We consider an energy harvesting two user cooperative Gaussian multiple access channel, where both of the users harvest energy from nature. The users cooperate at the physical layer (data cooperation) by establishing common messages through overheard signals and then cooperatively sending them. We study two scenarios within this model. In the first scenario, the data packets arrive intermittently over time. We find the optimal offline transmit power and rate allocation policy that maximize the departure region. We first show that there exists an optimal policy, in which the single user rate constraints in each time slot are tight, yielding a one-to-one relation between the powers and rates. Then, we formulate the departure region maximization problem as a weighted sum departure maximization in terms of rates only. Next, we propose a sequential convex approximation method to approximate the problem at each step and show that it converges to the optimal solution. We solve the approximate problems using an inner-outer decomposition method. In the second scenario, the data packets are available at the beginning of the transmission, but the users now have the ability to cooperate at the battery level (energy cooperation), in addition to data cooperation. The energy cooperation is facilitated by wireless energy transfer and is bidirectional. For this scenario, we find the jointly optimal offline transmit power and rate allocation policy together with the energy transfer policy that maximize the departure region. We provide necessary conditions for energy transfer and prove some properties of the optimal transmit policy, thereby shedding some light on the interplay between energy and data cooperation.

We consider an energy harvesting two user cooperative Gaussian multiple access channel (MAC), where both of the users harvest energy from nature. The data packets arrive intermittently over time. The users overhear each other's transmitted signals and can cooperate by forming common messages. We find the optimal offline transmit power and rate allocation policy that maximize the departure region. We first show that there exists an optimal policy, in which the single user rate constraints in each time slot are tight, yielding a one to one relation between the powers and rates. Then, we formulate the departure region maximization problem as a weighted sum rate maximization in terms of rates only. Next, we propose a sequential convex approximation method to approximate the problem at each step and show that it converges to the optimal solution. Finally, we solve the approximate problems using an inner outer decomposition method. Numerically, we observe that higher data rates can be supported with the same amount of energy.

We consider the energy harvesting two user Gaussian multiple access channel (MAC), where both users harvest energy from nature. The users cooperate at the physical layer (data cooperation) by establishing common messages through overheard signals and then cooperatively sending them. In addition, the users cooperate at the battery level (energy cooperation) by wirelessly transferring energy to each other. We find the jointly optimal offline transmit power and rate allocation policy together with the energy transfer policy that maximizes the departure region. We provide necessary conditions for energy transfer, and prove some properties of the optimal transmit policy, thereby shedding some light on the interplay between energy and data cooperation.

We consider the energy harvesting diamond channel, where the source and two relays harvest energy from nature and the physical layer is modeled as a concatenation of a broadcast and a multiple access channel. Since the broadcast channel is degraded, one of the relays has the message of the other relay and the multiple access channel can be modeled as a cooperative multiple access channel with common data. We find the optimal offline transmit power and rate allocations that maximize the end-to-end throughput. For the broadcast side, we show that there exists an optimal source power allocation, which is equal to the single-user optimal power allocation for the source energy arrivals. We then show that the fraction of the power spent on each broadcast link depends on the energy arrivals for the relays. For the multiple access side with no co-operation, with fixed source rates, we show that the problem can be cast as a multiple access channel with both data and energy arrivals and can be formulated in terms of data transmission rates only. We use a dual decomposition method to solve the overall problem efficiently. Finally, we focus on the diamond channel with co-operative multiple access capacity region and find the optimal rates and powers using a decomposition into inner and outer maximization problems.

We consider the delay minimization problem in an energy harvesting communication network with energy cooperation. In this network, nodes harvest energy from nature to sustain the power needed for data transmission, and may transfer a portion of their harvested energies to neighboring nodes through energy cooperation. For fixed data and energy routing topologies, we determine the optimum data rates, transmit powers, and energy transfers, subject to flow and energy conservation constraints, to minimize the network delay. We start with a simplified problem where data flows are fixed and optimize energy management at each node for the case of a single energy harvest per node. This is tantamount to distributing each node's available energy over its outgoing data links and energy transfers to neighboring nodes. For this case, with no energy cooperation, we show that each node should allocate more power to links with more noise and/or more data flow. In addition, when there is energy cooperation, our numerical results indicate that the energy is routed from nodes with lower data loads to nodes with higher data loads. We then extend this setting to the case of multiple energy harvests per node over time. In this case, we optimize each node's energy management over its outgoing data links and its energy transfers to neighboring nodes, over multiple time slots. For this case, with no energy cooperation, we show that, for any given node, the sum of powers on the outgoing links over time is equal to the single-link optimal power over time. Finally, we consider the problem of joint flow control and energy management for the entire network. We determine the necessary conditions for joint optimality of a power control, energy transfer, and routing policy. We provide an iterative algorithm that updates the data flows, energy flows, and power distribution over outgoing data links sequentially. We show that this algorithm converges to a Pareto-optimal operating point.

