Energy Receiver Research Articles

A Pricing-Based Approach for Energy-Efficiency Maximization in RIS-Aided Multi-User MIMO SWIPT-Enabled Wireless Networks

In this work, we investigate the performance of a reconfigurable intelligent surface (RIS)-aided multi-user simultaneous wireless information and power transfer (SWIPT) network, where a multiple-input multiple-output (MIMO) base station (BS) serves multiple MIMO information receivers (IRs) while ensuring a minimum harvested power at multiple MIMO energy receivers (ERs). In order to improve the energy efficiency (EE) of the network, we consider a pricing-based performance metric called network utility. We then establish an optimization framework to jointly optimize the transmit precoding matrix (TPM) and phase shift matrix (PSM) to maximize the network utility function with constraints on the available transmit power at BS, minimum harvested power required at each ER, and unit modulus phase shift condition at RIS. Due to the non-convex nature of this problem, we divide it into two sub-problems where a sub-optimal solution of TPM and PSM are obtained separately using successive convex approximation and bisection search-based algorithms. Further, we propose an EE maximization (EEM) algorithm based on the block coordinate descent method to achieve the optimal solution of the master problem by iteratively obtaining the sub-optimal TPM, PSM, and network price using their respective algorithms. Moreover, we also prove that the solution obtained for each problem using their respective algorithm converges to the Karush-Kuhn-Tucker (KKT) optimum point of that problem. We also show the efficacy of the proposed algorithm using simulation results. In particular, we highlight the importance of using RIS in a multi-user MIMO SWIPT network and demonstrate the effect of various parameters on the network’s EE performance.

Energy-Efficient Resource Allocation in Multi-UAV Networks With NOMA

This paper investigates the energy efficiency (EE) optimization in a wireless communication network where multiple UAVs serve different types of devices, namely, information receivers (IRs) and energy receivers (ERs). The UAVs transmit power signals towards the ERs, and then enable data transmission to IRs on the downlink and from ERs on the uplink with non-orthogonal multiple access (NOMA). The optimization problem to maximize the overall EE is formulated and solved using Lagrangian optimization and gradient-descent methods. The optimization is decomposed into two sub-problems. Firstly, by connecting the path loss of the devices’ channels with their rate demands, the UAVs’ optimal positions are obtained. Then, based on the obtained UAVs’ optimal positions and a closed-form expression for the EE, a resource allocation aiming to maximize EE is developed. For the simulations, two main scenarios for single and multiple UAVs are considered. Numerical results and comparisons are provided. In particular, for the single-UAV scenario, the results show an enhancement in EE for the operation with NOMA compared with OMA. For the multiple-UAV scenario, several cases depending on different combinations of the devices’ rate requirements are considered. The results show the superiority of NOMA over OMA in all use cases. The results also reveal the effect of considering the devices’ rate requirements on the EE, where the case with equal rate requirements has the best performance.

Beamforming optimization for RIS-aided SWIPT in cell-free MIMO networks

Reconfigurable intelligent surface (RIS) is a promising technology that utilizes massive low-cost elements to reflect incident signals to desired direction. In this paper, we consider a RIS-aided cell free multiple-input multiple-output (MIMO) network that composed of multiple access points (APs), multiple RISs, multiple information receivers (IRs), and multiple energy receivers (ERs). Under the maximum transmit power constraints of the APs and the minimum total energy harvesting power constraints of the ERs, we aim to maximize the weighted sum-rate (WSR) by jointly optimizing the beamforming matrices and the passive RIS reflection matrices. However, the formulated problem is nonconvex and very challenging to solve. Therefore, we propose an alternating optimization algorithm to obtain a suboptimal solution. Explicitly, the proposed algorithm decomposes the original optimization problem into three subproblems that can be efficiently solved. To overcome the nonconvexity of the subproblems, a successive convex approximation (SCA) based algorithm is proposed to tackle the energy harvesting constraints. Moreover, an alternating direction method of multipliers (ADMM) based algorithm is proposed to optimize the constant modulus constrained RIS reflecting elements. Finally, simulations are conducted to demonstrate the performance advantages of the proposed algorithms.

