Alexis Decurninge

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.

Median burg robust spectral estimation for inhomogeneous and stationary segments

In order to estimate parameters of Gaussian autoregressive processes, Burg method is often used in case of stationarity for its efficiency when few samples are available. We are interested in the case when multiple inhomogeneous (not necessarily Gaussian) segments of time series are available. We then study robust modification of Burg algorithms, especially based on Frechet medians defined for the Euclidean or the Poincare metric, to estimate the parameters of autoregressive processes in presence of outliers and/or contaminating distributions. Moreover, we will show that the introduced estimators are robust with respect to the power distribution of the time series. The considered modelization is motivated by radar applications, the performances of our methods will then be compared to the very popular Fixed Point and OS-CFAR estimators through radar simulated scenarios.

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.

Covariance estimation with projected data: Applications to CSI covariance acquisition and tracking

We consider the problem of covariance estimation with projected or missing data, and in particular the application to spatial channel covariance estimation in a multi-user Massive MIMO wireless communication system with arbitrary (possibly time-varying and/or non-orthogonal) pilot sequences. We introduce batch and online estimators based on the expectation-maximization (EM) approach, and provide sufficient conditions for their asymptotic (for large sample sizes) unbiasedness. We analyze their application to both uplink and downlink Massive MIMO, and provide numerical performance benchmarks.

Riemannian coding for covariance interpolation in massive MIMO frequency division duplex systems

In the context of multi-user Massive MIMO frequency division duplex (FDD) systems, the acquisition of channel state information cannot benefit from channel reciprocity. However, 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, it was also proposed to infer the downlink covariance based on the observed uplink covariance and a stored dictionary of uplink/downlink covariance matrices. This inference was performed through an interpolation in the Riemannian space of Hermitian positive definite matrices. We propose to rewrite the interpolation step as a Riemannian coding problematic. In this framework, we estimate the decomposition of the observed uplink matrix in the dictionary of uplink matrices and recover the corresponding downlink matrix assuming that its decomposition in the dictionary of downlink matrices is the same. Moreover, since this space is of large dimension in the Massive MIMO setting, it is expected that these decompositions will be sparse. We then propose new criteria based on this further constraint.

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.

Multivariate L-Moments Based on Transports

Univariate L-moments are expressed as projections of the quantile function onto an orthogonal basis of univariate polynomials. We present multivariate versions of L-moments expressed as collections of orthogonal projections of a multivariate quantile function on a basis of multivariate polynomials. We propose to consider quantile functions defined as transports from the uniform distribution on \([0;1]^d\) onto the distribution of interest and present some properties of the subsequent L-moments. The properties of estimated L-moments are illustrated for heavy-tailed distributions.