427 research outputs found
On embedded spheres of affine manifolds
This paper studies certain embedded spheres in closed affine manifolds. For n greater than or equal to 3, we investigate the dome bodies in a closed affine n-manifold M with its boundary homeomorphic to a sphere under the assumption that a developing map restricted to a component of the boundary of hat{M} is an embedding onto a strictly convex sphere in A^n. By using the recurrent property of an incomplete geodesic we show that dome bodies are compact. Then a maximal dome body is a closed solid ball bounded by a component of the boundary of hat{M}, and hence equals hat{M} . The main theorem is that the standard ball in an affine space can only bound one compact affine manifold inside, namely the solid ball
Secure Beamforming For MIMO Broadcasting With Wireless Information And Power Transfer
This paper considers a basic MIMO information-energy (I-E) broadcast system,
where a multi-antenna transmitter transmits information and energy
simultaneously to a multi-antenna information receiver and a dual-functional
multi-antenna energy receiver which is also capable of decoding information.
Due to the open nature of wireless medium and the dual purpose of information
and energy transmission, secure information transmission while ensuring
efficient energy harvesting is a critical issue for such a broadcast system.
Assuming that physical layer security techniques are applied to the system to
ensure secure transmission from the transmitter to the information receiver, we
study beamforming design to maximize the achievable secrecy rate subject to a
total power constraint and an energy harvesting constraint. First, based on
semidefinite relaxation, we propose global optimal solutions to the secrecy
rate maximization (SRM) problem in the single-stream case and a specific
full-stream case where the difference of Gram matrices of the channel matrices
is positive semidefinite. Then, we propose a simple iterative algorithm named
inexact block coordinate descent (IBCD) algorithm to tackle the SRM problem of
general case with arbitrary number of streams. We proves that the IBCD
algorithm can monotonically converge to a Karush-Kuhn-Tucker (KKT) solution to
the SRM problem. Furthermore, we extend the IBCD algorithm to the joint
beamforming and artificial noise design problem. Finally, simulations are
performed to validate the performance of the proposed beamforming algorithms.Comment: Submitted to journal for possible publication. First submission to
arXiv Mar. 14 201
- …