This paper investigates the offline packet-delay-minimization problem for an energy harvesting transmitter. To overcome the non-convexity of the problem, we propose a C2-diffeomorphic transformation and provide the necessary and sufficient condition for the transformed problem to a standard convex optimization problem. Based on this condition, a simple choice of the transformation is determined which allows an analytically tractable solution of the original non-convex problem to be easily obtained once the transformed convex problem is solved. We further study the structure of the optimal transmission policy in a special case and find it to follow a weighted-directional-water-filling structure. In particular, the optimal policy tends to allocate more power in earlier time slots and less power in later time slots. Our analytical insight is verified by simulation results.
Another interesting issue is the relationship among the pa-cket-delay-minimization, completion-time-minimization, and throughput-maximization problems. For the last two problems, they are linked through the maximum departure curve (see Section V in @cite_12 ). However, it is unclear whether the first problem has any correlation with the last two problems. Intuitively, the first two problems are related: the quicker the transmission is completed, the smaller the packet delay is. A similar observation was also made in the literature (e.g., @cite_15 @cite_8 ). Then, through the maximum departure curve, all these three problems appear to be highly related. Nevertheless, there has not been any analytical studied on the extent to which the three problems are related and, more importantly, whether the optimal offline transmission designs for the three problems have the similar behaviors.
@cite_15 @cite_12 @cite_8
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We consider the transmission completion time minimization problem in a single-user energy harvesting wireless communication system. In this system, both the data packets and the harvested energy are modelled to arrive at the source node randomly. Our goal is to adaptively change the transmission rate according to the traffic load and available energy, such that the transmission completion time is minimized. Under a deterministic system setting, we assume that the energy harvesting times and harvested energy amounts are known before the transmission starts. For the data traffic arrivals, we consider two different scenarios. In the first scenario, we assume that all bits have arrived and are ready at the transmitter before the transmission starts. In the second scenario we consider, packets arrive during the transmissions with known arriving times and sizes. We develop optimal off-line scheduling policies which minimize the overall transmission completion time under causality constraints on both data and energy arrivals. Wireless systems comprised of rechargeable nodes have a significantly prolonged lifetime and are sustainable. A distinct characteristic of these systems is the fact that the nodes can harvest energy throughout the duration in which communication takes place. As such, transmission policies of the nodes need to adapt to these harvested energy arrivals. In this paper, we consider optimization of point-to-point data transmission with an energy harvesting transmitter which has a limited battery capacity, communicating in a wireless fading channel. We consider two objectives: maximizing the throughput by a deadline, and minimizing the transmission completion time of the communication session. We optimize these objectives by controlling the time sequence of transmit powers subject to energy storage capacity and causality constraints. We, first, study optimal offline policies. We introduce a directional water-filling algorithm which provides a simple and concise interpretation of the necessary optimality conditions. We show the optimality of an adaptive directional water-filling algorithm for the throughput maximization problem. We solve the transmission completion time minimization problem by utilizing its equivalence to its throughput maximization counterpart. Next, we consider online policies. We use stochastic dynamic programming to solve for the optimal online policy that maximizes the average number of bits delivered by a deadline under stochastic fading and energy arrival processes with causal channel state feedback. We also propose near-optimal policies with reduced complexity, and numerically study their performances along with the performances of the offline and online optimal policies under various different configurations. Communication over a broadband fading channel powered by an energy harvesting transmitter is studied. Assuming non-causal knowledge of energy data arrivals and channel gains, optimal transmission schemes are identified by taking into account the energy cost of the processing circuitry as well as the transmission energy. A constant processing cost for each active sub-channel is assumed. Three different system objectives are considered: i) throughput maximization, in which the total amount of transmitted data by a deadline is maximized for a backlogged transmitter with a finite capacity battery; ii) energy maximization, in which the remaining energy in an infinite capacity battery by a deadline is maximized such that all the arriving data packets are delivered; iii) transmission completion time minimization, in which the delivery time of all the arriving data packets is minimized assuming infinite size battery. For each objective, a convex optimization problem is formulated, the properties of the optimal transmission policies are identified, and an algorithm which computes an optimal transmission policy is proposed. Finally, based on the insights gained from the offline optimizations, low-complexity online algorithms performing close to the optimal dynamic programming solution for the throughput and energy maximization problems are developed under the assumption that the energy data arrivals and channel states are known causally at the transmitter.