11 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
Power Allocation Based on SEP Minimization in Two-Hop Decode-and-Forward Relay Networks
The problem of optimal power allocation among the relays in a two-hop
decode-and-forward cooperative relay network with independent Rayleigh fading
channels is considered. It is assumed that only the relays that decode the
source message correctly contribute in data transmission. Moreover, only the
knowledge of statistical channel state information is available. A new simple
closed-form expression for the average symbol error probability is derived.
Based on this expression, a new power allocation method that minimizes the
average symbol error probability and takes into account the constraints on the
total average power of all the relay nodes and maximum instant power of each
relay node is developed. The corresponding optimization problem is shown to be
a convex problem that can be solved using interior point methods. However, an
approximate closed-form solution is obtained and shown to be practically more
appealing due to significant complexity reduction. The accuracy of the
approximation is discussed. Moreover, the so obtained closed-form solution
gives additional insights into the optimal power allocation problem. Simulation
results confirm the improved performance of the proposed power allocation
scheme as compared to other schemes.Comment: 27 pages, 5 figures, submitted to the IEEE Trans. Signal Processing
in Feb. 201
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
On the Optimal Precoding for MIMO Gaussian Wire-Tap Channels
We consider the problem of finding secrecy rate of a multiple-input
multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver,
and an eavesdropper are all equipped with multiple antennas. The channel states
from the transmitter to the legitimate user and to the eavesdropper are assumed
to be known at the transmitter. In this contribution, we address the problem of
finding the optimal precoder/transmit covariance matrix maximizing the secrecy
rate of the given wiretap channel. The problem formulation is shown to be
equivalent to a difference of convex functions programming problem and an
efficient algorithm for addressing this problem is developed.Comment: Published in Proceedings of the Tenth International Symposium on
Wireless Communication Systems (ISWCS 2013), Ilmenau, Germany, August 201