Optimal Time Allocation Research Articles

Completion time minimization for multi-antenna UAV-enabled data collection in uncorrelated Rician fading

In 5G, the unmanned aerial vehicle (UAV) is regarded as an essential way to support energy-saving, reliable, and low-cost data collection in wireless sensor networks. However, UAV-based data collection inevitably suffers from more significant data collection delays due to the UAV movement time in large application scenarios. In this paper, we consider a UAV-enabled wireless sensor network under the uncorrelated Rician fading channel, where a multi-antenna UAV is dispatched to collect data from ground sensor nodes (SNs). The objective is to minimize the mission completion time, including UAV flight and data collection time, by jointly optimizing UAV trajectory, UAV-SN transmission scheduling, and trajectory-based time allocation under the constraints of UAV speed, outage probability, data size, and transmission power. To solve this nonconvex problem, we decompose it into two subproblems: 1) trajectory optimization and 2) UAV-SN transmission scheduling and trajectory-based time allocation optimization. In the trajectory optimization, we first rewrite the outage probability constraint into the communication distance constraint and propose a Spiral-based method to find the shortest trajectory covering all SNs. Then, we propose a scheduling initialization algorithm and employ alternating optimization to solve the UAV-SN transmission scheduling and trajectory-based time allocation optimization. Finally, numerical results show that the proposed algorithm outperforms the benchmark and typical algorithms in terms of the mission completion time through a large number of experiments.

Energy-aware scheduling for dependent tasks in heterogeneous multiprocessor systems

Heterogeneous multiprocessor platform has been widely adopted as an effective approach to providing strong calculation capability while keeping complexity and energy consumption under control in large-scale systems. Although this platform is able to achieve efficient cost reduction and flexibility enhancement in the design and development process of real-time applications, it brings a serious and complex multi-task scheduling problem, especially for dependent tasks with energy consumption constraints. All tasks should be scheduled according to appropriate strategies such that their dependence requirements and energy consumption limitations would be satisfied even in the worst-case situations. In this work, we focus on the energy-aware scheduling problem of dependent tasks in heterogeneous multiprocessor systems. First, we model the dependent tasks and heterogeneous processors, and formulate the energy-aware scheduling problem as a constrained optimization one with an objective of minimizing the schedule length of tasks. Then, by adopting an efficient task prioritization strategy and a weight-based energy distribution strategy, we propose a list-based energy-aware scheduling algorithm to seek an approximate optimal start time and processor allocation for each task, guaranteeing that all tasks would be executed efficiently while meeting the dependence and energy requirements. Experiments with randomly generated tasks are conducted to evaluate the performances of the proposed approach in terms of schedule length, optimal solution ratio, and execution time.

Time Allocation and Optimization in UAV-Enabled Wireless Powered Communication Networks

Unmanned aerial vehicles (UAVs) have attracted great research attention due to their flexibility. In this paper, the use of UAVs in wireless sensor networks as an energy transmitter and a data collector is investigated. The UAV is first charged from a charging station, such as a base station (BS), before it flies to the sensors for data collection. Upon arrival, the UAV first charges the sensors via wireless power transfer (WPT) in the downlink, followed by data transmission from the sensors in the uplink. After that, the UAV flies back to the BS to offload data to the BS. We aim to maximize the amount of data offloaded to the BS by allocating optimal time slots to different tasks in this process, given a fixed total time. The maximization is solved in two steps as two convex optimization problems. In the first step, the time allocation between WPT to sensors and data collection from sensors is optimized. In the second step, the time allocation of BS charging, the total time in the first step, and BS data offloading is optimized. Unlike the previous works, our study takes into account the charging process from the BS to the UAV, the propulsion consumption at the UAV and the data offloading process to the BS. Both distance-dependent path loss and small-scale fading are considered. Numerical results show that the optimal time allocation can maximize the amount of data at the BS without wasting any time and energy.

Does Leisure Contribute to the Improvement of Individual Job Performance? A Field Tracking Study Based on the Chinese Manufacturing Industry

Theories of work–life balance (WLB) examine the dynamics of the relationship between work and life, but no universally accepted conclusion has yet been achieved. This study examines the effect of leisure time on job performance using first-hand data obtained in a field study in the Chinese manufacturing industry. The results reveal that the relationship between leisure participation and individual job performance presents an inverted U-shaped nonlinear relationship. Endogenous testing and robustness testing also demonstrated the reliability of the findings. In this study, we identified an “opportunity window” which promotes the best individual job performance, with an average daily leisure time threshold of 4.7 h. Our analysis of the underlying mechanism showed that leisure participation has an impact on job performance through physical health and happiness. This study advances the literature on the leisure economy and provides insights into work–life balance and optimal leisure time allocation on a daily basis.

