Alternate bounds on the resolvability constraints of spatial smoothing
Maria João Rendas, José M. F. Moura · IEEE Transactions on Acoustics Speech and Signal Processing · 1989
Bounds for the number of subarrays required by the spatial smoothing technique for direction finding are discussed. It is proved that for a source matrix of rank r, q directions can be resolved with M>or=q-r subarrays. It is also shown that when the source matrix is similar to a block-diagonal matrix through a permutation matrix, this bound can be further reduced to the largest rank deficiency presented by the diagonal blocks: M>or=(n/sub i/-r/sub i/) where n/sub i/ and r/sub i/ are, respectively, the dimension and the rank of the ith diagonal block. Another bound for M is derived, which relates to the number of nonzero components in the eigenvectors of the source covariance matrix.>