A self inversive array processing scheme for angle-of-arrival estimation

Eigenelement Statistics of Sample Covariance Matrix in the Correlated Data Case

“…In such cases one can use the eigenelement statistics derived under condition (2.2) to establish the statistical behavior of the parameter estimates of interest, even if the set of 5v i 6 i51 n used in the estimation is not guaranteed to satisfy (2.2). (See also [6,7] for a similar observation.) The above invariance property also applies to the ESPRIT algorithm [8] for estimating frequencies and directions-of-arrival.…”

“…Indeed, in applications 5v i 6 i51 n are unknown, which means that 5v i 6 cannot be selected to satisfy (2.2). Fortunately, the functions of 5v i 6 i51 n encountered in applications are invariant to the transformation for some a(u) vector (see, e.g., [5][6][7][8][9][10][11]), and it clearly satisfies the aforementioned invariance property. In such cases one can use the eigenelement statistics derived under condition (2.2) to establish the statistical behavior of the parameter estimates of interest, even if the set of 5v i 6 i51 n used in the estimation is not guaranteed to satisfy (2.2).…”

“…Of the analyses cited, the one in [6,7] appears to be the most general and complete. Yet that analysis is less general and more involved than that of the present paper.…”

“…Let 5l k 6 k51 m and 5v k 6 k51 m denote the eigenelements of R . The statistics of the principal eigenvalues 5l k 6 k51 n and their associated eigenvectors 5v k 6 k51 n play a central role in establishing the statistical behavior of a number of temporal or spatial frequency estimation algorithms such as MUSIC, ESPRIT, MIN-NORM, and TAM ( [5,6,12]). These statistics have been obtained, for example, in [1][2][3][4]6,7] under the assumptions that…”

“…for some n [ [1, m) (see, for example, [5][6][7][8][9][10][11][12]). Let 5l k 6 k51 m and 5v k 6 k51 m denote the eigenelements of R .…”