Energy Harvesting Systems With Continuous Energy and Data Arrivals: The Optimal Offline and Heuristic Online Algorithms

Abstract

Energy harvesting has been developed as an effective technology for communication systems in order to extend the lifetime of these systems. In this work, we consider a singleuser energy harvesting wireless communication system, in which arrival data and harvested energy curves are modeled as continuous functions. For the single-user model, our first goal is to find an offline algorithm, which maximizes the amount of data which is transmitted to the receiver node by a given deadline. If more than one scheme exists that transmits the maximum data, we choose the one with minimum utilized energy at the transmitter node. Next, we propose an online algorithm for this system. We also consider a multi-hop energy harvesting wireless communication system in a full-duplex mode and find the optimal offline algorithm to maximize the throughput.From (47) and (50), we have p * rd,Bsr (t 0 ) < p * rd,B * sr,s (t 0 ) which is a contradiction. Hence, proof is complete.Corollary 2. Theorem V.1 can be extended to n relays: Tx transmits maximum amount of data by proposed algorithm in Section IV, the first relay sends maximum amount of data to the second relay by the same algorithm and this procedure repeats until the Rx.An example: Assume that harvested energy curves in Tx and the relay nodes are E s (t) = e t − 1, E r (t) = 2e t − 2, respectively and r sr (p) = r rd (p) = 1 2 log(1 + p) in which

Optimal Transmission Policies for Multi-Hop Energy Harvesting Systems

“…The received data at the relay (from the source) can be modeled with an arrival data curve in the relay. Thus, knowing this curve (e.g.B sr (t)), the optimal strategy at the relay is a solution of the second hop's problem [20] (i.e., B * rd,Bsr (t)). Therefore, the question reduces to find the optimalB sr (t).…”

“…The proposed online algorithms from source to the relay in this paper is chosen as that in [20,Section V]. The difference between direct generalization of algorithm in [20,Section V] and our proposed algorithm is in the relay's policy.…”

“…We first prove that for any feasible B sr (t), we have: B * rd,Bsr (t) ≤ B * rd,B * sr,s (t). To prove, we use contradiction as well as the technique mentioned in [20,Remark 21].…”

“…In [0, T 1 ] based on (6), we haveB sr (t) = B * sr,s (t) and thusB sr (t) is feasible. For t ∈ [T 1 , T ],B sr (t) is linear and based on [20,Lemma 4], B * sr,s (t) is a convex curve. Thus, d dt l(t) ≤ d dt B * sr,s (t) holds for t ∈ [T 1 , T ], i.e., the slope of l(t) is not greater than d dt B * sr,s (t)| T + 1 .…”

On Optimal Online Algorithms for Energy Harvesting Systems With Continuous Energy and Data Arrivals

“…Besides, as we show in Section IV, the discretizing of harvested energy curve reduces the efficiency of system. In arXiv:1701.05392v1 [cs.IT] 19 Jan 2017 addition, the motivation of continuous model for data arrival comes from the rateless codes, network calculus and using relays in communications [4].…”