Refined Nonlinear Rectenna Modeling and Optimal Waveform Design for Multi-User Multi-Antenna Wireless Power Transfer

In this paper, we study the optimal waveform design for wireless power transfer (WPT) from a multi-antenna energy transmitter (ET) to multiple single-antenna energy receivers (ERs) simultaneously in multi-path frequency-selective channels. First, we propose a refined nonlinear current-voltage model of the diode in the ER rectifier, and accordingly derive new expressions for the output direct current (DC) voltage and corresponding harvested power at the ER. Leveraging this new rectenna model, we first consider the single-ER case and study the multisine-based power waveform design based on the wireless channel to maximize the harvested power at the ER. We propose two efficient algorithms for finding high-quality suboptimal solutions to this non-convex optimization problem. Next, we extend our formulated waveform design problem to the general multi-ER case for maximizing the weighted sum of the harvested powers by all ERs, and propose an efficient difference-of-convex-functions programming (DCP)-based algorithm for solving this problem. Finally, we demonstrate the superior performance of our proposed waveform designs based on the new rectenna model over existing schemes/models via simulations.

Wireless Energy Transfer in Extra-Large Massive MIMO Rician Channels

In application scenarios such as Internet of Things, a large number of energy receivers (ERs) exist and line-of-sight (LOS) propagation could be common. Considering this, we investigate wireless energy transfer (WET) in extra-large massive MIMO Rician channels. We derive analytical expressions of the received net energy for different schemes, including 1) training-based WET, where the ER sends beacon signal for channel training and the energy transmitter (ET) uses the channel estimate for energy beamforming, 2) LOS beamforming, where the ET transmits to the LOS direction of the ER, and 3) energy harvesting, which allows an ER to harvest the training energy from the other ERs. We derive a path loss threshold for switching between training and LOS beamforming-based WET. We further show that the WET scheme selection of one ER is not affected by the other ERs, and the energy harvested from training is minimal in practice. With these insights, we propose an algorithm for the multi-ER scenario, which minimizes the power consumption by iteratively updating the WET scheme selection and power allocation for all ERs. Simulations show that the proposed algorithm achieves near-optimal performance as compared to exhaustive searching, while with much lower implementation complexity.

Phase Aligned Time-Reversal for Multi-User Wireless Power Transfer Systems With Non-Linear Energy Harvesting

In this paper, we study a waveform design based on time-reversal (TR) for multi-user wireless power transfer (WPT) systems in multipath channels. The existing waveforms for WPT using the non-linear energy harvesting (EH) model have been designed in the frequency domain, whereas we design the waveform directly in the time domain by modifying TR to be suitable for WPT. In the non-linear EH model, the peak signal with the largest magnitude among the received signals is responsible for most of the harvested energy at the energy receiver (ER). Since the peak signal of TR for multi-user consists of the sum of the inter-user interference (IUI) signal and the desired signal, the phase difference between these signals can reduce the magnitude of the peak signal. Thus, we propose a novel waveform based on TR, called a phase aligned TR (PATR). The objective of the proposed PATR is to increase the harvested energy by aligning the phase between the desired signal and IUI signal as in-phase. We derive the optimal phase set to be pre-rotated for maximizing the peak signal, and design the PATR waveform by combining the modified TR and the derived optimal phase set. We prove the superior performance of the proposed PATR compared to the existing schemes in the multi-user WPT systems with the non-linear EH model by simulation. Moreover, we show that the gain for the harvested energy of the proposed PATR increases as the number of transmit antennas and the number of ERs increase.

