Blind channel estimation for precoded OFDM system

An orthogonal frequency division multiplex (OFDM) system with block-precoding is studied. It is observed that the correlation matrix of the post-DFT data is equal to the direct-product of the channel vector multiplied, element-by-element, by the product of the precoding matrix and its Hermitian. Therefore, an element-by-element division of the post-DFT correlation matrix by the product of the precoding matrix and its Hermitian gives a rank-one matrix whose only singular vector coincides the channel vector up to a phase ambiguity. The design criteria of the precoding matrix are discussed.