New Quaternary Cross Z-Complementary Sets with Flexible Sequence Lengths.

Most recently, cross Z-complementary pairs (CZCPs) were introduced and studied to achieve the lower bound on the channel estimation mean-squares-error (MSE) in the broadband spatial modulation (SM) systems. Owing to the front-end/tail-end zero-correlation zone (ZCZ) width for auto-correlation sums and tail-end ZCZ width for cross-correlation sums, CZCPs can offer optimal channel estimation MSE performance over quasi-static frequency-selective channels. In this work, we propose a new class of quaternary cross Z-complementary sets (QCZCSs) with more flexible sequence lengths and larger ZCZ widths as a potential alternative to existing CZCPs. More specifically, we present several new constructions based on $\mathcal{Z}{\text{ - transforms}}$ for QCZCSs with various sequence lengths, including lengths 3L, 7L, and 14L, where L is the length of the seed sequence. Finally, we study the minimum MSE performance of our proposed QCZCSs in broadband SM systems.