Robust Secure Energy Efficiency Optimization in the MIMO Wiretap Channel with Energy Harvesting

This work considers a secure multiple‐input multiple‐output (MIMO) channel where the energy receiver (ER) is a potential eavesdropper (Eve). Specifically, we aim to maximize the secrecy energy efficiency (SEE) via jointly designing the transmit precoding matrix and the artificial noise (AN) covariance at the base station (BS), as well as the power splitting (PS) ratio at the desired receiver (DR), subject to the constraints of the transmit power budget and harvested energy threshold. To handle the formulated highly nonconvex fractional problem, we apply the successive convex approximation (SCA) method to transform the objective and constraint into a tractable form. Then, a penalty‐based iterative algorithm is proposed. Finally, simulation results validate the performance of the proposed design.

Optimal SWIPT in RIS-Aided MIMO Networks

The use of simultaneous wireless information and power transfer (SWIPT) is a key enabler of achieving convenience and prolonging the energy supply lifetime of wireless networks. To address the low efficiencies of far-field power transfer, a reconfigurable intelligent surface (RIS) is adopted to enhance the energy harvesting (EH) performance, which can construct a favorable wireless propagation environment. In this paper, we consider an RIS-assisted SWIPT system with wireless transfer from the access point (AP) to multiple-antenna receivers, which include information receivers (IRs) and energy receivers (ERs). First, we formulate the problem of maximizing the minimum rates of the IRs as a nonconvex constrained optimization problem. For ideal and nonideal channels, we propose two different solutions. Second, we simplify the objective function and decompose the problem into several subproblems by using sorting and iterative optimization algorithms. Moreover, under optimal boundary and Karush-Kuhn-Tucker (KKT) conditions, we successfully solve this problem. The simulation results illustrate a promising approach for wireless communication by comparing ideal RIS and unsatisfactory situations with no RIS cases under various conditions.

Beamforming Optimization for Intelligent Reflecting Surface-Aided SWIPT IoT Networks Relying on Discrete Phase Shifts

Intelligent reflecting surface (IRS) is capable of constructing the favorable wireless propagation environment by leveraging massive low-cost reconfigurable reflect array elements. In this article, we investigate the IRS-aided multiple-input-multiple-output (MIMO) simultaneous wireless information and power transfer (SWIPT) for Internet-of-Things (IoT) networks, where the active base station (BS) transmits beamforming and the passive IRS reflection coefficients are jointly optimized for maximizing the minimum signal-to-interference-plus-noise ratio (SINR) among all information decoders (IDs), while maintaining the minimum total harvested energy at all energy receivers (ERs). Moreover, the IRS with practical discrete phase shifts is considered, and thereby the max-min SINR problem becomes an NP-hard combinatorial optimization problem with a strong coupling among optimization variables. To explore the insights and generality of this max-min design, both the single-ID single-ER (SISE) scenario and the multiple-IDs multiple-ERs (MIME) scenario are studied. In the SISE scenario, the classical combinatorial optimization techniques, namely, the special ordered set of type 1 (SOS1) and the reformulation-linearization (RL) technique, are applied to overcome the difficulty of this max-min design imposed by discrete optimization variables. Then, the optimal branch-and-bound algorithm and suboptimal alternating optimization algorithm are, respectively, proposed. We further extend the idea of alternating optimization to the MIME scenario. Moreover, to reduce the iteration complexity, a two-stage scheme is considered aiming to separately optimize the BS transmit beamforming and the IRS reflection coefficients. Finally, numerical simulations demonstrate the superior performance of the proposed algorithms over the benchmarks in both the two scenarios.

Joint 3D placement and multi-beam design for UAV-assisted wireless power transfer networks

This paper investigates an unmanned aerial vehicle (UAV)-enabled wireless power transfer (WPT) system, where a UAV acts as the energy transmitter (ET) to deliver radio frequency (RF) energy to a set of energy receivers (ERs). Our aim is to maximize the total harvested energy at all ERs by jointly optimizing the three-dimensional (3D) position of the UAV and beam pattern. However, the optimization problem which takes into account the coverage radius of the UAV and beam scanning range, is formulated as a non-convex problem and hence is difficult to solve. To address this problem, we propose a low-complexity iterative algorithm that decomposes the original problem into three sub-problems and solves the 2D position of the UAV, flight altitude and beam pattern in an iterative manner. In particular, we first apply the exhaustive search algorithm to find the global optimal 2D position of the UAV. Subsequently, we can obtain the optimal UAV’s flight altitude via monotonicity theory. Finally, by applying the Butler Matrix feed network, we propose a multi-beam generation scheme to optimize the beam patterns. Numerical results validate that the theoretical findings and demonstrate that significant performance gain in terms of energy harvesting of all ERs can be achieved by the proposed algorithm in UAV-assisted WPT networks.