Toward Hybrid Backscatter-Aided Wireless-Powered Internet of Things Networks: Cooperation and Coexistence Scenarios

The emerging hybrid backscatter and energy harvesting devices have been regarded as a promising scheme for green Internet-of-Things (IoT). In the interwoven primary and secondary wireless powered IoT networks, we develop a novel hybrid scheme that integrates the backscatter communication and the harvest-then-transmit (HTT) protocol. In order to mitigate the adverse effect on the primary user (PU), the secondary users (SUs) are classified into ‘Cooperation Scenario’ and ‘Coexistence Scenario’ based on their different levels of interference to the PU. In ‘Cooperation Scenario’, we propose a cooperation protocol where the SUs operate in the backscatter mode so as to relay information to the PU. Therefore, the SUs are rewarded for harvesting energy and obtaining the spectrum access time from the primary system. Also, in ‘Coexistence Scenario’, a coexistence strategy is developed to enable the SUs to operate in either ambient backscatter or energy harvesting mode during the channel busy time. When the primary channel becomes idle, the SUs are capable of active transmission by using the harvested energy. For each scenario, we investigate the sum-throughput maximization problem of the secondary system. Employing the Lambert W function and the block coordinate descent method, the optimal time allocation can be obtained via the Lagrangian dual method. Numerical results validate that the proposed hybrid backscatter and HTT scheme improves the performance of the secondary system evidently compared with benchmark methods.

Robust Beamforming Design and Time Allocation for IRS-Assisted Wireless Powered Communication Networks

In this paper, a novel intelligent reflecting surface (IRS)-assisted wireless powered communication network (WPCN) architecture is proposed for power-constrained Internet-of-Things (IoT) smart devices, where IRS is exploited to improve the performance of WPCN under imperfect channel state information (CSI). We formulate a hybrid access point (HAP) transmit energy minimization problem by jointly optimizing time allocation, HAP energy beamforming, receiving beamforming, user transmit power allocation, IRS energy reflection coefficient and information reflection coefficient under the imperfect CSI and non-linear energy harvesting model. On account of the high coupling of optimization variables, the formulated problem is a non-convex optimization problem that is difficult to solve directly. To address the above-mentioned challenging problem, alternating optimization (AO) technique is applied to decouple the optimization variables to solve the problem. Specifically, through AO, time allocation, HAP energy beamforming, receiving beamforming, user transmit power allocation, IRS energy reflection coefficient and information reflection coefficient are divided into three sub-problems to be solved alternately. The difference-of-convex (DC) programming is used to solve the non-convex rank-one constraint in solving IRS energy reflection coefficient and information reflection coefficient. Numerical simulations verify the superiority of the proposed optimization algorithm in decreasing HAP transmit energy compared with other benchmark schemes.

UAV-Assisted Cooperative & Cognitive NOMA: Deployment, Clustering, and Resource Allocation

Cooperative and cognitive non-orthogonal multiple access (CCR-NOMA) has been recognized as a promising technique to overcome issues of spectrum scarcity and support massive connectivity envisioned in next-generation wireless networks. In this paper, we investigate the deployment of an unmanned aerial vehicle (UAV) as a relay that fairly serves a large number of secondary users in a hot-spot region. The UAV deployment algorithm must jointly account for user clustering, channel assignment, and resource allocation sub-problems. We propose a solution methodology that obtains user clustering and channel assignment based on the optimal resource allocations for a given UAV location. To this end, we derive closed-form optimal power and time allocations and show it delivers optimal max-min fair throughput by consuming less energy and time than geometric programming. Based on optimal resource allocation, the optimal coverage probability is also provided in closed-form, which takes channel estimation errors, hardware impairments, and primary network interference into account. The optimal coverage probabilities are used by the proposed max-min fair user clustering and channel assignment approaches. The results show that the proposed method achieves 100% accuracy in more than five orders of magnitude less time than the optimal benchmark.

