21,766 research outputs found
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
Convex Relaxations for Permutation Problems
Seriation seeks to reconstruct a linear order between variables using
unsorted, pairwise similarity information. It has direct applications in
archeology and shotgun gene sequencing for example. We write seriation as an
optimization problem by proving the equivalence between the seriation and
combinatorial 2-SUM problems on similarity matrices (2-SUM is a quadratic
minimization problem over permutations). The seriation problem can be solved
exactly by a spectral algorithm in the noiseless case and we derive several
convex relaxations for 2-SUM to improve the robustness of seriation solutions
in noisy settings. These convex relaxations also allow us to impose structural
constraints on the solution, hence solve semi-supervised seriation problems. We
derive new approximation bounds for some of these relaxations and present
numerical experiments on archeological data, Markov chains and DNA assembly
from shotgun gene sequencing data.Comment: Final journal version, a few typos and references fixe
A Modified Levenberg-Marquardt Method for the Bidirectional Relay Channel
This paper presents an optimization approach for a system consisting of
multiple bidirectional links over a two-way amplify-and-forward relay. It is
desired to improve the fairness of the system. All user pairs exchange
information over one relay station with multiple antennas. Due to the joint
transmission to all users, the users are subject to mutual interference. A
mitigation of the interference can be achieved by max-min fair precoding
optimization where the relay is subject to a sum power constraint. The
resulting optimization problem is non-convex. This paper proposes a novel
iterative and low complexity approach based on a modified Levenberg-Marquardt
method to find near optimal solutions. The presented method finds solutions
close to the standard convex-solver based relaxation approach.Comment: submitted to IEEE Transactions on Vehicular Technology We corrected
small mistakes in the proof of Lemma 2 and Proposition
Push sum with transmission failures
The push-sum algorithm allows distributed computing of the average on a
directed graph, and is particularly relevant when one is restricted to one-way
and/or asynchronous communications. We investigate its behavior in the presence
of unreliable communication channels where messages can be lost. We show that
exponential convergence still holds and deduce fundamental properties that
implicitly describe the distribution of the final value obtained. We analyze
the error of the final common value we get for the essential case of two nodes,
both theoretically and numerically. We provide performance comparison with a
standard consensus algorithm
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