17 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
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
Twenty-Five Years of Advances in Beamforming: From Convex and Nonconvex Optimization to Learning Techniques
Beamforming is a signal processing technique to steer, shape, and focus an
electromagnetic wave using an array of sensors toward a desired direction. It
has been used in several engineering applications such as radar, sonar,
acoustics, astronomy, seismology, medical imaging, and communications. With the
advances in multi-antenna technologies largely for radar and communications,
there has been a great interest on beamformer design mostly relying on
convex/nonconvex optimization. Recently, machine learning is being leveraged
for obtaining attractive solutions to more complex beamforming problems. This
article captures the evolution of beamforming in the last twenty-five years
from convex-to-nonconvex optimization and optimization-to-learning approaches.
It provides a glimpse of this important signal processing technique into a
variety of transmit-receive architectures, propagation zones, paths, and
conventional/emerging applications
An alternative to diagonal loading for implementation of a white noise array gain constrained robust beamformer
Diagonal loading is one of the most popular methods of robust adaptive beamforming, and the solution to many different problems aimed at producing beamformers which are robust to finite samples effects or/and steering vector errors. Among the latter, constraining the white noise array gain (WNAG) is a meaningful approach. However, relating the loading level to the desired WNAG is not straightforward. In this communication, using a generalized sidelobe canceler structure of the beamformer, we prove that the WNAG constraint can be encoded directly in the beamformer, and the latter can be obtained in a rather simple way from a specific eigenvector and without going through the diagonal loading step
Principles of minimum variance robust adaptive beamforming design
Robustness is typically understood as an ability of adaptive beamforming algorithm to achieve high performance in the situations with imperfect, incomplete, or erroneous knowledge about the source, propagation media, and antenna array. It is also desired to achieve high performance with as little as possible prior information. In the last decade, several fruitful principles to minimum variance distortionless response (MVDR) robust adaptive beamforming (RAB) design have been developed and successfully applied to solve a number of problems in a wide range of applications. Such principles of MVDR RAB design are summarized here in a single paper. Prof. Gershman has actively participated in the development and applications of a number of such MVDR RAB design principles