Online Power Control for Block i.i.d. Energy Harvesting Channels

We study the problem of online power control for energy harvesting communication nodes with random energy arrivals and a finite battery. We assume a block i.i.d. stochastic model for the energy arrivals, in which the energy arrivals are constant for a fixed duration $T$, but are independent across different blocks, drawn from an arbitrary distribution. This model serves as a simple approximation to a random process with coherence time $T$. We propose a simple online power control policy, and prove that its performance gap to the optimal throughput is bounded by a constant which is independent of the parameters of the problem. This also yields a simple formula for the approximately optimal long-term average throughput, which sheds some light on the qualitative behavior of the throughput and how it depends on the coherence time of the energy arrival process. Our results show that, perhaps counter-intuitively, for a fixed mean energy arrival rate the throughput decreases with increasing coherence time $T$ of the energy arrival process. In particular, the battery size needed to approach the AWGN capacity of the channel increases linearly with the coherence time of the process. Finally, we show that our results can provide an approximation to the information-theoretic capacity of the same channel.Comment: submitted to IEEE Transactions on Information Theor

Power Management Policies for AWGN Channels with Slow-Varying Harvested Energy

In this paper, we study power management (PM) policies for an Energy Harvesting Additive White Gaussian Noise (EH-AWGN) channel. The arrival rate of the harvested energy is assumed to remain unchanged during each data frame (block code) and to change independently across block codes. The harvested energy sequence is known causally (online) at the transmitter. The transmitter is equipped with a rechargeable battery with infinite energy storage capacity. The transmitter is able to adapt the allocated energy and the corresponding transmission rate of each block according to a PM policy. Three novel online PM policies are established. The policies are universal, in the sense of the distribution of the harvested energy, and simple, in the sense of complexity, and asymptotically optimal, in the sense of maximum achievable average rates (throughput) taken over a long-term horizon of blocks.Comment: 4 Figures, 6 page

Capacity of the Energy Harvesting Channel with a Finite Battery

We consider an energy harvesting channel, in which the transmitter is powered by an exogenous stochastic energy harvesting process $E_t$, such that $0\leq E_t\leq\bar{E}$, which can be stored in a battery of finite size $\bar{B}$. We provide a simple and insightful formula for the approximate capacity of this channel with bounded guarantee on the approximation gap independent of system parameters. This approximate characterization of the capacity identifies two qualitatively different operating regimes for this channel: in the large battery regime, when $\bar{B}\geq \bar{E}$, the capacity is approximately equal to that of an AWGN channel with an average power constraint equal to the average energy harvesting rate, i.e. it depends only on the mean of $E_t$ and is (almost) independent of the distribution of $E_t$ and the exact value of $\bar{B}$. In particular, this suggests that a battery size $\bar{B}\approx\bar{E}$ is approximately sufficient to extract the infinite battery capacity of the system. In the small battery regime, when $\bar{B}<\bar{E}$, we clarify the dependence of the capacity on the distribution of $E_t$ and the value of $\bar{B}$. There are three steps to proving this result which can be of interest in their own right: 1) we characterize the capacity of this channel as an $n$-letter mutual information rate under various assumptions on the availability of energy arrival information; 2) we characterize the approximately optimal online power control policy that maximizes the long-term average throughput of the system; 3) we show that the information-theoretic capacity of this channel is equal, within a constant gap, to its long-term average throughput. This last result provides a connection between the information- and communication-theoretic formulations of the energy-harvesting communication problem that have been so far studied in isolation.Comment: submitted to IEEE Transactions on Information Theory; revised following reviewers' comment

