Aperiodic autocorrelation functions of real‐valued shift‐orthogonal finite‐length sequences with round‐off errors

Abstract

SUMMARYA real-valued shift-orthogonal finite-length sequence is a sequence for which the side-lobe of the aperiodic autocorrelation function is zero except at the two ends. It is effectively used in spread-spectrum communications and other applications. This type of sequence can be synthesized by using element sequences of adequate lengths. Consequently, fast correlation processing can be realized by dividing the process for each element sequence. A problem in this sequence is that the round-off error of its real values has an effect on the correlation characteristics. Therefore, this paper investigates the effect of the round-off error on integrated correlation processing and divided correlation processing. In the former, the mean-square error of the correlation output is inversely proportional to the sequence length. In the latter, it is the sum of the mean-square errors of the element sequences, which are inversely proportional to the respective sequence lengths. Thus, we see that the error of shorter element sequences should be reduced in the latter method in order to speed up correlation processing. This paper considers in particular a method by which the mean-square error is reduced without significantly enlarging the circuit scale.