Recovery from Linear Measurements with Complexity-Matching Universal Signal Estimation

We study the compressed sensing (CS) signal estimation problem where an input signal is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the input signal during recovery, the signal structure that can be leveraged is often not known a priori. In this paper, we consider universal CS recovery, where the statistics of a stationary ergodic signal source are estimated simultaneously with the signal itself. Inspired by Kolmogorov complexity and minimum description length, we focus on a maximum a posteriori (MAP) estimation framework that leverages universal priors to match the complexity of the source. Our framework can also be applied to general linear inverse problems where more measurements than in CS might be needed. We provide theoretical results that support the algorithmic feasibility of universal MAP estimation using a Markov chain Monte Carlo implementation, which is computationally challenging. We incorporate some techniques to accelerate the algorithm while providing comparable and in many cases better reconstruction quality than existing algorithms. Experimental results show the promise of universality in CS, particularly for low-complexity sources that do not exhibit standard sparsity or compressibility.Comment: 29 pages, 8 figure

Non-convex approach to binary compressed sensing

We propose a new approach to the recovery of binary signals in compressed sensing, based on the local minimization of a non-convex cost functional. The desired signal is proved to be a local minimum of the functional under mild conditions on the sensing matrix and on the number of measurements. We develop a procedure to achieve the desired local minimum, and, finally, we propose numerical experiments that show the improvement obtained by the proposed approach with respect to the classical convex approach, i.e., Lasso

Recovery of binary sparse signals from compressed linear measurements via polynomial optimization

The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been recently proposed to deal with the case of finite-valued sparse signals. In this work, we focus on binary sparse signals and we propose a novel formulation, based on polynomial optimization. This approach is analyzed and compared to the state-of-the-art binary compressed sensing methods

Sparse Signal Processing Concepts for Efficient 5G System Design

As it becomes increasingly apparent that 4G will not be able to meet the emerging demands of future mobile communication systems, the question what could make up a 5G system, what are the crucial challenges and what are the key drivers is part of intensive, ongoing discussions. Partly due to the advent of compressive sensing, methods that can optimally exploit sparsity in signals have received tremendous attention in recent years. In this paper we will describe a variety of scenarios in which signal sparsity arises naturally in 5G wireless systems. Signal sparsity and the associated rich collection of tools and algorithms will thus be a viable source for innovation in 5G wireless system design. We will discribe applications of this sparse signal processing paradigm in MIMO random access, cloud radio access networks, compressive channel-source network coding, and embedded security. We will also emphasize important open problem that may arise in 5G system design, for which sparsity will potentially play a key role in their solution.Comment: 18 pages, 5 figures, accepted for publication in IEEE Acces

Non-convex approach to binary compressed sensing

We propose a new approach for the recovery of binary signals in compressed sensing, based on the local minimization of a non-convex cost functional. The desired signal is proved to be a local minimum of the functional under mild conditions on the sensing matrix and on the number of measurements. We develop a procedure to achieve the desired local minimum, and, finally, we propose numerical experiments that show the improvement obtained by the proposed approach with respect to classical convex methods

Some MIMO applications in cognitive radio networks

In the last decade, the wireless communication technology has witnessed a rapid development, which led to a rapid growth in wireless applications and services. However, the radio spectrum resources scarcity resulting from using the traditional methods of fixed spectrum resources allocation has potential constraints on this wireless services rapid growth. Consequently, cognitive radio has been emerged as a possible solution for alleviating this spectrum scarcity problem by employing dynamic resource allocation strategies in order to utilize the available spectrum in a more efficient way so that finding opportunities for new wireless application services could be achieved. In cognitive radio networks, the radio spectrum resources utilization is improved by allowing unlicensed users, known as secondary users, to share the spectrum with licensed users, known as primary users, as long as this sharing do not induce harmful interference on the primary users, which completely entitled to utilize the spectrum. Motivated by MIMO techniques that have been used in practical systems as a means for high data rate transmission and a source for spatial diversity, and by its ease implementation with OFDM, different issues in multi-user MIMO (MU-MIMO) in both the uplink and downlink in the context of cognitive radio are studied in this thesis. More specifically, in the first thrust of this thesis, the spectrum spatial holes which could exist in an uplink MU-MIMO cell as a result of the possible free spatial dimensions resulted from the sparse activity of the primary users is studied; a modified sensing algorithm for these spectrum spatial holes that exploit both the block structure of the OFDM signals and the correlation of their activity states along time are proposed. The second thrust is concerned with cognitive radio relaying in the physical layer where the cognitive radio base station (CBS) relays the PU signal while transmitting its own signals to its SUs. We define secondary users with different priorities (different quality of service requirements); the different levels of priority for SUs are achieved by a newly proposed simple linear scheme based on zero forcing called Hierarchal Priority Zero Forcing scheme HPZF