Harvest-on-Sky: An AoI-Driven UAV-Assisted Wireless Communication System

The 5G cellular network provides a sufficient data rate to support the ever growing number of devices that will be connected to the Internet. To enable Internet of Things (IoT) applications in remote locations, it is very crucial to increase the coverage of the cellular networks. This article proposes a wireless communication system that exploits a full-duplex enabled unmanned aerial vehicle (FD-UAV) integrated into a communication network as a mobile relay to expand network coverage. With the deployment of IoT devices, a large volume of data is introduced into the network, causing a delay in data delivery due to scarcity of resources. Real-time information updates play an important role in modern IoT applications including connected vehicles in intelligent transportation systems, digital healthcare, real-time tracking, and so on. Decision making based on the latest fresh information is critically important for these applications. We quantify the freshness of data in IoT applications using a new performance metric, the age of information (AoI). This work proposes a new mathematical model to estimate the average AoI (AAoI) in the FD-UAV assisted cooperative wireless communication system. Here, sensors located in a transport infrastructure harvest energy from radio frequency (RF) signals transmitted by the FD-UAV via a wireless power transmission RF energy harvesting (EH) technique. Then sensors consume this energy to transmit their sensed real-time observations to the access point with the aid of FD-UAV. A closed-form expression for the AAoI is derived as a function of time allocated for energy harvesting. The optimal time allocation for EH that minimizes the AAoI is identified together with the effect of self-interference experienced by the UAV.

Energy provision minimization of energy-harvesting cognitive radio networks with minimal throughput demands

The newly emerging energy-harvesting cognitive radio networks (EH-CRNs) have drawn significant research interests in the fields of spectrum reuse and lifetime prolongation. This paper focuses on the EH-CRN with a pair of primary users (PUs) and multiple pairs of secondary users (SUs), and aims to minimize the primary transmitter (PT)’s energy provision (EP) while satisfying the network’s or users’ minimal throughput demands. Specifically, under the network’s minimal throughput demand, we first formulate the EP minimization (EPM) problems as non-linear optimization problems, then transform them into convex problems, and finally propose an algorithm that jointly uses the golden-section search and bisection search method to obtain the optimal time allocation of PT’s energy transfer and each SU’s packet transmission. Under the users’ minimal throughput demands, we jointly use the golden-section search, bisection search methods, and the dual sub-gradient algorithm to derive the optimal time allocation of PUs and SUs. Simulation results demonstrate the effectiveness of our algorithms from the perspective of reducing EP.

Spatial-temporal distribution of carbon, nitrogen and phosphorus concentrations and eutrophication evaluation of mountainous small river in a cascaded damming

