Energy Harvesting Communication Systems Research Articles

Joint Sleep and Rate Scheduling With Booting Costs for Energy Harvesting Communication Systems

Joint Sleep and Rate Scheduling With Booting Costs for Energy Harvesting Communication Systems

Resource Allocation Policies for Battery Constrained Energy Harvesting Communication Systems With Co-Channel Interference

This paper studies resource allocation policies for energy harvesting (EH) multi-user multiple input single output (MU- MISO) communication systems. The multi-antenna EH base station (BS) is equipped with a limited-capacity battery. Though employing the multi-antenna at the BS provides the channel diversity, this leads to the co-channel interference which makes the resource allocation problem hard to solve. For this challenging scenario, we first consider off-line policies based on full channel state information (CSI) and energy arrival information (EAI) to obtain the best performance for any feasible resource allocation policies. We propose an iterative algorithm using generalized linear fractional programming to obtain an optimal policy. To achieve a low-complexity sub-optimal policy, we propose another iterative algorithm using the successive convex approximation. Based on the off-line policies, we develop on-line policies in which only statistical CSI and EAI are available. The complexity of the proposed policies is derived. Finally, simulation results evaluate the performance of the proposed approaches and show that the proposed polices outperform the benchmark.

On Optimal Power Control for Energy Harvesting Communications With Lookahead

Consider the problem of power control for an energy harvesting communication system, where the transmitter is equipped with a finite-sized rechargeable battery and is able to look ahead to observe a fixed number of future energy arrivals. An implicit characterization of the maximum average throughput over an additive white Gaussian noise channel and the associated optimal power control policy is provided via the Bellman equation under the assumption that the energy arrival process is stationary and memoryless. A more explicit characterization is obtained for the case of Bernoulli energy arrivals by means of asymptotically tight upper and lower bounds on both the maximum average throughput and the optimal power control policy. Apart from their pivotal role in deriving the desired analytical results, such bounds are highly valuable from a numerical perspective as they can be efficiently computed using convex optimization solvers.

SWIPT-Enabled Multiple Access Channel: Effects of Decoding Cost and Non-Linear EH Model

We studied power splitting-based simultaneous wireless information and power transfer (PS-SWIPT) in multiple access channels (MACs), considering the decoding cost and non-linear energy harvesting (EH) constraints at the receiving nodes to study practical limitations of an EH communication system. Under these restrictions, we formulated and analyzed the achievable rate and maximum departure regions in two well-studied scenarios, i.e., a classical PS-SWIPT MAC and a PS-SWIPT MAC with user cooperation. In the classical PS-SWIPT MAC setting, closed-form expressions for the optimal values of the PS factors are derived for two fundamental decoding schemes: simultaneous decoding and successive interference cancellation. In the PS-SWIPT MAC with user cooperation, the joint optimal power allocation for users as well as the optimal PS factor are derived. This reveals that one decoding scheme outperforms the other in the classical PS-SWIPT MAC, depending on the function type of the decoding cost. Finally, it is shown that the cooperation between users can potentially boost the performance of a PS-SWIPT MAC under decoding cost and non-linear EH constraints. Moreover, effects of the decoding cost functions, non-linear EH model and channel quality between the users are studied, and performance characteristics of the system are discussed.

On the Optimality of the Greedy Policy for Battery Limited Energy Harvesting Communications

Consider a battery limited energy harvesting communication system with online power control. Assuming independent and identically distributed (i.i.d.) energy arrivals and the harvest-store-use architecture, it is shown that the greedy policy achieves the maximum throughput if and only if the battery capacity is below a certain positive threshold that admits a precise characterization. Simple lower and upper bounds on this threshold are established. The asymptotic relationship between the threshold and the mean of the energy arrival process is analyzed for several examples.

