Abstract
In this paper, to maximize the energy efficiency (EE) in the two-hop multi-relay cooperative decoding and forwarding (DF) system for simultaneous wireless information and power transmission (SWIPT), an optimal power allocation algorithm is proposed, in which the relay energy harvesting (EH) adopts a nonlinear model. Under the constraints, including energy causality, the minimum transmission quality of information and the total transmission power at the relays, an optimization problem is constructed to jointly optimize the transmit power and power-splitting (PS) ratios of multiple relays. Although this problem is a nonlinear fractional programming problem, an iterative algorithm is developed to obtain the optimal power allocation. In particular, the joint power allocation at multiple relays is first decoupled into a single relay power allocation, and then single-relay power allocation is performed by the Dinkelbach iteration algorithm, which can be proven that it is a convex programming problem. Its closed form solutions for different polylines of EH models are obtained by using mathematical methods, such as monotonicity, Lagrange multipliers, the KKT condition and the Cardan formula. The simulation results show the superiority of the power allocation algorithm proposed in this paper in terms of EE.
Highlights
This paper presents a power allocation algorithm based on the nonlinear energy harvesting (EH) model for maximizing the EE in a two-hop multi-relay cooperative forwarding system
: ∑ Pi ≤ Pmax i =1 where γmin = 2Rmin − 1 and Rmin is the minimum required rate for S − R − D, Pmax is the threshold of the relay nodes’ total transmit power, constraint C2 means the energy causality, C3 is the constraint of the quality of information transmission, C4 is the constraint that the energy harvester works in the l − th linear regions and C5 is the constraint of the total transmit power of all relays, and it is a requirement to consider interference across the network [18]
Superior EE performance of the multi-relay system was verified by comparison with different numbers of relays
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. In [11], a power allocation algorithm for a nonlinear EH model that maximized the total harvesting power of the energy harvester was presented. This paper presents a power allocation algorithm based on the nonlinear EH model for maximizing the EE in a two-hop multi-relay cooperative forwarding system. The EE maximization problem with quality of service (QoS) guaranteed is a complex, nondeterministic polynomial (NP) problem and can be decoupled into a single-relay power allocation problem. It is optimized based on the Dinkelbach iteration algorithm, and the optimization problem after iteration simplification is proven to be a convex programming problem.
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