139 research outputs found
Robust Adaptive Beamforming for General-Rank Signal Model with Positive Semi-Definite Constraint via POTDC
The robust adaptive beamforming (RAB) problem for general-rank signal model
with an additional positive semi-definite constraint is considered. Using the
principle of the worst-case performance optimization, such RAB problem leads to
a difference-of-convex functions (DC) optimization problem. The existing
approaches for solving the resulted non-convex DC problem are based on
approximations and find only suboptimal solutions. Here we solve the non-convex
DC problem rigorously and give arguments suggesting that the solution is
globally optimal. Particularly, we rewrite the problem as the minimization of a
one-dimensional optimal value function whose corresponding optimization problem
is non-convex. Then, the optimal value function is replaced with another
equivalent one, for which the corresponding optimization problem is convex. The
new one-dimensional optimal value function is minimized iteratively via
polynomial time DC (POTDC) algorithm.We show that our solution satisfies the
Karush-Kuhn-Tucker (KKT) optimality conditions and there is a strong evidence
that such solution is also globally optimal. Towards this conclusion, we
conjecture that the new optimal value function is a convex function. The new
RAB method shows superior performance compared to the other state-of-the-art
general-rank RAB methods.Comment: 29 pages, 7 figures, 2 tables, Submitted to IEEE Trans. Signal
Processing on August 201
Robust Design of Transmit Waveform and Receive Filter For Colocated MIMO Radar
We consider the problem of angle-robust joint transmit waveform and receive
filter design for colocated Multiple-Input Multiple-Output (MIMO) radar, in the
presence of signal-dependent interferences. The design problem is cast as a
max-min optimization problem to maximize the worst-case output
signal-to-interference-plus-noise-ratio (SINR) with respect to the unknown
angle of the target of interest. Based on rank-one relaxation and semi-definite
programming (SDP) representation of a nonnegative trigonometric polynomial, a
cyclic optimization algorithm is proposed to tackle this problem. The
effectiveness of the proposed method is illustrated via numerical examples.Comment: 6 pages, 13 figures, part of this work was submitted to IEEE Signal
Processing Letters; (short introduction; typos corrected; revised statement
in section III-B and IV; revised figure labels
Efficient Transmit Beamspace Design for Search-free Based DOA Estimation in MIMO Radar
In this paper, we address the problem of transmit beamspace design for
multiple-input multiple-output (MIMO) radar with colocated antennas in
application to direction-of-arrival (DOA) estimation. A new method for
designing the transmit beamspace matrix that enables the use of search-free DOA
estimation techniques at the receiver is introduced. The essence of the
proposed method is to design the transmit beamspace matrix based on minimizing
the difference between a desired transmit beampattern and the actual one under
the constraint of uniform power distribution across the transmit array
elements. The desired transmit beampattern can be of arbitrary shape and is
allowed to consist of one or more spatial sectors. The number of transmit
waveforms is even but otherwise arbitrary. To allow for simple search-free DOA
estimation algorithms at the receive array, the rotational invariance property
is established at the transmit array by imposing a specific structure on the
beamspace matrix. Semi-definite relaxation is used to transform the proposed
formulation into a convex problem that can be solved efficiently. We also
propose a spatial-division based design (SDD) by dividing the spatial domain
into several subsectors and assigning a subset of the transmit beams to each
subsector. The transmit beams associated with each subsector are designed
separately. Simulation results demonstrate the improvement in the DOA
estimation performance offered by using the proposed joint and SDD transmit
beamspace design methods as compared to the traditional MIMO radar technique.Comment: 32 pages, 10 figures, submitted to the IEEE Trans. Signal Processing
in May 201
Sum-Rate Maximization in Two-Way AF MIMO Relaying: Polynomial Time Solutions to a Class of DC Programming Problems
Sum-rate maximization in two-way amplify-and-forward (AF) multiple-input
multiple-output (MIMO) relaying belongs to the class of difference-of-convex
functions (DC) programming problems. DC programming problems occur as well in
other signal processing applications and are typically solved using different
modifications of the branch-and-bound method. This method, however, does not
have any polynomial time complexity guarantees. In this paper, we show that a
class of DC programming problems, to which the sum-rate maximization in two-way
MIMO relaying belongs, can be solved very efficiently in polynomial time, and
develop two algorithms. The objective function of the problem is represented as
a product of quadratic ratios and parameterized so that its convex part (versus
the concave part) contains only one (or two) optimization variables. One of the
algorithms is called POlynomial-Time DC (POTDC) and is based on semi-definite
programming (SDP) relaxation, linearization, and an iterative search over a
single parameter. The other algorithm is called RAte-maximization via
Generalized EigenvectorS (RAGES) and is based on the generalized eigenvectors
method and an iterative search over two (or one, in its approximate version)
optimization variables. We also derive an upper-bound for the optimal values of
the corresponding optimization problem and show by simulations that this
upper-bound can be achieved by both algorithms. The proposed methods for
maximizing the sum-rate in the two-way AF MIMO relaying system are shown to be
superior to other state-of-the-art algorithms.Comment: 35 pages, 10 figures, Submitted to the IEEE Trans. Signal Processing
in Nov. 201
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