arXiv subjects

François Horlin

Publications and source records attributed to François Horlin.

23 records · Page 2Linked to original sources

arXiv2017

On the Noise Robustness of Simultaneous Orthogonal Matching Pursuit

In this paper, the joint support recovery of several sparse signals whose supports present similarities is examined. Each sparse signal is acquired using the same noisy linear measurement process, which returns fewer observations than the dimension of the sparse signals. The measurement noise is assumed additive, Gaussian, and admits different variances for each sparse signal that is measured. Using the theory of compressed sensing, the performance of simultaneous orthogonal matching pursuit (SOMP) is analysed for the envisioned signal model. The cornerstone of this paper is a novel analysis method upper bounding the probability that SOMP recovers at least one incorrect entry of the joint support during a prescribed number of iterations. Furthermore, the probability of SOMP failing is investigated whenever the number of sparse signals being recovered simultaneously increases and tends to infinity. In particular, convincing observations and theoretical results suggest that SOMP committing no mistake in the noiseless case does not guarantee the absence of error in the noisy case whenever the number of acquired sparse signals scales to infinity. Finally, simulation results confirm the validity of the theoretical results.

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arXiv2016

Single-Tap Precoders and Decoders for Multi-User MIMO FBMC-OQAM under Strong Channel Frequency Selectivity

The design of linear precoders or decoders for multiuser (MU) multiple-input multiple-output (MIMO) filterbank multicarrier (FBMC) modulations in the case of strong channel frequency selectivity is presented. The users and the base station (BS) communicate using space division multiple access (SDMA). The low complexity proposed solution is based on a single tap per-subcarrier precoding/decoding matrix at the base station (BS) in the downlink/uplink. As opposed to classical approaches that assume flat channel frequency selectivity at the subcarrier level, the BS does not make this assumption and takes into account the distortion caused by channel frequency selectivity. The expression of the FBMC asymptotic mean squared error (MSE) in the case of strong channel selectivity derived in earlier works is developed and extended. The linear precoders and decoders are found by optimizing the MSE formula under two design criteria, namely zero forcing (ZF) or minimum mean squared error (MMSE). Finally, simulation results demonstrate the performance of the optimized design. As long as the number of BS antennas is larger than the number of users, it is shown that those extra degrees of freedom can be used to compensate for the channel frequency selectivity.

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arXiv2016

Improving the Correlation Lower Bound for Simultaneous Orthogonal Matching Pursuit

The simultaneous orthogonal matching pursuit (SOMP) algorithm aims to find the joint support of a set of sparse signals acquired under a multiple measurement vector model. Critically, the analysis of SOMP depends on the maximal inner product of any atom of a suitable dictionary and the current signal residual, which is formed by the subtraction of previously selected atoms. This inner product, or correlation, is a key metric to determine the best atom to pick at each iteration. This paper provides, for each iteration of SOMP, a novel lower bound of the aforementioned metric for the atoms belonging to the correct and common joint support of the multiple signals. Although the bound is obtained for the noiseless case, its main purpose is to intervene in noisy analyses of SOMP. Finally, it is shown for specific signal patterns that the proposed bound outperforms state-of-the-art results for SOMP, and orthogonal matching pursuit (OMP) as a special case.

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arXiv2015

On The Exact Recovery Condition of Simultaneous Orthogonal Matching Pursuit

Several exact recovery criteria (ERC) ensuring that orthogonal matching pursuit (OMP) identifies the correct support of sparse signals have been developed in the last few years. These ERC rely on the restricted isometry property (RIP), the associated restricted isometry constant (RIC) and sometimes the restricted orthogonality constant (ROC). In this paper, three of the most recent ERC for OMP are examined. The contribution is to show that these ERC remain valid for a generalization of OMP, entitled simultaneous orthogonal matching pursuit (SOMP), that is capable to process several measurement vectors simultaneously and return a common support estimate for the underlying sparse vectors. The sharpness of the bounds is also briefly discussed in light of previous works focusing on OMP.

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arXiv2014

Iterative pre-distortion of the non-linear satellite channel

Digital Video Broadcasting - Satellite - Second Generation (DVB-S2) is the current European standard for satellite broadcast and broadband communications. It relies on high order modulations up to 32-amplitude/phase-shift-keying (APSK) in order to increase the system spectral efficiency. Unfortunately, as the modulation order increases, the receiver becomes more sensitive to physical layer impairments, and notably to the distortions induced by the power amplifier and the channelizing filters aboard the satellite. Pre-distortion of the non-linear satellite channel has been studied for many years. However, the performance of existing pre-distortion algorithms generally becomes poor when high-order modulations are used on a non-linear channel with a long memory. In this paper, we investigate a new iterative method that pre-distorts blocks of transmitted symbols so as to minimize the Euclidian distance between the transmitted and received symbols. We also propose approximations to relax the pre-distorter complexity while keeping its performance acceptable.

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