Doppler tolerance, complementary code sets, and generalised Thue–Morse sequences
Hieu Duc Nguyen, Gregory Emmett Coxson · IET Radar Sonar & Navigation · 2016
The authors generalise the construction of Doppler‐tolerant Golay complementary waveforms by Pezeshki–Calderbank–Moran–Howard to complementary code sets having more than two codes, which they call Doppler‐null codes. This is accomplished by exploiting number‐theoretic results involving the sum‐of‐digits function and a generalisation to more than two symbols of the classical two‐symbol Thue–Morse sequence. Two approaches are taken to establish higher‐order nulls of the composite ambiguity function: one by rewriting it in terms of equal sums of powers (ESP) and the other by factoring it in product form to reveal a higher‐order zero, analogous to spectral‐null codes. They conclude by describing an application of minimal ESP sets to multiple‐input–multiple‐output radar.