Ahmed Arafa

Optimal Policies for Wireless Networks With Energy Harvesting Transmitters and Receivers: Effects of Decoding Costs

We consider the effects of decoding costs in energy-harvesting communication systems. In our setting, receivers, in addition to transmitters, rely solely on energy harvested from nature, and need to spend some energy in order to decode their intended packets. We model the decoding energy as an increasing convex function of the rate of the incoming data. In this setting, in addition to the traditional energy causality constraints at the transmitters, we have the decoding causality constraints at the receivers, where energy spent by the receiver for decoding cannot exceed its harvested energy. We first consider the point-to-point single-user problem where the goal is to maximize the total throughput by a given deadline subject to both energy and decoding causality constraints. We show that decoding costs at the receiver can be represented as generalized data arrivals at the transmitter, and thereby moving all system constraints to the transmitter side. Then, we consider several multiuser settings. We start with a two-hop network where the relay and the destination have decoding costs, and show that separable policies, where the transmitters throughput is maximized irrespective of the relays transmission energy profile, are optimal. Next, we consider the multiple access channel (MAC) and the broadcast channel (BC) where the transmitters and the receivers harvest energy from nature, and characterize the maximum departure region. In all multiuser settings considered, we decompose our problems into inner and outer problems. We solve the inner problems by exploiting the structure of the particular model, and solve the outer problems by water-filling algorithms.

Energy Harvesting Two-Way Channels With Decoding and Processing Costs

We study the effects of decoding and processing costs in an energy harvesting two-way channel. We design the optimal offline power scheduling policies that maximize the sum throughput by a given deadline, subject to energy causality constraints, decoding causality constraints, and processing costs at both users. In this system, each user spends energy to transmit data to the other user, and also to decode data coming from the other user; that is, each user divides its harvested energy for transmission and reception. Further, each user incurs a processing cost per unit time as long as it communicates. The power needed for decoding the incoming data is modeled as an increasing convex function of the incoming data rate; and the power needed to be on, i.e., the processing cost, is modeled to be a constant per unit time. We solve this problem by first considering the cases with decoding costs only and processing costs only individually. In each case, we solve the single energy arrival scenario, and then use the solution’s insights to provide an iterative algorithm that solves the multiple energy arrivals scenario. Then, we consider the general case with both decoding and processing costs in a single setting, and solve it for the most general scenario of multiple energy arrivals.

Single-user and multiple access channels with energy harvesting transmitters and receivers

We consider the effects of decoding costs in energy harvesting communication systems. In our setting, receivers, in addition to transmitters, rely solely on energy harvested from nature, and need to spend some energy in order to decode their intended packets. We model the decoding energy as an increasing convex function of the rate of the incoming data. In this setting, in addition to the traditional energy causality constraints at the transmitters, we have the decoding causality constraints, where energy spent by the receiver for decoding cannot exceed its harvested energy. We first consider the point-to-point single-user problem where the goal is to maximize the total throughput by a given deadline subject to both energy and decoding causality constraints. We then consider the multiple access channel (MAC) where the transmitters and the receiver harvest energy from nature, and characterize the maximum departure region.

Optimal policies in energy harvesting two-way channels with processing costs

We consider a two-way communication channel in which both users rely solely on energy harvested from nature. Each user incurs a processing cost per unit time as long as it communicates; that is, each users energy consumption includes energy spent for transmission and energy spent for processing. We maximize the sum throughput by a given deadline subject to energy causality constraints. We first show that the optimal power policy is bursty; the two users communicate only during a portion of the time that is uniquely determined by their available energies and processing costs. We show that it is optimal for the two users to be fully synchronized; they turn on and exchange data during the same portion of time, and then turn off together. We first solve the single energy arrival case, and then extend it to solve the multiple energy arrival throughput maximization problem. We show that it is optimal for the users to communicate in a deferred fashion; users postpone their energy consumption to utilize later time slots first. We present an algorithm that gives the optimal deferred policy by iteratively applying a modified version of the single energy arrival result in a backward manner.

