Communicating Using an Energy Harvesting Transmitter: Optimum Policies Under Energy Storage Losses

In this paper, short-term throughput optimal power allocation policies are derived for an energy harvesting transmitter with energy storage losses. In particular, the energy harvesting transmitter is equipped with a battery that loses a fraction of its stored energy. Both single user, i.e. one transmitter-one receiver, and the broadcast channel, i.e., one transmitter-multiple receiver settings are considered, initially with an infinite capacity battery. It is shown that the optimal policies for these models are threshold policies. Specifically, storing energy when harvested power is above an upper threshold, retrieving energy when harvested power is below a lower threshold, and transmitting with the harvested energy in between is shown to maximize the weighted sum-rate. It is observed that the two thresholds are related through the storage efficiency of the battery, and are nondecreasing during the transmission. The results are then extended to the case with finite battery capacity, where it is shown that a similar double-threshold structure arises but the thresholds are no longer monotonic. A dynamic program that yields an optimal online power allocation is derived, and is shown to have a similar double-threshold structure. A simpler online policy is proposed and observed to perform close to the optimal policy.Comment: Submitted to IEEE Transactions on Wireless Communications, August 201

The Binary Energy Harvesting Channel with a Unit-Sized Battery

We consider a binary energy harvesting communication channel with a finite-sized battery at the transmitter. In this model, the channel input is constrained by the available energy at each channel use, which is driven by an external energy harvesting process, the size of the battery, and the previous channel inputs. We consider an abstraction where energy is harvested in binary units and stored in a battery with the capacity of a single unit, and the channel inputs are binary. Viewing the available energy in the battery as a state, this is a state-dependent channel with input-dependent states, memory in the states, and causal state information available at the transmitter only. We find an equivalent representation for this channel based on the timings of the symbols, and determine the capacity of the resulting equivalent timing channel via an auxiliary random variable. We give achievable rates based on certain selections of this auxiliary random variable which resemble lattice coding for the timing channel. We develop upper bounds for the capacity by using a genie-aided method, and also by quantifying the leakage of the state information to the receiver. We show that the proposed achievable rates are asymptotically capacity achieving for small energy harvesting rates. We extend the results to the case of ternary channel inputs. Our achievable rates give the capacity of the binary channel within 0.03 bits/channel use, the ternary channel within 0.05 bits/channel use, and outperform basic Shannon strategies that only consider instantaneous battery states, for all parameter values.Comment: Submitted to IEEE Transactions on Information Theory, August 201

Improved capacity bounds for the binary energy harvesting channel

Abstract—We consider a binary energy harvesting channel (BEHC) where the encoder has unit energy storage capacity. We first show that an encoding scheme based on block indexing is asymptotically optimal for small energy harvesting rates. We then present a novel upper bounding technique, which upper bounds the rate by lower-bounding the rate of information leakage to the receiver regarding the energy harvesting process. Finally, we propose a timing based hybrid encoding scheme that achieves rates within 0.03 bits/channel use of the upper bound; hence determining the capacity to within 0.03 bits/channel use. I

Multiple Access and Two-way Channels with Energy Harvesting and Bi-directional Energy Cooperation

Abstract—This paper considers the multiple access and twoway channels with energy harvesting transmitters that can cooperate by transferring energy to each other. Specifically, the jointly optimal transmit power allocation and energy transfer policies that achieve the sum-capacity in both models are found. These models were first considered in previous work with unidirectional energy transfer, and optimal policies were found using a two-dimensional water-filling algorithm. In this paper, the bi-directional extension of the energy cooperation model is considered. Using an equivalent energy transfer efficiency representation, it is found that in the optimal policy, a node cannot simultaneously send and receive energy. It is shown that a class of power policies termed procrastinating policies include at least one optimal policy, leading to the insight that the resulting power allocation problem can be solved by a one-dimensional directional water-filling algorithm. It is observed that in the multiple access channel, a node either transfers no energy, or transfers all of its energy to a single user to achieve sum-capacity. For the two-way channel, the optimal policy is found to have a directional water-filling interpretation with two non-mixing fluids whenever optimal energy transfer is non-zero. Index Terms—Energy harvesting, energy cooperation, energy transfer, optimal power allocation, wireless networks, multiple access channel, two-way channel. I

The energy harvesting and energy cooperating two-way channel with finite-sized batteries

In this paper, we consider the energy allocation problem for energy harvesting and energy cooperating nodes with finite-sized batteries. In particular, we solve the sumthroughput maximization problem in a two-way channel with energy harvesting nodes that can also transfer energy to one another. To do so, we non-trivially extend a class of policies which originally rely on an infinite-sized battery to be optimal, to the finite battery case. We observe that when we partition transferred energy into immediately used and stored components, an optimal policy has a non-zero stored component only when the battery of the transferring user is full. This enables the decomposition of the sum-throughput maximization problem into separate energy transfer and power allocation problems. Utilizing properties of this optimal class of policies, we solve the power allocation problem using a two dimensional directional water-filling algorithm with restricted transfers, where energy transfers only take place at full battery instances. Numerical results demonstrate that energy cooperation notably improves sum-throughput as one node gets energy deprived