15,949 research outputs found
A Non-Convex Relaxation for Fixed-Rank Approximation
This paper considers the problem of finding a low rank matrix from
observations of linear combinations of its elements. It is well known that if
the problem fulfills a restricted isometry property (RIP), convex relaxations
using the nuclear norm typically work well and come with theoretical
performance guarantees. On the other hand these formulations suffer from a
shrinking bias that can severely degrade the solution in the presence of noise.
In this theoretical paper we study an alternative non-convex relaxation that
in contrast to the nuclear norm does not penalize the leading singular values
and thereby avoids this bias. We show that despite its non-convexity the
proposed formulation will in many cases have a single local minimizer if a RIP
holds. Our numerical tests show that our approach typically converges to a
better solution than nuclear norm based alternatives even in cases when the RIP
does not hold
Multicast Multigroup Beamforming for Per-antenna Power Constrained Large-scale Arrays
Large in the number of transmit elements, multi-antenna arrays with
per-element limitations are in the focus of the present work. In this context,
physical layer multigroup multicasting under per-antenna power constrains, is
investigated herein. To address this complex optimization problem
low-complexity alternatives to semi-definite relaxation are proposed. The goal
is to optimize the per-antenna power constrained transmitter in a maximum
fairness sense, which is formulated as a non-convex quadratically constrained
quadratic problem. Therefore, the recently developed tool of feasible point
pursuit and successive convex approximation is extended to account for
practical per-antenna power constraints. Interestingly, the novel iterative
method exhibits not only superior performance in terms of approaching the
relaxed upper bound but also a significant complexity reduction, as the
dimensions of the optimization variables increase. Consequently, multicast
multigroup beamforming for large-scale array transmitters with per-antenna
dedicated amplifiers is rendered computationally efficient and accurate. A
preliminary performance evaluation in large-scale systems for which the
semi-definite relaxation constantly yields non rank-1 solutions is presented.Comment: submitted to IEEE SPAWC 2015. arXiv admin note: substantial text
overlap with arXiv:1406.755
Designing Precoding and Receive Matrices for Interference Alignment in MIMO Interference Channels
Interference is a key bottleneck in wireless communication
systems. Interference alignment is a management
technique that align interference from other transmitters in
the least possibly dimension subspace at each receiver and
provides the remaining dimensions for free interference signal.
An uncoordinated interference is an example of interference
which cannot be aligned coordinately with interference from
coordinated part; consequently, the performance of interference
alignment approaches are degraded. In this paper, we propose a
rank minimization method to enhance the performance of interference
alignment in the presence of uncoordinated interference
sources. Firstly, to obtain higher multiplexing gain, a new rank
minimization based optimization problem is proposed; then, a
new class of convex relaxation is introduced which can reduce
the optimal value of the problem and obtain lower rank solutions
by expanding the feasibility set. Simulation results show that our
proposed method can obtain considerably higher multiplexing
gain and sum rate than other approaches in the interference
alignment framework
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