梯级筑坝对河流水环境演化的影响是国内外关注的热点.小型山区河流高密度梯级开发对水体生源要素的空间格局以及水环境演化的累积影响特征尚不清楚.以重庆市五布河为研究对象，对流域内8个“河流-水库-下泄水”交替系统中表层水体理化因子及碳（C）、氮（N）、磷（P）形态组成进行季节性监测，探讨了梯级筑坝对小型河流生源要素空间格局及水体富营养化风险影响的累积特征及驱动机制.结果表明：梯级水电开发对五布河流域水生生境和生源要素空间分配的影响具有潜在的累积效应，各库区水体碳氮磷浓度均呈逐级增加的空间规律；水库段的有机碳及不同形态的氮、磷浓度均高于入库河流，因此水体养分浓度呈现出河段尺度（即单个河流-水库-下泄水系统）和流域尺度（即上游至下游）耦合的空间变异模式.上游水库中溶解性氮、磷的再释放及下泄输移能够补给下游库区，加之下游水库泥沙对氮、磷的吸附-沉积作用的减弱，导致水体氮、磷总量及溶解性氮、磷的占比沿程增加，呈现梯级筑坝对水环境演化的累积影响.梯级筑坝影响下河流碳氮磷总量的相关性减弱，而溶解性养分间的相关性增强，形成了特殊的养分协同演化；水库群之间水力滞留时间的差异与水体碳氮磷浓度具有较好的线性关系，是影响流域养分分配的关键因素.五布河流域水体均为高富营养化风险，由于梯级筑坝下水体溶解性养分的逐级增加，下游水库水华风险更大；水力滞留时间与水体富营养化指数及叶绿素a浓度呈显著正向关，结合氮磷比特征的分析，本研究认为外源磷输入控制及水力滞留时间的调节是五布河梯级水库富营养化防控的有效途径.;Rivers, as the channel connecting terrestrial and marine ecosystems and transporting a large amount of nutrients to ocean, are important for maintaining the global material cycle. The construction of cascade dams leads to river fragmentation and changes the distribution of carbon, nitrogen and phosphorus in the water. At present, a lot of studies have been conducted on the ecological effects of cascade development in large rivers, but few studies focus on small mountainous rivers. The spatial-temporal patterns and controls of the distribution of carbon, nitrogen and phosphorus from cascade river-reservoir systems in the small mountainous rivers remain unclear. In this study, we investigated the spatial-temporal variations of carbon(C), nitrogen(N) and phosphorus(P) concentrations along a cascade damming river (Wubu River) in Southwest China. The results showed that carbon, nitrogen and phosphorus showed an obvious cumulative effect, that was, the contents of C, N and P gradually increased from the first reservoir upstream to the last reservoir downstream underlying cascade dams. And, the organic carbon, as well as nitrogen and phosphorus in the reservoir section, were higher than in those inflow rivers. Thus, different forms of carbon, nitrogen, and phosphorus concentration in the reach (river-reservoir-release water system) scale and river basin scale (the upstream to downstream) displayed the double coupling variation pattern. Primary production and plankton proliferation were the main mechanisms of organic carbon accumulation in the river. At the same time, cascade reservoirs may form a series of nitrogen and phosphorus storage tanks and reactors to promote the release and transport of dissolved nitrogen and phosphorus. The re-release and transport of dissolved N and P in the upstream reservoir can replenish the downstream reservoir, increasing the content of N and P in the downstream reservoir and the proportion of dissolved N and P, thus leading to the cumulative effect of water deterioration. The decrease in the adsorption-deposition effect of sediment on nitrogen and phosphorus nutrients in downstream reservoirs also leads to the accumulation of soluble nitrogen and phosphorus concentrations. The correlation of C, N and P in the river was weakened, but there was a significant relationship between dissolved nutrients, forming a special nutrient co-evolution. Furthermore, the hydraulic retention time of the reservoir groups had a good linear relationship with water C, N and P contents, which was the key factor affecting nutrient allocation in the watershed. Seasonal variations of total organic carbon and dissolved organic carbon were highest in spring and lowest in winter in Wubu River Basin. Total nitrogen and nitrate nitrogen in the dry season (winter and spring) were significantly higher than those in the wet season (summer and autumn), and other nutrient forms had no obvious seasonal pattern. Rainfall dilution, algal reproduction, microbial decomposition and re-release were the main processes leading to the seasonal variation of nutrients. The eutrophication risk also presented an increasing trend from upstream to downstream because of the dam. There was also a good linear relationship between hydraulic retention time and eutrophication risk. Combining the analysis of N:P ratio characteristics, it was suggested that exogenous P control and optimal allocation of hydraulic retention time are effective approaches for eutrophication control in the Wubu River Basin.

Secrecy Performance Maximization for Underlay CR Networks with an Energy Harvesting Jammer.

This paper investigates the secrecy communication in an underlay cognitive radio (CR) networks with one primary user (PU) as well as multiple PUs, where the radio frequency (RF) energy-harvesting secondary user (SU) transmits the confidential information to the destination in the presence of a potential eavesdropper. We introduce a RF energy-harvesting secondary jammer (SJ) to secure the SU transmissions. The system works in time slots, where each time slot is divided into the energy transfer (ET) phase and the information transfer (IT) phase. In ET phase, the SU and SJ capture energy from the PU transmissions; in the IT phase, the SU uses the harvested energy to transmit information to the destination without causing the harmful interference to the PU transmissions, while the SJ utilizes the captured energy to generate jamming signals to the eavesdropper to secure the SU transmissions. We aim to maximize the secrecy rate for SU transmissionsby jointly optimizing the time allocation between ET phase and IT phase and the transmit power allocation at the SU and SJ. We first formulate the secrecy rate maximization as non-convex optimization problems. Then, we propose efficient nested form algorithms for the non-convex problems. In the outer layer, we obtain the optimal time allocation by the one dimension search method. In the inner layer, we obtain the optimal transmit power allocation by the DC programming, where the Lagrange duality method is employed to solve the convex approximation problem. Simulation results verify that the proposed schemes essentially improve the secrecy rate of the secondary network as compared to the benchmark schemes.

