Doppler tolerance, complementary code sets, and generalised Thue-Morse sequences

Hieu Duc Nguyen, Gregory Emmett Coxson

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1603-1610
Number of pages8
JournalIET Radar, Sonar and Navigation
Issue number9
StatePublished - 2016

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


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