3,009 research outputs found
Semidefinite approximation for mixed binary quadratically constrained quadratic programs
Motivated by applications in wireless communications, this paper develops
semidefinite programming (SDP) relaxation techniques for some mixed binary
quadratically constrained quadratic programs (MBQCQP) and analyzes their
approximation performance. We consider both a minimization and a maximization
model of this problem. For the minimization model, the objective is to find a
minimum norm vector in -dimensional real or complex Euclidean space, such
that concave quadratic constraints and a cardinality constraint are
satisfied with both binary and continuous variables. {\color{blue}By employing
a special randomized rounding procedure, we show that the ratio between the
norm of the optimal solution of the minimization model and its SDP relaxation
is upper bounded by \cO(Q^2(M-Q+1)+M^2) in the real case and by
\cO(M(M-Q+1)) in the complex case.} For the maximization model, the goal is
to find a maximum norm vector subject to a set of quadratic constraints and a
cardinality constraint with both binary and continuous variables. We show that
in this case the approximation ratio is bounded from below by
\cO(\epsilon/\ln(M)) for both the real and the complex cases. Moreover, this
ratio is tight up to a constant factor
Input Design for System Identification via Convex Relaxation
This paper proposes a new framework for the optimization of excitation inputs
for system identification. The optimization problem considered is to maximize a
reduced Fisher information matrix in any of the classical D-, E-, or A-optimal
senses. In contrast to the majority of published work on this topic, we
consider the problem in the time domain and subject to constraints on the
amplitude of the input signal. This optimization problem is nonconvex. The main
result of the paper is a convex relaxation that gives an upper bound accurate
to within of the true maximum. A randomized algorithm is presented for
finding a feasible solution which, in a certain sense is expected to be at
least as informative as the globally optimal input signal. In the case
of a single constraint on input power, the proposed approach recovers the true
global optimum exactly. Extensions to situations with both power and amplitude
constraints on both inputs and outputs are given. A simple simulation example
illustrates the technique.Comment: Preprint submitted for journal publication, extended version of a
paper at 2010 IEEE Conference on Decision and Contro
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
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