Design of Ambient Backscatter Training for Wireless Power Transfer

Wireless power transfer (WPT) using energy beamforming is a promising solution for low power Internet of Things (IoT) devices. In this work, we consider WPT from an energy transmitter (ET) employing retrodirective WPT using a large phased antenna array to an energy receiver (ER) capable of ambient backscatter. The advantage of retrodirective WPT is that no explicit channel estimation is needed at the ET and the use of ambient backscattering eliminates the need for active transmission at the ER. We propose a training sequence design, i.e., pattern of varying the reflection coefficient at the ER, to eliminate the direct-link interference from the ambient source. We show that when the ambient symbol duration is known, the ambient interference is fully cancelled by the proposed design. We analytically model the system and find the average harvested power at the ER considering Nakagami-m fading channels and non-linear energy harvesting model. Our results clearly show that the proposed solution is robust to a small timing offset mismatch at the correlator. When interference from undesired neighbouring sources in the ambient environment is not significant, the ER can successfully harvest tens to hundreds of μW of power, which is an important improvement for low-power IoT devices.

Time-Division Energy Beamforming for Multiuser Wireless Power Transfer With Non-Linear Energy Harvesting

Energy beamforming has emerged as a promising technique for enhancing the energy transfer efficiency of radio-frequency (RF) enabled wireless power transfer (WPT). However, the performance of conventional energy beamforming may seriously degrade due to the non-linear RF to direct current (DC) conversion at energy receivers (ERs). To tackle this issue, this letter proposes a new time-division energy beamforming scheme, in which different energy beamforming matrices (of high ranks in general) are time shared to exploit the “convex-concave” shape of the RF-DC power relation at ERs. In particular, we maximize the minimum harvested DC energy among all ERs, by jointly optimizing the energy beamforming matrices and the corresponding time allocation subject to a given charging time duration (e.g., a second). To solve the formulated non-convex min-DC-energy maximization problem, we propose an efficient solution by using the techniques of alternating optimization and successive convex approximation (SCA). Numerical results show that the proposed time-division energy beamforming design indeed outperforms the conventional multi-beam and time-division-multiple-access (TDMA)-based energy transmissions.

Efficient, Fair, and QoS-Aware Policies for Wirelessly Powered Communication Networks

In this paper, we propose efficient wireless power transfer (WPT) policies for various practical scenarios in wirelessly powered communication networks (WPCNs). First, we consider WPT from an energy access point (E-AP) to multiple energy receivers (E-Rs). We formulate the problem of maximizing the total average received power of the E-Rs subject to power constraints of the E-AP, which is a non-convex stochastic optimization problem. Using eigenvalue decomposition techniques, we derive a closed-form expression for the optimal policy, which requires the distribution of the channel state information (CSI) in the network. We then propose a near-optimal policy that does not require this knowledge and prove that its optimality gap can be decreased at the cost of increment in its convergence time. Next, we consider fairness among the E-Rs and propose a quality of service (QoS) aware fair policy that provides fairness and guarantees the required QoS of each E-R. Finally, we study a WPCN where the E-Rs utilize their received energy to transmit information to the E-AP. We maximize a generic fair network utility under the E-Rs’ QoS constraints and the E-AP’s power constraints. Numerical results show a significant improvement of $O(\log {N})$ in the total throughput compared to the state-of-the-art baselines.

