Fast aperiodic correlation algorithm for real-valued shift-orthogonal finite-length sequence of length 2ν+1

Abstract

Real-valued shift-orthogonal finite-length sequences are sequences in which the side lobes of the aperiodic autocorrelation function become 0, except for the endpoints of the shift to both sides, and can be applied in pulse compression radar and spread spectrum communications. In this paper, a fast correlation algorithm for efficiently calculating the periodic correlation function is discussed for real-valued shift-orthogonal finite-length sequences with length M=2^ν+1. For input data, including a real-valued shift-orthogonal finite-length sequence over a certain range, the value of the aperiodic correlation function is found in a certain shift range. Based on the synthesis of this sequence by the convolution of ν+1 partial sequences, the correlation processing is broken down into correlation processing of the ν+1 stages of partial sequences. As a result, the number of multiplications and the number of additions can be suppressed on the order Mlog₂M. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(9): 18– 30, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20301