arXiv subjects

Alexis Decurninge

Publications and source records attributed to Alexis Decurninge.

24 records · Page 2Linked to original sources

arXiv2016

Cube-Split: Structured Quantizers on the Grassmannian of Lines

This paper introduces a new quantization scheme for real and complex Grassmannian sources. The proposed approach relies on a structured codebook based on a geometric construction of a collection of bent grids defined from an initial mesh on the unit-norm sphere. The associated encoding and decoding algorithms have very low complexity (equivalent to a scalar quantizer), while their efficiency (in terms of the achieved distortion) is on par with the best known structured approaches, and compares well with the theoretical bounds. These properties make this codebook suitable for high-resolutions, real-time applications such as channel state feedback in massive multiple-input multiple-output (MIMO) wireless communication systems.

cs.IT↗

arXiv2016

SNOPS: Short Non-Orthogonal Pilot Sequences for Downlink Channel State Estimation in FDD Massive MIMO

Channel state information (CSI) acquisition is a significant bottleneck in the design of Massive MIMO wireless systems, due to the length of the training sequences required to distinguish the antennas (in the downlink) and the users (for the uplink where a given spectral resource can be shared by a large number of users). In this article, we focus on the downlink CSI estimation case. Considering the presence of spatial correlation at the base transceiver station (BTS) side, and assuming that the per-user channel statistics are known, we seek to exploit this correlation to minimize the length of the pilot sequences. We introduce a scheme relying on non-orthogonal pilot sequences and feedback from the user terminal (UT), which enables the BTS to estimate all downlink channels. Thanks to the relaxed orthogonality assumption on the pilots, the length of the obtained pilot sequences can be strictly lower than the number of antennas at the BTS, while the CSI estimation error is kept arbitrarily small. We introduce two algorithms to dynamically design the required pilot sequences, analyze and validate the performance of the proposed CSI estimation method through numerical simulations using a realistic scenario based on the one-ring channel model.

cs.IT↗

arXiv2016

Robust Burg Estimation of Radar Scatter Matrix for Autoregressive structured SIRV based on Fréchet medians

We address the estimation of the scatter matrix of a scale mixture of Gaussian stationary autoregressive vectors. This is equivalent to consider the estimation of a structured scatter matrix of a Spherically Invariant Random Vector (SIRV) whose structure comes from an autoregressive modelization. The Toeplitz structure representative of stationary models is a particular case for the class of structures we consider. For Gaussian autoregressive processes, Burg method is often used in case of stationarity for its efficiency when few samples are available. Unfortunately, if we directly apply these methods to estimate the common scatter matrix of N vectors coming from a non-Gaussian distribution, their efficiency will strongly decrease. We propose then to adapt these methods to scale mixtures of autoregressive vectors by changing the energy functional minimized in the Burg algorithm. Moreover, we study several approaches of robust modification of the introduced Burg algorithms, based on Fréchet medians defined for the Euclidean or the Poincaré metric, in presence of outliers or contaminating distributions. The considered structured modelization is motivated by radar applications, the performances of our methods will then be compared to the very popular Fixed Point estimator and OS-CFAR detector through radar simulated scenarios.

math.ST↗

arXiv2016

Channel Covariance Estimation in Massive MIMO Frequency Division Duplex Systems

Channel covariance is emerging as a critical ingredient of the acquisition of instantaneous channel state information (CSI) in multi-user Massive MIMO systems operating in frequency division duplex (FDD) mode. In this context, channel reciprocity does not hold, and it is generally expected that covariance information about the downlink channel must be estimated and fed back by the user equipment (UE). As an alternative CSI acquisition technique, we propose to infer the downlink covariance based on the observed uplink covariance. This inference process relies on a dictionary of uplink/downlink covariance matrices, and on interpolation in the corresponding Riemannian space; once the dictionary is known, the estimation does not rely on any form of feedback from the UE. In this article, we present several variants of the interpolation method, and benchmark them through simulations.

cs.IT↗

arXiv2015

Estimation for models defined by conditions on their L-moments

This paper extends the empirical minimum divergence approach for models which satisfy linear constraints with respect to the probability measure of the underlying variable (moment constraints) to the case where such constraints pertain to its quantile measure (called here semi parametric quantile models). The case when these constraints describe shape conditions as handled by the L-moments is considered and both the description of these models as well as the resulting non classical minimum divergence procedures are presented. These models describe neighborhoods of classical models used mainly for their tail behavior, for example neighborhoods of Pareto or Weibull distributions, with which they may share the same first L-moments. A parallel is drawn with similar problems held in elasticity theory and in optimal transport problems. The properties of the resulting estimators are illustrated by simulated examples comparing Maximum Likelihood estimators on Pareto and Weibull models to the minimum Chi-square empirical divergence approach on semi parametric quantile models, and others.

math.ST↗

arXiv2015

Multivariate quantiles and multivariate L-moments

Univariate L-moments are expressed as projections of the quantile function onto an orthogonal basis of polynomials in $L_2([0;1],\mathbb{R})$. We present multivariate versions of L-moments expressed as collections of orthogonal projections of a multivariate quantile function on a basis of multivariate polynomials in $L_2([0;1]^d,\mathbb{R})$. We propose to consider quantile functions defined as transport from the uniform distribution on $[0;1]^d$ onto the distribution of interest. In particular, we present the quantiles defined by the transport of Rosenblatt and the optimal transport and the properties of the subsequent L-moments.

math.ST↗