Robust Secure Beamforming for Wireless Powered Cognitive Satellite-Terrestrial Networks

This article addresses the security problem for wireless powered cognitive satellite-terrestrial network, where a multibeam satellite sub-network shares the portion of millimeter wave bands with multiple cellular networks, each consisting of a base station, several mobile users (MUs) and energy receivers (ERs). Considering that the ERs are potential eavesdroppers of the MUs, and only imperfect knowledge of the angles of departure for the wiretap channels is available, we aim at maximizing aggregated rate of the considered network while guaranteeing the signal-to-interference-plus-noise ratio requirements of the MUs, the energy harvesting thresholds and the secrecy constraints at ERs. Since the formulated optimization problem is mathematically intractable, we exploit a discretization method and the Taylor expansion method to transform the non-convex objective and constraints into convex ones, and then propose an iterative beamforming (BF) algorithm to solve the problem. Furthermore, we present a combined multibeam scheme to obtain suboptimal BF weight vectors with low computational burden. Finally, simulation results reveal that the proposed BF schemes can efficiently improve the aggregated rate with fast convergence compared to the benchmark schemes.

Intelligent Reflecting Surface Aided MIMO Broadcasting for Simultaneous Wireless Information and Power Transfer

An intelligent reflecting surface (IRS) is invoked for enhancing the energy harvesting performance of a simultaneous wireless information and power transfer (SWIPT) aided system. Specifically, an IRS-assisted SWIPT system is considered, where a multi-antenna aided base station (BS) communicates with several multi-antenna assisted information receivers (IRs), while guaranteeing the energy harvesting requirement of the energy receivers (ERs). To maximize the weighted sum rate (WSR) of IRs, the transmit precoding (TPC) matrices of the BS and passive phase shift matrix of the IRS should be jointly optimized. To tackle this challenging optimization problem, we first adopt the classic block coordinate descent (BCD) algorithm for decoupling the original optimization problem into several subproblems and alternately optimize the TPC matrices and the phase shift matrix. For each subproblem, we provide a low-complexity iterative algorithm, which is guaranteed to converge to the Karush-Kuhn-Tucker (KKT) point of each subproblem. The BCD algorithm is rigorously proved to converge to the KKT point of the original problem. We also conceive a feasibility checking method to study its feasibility. Our extensive simulation results confirm that employing IRSs in SWIPT beneficially enhances the system performance and the proposed BCD algorithm converges rapidly, which is appealing for practical applications.

Joint 3D Trajectory Design and Time Allocation for UAV-Enabled Wireless Power Transfer Networks

This paper considers a rotary-wing unmanned aerial vehicle (UAV)-enabled wireless power transfer system, where a UAV is dispatched as an energy transmitter (ET), transferring radio frequency (RF) signals to a set of energy receivers (ERs) periodically. We aim to maximize the energy harvested at all ERs by jointly optimizing the UAV's three-dimensional (3D) placement, beam pattern and charging time. However, the considered optimization problem taking into account the drone flight altitude and the wireless coverage performance is formulated as a non-convex problem. To tackle this problem, we propose a low-complexity iterative algorithm to decompose the original problem into four sub-problems in order to optimize the variables sequentially. In particular, we first use the sequential unconstrained convex minimization based algorithm to find the globally optimal UAV two-dimensional (2D) position. Subsequently, we can directly obtain the optimal UAV altitude as the objective function of problem is monotonic decreasing with respect to UAV altitude. Then, we propose the multiobjective evolutionary algorithm based on decomposition (MOEA/D) based algorithm to control the phase of antenna array elements, in order to achieve high steering performance of multi-beams. Finally, with the above solved variables, the original problem is reformulated as a single-variable optimization problem where charging time is the optimization variable, and can be solved using the standard convex optimization techniques. Furthermore, we use the branch and bound method to design the UAV trajectory which can be constructed as traveling salesman problem (TSP) to minimize flight distance. Numerical results validate the theoretical findings and demonstrate that significant performance gain in terms of sum received power of ERs can be achieved by the proposed algorithm in UAV-enabled wireless power transfer networks.