Low-Complexity Algorithm for Outage Optimal Resource Allocation in Energy Harvesting-Based UAV Identification Networks

We study an unmanned aerial vehicle (UAV) identification network equipped with an energy harvesting (EH) technique. In the network, the UAVs harvest energy through radio frequency (RF) signals transmitted from ground control stations (GCSs) and then transmit their identification information to the ground receiver station (GRS). Specifically, we first derive a closed-form expression of the outage probability to evaluate the network performance. Then we obtain the closed-form expression of the optimal time allocation when the bandwidth is equally allocated to the UAVs. We also propose a fast-converging algorithm for time and the bandwidth allocation, which is necessary for the UAV environment with high mobility, to optimize the outage performance of EH-based UAV identification network. Simulation results show that the proposed algorithm outperforms the conventional bisection algorithm and achieves near-optimal performance.

Time allocation of a three-bed adsorption chiller using an artificial neural network

3-bed adsorption cooling systems have the advantage of maintaining a uniform chilled water temperature. Because the number of parameters in a 3-bed system is very large, using artificial neural networks (ANN) is often suggested as an alternative to conducting experiments in many recent studies. We systematically determined the optimal time allocation for a 3-bed, 2-evaporation adsorption cooling system, using ANN with five variables, i.e., adsorption/desorption time ratio (fad), high/low evaporator time ratio (fp), cycle time (τ), and the time lag between each adsorption bed (δ2, δ3). Each case was methodically modeled using a process that our research team had previously developed and verified. When the coefficient of performance (COP) and specific cooling power (SCP) estimated by ANN were compared with the actual results, errors were within ±4%. Finally, the best strategy for each performance indicator, i.e., COP, SCP, and standard deviation of chilled-out temperature, was proposed for the 5 operating parameters of fad, fp, τ, δ2, and δ3. The cycle time was found to have 42.9% relative importance for the COP, and 33.1% relative importance for the SCP, but the most influential factor to the SCP was the high/low pressure evaporator time ratio with a relative importance of 33.3%.

Robust Energy-Efficient Transmission for Wireless-Powered D2D Communication Networks

This paper considers optimal joint time, frequency, and power allocation for energy-efficient device-to-device (D2D) communications in an overlay cellular network, where multiple D2D transmitters communicate with their corresponding D2D receivers while utilizing the energy harvested from a cellular base station (BS). Due to channel estimation error and feedback delays, the channel state information (CSI) available at the transmitters is usually imperfect, which can significantly deteriorate the energy efficiency (EE) of the considered system. To mitigate the impact of imperfect CSI, we formulate a non-convex robust optimization problem for the maximization of the EE (in bits/Joule) of the system while ensuring quality of service (QoS) requirements on the minimum data rata and the minimum amount of harvested energy for cellular and D2D users, respectively. We reveal that the optimal energy-efficient D2D transmission should exhaust all the harvested energy of each D2D transmitter. Exploiting this fact, we propose an efficient iterative algorithm for obtaining the optimal solution. To strike a balance between performance and computational complexity, we further propose a low-complexity suboptimal algorithm. Simulation results show that compared with several baseline schemes, both the proposed optimal and suboptimal algorithms can significantly improve the EE of wireless-powered D2D communications under imperfect CSI. Moreover, the proposed suboptimal algorithm is close-to-optimal when the number of cellular users are small or the channel estimation error is large.

Optimal time allocation for throughput maximization in backscatter assisted wireless powered communication networks

Optimal time allocation for throughput maximization in backscatter assisted wireless powered communication networks

Throughput optimization of multi-hop and multi-path cooperation in WPSNs with hardware noises

This paper proposes a novel multi-path and multi-hop wireless powered sensor network in case of hardware impairment, constituting an energy node, one source node, single sink node, and a series of distributed relay sensor nodes, where the energy node transmits wireless energy to all terminals in the first stage, and the relay sensor nodes relay the information of the source node to the sink node in the second stage. There exists M available paths between the source node and sink node, one of which is chosen for serving source-sink communication. To enhance the minimum achievable data rate, we propose a multi-hop communication protocol based on time-division-multiple-access and an optimal throughput path algorithm. We formulate the time allocation optimization problem about energy and information transmission of the proposed multi-hop cooperation, and confirm through abundant simulation experiments that the proposed scheme can availably improve user unfairness and spectral efficiency, and thus enhance its throughput performance.

