Music using off-origin hessians of the second characteristic function

Arie Yeredor*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations

Abstract

In its classical form, the Multiple Signal Classification (MUSIC) algorithm applies eigen-decomposition to the estimated correlation matrix of the noisy sensors' outputs in order to estimate the directions of arrival (DOAs) of several sources. When the noise is spatially white, consistent estimates of the DOAs are obtained. However, when the noise is spatially correlated (and / or has different variances at different sensors), the correlation-based MUSIC cannot produce consistent DOA estimates, unless the noise covariance is known in advance. To mitigate this drawback, the use of certain matrices of Higher Order Statistics (HOS), mainly fourth-order cumulants, has been proposed, which can still lead to consistent DOA estimates when the noise is not spatially white, as long as it has a Gaussian distribution. However, estimates of the required HOS often introduce larger variances; Moreover, if the sources happen to have null cumulants of the chosen order, they remain unaccounted for in the algorithm. In this paper we propose a new target-matrix to substitute HOS as the input to MUSIC. Our target matrix is based on subtracting the observations' correlation matrix from Hessians of their second characteristic function, evaluated at several "processing points". These Hessians are related to the array steering-vectors (hence to the DOAs) in the same way as the correlation matrix, and can be easily estimated from the data. The subtraction of the correlation matrices eliminates (asymptotically) the effect of any additive independent Gaussian noise, hence maintaining consistency. We demonstrate the attainable improvement in comparative simulation.

Original languageEnglish
Title of host publication2006 IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAM 2006
Pages176-180
Number of pages5
DOIs
StatePublished - 2006
Event4th IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAM 2006 - Waltham, MA, United States
Duration: 12 Jul 200614 Jul 2006

Publication series

Name2006 IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAM 2006

Conference

Conference4th IEEE Sensor Array and Multichannel Signal Processing Workshop Proceedings, SAM 2006
Country/TerritoryUnited States
CityWaltham, MA
Period12/07/0614/07/06

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