Techniques for deriving eigenvectors based on steered reference and used for spatial processing. A steered reference is a pilot transmission on one eigenmode of a MIMO channel per symbol period using a steering vector for that eigenmode. The steered reference is used to estimate both a matrix Σ of singular values and a matrix U of left eigenvectors of a channel response matrix H . A matrix U with orthogonalized columns may be derived based on the estimates of Σ and U, e.g., using QR factorization, minimum square error computation, or polar decomposition. The estimates of Σ and U (or the estimate of Σ and the matrix U ) may be used for matched filtering of data transmission received via a first link. The estimate U of or the matrix U may also be used for spatial processing of data transmission on a second link (for reciprocal first and second links).