Online Power Control and Optimization for Energy Harvesting Communication System Based on State of Charge

In this paper, the online power control problem for energy harvesting wireless communication system with a finite storage capacity battery is addressed, where the channel state and energy harvesting rate are both unknown. A low complexity algorithm based online convex optimization is proposed to guarantee energy availability of energy harvesting node and maximize average long-term throughput. The proposed algorithm restricts maximum transmission power with the information of state of charge, and allocates transmission power based on historical information. In addition, energy availability constraint is given by rigorous theoretical analysis to guarantee the optimization of average long-term throughput. Simulations have been conducted to demonstrate the effectiveness of the algorithm without considering probability distribution of energy arrival or channel coefficients. The proposed algorithm outperforms counterparts in different energy harvested rates.

RF energy modelling using machine learning for energy harvesting communications systems

SummaryMachine learning (ML) theories and methods are mainly based on probability theory and statistics. It is a very powerful tool for data modelling. On the other hand, energy harvesting has been regarded as a viable solution to extending battery lifetime of wireless sensor network. Motivated by these, modelling of the radio frequency (RF) energy available to the wireless nodes is required for efficient operation of wireless networks. In this work, we will use different ML algorithms to model the RF energy data for efficient operation of energy harvesting communication systems. Four ML algorithms are studied and compared in terms of the accuracy for RF energy modelling using the energy data in the band between 1805 and 1880 MHz. The results show that linear regression (LR) has the highest accuracy and the most stable performance, while decision tree is the worst model. Also, in terms of the operation efficiency of the system, LR has the best performance, followed by support vector machine and random forest algorithm.

Battery-Level-Triggered Transmit Power Control for Energy Harvesting Communications

We consider a continuous-time energy harvesting (EH) communication system consisting of an EH transmitter with random lifetime and a receiver. We assume that neither the fading channel state nor the EH state is available to the transmitter and the transmitter can only observe its battery level, based on which it adjusts its transmit power. Specifically, we quantize the battery capacity of the transmitter into a number of levels, and whenever the energy in the battery hits a certain level, the EH transmitter updates its transmit power. Our main objective is to find the optimal battery-level-triggered (BLT) control policy to maximize the expected total throughput of the transmitter in its lifetime. We model the system as an extended two-dimensional stochastic fluid model (2D-SFM), and derive the Laplace-Stieltjes Transform (LST) matrices of the imbedded process on the decision time sequence, based on which, we formulate the power control problem as a Markov decision process (MDP). We obtain the BLT control policy and the maximum expected throughput by solving the 2D-SFM induced MDP. We evaluate the performance of the BLT policy by comparing it with the conventional uniform-in-time control policies, and results show that the proposed BLT power control policy provides significantly higher expected throughput under the same total energy consumption and the same average control frequency.

On maximizing information reliability in wireless powered cooperative networks

Unpredictable nature of fading channels and difficulty in tracking channel state information pose major challenge in wireless energy harvesting communication system design. In this work, we address relay selection problem for wireless powered communication networks, where the relays harvest energy from the source radio frequency signals. A single source–destination pair is considered without a direct link. The connecting relay nodes are equipped with storage batteries of infinite size. We assume that the channel state information (CSI) on the source–relay link is available at the relay nodes. Depending on the availability of the CSI on the relay–destination link at the relay node, we propose two relay selection schemes and evaluate their outage probability. Availability of the CSI at the relay node on the relay–destination link considerably improves the performance due to additional flexibility in the relay selection mechanism. Due to absence of CSI throughout the network at the time of transmission path selection, the analysis of the problem is not tractable. Therefore, we relax our assumptions on availability of CSI and closed-form expressions of the outage probability as a function of the amount of the available harvested energy are derived for both CSI availability cases. Finally, we numerically quantify the performance for the proposed schemes and compare the outage probability for fixed and equal number of wireless powered forwarding relays.

On the Design of Tailored Neural Networks for Energy Harvesting Broadcast Channels: A Reinforcement Learning Approach

In this paper, we consider a power allocation optimization technique for a time-varying fading broadcast channel in energy harvesting communication systems, in which a transmitter with a rechargeable battery transmits messages to receivers using the harvested energy. We first prove that the optimal online power allocation policy for the sum-rate maximization of the transmitter is a monotonically increasing function of harvested energy, remaining battery, and the channel gain of each user. We then construct a lightweight neural network architecture to take advantage of the monotonicity of the optimal policy. This two-step approach, which relies on effective function approximation to provide a mathematical guideline for neural network design, can prevent us from wasting the representational capacity of neural networks. The tailored neural network architectures enable stable learning and eliminate the heuristic network design. For performance assessment, the proposed approach is compared with the closed-form optimal policy for a partially observable Markov problem. Through additional experiments, it is observed that our online solution achieves a performance close to the theoretical upper bound of the performance in a time-varying fading broadcast channel.