We consider the energy harvesting two user Gaussian multiple access channel (MAC), where both of the users harvest energy from nature and their data packets arrive intermittently over time. We find the optimal offline transmit power and rate allocations that maximize the sum rate. First, we show that the optimization problem can be formulated in terms of the data rates only, instead of both transmission powers and data rates. Next, we show that the optimal sum rates are non-decreasing in time, similar to the single-user optimal powers. Then, we use a dual decomposition method to solve this problem efficiently. Specifically, we show that this problem is equivalent to three subproblems where each subproblem is a throughput maximization problem with fading, data and energy arrival constraints. We decompose the problem into inner and outer optimization problems and solve the overall problem using the subgradient descent method. Finally, we consider a relaxed problem where the data and energy arrivals to both of the users are merged into single energy and data queues and show that the optimal sum rates of the original problem are majorized by the solution to this relaxed problem.

We consider the energy harvesting diamond channel, where the source and two relays harvest energy from nature. The physical layer is modeled as a concatenation of a broadcast and a multiple access channel. We find the optimal offline transmit power and rate allocations that maximize the end-to-end throughput. First, we show that there exists an optimal source power allocation which is equal to the single-user optimal power allocation for the source energy arrivals and does not depend on the relay energy arrivals. Second, we show that the fraction of the power spent on each broadcast link depends on the energy arrivals for the relays. Specifically, we show that the optimal source rate allocation can be found by solving an optimal broadcasting problem with slot-dependent user priorities and these priorities can change only at instants where one of the relay data buffers is empty. Finally, we decompose the problem into inner and outer optimization problems and solve the overall problem by iterating between the two.

We consider the energy harvesting diamond channel, where the source and two relays harvest energy from nature, the relays help deliver the source's messages via signal cooperation, and the source has the option of wirelessly transferring some of its energy to the relays via energy cooperation. We find the optimal offline transmit power allocations and energy transfer policies that maximize the end-to-end throughput. For the case of no energy cooperation, we decompose the problem into inner and outer maximization problems, and solve the overall problem iterating between the two. We show that the class of procrastinating policies, where energy is transferred only when it will be immediately used, is optimal. We then show that the problem with energy cooperation is equivalent to a problem without energy cooperation with suitably modified rate expressions. We show that, in this system, if the source sends more energy to a relay, then it sends less data, showing us how data and energy should flow together optimally in this network.

In this paper, we investigate a two-way communication channel where users can harvest energy from nature and energy can be transferred in one-way from one of the users to the other. Energy required for data transmission is randomly harvested by the users throughout the communication duration and users have unlimited batteries to store energy for future use. In addition, there is a separate wireless energy transfer unit that facilitates energy transfer only in one-way and with efficiency α. We study the energy cooperation made possible by wireless energy transfer in the two-way channel. Assuming that both users know the energy arrivals in advance, we find jointly optimal offline energy management policies that maximize the sum throughput of the users. We show that this problem is a convex optimization problem, and find the solution by a generalized two-dimensional directional water-filling algorithm which transfers energy from one user to another while maintaining that the energy is allocated in the time dimension optimally. Optimal solution equalizes the energy levels as much as possible both among users and among slots, permitted by causality constraints of the energy arrivals and one-way energy transfer.

In energy harvesting communications, users transmit messages using energy harvested from nature during the course of communication. With an optimum transmit policy, the performance of the system depends only on the energy arrival profiles. In this paper, we introduce the concept of energy cooperation, where a user wirelessly transmits a portion of its energy to another energy harvesting user. This enables shaping and optimization of the energy arrivals at the energy-receiving node, and improves the overall system performance, despite the loss incurred in energy transfer. We consider several basic multi-user network structures with energy harvesting and wireless energy transfer capabilities: relay channel, two-way channel and multiple access channel. We determine energy management policies that maximize the system throughput within a given duration using a Lagrangian formulation and the resulting KKT optimality conditions. We develop a two-dimensional directional water-filling algorithm which optimally controls the flow of harvested energy in two dimensions: in time (from past to future) and among users (from energy-transferring to energy-receiving) and show that a generalized version of this algorithm achieves the boundary of the capacity region of the two-way channel.

We consider a simple multi-hop communication scenario composed of a source node, a relay node and a destination node where the source and the relay can harvest energy from the nature. Energy required for communication arrives (is harvested) at the transmitter and an unlimited battery stores it before being consumed for transmission. In addition, the source can assist the relay by transferring a portion of its energy to the relay through a separate energy transfer unit. We address this energy cooperation between the source and the relay in a deterministic setting. Assuming that the source and the relay nodes are informed of the energy arrivals in advance, we find jointly optimal offline energy management policies for the source and the relay that maximize the end-to-end throughput. We show that this problem is a convex problem. In order to gain insight about the structure of the solution, we consider specific scenarios. In particular, we show that if the relay energy profile is higher at the beginning and lower at the end with only one intersection, then matching the power sequences of the source and the relay slot-by-slot is optimal. We also consider the case when the energy of the source is available at the beginning and show that transferring energy in the first slot is optimal.