SWIPT using Hybrid ARQ over Time Varying Channels

We consider a class of wireless powered devices employing Hybrid Automatic Repeat reQuest (HARQ) to ensure reliable end-to-end communications over a two-state time-varying channel. A receiver, with no power source, relies on the energy transferred by a Simultaneous Wireless Information and Power Transfer (SWIPT) enabled transmitter to \emph{receive} and \emph{decode} information. Under the two-state channel model, information is received at two different rates while it is only possible to harvest energy in one of the states. The receiver aims to decode its messages with minimum expected number of re-transmissions. Dynamic and continuous nature of the problem motivated us to use a novel Markovian framework to bypass the complexities plaguing the conventional approaches such as MDP. Using the theory of absorbing Markov chains, we show that there exists an optimal policy utilizing the incoming RF signal solely to harvest energy or to accumulate mutual information. Hence, we convert the original problem with continuous action and state space into an equivalent one with discrete state and action space. For independent and identically distributed channels, we prove the optimality of a simple-to-implement {\em harvest-first-store-later} type policy. However, for time-correlated channels, we demonstrate that statistical knowledge of the channel may significantly improve the performance over such policies

Closed-Form Delay-Optimal Power Control for Energy Harvesting Wireless System with Finite Energy Storage

In this paper, we consider delay-optimal power control for an energy harvesting wireless system with finite energy storage. The wireless system is powered solely by a renewable energy source with bursty data arrivals, and is characterized by a data queue and an energy queue. We consider a delay-optimal power control problem and formulate an infinite horizon average cost Markov Decision Process (MDP). To deal with the curse of dimensionality, we introduce a virtual continuous time system and derive closed-form approximate priority functions for the discrete time MDP at various operating regimes. Based on the approximation, we obtain an online power control solution which is adaptive to the channel state information as well as the data and energy queue state information. The derived power control solution has a multi-level water-filling structure, where the water level is determined jointly by the data and energy queue lengths. We show through simulations that the proposed scheme has significant performance gain compared with various baselines.Comment: 17 pages, 9 figures, 1 table. Accepted for publication in IEEE Transactions on Signal Processin

Optimal Power Allocation for Outage Minimization in Fading Channels with Energy Harvesting Constraints

This paper studies the optimal power allocation for outage minimization in point-to-point fading channels with the energy-harvesting constraints and channel distribution information (CDI) at the transmitter. Both the cases with non-causal and causal energy state information (ESI) are considered, which correspond to the energy harvesting rates being known and unknown prior to the transmissions, respectively. For the non-causal ESI case, the average outage probability minimization problem over a finite horizon is shown to be non-convex for a large class of practical fading channels. However, the globally optimal "offline" power allocation is obtained by a forward search algorithm with at most $N$ one-dimensional searches, and the optimal power profile is shown to be non-decreasing over time and have an interesting "save-then-transmit" structure. In particular, for the special case of N=1, our result revisits the classic outage capacity for fading channels with uniform power allocation. Moreover, for the case with causal ESI, we propose both the optimal and suboptimal "online" power allocation algorithms, by applying the technique of dynamic programming and exploring the structure of optimal offline solutions, respectively.Comment: submitted for possible Journal publicatio

Grid Energy Consumption and QoS Tradeoff in Hybrid Energy Supply Wireless Networks

Hybrid energy supply (HES) wireless networks have recently emerged as a new paradigm to enable green networks, which are powered by both the electric grid and harvested renewable energy. In this paper, we will investigate two critical but conflicting design objectives of HES networks, i.e., the grid energy consumption and quality of service (QoS). Minimizing grid energy consumption by utilizing the harvested energy will make the network environmentally friendly, but the achievable QoS may be degraded due to the intermittent nature of energy harvesting. To investigate the tradeoff between these two aspects, we introduce the total service cost as the performance metric, which is the weighted sum of the grid energy cost and the QoS degradation cost. Base station assignment and power control is adopted as the main strategy to minimize the total service cost, while both cases with non-causal and causal side information are considered. With non-causal side information, a Greedy Assignment algorithm with low complexity and near-optimal performance is proposed. With causal side information, the design problem is formulated as a discrete Markov decision problem. Interesting solution structures are derived, which shall help to develop an efficient monotone backward induction algorithm. To further reduce complexity, a Look-Ahead policy and a Threshold-based Heuristic policy are also proposed. Simulation results shall validate the effectiveness of the proposed algorithms and demonstrate the unique grid energy consumption and QoS tradeoff in HES networks.Comment: 14 pages, 7 figures, to appear in IEEE Transactions on Wireless Communication