Look-Ahead and Learning Approaches for Energy Harvesting Communications Systems

This work investigates the performance of an energy harvesting communications system. This system consists of a transmitter and a receiver. The transmitter is equipped with an infinite buffer to store data, and energy harvesting capability to harvest renewable energy and store it in a finite battery. The goal is to maximize the expected cumulative throughput of such systems. The problem of finding an optimal power allocation policy is formulated as a Markov decision process. Two cases are considered based on the availability of statistical knowledge about the channel gain and energy harvesting processes. When this knowledge is available, an algorithm is designed to maximize the expected throughput, while reducing the complexity of traditional methods (e.g., value iteration). This algorithm exploits instant knowledge about the channel, harvested energy, and current battery level to find a near-optimal policy. For the second scenario, when the statistical knowledge is unavailable, reinforcement learning is used. Two different exploration algorithms, convergence-based and the epsilon-greedy algorithms, are used. Simulations and comparisons with conventional algorithms show the effectiveness of the look-ahead algorithm when the statistical knowledge is available, and the effectiveness of reinforcement learning in optimizing the system performance when this knowledge is unavailable.

Energy Harvesting Communications With Batteries Having Cycle Constraints

Practical energy harvesting (EH) based communication systems typically use a battery to temporarily store the harvested energy prior to its use for communication. The battery capacity can quickly degrade with time if it is subject to repeated shallow charge-discharge cycles. This motivates the cycle constraint which mandates that a battery must be charged only after it is sufficiently discharged and vice versa. We consider a Bernoulli energy arrival model, and a half-duplex battery constraint. In this context, we study EH communication systems with: (a) a single battery with capacity $2{B}$ units and (b) dual batteries , each having capacity of ${B}$ units. The aim is to obtain the best possible long-term average throughputs in point-to-point (P2P) channels and multiple access channels (MAC). For the P2P channel, we obtain an analytical optimal solution in the single battery case, and propose optimal and suboptimal power allocation policies for the dual battery case. We extend these policies to obtain achievable throughput regions in MACs by jointly allocating rates and powers. From numerical simulations, we find that the optimal throughput in the dual battery case can be more than twice of that in the single battery case, although the total energy storage capacity in both cases is $2{B}$ units.

Modeling of Hybrid Energy Harvesting Communication Systems

Energy harvesting is considered as a prominent technology, particularly for low-power wireless nodes. In this paper, we propose the use of hybrid energy harvesting (HEH) utilizing multiple type energy sources and present the modeling of HEH communication systems based on their probabilistic natures. According to our approach, received energy levels of an HEH system for possible combinations of energy arrivals are characterized by using Gaussian mixture models, which are used to determine harvested energy levels. The range of harvested energy is partitioned, and probabilities of partitioning intervals are used to form a finite-state Markov energy channel (FSMEC) model as an energy channel. Similar to the energy arrival, we also include the probabilistic energy consumption of wireless node in this model, depending on multiple application services, by means of the FSMEC model. Thus, we develop an integrated Markov energy model for HEH communication systems corresponding to the energy harvesting and energy consumption profiles. To evaluate the performance of an HEH communication system, we derive the expressions of energy outage, energy shortage, and service loss probabilities analytically. In numerical studies, the derived expressions are verified by matching simulation results, and it is shown that the performance improves significantly with energy source diversity.

