Meromorphic solutions of a third order nonlinear differential equation

We prove that all the meromorphic solutions of the nonlinear differential equation c0 u"' + 6 u^4 + c1 u" + c2 u u' + c3 u^3 + c4 u'+ c5 u^2 + c6 u +c7=0 are elliptic or degenerate elliptic, and we build them explicitly.Comment: 12 pages, to appear, Journal of Mathematical Physic

Resource Allocation for Secure Communication in Systems with Wireless Information and Power Transfer

This paper considers secure communication in a multiuser multiple-input single-output (MISO) downlink system with simultaneous wireless information and power transfer. We study the design of resource allocation algorithms minimizing the total transmit power for the case when the receivers are able to harvest energy from the radio frequency. In particular, the algorithm design is formulated as a non-convex optimization problem which takes into account artificial noise generation to combat potential eavesdroppers, a minimum required signal-to-interference-plus-noise ratio (SINR) at the desired receiver, maximum tolerable SINRs at the potential eavesdroppers, and a minimum required power delivered to the receivers. We adopt a semidefinite programming (SDP) relaxation approach to obtain an upper bound solution for the considered problem. The tightness of the upper bound is revealed by examining a sufficient condition for the global optimal solution. Inspired by the sufficient condition, we propose two suboptimal resource allocation schemes enhancing secure communication and facilitating efficient energy harvesting. Simulation results demonstrate a close-to-optimal performance achieved by the proposed suboptimal schemes and significant transmit power savings by optimization of the artificial noise generation.Comment: 7 pages, 5 figures, and 1 table. Submitted for possible conference publicatio

Max-min Fair Wireless Energy Transfer for Secure Multiuser Communication Systems

This paper considers max-min fairness for wireless energy transfer in a downlink multiuser communication system. Our resource allocation design maximizes the minimum harvested energy among multiple multiple-antenna energy harvesting receivers (potential eavesdroppers) while providing quality of service (QoS) for secure communication to multiple single-antenna information receivers. In particular, the algorithm design is formulated as a non-convex optimization problem which takes into account a minimum required signal-to-interference-plus-noise ratio (SINR) constraint at the information receivers and a constraint on the maximum tolerable channel capacity achieved by the energy harvesting receivers for a given transmit power budget. The proposed problem formulation exploits the dual use of artificial noise generation for facilitating efficient wireless energy transfer and secure communication. A semidefinite programming (SDP) relaxation approach is exploited to obtain a global optimal solution of the considered problem. Simulation results demonstrate the significant performance gain in harvested energy that is achieved by the proposed optimal scheme compared to two simple baseline schemes.Comment: 5 pages, invited paper, IEEE Information Theory Workshop 2014, Hobart, Tasmania, Australia, Nov. 201