Energy harvesting two-way channel with decoding costs

We consider an energy harvesting two-way channel with decoding costs. In this system, each node spends energy to transmit data to the other user, and also to decode data coming from the other user; that is, each user divides its harvested energy for transmission and reception. The power needed for decoding the incoming data is a function of the incoming data rate. We determine the optimal offline power scheduling policies for both users that maximize the sum throughput of the system by a given deadline. We first consider the case with a single energy arrival at each user. We show that the transmission is limited by the user with the smaller energy. In this case, the user with larger energy may not consume all of its energy. We next consider the case with multiple energy arrivals at both users. We show that the optimal power allocations are non-decreasing over time, and they increase synchronously at both users. We then develop an iterative algorithm based on two-slot updates to obtain the optimal power allocations for both users.

Delay minimal policies in energy harvesting broadcast channels

We consider a two-user energy harvesting broadcast channel, and characterize the delay minimal transmission policies that minimize the total delay experienced by the data packets in the system. 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 consider the case where all data packets are available at the transmitter at the beginning of the communication session. We characterize the optimal solution in terms of the Lagrange multipliers, and present an iterative algorithm that optimally 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 the strong user or only the weak user is served alone. We also show that the optimal policy may have gaps in transmission where none of the users is served until the next energy arrival.

Energy harvesting networks with general utility functions: Near optimal online policies

We consider online 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 some general concave and monotonically increasing utility function. In our setting, 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 energy. Energy packets are independent and identically distributed (i.i.d.) over time slots, and are revealed causally to the transmitter. Only the average arrival rate is known a priori. 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 [1] 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.

Mobile Energy Harvesting Nodes: Offline and Online Optimal Policies

We consider a mobile energy harvesting transmitter where movement is motivated by trying to find better energy harvesting locations. Movement comes with an energy cost expenditure, and hence there exists a throughput-movement tradeoff. On one hand, the transmitter may opt not to move and use all its available energy for transmission; on the other hand, it can choose to move to a potentially better location, spending some of its available energy during the movement process, and yet harvest larger amounts of energy at the new location and achieve higher throughput. In this paper, we characterize this tradeoff by designing throughput optimal power allocation policies subject to energy causality constraints and moving costs. In our setup, the transmitter moves along a straight line, where two energy sources are located at the opposite ends of the line. We first study the offline version of this problem where the goal is to maximize the throughput by a given deadline. We find a closed form solution for the case of single energy arrival at each source, and provide an iterative solution for the case of multiple energy arrivals. Then, we study the online version of this problem with independent and identically distributed (i.i.d.) energy arrivals at each source, and the goal is to maximize the long term average throughput. We propose an optimal move-then-transmit scheme where the transmitter first moves towards the source with higher mean energy arrival, stays at that source, and then starts transmission.

Near optimal online distortion minimization for energy harvesting nodes

We consider online scheduling for an energy harvesting communication system where a sensor node collects samples from a Gaussian source and sends them to a destination node over a Gaussian channel. The sensor is equipped with a finite-sized battery that is recharged by an independent and identically distributed (i.i.d.) energy harvesting process over time. The goal is to minimize the long term average distortion of the source samples received at the destination. We study two problems: the first is when sampling is cost-free, and the second is when there is a sampling cost incurred whenever samples are collected. We show that fixed fraction policies [1], in which a fixed fraction of the battery state is consumed in each time slot, are near-optimal in the sense that they achieve a long term average distortion that lies within a constant additive gap from the optimal solution for all energy arrivals and battery sizes. For the problem with sampling costs, the transmission policy is bursty; the sensor can collect samples and transmit for only a portion of the time.

Mobile energy harvesting nodes

We consider a mobile energy harvesting transmitter where movement is motivated by finding better energy harvesting locations. Movement comes with an energy cost expenditure, and hence there exists a tradeoff between staying at the same location and moving to a new one. On one hand, the transmitter may opt not to move and use all its available energy for transmission; on the other hand, it can choose to move to a potentially better location, spending some of its available energy during the movement process, and yet harvest larger amounts of energy at the new location and achieve higher throughput. In this paper, we characterize this tradeoff by designing throughput-optimal power allocation policies subject to energy causality constraints and moving costs. In our setup, the transmitter moves along a straight line, where two energy sources are located at the opposite ends of the line. We first study the case of a single energy arrival at both sources, and then generalize it to the case of multiple energy arrivals.