Cooperative Power Management in Energy Harvesting Communication Systems in Presence of a Helper

We investigate end-to-end throughput maximization problem for an energy harvesting (EH) single user channel in presence of an energy cooperating helper. The EH helper transfers energy to the EH battery-limited transmitter and receiver nodes. These nodes impose energy causality and energy saving constraints on the power consumption. Both of the transmitter and the receiver harvest energy from nature, and also from the helper via energy cooperation links. The EH receiver requires energy for message decoding process which is called the decoding cost. Then, based on status of the batteries at the transmitter and the receiver, five scenarios are investigated. To maximize the achievable throughput, we propose iterative directional waterfilling algorithms based on minimum and maximum constraint violations. Then as a general model, a backward iterative algorithm (based on combination of optimization in feasibility tunnel and directional waterfilling with variable minimum constraints) is presented. Finally, numerical results are presented to highlight the advantages of energy cooperating helper.

Optimal Rate Control for Energy-Harvesting Systems with Random Data and Energy Arrivals

Due to the random and dynamic energy-harvesting process, it is challenging to conduct optimal rate control in Energy-Harvesting Communication Systems (EHCSs). Existing works mainly focus on two cases: (1) the traffic load is infinite (as long as there is energy, there is data to transmit), in which the objective is to optimize the rate control policy subject to the dynamic energy arrivals, thus maximizing the average system throughput; and (2) the traffic load is finite, in which the objective is to optimize the rate control policy, thus minimizing the time by which all packets are delivered. In this work, we focus on the optimal rate control of EHCSs from another important and practical perspective, where the data and energy arrivals are both random. Given any deadline of T , our goal is to maximize the total throughput in [0, T ]. Specifically, two scenarios are considered: (1) energy is ready before the transmission; and (2) energy arrives randomly during the transmission. In both scenarios, we assume that the data arrive randomly during the transmission. For the first scenario, we develop a novel Stepwise Searching Algorithm (SSA) based on the cumulative curve methodology, which is shown to achieve the optimal solution and the complexity grows only linearly with the problem size. In addition, the SSA can provide a simple and appealing graphical visualization of approximating the optimal solution. For the second scenario, we provide a simplified case study that can be solved by the SSA with low computation overhead and demonstrate the difficulties in solving the general setting, which initiates a first step toward the full understanding of the scenario when energy arrives randomly during the transmission.

Energy Harvesting Communications Under Explicit and Implicit Temperature Constraints

With a motivation to understand the effects of temperature sensitivity on wireless data transmission performance, we consider an energy harvesting communication system, where the temperature dynamics are governed by the transmission power policy. Different from the previous work, we consider a discrete time system where transmission power is kept constant in each slot. We consider two models that capture different effects of temperature. In the first model, the temperature is constrained to be below a critical temperature at all time instants; we coin this the explicit temperature constrained model . We investigate throughput optimal power allocation for multiple energy arrivals under general, as well as temperature and energy limited regimes. We show that the optimal power allocation for the temperature limited case is monotone decreasing. In the second model, we consider the effect of the temperature on the channel quality via its influence on additive noise power; we coin this the implicit temperature constrained model . In this model, the change in the variance of the additive noise due to previous transmissions is non-negligible. In particular, transmitted signals contribute as interference for all subsequent slots and thus affect the signal to interference plus noise ratio (SINR). In this case, we investigate throughput optimal power allocation under general, as well as low and high SINR regimes. We show in the low SINR regime that the optimal allocation dictates the transmitter to save its harvested energy till the last slot. In the high SINR regime, we show that the optimal power sequence is monotone increasing. Finally, we consider the case in which implicit and explicit temperature constraints are simultaneously active and we show under certain conditions that the optimal power sequence is monotone decreasing.

Battery and supercapacitor imperfections modeling and comparison for RF energy harvesting wireless sensor network

In an energy harvesting communication system, the main challenge is to improve network lifetime and maximize throughput by allocating optimal power over a finite span of time, with varying channel and energy. Considering (1) causal state information (SI) of channel and energy (CSI and ESI) and (2) energy storage device imperfections, the problem of power allocation is solved using dynamic programming. As compared to the battery, the supercapacitor is a good alternative for network lifetime improvement, but the imperfections hinder the performance. In this paper, imperfections (storage inefficiency and energy leakage equation) are modeled for supercapacitor and battery. We consider a constant leakage rate for battery. Also, the imperfections of battery and supercapacitor are compared to find which imperfection of supercapacitor is a bottleneck in system performance in different settings (varying channel conditions). The analysis is supported by numerical results.

