Generation and Correlation Architectures of Multilevel Complementary Sets of Sequences

Complementary sets of sequences (CSS) are used extensively in many applications, as channel estimation and synchronization preamble or as a basic block for the generation of generalized orthogonal (GO) sequences. Nevertheless, binary CSS exist for very limited lengths, while for multilevel CSS there are fewer limitations in the sequence length. This paper presents two modular architectures for the generation and correlation of $K$ multilevel CSS: an algorithm for $K=2^{k}$ , $k\inBBN-{0}$ multilevel CSS, and another for $K\geq 3-{4}$ multilevel CSS. In contrast to previous generation algorithms, the proposed architectures reduce the number of computations needed to perform the correlation of $K$ multilevel CSS when compared to those required with a straightforward architecture. Furthermore, these architectures can be used as a starting point for the search of multilevel CSS with low peak-to-average power ratio (PAPR) and flexible length.