3,161 research outputs found
Estimation of Collision Multiplicities in IEEE 802.11-based WLANs
Abstract—Estimating the collision multiplicity (CM), i.e. the number of users involved in a collision, is a key task in multipacket reception (MPR) approaches and in collision resolution (CR) techniques. A new technique is proposed for IEEE 802.11 networks. The technique is based on recent advances in random matrix theory and rely on eigenvalue statistics. Provided that the eigenvalues of the covariance matrix of the observations are above a given threshold, signal eigenvalues can be separated from noise eigenvalues since their respective probability density functions are converging toward two different laws: a Gaussian law for the signal eigenvalues and a Tracy-Widom law for the noise eigenvalues. The proposed technique outperforms current estimation techniques in terms of underestimation rate. Moreover, this paper reveals that, contrary to what is generally assumed in current MPR techniques, a single observation of the colliding signals is far from being sufficient to perform a reliable CM estimation
Random Matrix Theory applied to the Estimation of Collision Multiplicities
This paper presents two techniques in order to estimate the collision multiplicity, i.e., the number of users involved in a collision [1]. This estimation step is a key task in multi-packet reception approaches and in collision resolution techniques. The two techniques are proposed for IEEE 802.11 networks but they can be used in any OFDM-based system. The techniques are based on recent advances in random matrix theory and rely on eigenvalue statistics. Provided that the eigenvalues of the covariance matrix of the observations are above a given threshold, signal eigenvalues can be separated from noise eigenvalues since their respective probability density functions are converging toward two different laws: a Gaussian law for the signal eigenvalues and a Tracy-Widom law for the
noise eigenvalues. The first technique has been designed for the white noise case, and the second technique has been designed for the colored noise case. The proposed techniques outperform current estimation techniques in terms of mean square error. Moreover, this paper reveals that, contrary to what is generally assumed in current multi-packet reception techniques, a single observation of the colliding signals is far from being sufficient to
perform a reliable estimation of the collision multiplicities
Model Order Selection for Collision Multiplicity Estimation
The collision multiplicity (CM) is the number of users involved in a collision. The CM estimation is an essential step in multi-packet reception (MPR) techniques and in collision resolution (CR) methods. We propose two techniques to estimate collision multiplicities in the context of IEEE 802.11 networks. These two techniques have been initially designed in the context of source separation. The first estimation technique is based on eigenvalue statistics. The second technique is based on the exponentially embedded family (EEF). These two techniques outperform current estimation techniques in terms of underestimation rate (UNDER). The reason for this is twofold. First, current techniques are based on a uniform distribution of signal samples whereas the proposed methods rely on a Gaussian distribution. Second, current techniques use a small number of observations whereas the proposed methods use a number of observations much greater than the number of signals to be separated. This is in accordance with typical source separation techniques
Statistical Inference in Large Antenna Arrays under Unknown Noise Pattern
In this article, a general information-plus-noise transmission model is
assumed, the receiver end of which is composed of a large number of sensors and
is unaware of the noise pattern. For this model, and under reasonable
assumptions, a set of results is provided for the receiver to perform
statistical eigen-inference on the information part. In particular, we
introduce new methods for the detection, counting, and the power and subspace
estimation of multiple sources composing the information part of the
transmission. The theoretical performance of some of these techniques is also
discussed. An exemplary application of these methods to array processing is
then studied in greater detail, leading in particular to a novel MUSIC-like
algorithm assuming unknown noise covariance.Comment: 25 pages, 5 figure
Universality for the largest eigenvalue of sample covariance matrices with general population
This paper is aimed at deriving the universality of the largest eigenvalue of
a class of high-dimensional real or complex sample covariance matrices of the
form . Here, is
an random matrix with independent entries such that , . On
dimensionality, we assume that and as
. For a class of general deterministic positive-definite
matrices , under some additional assumptions on the
distribution of 's, we show that the limiting behavior of the largest
eigenvalue of is universal, via pursuing a Green function
comparison strategy raised in [Probab. Theory Related Fields 154 (2012)
341-407, Adv. Math. 229 (2012) 1435-1515] by Erd\H{o}s, Yau and Yin for Wigner
matrices and extended by Pillai and Yin [Ann. Appl. Probab. 24 (2014) 935-1001]
to sample covariance matrices in the null case (). Consequently, in
the standard complex case (), combing this universality
property and the results known for Gaussian matrices obtained by El Karoui in
[Ann. Probab. 35 (2007) 663-714] (nonsingular case) and Onatski in [Ann. Appl.
Probab. 18 (2008) 470-490] (singular case), we show that after an appropriate
normalization the largest eigenvalue of converges weakly to the
type 2 Tracy-Widom distribution . Moreover, in the real case, we
show that when is spiked with a fixed number of subcritical spikes,
the type 1 Tracy-Widom limit holds for the normalized largest
eigenvalue of , which extends a result of F\'{e}ral and
P\'{e}ch\'{e} in [J. Math. Phys. 50 (2009) 073302] to the scenario of
nondiagonal and more generally distributed .Comment: Published in at http://dx.doi.org/10.1214/14-AOS1281 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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