40 research outputs found
Towards Dual-functional Radar-Communication Systems: Optimal Waveform Design
We focus on a dual-functional multi-input-multi-output (MIMO)
radar-communication (RadCom) system, where a single transmitter communicates
with downlink cellular users and detects radar targets simultaneously. Several
design criteria are considered for minimizing the downlink multi-user
interference. First, we consider both the omnidirectional and directional
beampattern design problems, where the closed-form globally optimal solutions
are obtained. Based on these waveforms, we further consider a weighted
optimization to enable a flexible trade-off between radar and communications
performance and introduce a low-complexity algorithm. The computational costs
of the above three designs are shown to be similar to the conventional
zero-forcing (ZF) precoding. Moreover, to address the more practical constant
modulus waveform design problem, we propose a branch-and-bound algorithm that
obtains a globally optimal solution and derive its worst-case complexity as a
function of the maximum iteration number. Finally, we assess the effectiveness
of the proposed waveform design approaches by numerical results.Comment: 13 pages, 10 figures. This work has been submitted to the IEEE for
possible publication. Copyright may be transferred without notice, after
which this version may no longer be accessibl
S-Lemma with Equality and Its Applications
Let and be two quadratic functions
having symmetric matrices and . The S-lemma with equality asks when the
unsolvability of the system implies the existence of a real
number such that . The
problem is much harder than the inequality version which asserts that, under
Slater condition, is unsolvable if and only if for some . In this paper, we
show that the S-lemma with equality does not hold only when the matrix has
exactly one negative eigenvalue and is a non-constant linear function
(). As an application, we can globally solve as well as the two-sided generalized trust region subproblem
without any condition. Moreover, the
convexity of the joint numerical range where is a (possibly non-convex) quadratic
function and are affine functions can be characterized
using the newly developed S-lemma with equality.Comment: 34 page
Robust Joint Precoder and Equalizer Design in MIMO Communication Systems
We address joint design of robust precoder and equalizer in a MIMO
communication system using the minimization of weighted sum of mean square
errors. In addition to imperfect knowledge of channel state information, we
also account for inaccurate awareness of interference plus noise covariance
matrix and power shaping matrix. We follow the worst-case model for imperfect
knowledge of these matrices. First, we derive the worst-case values of these
matrices. Then, we transform the joint precoder and equalizer optimization
problem into a convex scalar optimization problem. Further, the solution to
this problem will be simplified to a depressed quartic equation, the
closed-form expressions for roots of which are known. Finally, we propose an
iterative algorithm to obtain the worst-case robust transceivers.Comment: 2 figures, 5 pages, conferenc
On the local stability of semidefinite relaxations
We consider a parametric family of quadratically constrained quadratic
programs (QCQP) and their associated semidefinite programming (SDP)
relaxations. Given a nominal value of the parameter at which the SDP relaxation
is exact, we study conditions (and quantitative bounds) under which the
relaxation will continue to be exact as the parameter moves in a neighborhood
around the nominal value. Our framework captures a wide array of statistical
estimation problems including tensor principal component analysis, rotation
synchronization, orthogonal Procrustes, camera triangulation and resectioning,
essential matrix estimation, system identification, and approximate GCD. Our
results can also be used to analyze the stability of SOS relaxations of general
polynomial optimization problems.Comment: 23 pages, 3 figure