Singular Gaussian Measures in Detection Theory

No abstract availabl

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

Processing and Transmission of Information

Contains reports on three research projects.Lincoln Laboratory, Purchase Order DDL B-00283U. S. ArmyU. S. NavyU. S. Air Force under Air Force Contract AF 19(604)-5200Office of Naval Research under Contract Nonr-1841(57

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

Digital matched filters for detecting Gaussian signals in Gaussian noise

Digital filters for detecting random signals in random nois