Optimal Transmit Strategy for Multi-User MIMO WPT Systems With Non-Linear Energy Harvesters

In this paper, we study multi-user multi-antenna wireless power transfer (WPT) systems, where each antenna at the energy harvesting (EH) nodes is connected to a dedicated non-linear rectifier. We propose an optimal transmit strategy which maximizes a weighted sum of the average harvested powers at the EH nodes under a constraint on the power budget of the transmitter. First, for multiple-input single-output (MISO) WPT systems, we show that it is optimal to transmit scalar symbols with an arbitrary phase and an amplitude, whose probability density function (pdf) has at most two mass points, using maximum ratio transmission (MRT) beamforming. Then, we prove that for single-input multiple-output (SIMO) WPT systems, the optimal transmit symbol amplitudes are discrete random variables, whose pdf also has no more than two mass points. For general multi-user MIMO WPT systems, we show that the optimal transmit strategy involves scalar unit-norm symbols with arbitrary phase and at most two beamforming vectors. In order to determine these vectors, we formulate a non-convex optimization problem and obtain an optimal solution based on monotonic optimization. Since the computational complexity of the optimal solution is high, we also propose a low-complexity iterative algorithm to obtain a suboptimal solution, which achieves nearly optimal performance. Our simulation results reveal that the proposed transmit strategy for multi-user MIMO WPT systems outperforms two baseline schemes, which are based on a linear EH model and a single beamforming vector, respectively. For a given transmit power budget, we show that the harvested power saturates when increasing the number of transmit antennas. Finally, we observe that the harvested power region spanned by multiple EH nodes is convex and the power harvested at one EH node can be traded for a higher harvested power at the other nodes. This paper was submitted in part to the Biennial Symposium on Communications, Saskatoon, Canada, 2021 [1] and the IEEE 3rd International Workshop on Wirelessly Powered Systems and Networks, 2021 [2]. ar X iv :2 10 5. 04 83 3v 1 [ cs .I T ] 1 1 M ay 2 02 1

[1]  Tamás Terlaky,et al.  Interior Point Methods for Nonlinear Optimization , 2010 .

[2]  Robert Schober,et al.  Markov Decision Process Based Design of SWIPT Systems: Non-linear EH Circuits, Memory, and Impedance Mismatch , 2020, ArXiv.

[3]  Prabhu Babu,et al.  Majorization-Minimization Algorithms in Signal Processing, Communications, and Machine Learning , 2017, IEEE Transactions on Signal Processing.

[4]  A. Pugh.  The art of electronics. 2nd edn: By Paul Horowitz and Winfield Hill. Pp. 1125. Cambridge University Presss. 1989. £29.95, US$49.50 , 1990 .

[5]  Liang-Hung Lu,et al.  A miniaturized Wilkinson power divider with CMOS active inductors , 2005, IEEE Microwave and Wireless Components Letters.

[6]  H. Vincent Poor,et al.  Fundamentals of Wireless Information and Power Transfer: From RF Energy Harvester Models to Signal and System Designs , 2018, IEEE Journal on Selected Areas in Communications.

[7]  Vahid Jamali,et al.  Resource Allocation for Secure Multi-User Downlink MISO-URLLC Systems , 2020, ICC 2020 - 2020 IEEE International Conference on Communications (ICC).

[8]  Bruno Clerckx,et al.  Wireless Information and Power Transfer: Nonlinearity, Waveform Design, and Rate-Energy Tradeoff , 2016, IEEE Transactions on Signal Processing.

[9]  Christoph Schenk,et al.  Advanced Electronic Circuits , 1978 .

[10]  Anant Sahai,et al.  Shannon meets Tesla: Wireless information and power transfer , 2010, 2010 IEEE International Symposium on Information Theory.

[11]  Bruno Clerckx,et al.  Waveform Design for Wireless Power Transfer , 2016, IEEE Transactions on Signal Processing.

[12]  Gert R. G. Lanckriet,et al.  On the Convergence of the Concave-Convex Procedure , 2009, NIPS.

[13]  David P. Morton,et al.  Higher-Order Upper Bounds on the Expectation of a Convex Function , 2002 .

[14]  Ian F. Akyildiz,et al.  6G and Beyond: The Future of Wireless Communications Systems , 2020, IEEE Access.

[15]  Robert Schober,et al.  Harvested Power Region of Two-user MISO WPT Systems With Non-linear EH Nodes , 2021, ArXiv.

[16]  Bruno Clerckx,et al.  Beamforming Optimization for MIMO Wireless Power Transfer With Nonlinear Energy Harvesting: RF Combining Versus DC Combining , 2020, IEEE Transactions on Wireless Communications.

[17]  C. J. Price,et al.  On the Convergence of Grid-Based Methods for Unconstrained Optimization , 2000, SIAM J. Optim..

[18]  Derrick Wing Kwan Ng,et al.  Conditional Capacity and Transmit Signal Design for SWIPT Systems With Multiple Nonlinear Energy Harvesting Receivers , 2020, IEEE Transactions on Communications.

[19]  Bruno Clerckx,et al.  Signal and System Design for Wireless Power Transfer: Prototype, Experiment and Validation , 2019, IEEE Transactions on Wireless Communications.

[20]  Derrick Wing Kwan Ng,et al.  Practical Non-Linear Energy Harvesting Model and Resource Allocation for SWIPT Systems , 2015, IEEE Communications Letters.

[21]  Bruno Clerckx.  Waveform Optimization for SWIPT with Nonlinear Energy Harvester Modeling , 2016, WSA.

[22]  Jianwei Huang,et al.  Monotonic Optimization in Communication and Networking Systems , 2013 .

[23]  Jie Xu,et al.  A Generic Receiver Architecture for MIMO Wireless Power Transfer With Nonlinear Energy Harvesting , 2018, IEEE Signal Processing Letters.

[24]  Bruno Clerckx,et al.  Waveform Design for Wireless Power Transfer With Limited Feedback , 2017, IEEE Transactions on Wireless Communications.

[25]  Rui Zhang,et al.  MIMO Broadcasting for Simultaneous Wireless Information and Power Transfer , 2011, IEEE Transactions on Wireless Communications.

[26]  Robert Schober,et al.  Optimal Transmit Strategy for MIMO WPT Systems With Non-linear Energy Harvesting , 2021, 2021 17th International Conference on Distributed Computing in Sensor Systems (DCOSS).

[27]  K. J. Ray Liu,et al.  Rate-Energy Region of SWIPT for MIMO Broadcasting Under Nonlinear Energy Harvesting Model , 2017, IEEE Transactions on Wireless Communications.

[28]  Bruno Clerckx,et al.  Large-Scale Multiantenna Multisine Wireless Power Transfer , 2016, IEEE Transactions on Signal Processing.

[29]  Abbas Jamalipour,et al.  Wireless communications , 2005, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

[30]  Derrick Wing Kwan Ng,et al.  On the Capacity of SWIPT Systems with a Nonlinear Energy Harvesting Circuit , 2017, 2018 IEEE International Conference on Communications (ICC).