Optimal Relay Placement in Two-Hop RF Energy Transfer

Recently, wireless radio frequency energy transfer (RFET) has emerged as an effective technology for prolonging lifetime of the energy-limited wireless sensor networks. However, low RFET efficiency is still a fundamental bottleneck in its widespread usage. Multi-hop RF energy transfer (MHET) can improve the RFET efficiency by deploying relay nodes that scavenge the dispersed energy and transfer it to the nearby sensor node. The efficiency of MHET is strongly influenced by the relay node's placement. To maximize the RFET efficiency for a two-hop scenario, in this paper a novel optimization model is proposed to determine the optimal relay placement (ORP) on an Euclidean x-y plane. Nontrivial tradeoff between the energy scavenged at the relay versus the effective energy delivered by the relay to the target node is investigated. Due to the nonconvex and highly nonlinear nature of the optimization problem, an α-based branch and bound algorithm has been used. The proposed optimization model is further extended by incorporating distributed beamforming to enhance the RFET efficiency. Numerical results illustrate that the proposed algorithm provides convergence to the ϵ-global optimal solution in a few iterations, and ORP provides significant energy saving over arbitrary relay positions for commercial RF energy harvesting systems.

[1]  A. Belegundu,et al.  Optimization Concepts and Applications in Engineering , 2011 .

[2]  Swades De,et al.  Experimental demonstration of multi-hop RF energy transfer , 2013, 2013 IEEE 24th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC).

[3]  Salama Ikki,et al.  A Study of Optimization Problem for Amplify-and-Forward Relaying over Weibull Fading Channels with Multiple Antennas , 2011, IEEE Communications Letters.

[4]  Ali A. Nasir,et al.  Relaying Protocols for Wireless Energy Harvesting and Information Processing , 2012, IEEE Transactions on Wireless Communications.

[5]  Ioannis Krikidis,et al.  Simultaneous Information and Energy Transfer in Large-Scale Networks with/without Relaying , 2013, IEEE Transactions on Communications.

[6]  Christodoulos A Floudas,et al.  Global minimum potential energy conformations of small molecules , 1994, J. Glob. Optim..

[7]  Chinmoy Kundu,et al.  Joint Optimal Power Allocation and Relay Location for Amplify-and-Forward Multihop Relaying over Lognormal Channel , 2013, 2013 IEEE 77th Vehicular Technology Conference (VTC Spring).

[8]  Raghuraman Mudumbai,et al.  On the Feasibility of Distributed Beamforming in Wireless Networks , 2007, IEEE Transactions on Wireless Communications.

[9]  H. Vincent Poor,et al.  Power Allocation Strategies in Energy Harvesting Wireless Cooperative Networks , 2013, IEEE Transactions on Wireless Communications.

[10]  Murat Uysal,et al.  Joint Optimization of Power Allocation and Relay Location for Decode-and-Forward Dual-Hop Systems over Nakagami-m Fading Channels , 2009, GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference.

[11]  Mohamed K. Watfa,et al.  Multi-Hop Wireless Energy Transfer in WSNs , 2011, IEEE Communications Letters.

[12]  Yacine Challal,et al.  Multi-hop wireless charging optimization in low-power networks , 2013, 2013 IEEE Global Communications Conference (GLOBECOM).

[13]  Raghuraman Mudumbai,et al.  A Scalable Architecture for Distributed Transmit Beamforming with Commodity Radios: Design and Proof of Concept , 2013, IEEE Transactions on Wireless Communications.

[14]  M. Soljačić,et al.  Wireless Power Transfer via Strongly Coupled Magnetic Resonances , 2007, Science.

[15]  A. Neumaier,et al.  A global optimization method, αBB, for general twice-differentiable constrained NLPs — I. Theoretical advances , 1998 .

[16]  Gregory W. Wornell,et al.  Cooperative diversity in wireless networks: Efficient protocols and outage behavior , 2004, IEEE Transactions on Information Theory.

[17]  M. Powell.  Convergence properties of algorithms for nonlinear optimization , 1986 .

[18]  Swades De,et al.  Toward Uninterrupted Operation of Wireless Sensor Networks , 2012, Computer.

[19]  Rui Zhang,et al.  MIMO Broadcasting for Simultaneous Wireless Information and Power Transfer , 2013 .

[20]  Prusayon Nintanavongsa,et al.  Design Optimization and Implementation for RF Energy Harvesting Circuits , 2012, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[21]  Kai Han,et al.  Fueling Wireless Networks perpetually: A case of multi-hop wireless power distribution∗ , 2013, 2013 IEEE 24th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC).

[22]  Robert Schober,et al.  Relay Selection for Simultaneous Information Transmission and Wireless Energy Transfer: A Tradeoff Perspective , 2013, IEEE Journal on Selected Areas in Communications.

[23]  E. Weisstein.  Least Squares Fitting--Polynomial , 2002 .

[24]  D.C. Jenn,et al.  Transmission Equation for Multiple Cooperative Transmitters and Collective Beamforming , 2008, IEEE Antennas and Wireless Propagation Letters.

[25]  Christodoulos A. Floudas,et al.  Deterministic global optimization - theory, methods and applications , 2010, Nonconvex optimization and its applications.

[26]  Swades De,et al.  Implementation of multi-path energy routing , 2014, 2014 IEEE 25th Annual International Symposium on Personal, Indoor, and Mobile Radio Communication (PIMRC).

[27]  Michael R. Mullen,et al.  Structural equation modelling: guidelines for determining model fit , 2008 .

[28]  John. Ruze.  Physical limitations on antennas , 1952 .

[29]  Xianfu Chen,et al.  Energy-Efficient Optimization for Wireless Information and Power Transfer in Large-Scale MIMO Systems Employing Energy Beamforming , 2013, IEEE Wireless Communications Letters.