Distributed Opportunistic Scheduling for Energy Harvesting Based Wireless Networks: A Two-Stage Probing Approach

This paper considers a heterogeneous ad hoc network with multiple transmitter-receiver pairs, in which all transmitters are capable of harvesting renewable energy from the environment and compete for one shared channel by random access. In particular, we focus on two different scenarios: the constant energy harvesting (EH) rate model where the EH rate remains constant within the time of interest and the i.i.d. EH rate model where the EH rates are independent and identically distributed across different contention slots. To quantify the roles of both the energy state information (ESI) and the channel state information (CSI), a distributed opportunistic scheduling (DOS) framework with two-stage probing and save-then-transmit energy utilization is proposed. Then, the optimal throughput and the optimal scheduling strategy are obtained via one-dimension search, i.e., an iterative algorithm consisting of the following two steps in each iteration: First, assuming that the stored energy level at each transmitter is stationary with a given distribution, the expected throughput maximization problem is formulated as an optimal stopping problem, whose solution is proved to exist and then derived for both models; second, for a fixed stopping rule, the energy level at each transmitter is shown to be stationary and an efficient iterative algorithm is proposed to compute its steady-state distribution. Finally, we validate our analysis by numerical results and quantify the throughput gain compared with the best-effort delivery scheme.Comment: 14 pages, 5 figures, accepted by IEEE/ACM Transactions on Networkin

On Lossy Joint Source-Channel Coding In Energy Harvesting Communication Systems

We study the problem of lossy joint source-channel coding in a single-user energy harvesting communication system with causal energy arrivals and the energy storage unit may have leakage. In particular, we investigate the achievable distortion in the transmission of a single source via an energy harvesting transmitter over a point-to-point channel. We consider an adaptive joint source-channel coding system, where the length of channel codewords varies based on the available battery charge. We first establish a lower bound on the achievable distortion. Then, as necessary conditions for local optimality, we obtain two coupled equations that determine the mismatch ratio between channel symbols and source symbols as well as the transmission power, both as functions of the battery charge. As examples of continuous and discrete sources, we consider Gaussian and binary sources respectively. For the Gaussian case, we obtain a closed-form expression for the mismatch factor in terms of the $Lambert W$ function, and show that an increasing transmission power policy results in a decreasing mismatch factor policy and vice versa. Finally, we numerically compare the performance of the adaptive mismatch factor scheme to the case of a constant mismatch factor.Comment: 15 pages, 7 figures. To be published in IEEE Transactions on Communication

Opportunistic Multi-Channel Access in Heterogeneous 5G Network with Renewable Energy Supplies

A heterogeneous system, where small networks (e.g., small cell or WiFi) boost the system throughput under the umbrella of a large network (e.g., large cell), is a promising architecture for the 5G wireless communication networks, where green and sustainable communication is also a key aspect. Renewable energy based communication via energy harvesting (EH) devices is one of such green technology candidates. In this paper, we study an uplink transmission scenario under a heterogeneous network hierarchy, where each mobile user (MU) is powered by a sustainable energy supply, capable of both deterministic access to the large network via one private channel, and dynamic access to a small network with certain probability via one common channel shared by multiple MUs. Considering a general EH model, i.e., energy arrivals are time-correlated, we study an opportunistic transmission scheme and aim to maximize the average throughput for each MU, which jointly exploits the statistics and current states of the private channel, common channel, battery level, and EH rate. Applying a simple yet efficient "save-then-transmit" scheme, the throughput maximization problem is cast as a "rate-of-return" optimal stopping problem. The optimal stopping rule is proved to has a time-dependent threshold-based structure for the case with general Markovian system dynamics, and degrades to a pure threshold policy for the case with independent and identically distributed system dynamics. As performance benchmarks, the optimal power allocation scheme with conventional power supplies is also examined. Finally, numerical results are presented, and a new concept of "EH diversity" is discussed.Comment: 28 pages, 8 figure