Doppler Tolerance, Complementary Code Sets and the Generalized Thue-Morse Sequence

TL;DR

This paper extends the design of Doppler-tolerant waveforms from pairs to larger sets using advanced number theory and sequence generalizations, enhancing radar signal processing capabilities.

Contribution

It introduces a novel construction method for Doppler-tolerant complementary code sets based on generalized Thue-Morse sequences and number-theoretic principles.

Findings

New construction of complementary code sets with more than two codes.

Enhanced Doppler tolerance in radar waveforms.

Application of number theory to sequence design.

Abstract

We generalize the construction of Doppler-tolerant Golay complementary waveforms by Pezeshki-Calderbank-Moran-Howard to complementary code sets having more than two codes. This is accomplished by exploiting number-theoretic results involving the sum-of-digits function, equal sums of like powers, and a generalization to more than two symbols of the classical two-symbol Prouhet-Thue-Morse sequence.