Optimal Transmission Policies for Multi-Hop Energy Harvesting Systems

In this paper, we consider a multi-hop energy harvesting (EH) communication system in a full-duplex mode, considering arrival data and harvested energy curves in the source and the relays. Our model covers all possible harvesting profiles by considering a general function (including both continuous and discrete functions). This model includes the EH system with discrete arrival processes as a special case. We investigate the throughput maximization problem considering least utilized energy in the source and relays and find the optimal offline algorithm. We propose a three-step algorithm: 1) solving a point-to-point throughput maximization problem at the source; 2) solving a point-to-point throughput maximization problem at the relay (after applying the solution of first step as the input of this second problem); and 3) minimizing utilized energy in the source. We show this algorithm gives the optimal throughput. In addition, we find the relation between the optimal algorithm for the completion time minimization problem and the proposed algorithm for the throughput maximization problem. Further, for the throughput maximization problem, we propose an online algorithm and show that it is more efficient than the benchmark one (which is a direct application of an existing point-to-point online algorithm to the multi-hop system).

Delay Minimal Policies in Energy Harvesting Communication Systems

We characterize delay minimal power scheduling policies in energy harvesting communication systems. We consider a continuous-time system, where the delay experienced by each bit is given by the time spent by the bit in the queue waiting to be transmitted to its receiver. We first consider a single-user channel, where the transmitter has a finite-sized battery to save its harvested energy. Data arrives during the course of communication and are saved in a finite data buffer as well. We find the optimal power policy that minimizes the average delay experienced by the bits subject to energy and data causality constraints. We characterize the optimal solution in terms of Lagrange multipliers, and calculate their values in a recursive manner. We show that, different from the existing literature, the optimum transmission power is not constant between the energy and data arrival events; the transmission power starts high, decreases linearly, and potentially reaches zero between energy and data arrivals. Intuitively, untransmitted bits experience cumulative delay due to the bits to be transmitted ahead of them, and hence the reason for transmission power starting high and decreasing over time. Next, we study a multiuser version of this problem, namely, a two-user broadcast channel, and characterize the optimal transmission policies that minimize the sum delay. For this setting, we consider the case, where the transmitter has an infinite-sized battery, and that all data packets intended for the receivers are available at the beginning of the communication session. We characterize the optimal solution in terms of Lagrange multipliers, and present an iterative solution that calculates their values. Our results show that in the optimal policy, both users may not be served simultaneously all the time; there may be times, where only one of the two users is served alone. We also show that the optimal policy may have gaps in transmission in between energy arrivals, where none of the users is served, echoing the results of the single-user setting.

Online Fixed Fraction Policies in Energy Harvesting Communication Systems

We consider power scheduling policies for single-user energy harvesting communication systems, where the goal is to characterize online policies that maximize the long term average utility, for general concave and monotonically increasing utility functions. The transmitter relies on energy harvested from nature to send its messages to the receiver, and is equipped with a finite-sized battery to store its harvested energy. Energy packets are independent and identically distributed (i.i.d.) over time slots, and are revealed causally to the transmitter. We first characterize the optimal solution for the case of Bernoulli arrivals. Then, for general i.i.d. arrivals, we first show that fixed fraction policies , in which a fixed fraction of the battery state is consumed in each time slot, are within a constant multiplicative gap from the optimal solution for all energy arrivals and battery sizes. We then derive a set of sufficient conditions on the utility function to guarantee that fixed fraction policies are within a constant additive gap as well from the optimal solution. We then apply these results to a specific scenario where a sensor node collects samples from a Gaussian source and sends them to a destination node over a Gaussian channel, and the goal is to minimize the long term average distortion of the source samples received at the destination. We study two problem settings for this case: the first is when sampling is cost-free, and the second is when there is a sampling cost incurred whenever samples are collected. For the problem with sampling costs, the transmission policy can be bursty; the sensor may collect samples and transmit for only a portion of the time. Finally, we present an alternative analysis approach that is more tailored to these distortion problems to show that fixed fraction policies achieve an additive gap that is independent of the sampling cost.