Function-Based Construction of Two-Dimensional Binary Golay-ZCZ Array Pair of Length Non-Power-of-Two

In this paper, we propose the construction of Golay complementary array pairs (GCAP) with zero correlation zone ($\text{Z C Z}$) properties, having array lengths of $\left(2^{n_{1}+2}, 10 \cdot 2^{n_{2}-4}\right)$ and $\left(2^{n_{1}+2}, 26 \cdot 2^{n_{2}-5}\right)$, and corresponding $\text{Z C Z}$ widths of the forms $\left(2^{n_{1}}, 10 \cdot 2^{n_{2}-4}-1\right)$ and $\left(2^{n_{1}}, 26 \cdot 2^{n_{2}-5}-1\right)$, respectively. These flexible Golay-ZCZ arrays have potential applications in multiple-input multiple-output (MIMO) omnidirectional transmission as precoding matrices, sound source arrays, phased array antennas, and orthogonal time frequency space (OTFS) communication systems as a two-dimensional (2-D) pilot to improve channel estimation. For the first time, we propose the construction of Golay-ZCZ arrays based on generalized Boolean functions (GBFs), constructing the arrays with non-power-oftwo lengths through truncation techniques. Further, we show that, under specific constraints, we construct one-dimensional (1-D) and 2-D Golay-ZCZ sequences and array pairs for lengths, powers of two as well.