On the Performance of MUSIC With Toeplitz Rectification in the Context of Large Arrays

Abstract : —When using subspace methods for DoA estimation such as MUSIC, it is well known that a performance loss occurs when the number of available samples N is not large compared to the number of sensors M. This degradation is mainly due to the use of the Sample Correlation Matrix (SCM), which is a poor estimator of the true correlation matrix of the observations in this situation. When the latter exhibits a Toeplitz structure, a standard trick consists in correcting the structure of the SCM by averaging its entries along the subdiagonals. This procedure, known as Toeplitz rectification, is widely known to improve the estimation of the true correlation matrix, hence the performance of the corresponding subspace methods. In this paper, we propose a statistical analysis of the MUSIC method using Toeplitz rectified SCM (refered to as R-MUSIC), in the context where M, N are of the same order of magnitude. More precisely, considering the asymptotic regime in which M, N converge to infinity at the same rate, we prove the consistency and asymptotic normality of the R-MUSIC DoA estimates. Numerical simulations show the accurate prediction provided by the proposed theoretical analysis.
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Pascal Vallet, Philippe Loubaton. On the Performance of MUSIC With Toeplitz Rectification in the Context of Large Arrays. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2017, 65 (22), pp.5848 - 5859. ⟨10.1109/TSP.2017.2742988⟩. ⟨hal-01617757⟩

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