Synthesis of a set of real-valued shift-orthogonal finite-length PN sequences

The finite-length sequence whose non-periodic autocorrelation function takes zero sidelobes except at left and right shift ends can be called the shift-orthogonal finite-length sequence, and is effective to reduce the intersymbol interference in a direct-sequence spread-spectrum communication system. This paper proposes the synthesis of a set of real-valued shift-orthogonal finite-length sequences which has family size 2^ν or 2^ν+1 and length 2^ν+1, ν=1, 2, 3, ... and is suitable for the fast correlation processing. A sequence is synthesized by convolving the ν+1 original or order-reversed elementary sequences from the sequences of lengths 2 and 5. The fast correlation for the sequence is decomposed to the (ν+1)-stage correlations