Intelligent Reflect Surface Aided Secure Transmission in MIMO Channel With SWIPT

This paper considers a multiple-input multiple-output (MIMO) secure simultaneous wireless information and power transfer (SWIPT) system aided by the intelligent reflecting surface (IRS), where the transmitter (T), the information receiver (IR) and energy receiver (ER) are all equipped with multiple antennas. Assuming that the ER may be potential eavesdropper (Eve), we aim to maximize the secrecy rate via jointly designing the precoding matrix, the artificial noise (AN) covariance, and the phase shift matrix, subject to the harvested energy and unit modulus reflect coefficient (RC) constraints. The formulated secrecy rate maximization (SRM) problem is non-convex with multiple coupled variables. To tackle it, an inexact block coordinate descent (IBCD) method is proposed, where the unit modulus constraint is handled by the penalty majorization-minimization (MM) and the complex circle manifold (CCM) methods. Finally, simulation results validate the effectiveness of IRS in enhancing the security.

Multi-Objective Optimization for Full-Duplex SWIPT Systems

This paper studies a multi-objective optimization (MOO) problem in full-duplex (FD) networks with simultaneous wireless information and power transfer (SWIPT). In the considered networks, an FD base station (BS) communicates with multiple half-duplex (HD) uplink (UL) and downlink (DL) users simultaneously. The energy receivers (ERs) harvest energy from the ambient radio frequency (RF) signals and may act as potential eavesdroppers. Specifically, there exists two conflicting yet important system design objectives, i.e., secrecy energy efficiency (SEE) maximization and energy harvesting efficiency (EHE) maximization. An MOO design based on the weighted Tchebycheff approach is proposed to investigate the tradeoff between these two design objectives. The proposed design takes into account the quality-of-service (QoS) guarantees of secrecy rate and energy harvesting (EH) under the imperfect channel state information (CSI) of ERs. The formulated MOO problem is solved with a two-layer optimization algorithm, where the modified Dinkelbach method is applied to deal with the generalized fractional programming (FP) in the outer layer problem and semidefinite relaxation (SDR), successive convex approximation (SCA) as well as S-procedure methods are applied to transfer the inner layer problem into a convex iterative program. Moreover, we propose a suboptimal solution to the formulated problem and analyze the computational complexities. Finally, numerical results are provided to demonstrate the effectiveness of the proposed algorithms and reveal a tradeoff region between SEE and EHE.

Optimal energy beamforming under per‐antenna power constraint

AbstractEnergy beamforming (EB) is a key technique to enhance the efficiency of wireless power transfer. In this paper, we study the optimal EB under per‐antenna power constraint (PAC), which is more practical than the conventional sum‐power constraint. We consider a multiantenna energy transmitter with PAC that broadcasts wireless energy to multiple energy receivers (ER)s. We consider sum‐energy maximization problem with PAC and provide the optimal solution structure for the general case. This optimal structure implies that sending one energy beam is optimal under PAC, which means that the rank of transmit covariance matrix is one similar to sum‐power constraint. We also derive closed‐form solutions for two special cases and propose two suboptimal solutions for general case, which performs very close to optimal beamforming.

Outage Constrained Robust Secrecy Energy Efficiency Maximization for EH Cognitive Radio Networks

In this letter, we investigate the outage-constrained robust secure design in a multiple-input single-output (MISO) energy harvesting (EH) cognitive radio network (CRN), where the malicious energy receivers (ERs) may wiretap the desired information and hence can be treated as potential eavesdroppers (Eves). In particular, considering a non-linear energy harvesting (EH) model, our objective is to design the transmit covariance matrix to maximize the secrecy energy efficiency (SEE) under the given outage probability and transmit power constraints, while satisfying the EH and quality-of-service (QoS) requirements. To tackle the original non-convex problem, we resort to semi-definite relaxation (SDR) and Bernstein-type inequality (BTI)-based approximations to reformulate it into a tractable form. Then, the original problem becomes decomposable and can be efficiently solved by handling a two-stage optimization problem. At last, numerical results are provided to demonstrate the effectiveness and superior performance of the proposed design in comparison with the existing schemes.