Joint Uplink-and-Downlink Optimization of 3-D UAV Swarm Deployment for Wireless-Powered IoT Networks

This article investigates a full-duplex orthogonal-frequency-division multiple access (OFDMA)-based multiple unmanned-aerial-vehicles (UAVs)-enabled wireless-powered Internet-of-Things (IoT) networks. In this paper, a swarm of UAVs is first deployed in 3-D to simultaneously charge all devices, i.e., a downlink (DL) charging period, and then flies to new locations within this area to collect information from scheduled devices in several epochs via OFDMA due to potential limited number of channels available in IoT during an uplink (UL) communication period. To maximize the UL throughput of IoT devices, we jointly optimize the UL-and-DL 3-D deployment of the UAV swarm, including the device-UAV association, the scheduling order, and the UL-DL time allocation. In particular, the DL energy harvesting threshold of devices and the UL signal decoding threshold of UAVs are taken into consideration when studying the problem. Besides, both line-of-sight and non-line-of-sight channel models are studied depending on the position of sensors and UAVs. The influence of potential limited number of channels in IoT is also considered. Guidelines on the 3-D placement of UAVs in the DL charging and the UL communications are also given. Finally, simulation results show that the proposed optimal time allocation OFDMA-UAV scheme achieves significant throughput gains compared with conventional schemes.

Efficient Large-Scale Multi-Drone Delivery using Transit Networks

We consider the problem of routing a large fleet of drones to deliver packages simultaneously across broad urban areas. Besides flying directly, drones can use public transit vehicles such as buses and trams as temporary modes of transportation to conserve energy. Adding this capability to our formulation augments effective drone travel range and the space of possible deliveries but also increases problem input size due to the large transit networks. We present a comprehensive algorithmic framework that strives to minimize the maximum time to complete any delivery and addresses the multifaceted computational challenges of our problem through a two-layer approach. First, the upper layer assigns drones to package delivery sequences with an approximately optimal polynomial time allocation algorithm. Then, the lower layer executes the allocation by periodically routing the fleet over the transit network, using efficient, bounded suboptimal multi-agent pathfinding techniques tailored to our setting. We demonstrate the efficiency of our approach on simulations with up to 200 drones, 5000 packages, and transit networks with up to 8000 stops in San Francisco and the Washington DC Metropolitan Area. Our framework computes solutions for most settings within a few seconds on commodity hardware and enables drones to extend their effective range by a factor of nearly four using transit.

Performance Analysis of UAV‐Assisted Wireless Powered Sensor Network over Shadowed κ − μ Fading Channels

In this work, we analyze performances of the unmanned aerial vehicle‐ (UAV‐) assisted wireless powered sensor communication, where sensor transmission ability is supported by the UAV. Harvested energy from the UAV‐broadcasted signal is further used at the sensor nodes for uplink information transmission to the UAV, over assumed shadowed κ − μ fading channels. Here, we observe a general scenario in which due to the flight conditions of the UAV, the channel’s content include the LOS components affected by the shadowing effect, modeled by the general shadowed κ − μ channel model, which can be reduced to other well‐known channel models as its special cases. We derive closed‐form expressions for the outage probability (OP) of such wireless sensor network (WSN) operating in shadowed κ − μ fading environments. Further, we analyze the optimization of time allocation to minimize OP subjected to UAV’s energy constraints. The impact of channel parameters on observed performance measures is analyzed, and obtained results are numerically validated.

Beamforming and Resource Allocation for Charging Power Minimization in Multiuser Wireless-Powered Networks

In this paper, a multi-antenna base station (BS) concurrently serves uplink users with harvested energy in wireless-powered communication networks (WPCNs). We minimize the average power consumption of the BS due to wirelessly charging under the quality-of-service (QoS) requirements for uplink users. Based on this, the downlink/uplink beamforming, downlink/uplink time allocation, and uplink multiuser power control are jointly designed. The non-convex problem is first solved with fixed time allocation and uplink receive beamforming via a semi-definite relaxation (SDR) approach, based on which an iterative algorithm is proposed for updating the optimal time allocation and the receive beamforming. The feasibility condition and the equivalence condition between the original and relaxed problems are analyzed. Simulation results show that the average charging power consumption of the BS is significantly reduced compared with a heuristic scheme that adopts the average user channel gain as energy beamforming in the downlink and exhausts the harvested energy for multiuser power control with zero-forcing (ZF) receive beamforming in the uplink.