provides a theoretical analysis for the static beamforming problem when the base station is equipped with two antennas. It is assumed that the base station cannot change the beamforming vector dynamically due to hardware restrictions. The objective is to find the static beamforming vector that maximizes network utility when long-term information about the user location is available. Non-linear optimization techniques are used to find the solution of the problem for two different network utility functions: average SNR and average rate. Numerical results are provided to support the analysis.

Low Complexity Algorithms for Robust Multigroup Multicast Beamforming

Existing methods for robust multigroup multicast beamforming obtain feasible points using semidefinite relaxation (SDR) and Gaussian randomization, and have high computational complexity. In this letter, we consider the robust multigroup multicast beamforming design to minimize the sum power (SP) or per-antenna power (PAP) under the signal-to-interference-plus-noise ratio (SINR) constraints and to maximize the worst-case SINR under the SP constraint or PAP constraints, respectively. The resulting optimization problems are challenging non-convex problems with infinitely many constraints. For each problem, using the majorization-minimization (MM) approach, we propose an iterative algorithm to obtain a feasible solution which is shown to be a stationary point under certain conditions. We also show that the proposed algorithms have much lower computational complexity than existing SDR-based algorithms.

Optimal Transmit Strategies for Gaussian MISO Wiretap Channels

This paper studies the optimal tradeoff between secrecy and non-secrecy rates of the MISO wiretap channels for different power constraint settings: sum power constraint only, per-antenna power constraints only, and joint sum and per-antenna power constraints. The problem is motivated by the fact that channel capacity and secrecy capacity are generally achieved by different transmit strategies. First, a necessary and sufficient condition to ensure a positive secrecy capacity is shown. The optimal tradeoff between secrecy rate and transmission rate is characterized by a weighted rate sum maximization problem. Since this problem is not necessarily convex, equivalent problem formulations are introduced to derive the optimal transmit strategies. Under sum power constraint only, a closed-form solution is provided. Under per-antenna power constraints, necessary conditions to find the optimal power allocation are derived. Sufficient conditions are provided for the special case of two transmit antennas. For the special case of aligned channels, the optimal transmit strategies can deduced from an equivalent point-to-point channel problem. Last, the theoretical results are illustrated by numerical simulations.

A zero-forcing beamforming based time switching protocol for wireless powered internet of things system

In this paper, a time switching (TS) protocol for the wireless powered communications system with per-antenna power constraints is considered. To eliminate the multi-user interference, we adopt the zero-forcing beamforming scheme to maximize the sum rate performance. A two-step algorithm is proposed to solve the sum rate maximization problem with per-antenna power constraints. More specifically, golden section search method is used to find optimal time switching factor in the first step. For each given TS factor, the sub-problem in the second step is convex, which can be efficiently solved by standard software package. Numerical results are provided to demonstrate the effectiveness of the proposed methods, and some interesting results are also observed.

Improved ADMM-based algorithms for multi-group multicasting in large-scale antenna systems with extension to hybrid beamforming

In this paper, multi-group multicast beamforming is considered for the full digital and hybrid beamforming. The wireless system comprises of a multiple-antenna base station and single-antenna users. Quality-of-service (QoS)-aware design is investigated where the optimization objective is to minimize the total transmitted power subject to the signal-to-interference-plus-noise ratio (SINR) constraint at each user. In addition to the SINR constraints, per-antenna power constraint is included for each antenna of the base station. The original optimization problem for full digital beamforming is transformed into an equivalent form such that the alternating direction method of multipliers (ADMM) can be applied in an effective and computationally inexpensive manner for the large-scale antenna systems. In this new formulation, the beamformer weight vectors are decomposed into two subspaces in order to decrease the number of dual variables and multiplications. The optimum update equations are obtained for the proposed ADMM algorithm. This new reformulation is used for two different hybrid beamforming structures employing phase shifters and vector modulators. Optimum updates are derived for each system. The proposed algorithms decrease computational complexity of the existing ADMM algorithms due to the effective reformulation as well as the direct solution of the nonconvex problem. In the simulation results, it is shown that the proposed methods have better convergence behavior and less computational time than the benchmark algorithms. Furthermore, the proposed method for hybrid beamforming with vector modulators performs better than its counterpart in the literature in terms of transmitted power.

Space–time line coded regenerative two‐way relay systems with power control

In this Letter, a general space–time line code (STLC)-based two-way relay (TWR) method is proposed to enable a power control for individual data streams transmitted to source nodes. Optimal power control factors are derived to ensure fairness between two source nodes under per-antenna power constraints. When the two-way channels are unbalanced, numerical results verify that the proposed method outperforms the existing TWR methods, an STLC TWR method without power control, and a space division multiple-access-based TWR method.

Space–Time Line Codes With Power Allocation for Regenerative Two-Way Relay Systems

In this paper, a general two-way relay (TWR) transmission method is proposed under per-antenna power constraints by combining space-time line codes (STLCs) with transmit power allocation for two source nodes. We introduce a general STLC-based encoding scheme for a decode-and-forward TWR and derive the detection signal-to-interference-plus-noise ratio (SINR) values at two source nodes. An optimal encoder structure with power allocation is proposed in terms of maximizing the minimum SINRs, and it is verified that the optimal encoder is identical to the superposition of two conventional STLCs. An iterative method is proposed to find the optimal power allocation for detection at two source nodes. Moreover, a low-complexity suboptimal encoder is proposed for practical implementation. Numerical simulations present that the proposed STLC-based transmission method outperforms a conventional eigen-beamforming scheme with nulling and an STLC-based scheme with equal power allocation, in terms of the average bit error rate of source nodes, regardless of the distribution of source nodes, the number of TWR antennas, and the transmit power.