Improved correlation algorithm of multilevel complementary set of sequences

Complementary sets of sequences (CSS) are widely used in communications field due to their good correlation properties. The use of multilevel CSS reduces the binary CSS limitations in length and number of sequences per set, giving more flexibility in their applications, but with a higher computational complexity in the implementation of the generation and/or correlation algorithms. Although efficient recursive algorithms have been developed for these tasks, there is a continuous interest in reducing the calculations involved in these algorithms. This work presents a new recursive algorithm that allows obtaining the sum of the autocorrelation functions (SACF) of the K sequences belonging to a multilevel CSS. From this algorithm, two efficient correlation architectures are presented, reducing the number of operations needed to perform the SACF in comparison to straightforward and previous proposed architectures. The use of the new correlation algorithm improves the practical implementation of correlators in the well-known applications of the CSS.