# Pseudo-polyphase orthogonal sequence sets with good cross-correlation property

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## Abstract

This paper proposes a class of pseudo-polyphase orthogonal sequence sets with good cross-correlation property. Each set, composed of *N* pseudo-polyphase orthogonal sequences, is introduced from a maximum length sequence (m-sequence) by the inverse DFT, where *N* is the period of sequences.

A periodic sequence is called an orthogonal sequence, when the autocorrelation function is 0 in every term except for period-multiple-shift terms. It is known that a polyphase periodic sequence is transformed into an orthogonal sequence by the DFT or by the inverse DFT. There are *N* way for transforming a shifted m-sequence by the inverse DFT matrix, because an m-sequence is a periodic sequence of period *N*. So, we obtain *N* pseudo-polyphase orthogonal sequences by transforming the shifted m-sequences with the inverse DFT.

The absolute values of (*N*−1) terms in any obtained sequence are the same value \(\sqrt {\frac{{N + 1}}{N}}\). The absolute value of remained one term in the sequence is \(\sqrt {\frac{1}{N}}\). So, the obtained sequences can be called a pseud-polyphase orthogonal sequence.

The absolute values of (*N*−1) terms in any crosscorrelation function between two different sequences in a set are the same value \(\sqrt {\frac{{N + 1}}{N}}\). The absolute value of the remained one term is 1/*N*. So, these sequences have good crosscorrelation property.

## Keywords

Discrete Fourier Transform Binary Sequence Periodic Sequence Orthogonal Sequence Maximum Length Sequence## Preview

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