Alternate bounds on the resolvability constraints of spatial smoothing

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⩾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 ⩾(n_i-r_i) where n _i and r_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