Non-standard Golay Complementary Sequence Pair over QAM

TL;DR

This paper extends the construction of Golay complementary sequences to 4^q-QAM constellations using para-unitary matrices, addressing open questions and generating new array pairs beyond known results.

Contribution

It generalizes a three-stage process for Golay sequence construction to higher-order QAM, including non-standard pairs, based on para-unitary matrices.

Findings

Includes known Golay sequences over QPSK and 4^q-QAM.

Generates new Golay array pairs over 4^q-QAM.

Partly solves open questions from prior research.

Abstract

We generalize the three-stage process for constructing and enumerating Golay array and sequence pairs given in 2008 by Frank Fiedler et al. [A multi-dimensional approach to the construction and enumeration of Golay complementary sequences, Journal of Combinatorial Theory, Series A 115 (2008) 753-776] to $4^{q}$-QAM constellation based on para-unitary matrix method, which partly solves their open questions. Our work not only includes the main part of known results of Golay complementary sequences over $4^{q}$-QAM based on Boolean functions and standard Golay sequence pairs over QPSK, but also generates new Golay complementary arrays (sequences) over $4^{q}$-QAM based on non-standard Golay array pairs over QPSK.