Uniquely generated paraunitary-based complementary QAM sequences

Predrag Spasojević, Srdjan Z. Budišin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


A Boolean generator for a broad set of standard pairs of complex valued complementary sequences of length 2K is proposed. Binary, M-PSK and QAM sequences can be generated. The Boolean generator is derived from our earlier paraunitary algorithm from 2013 that is based on matrix multiplication. Both algorithms are based on unitary matrices. In contrast to previous Boolean QAM algorithms, which have an additive form, our algorithm has a multiplicative form. Any element of the sequence can be efficiently generated by indexing entries of K unitary matrices using a binary counter. MQum generation algorithm uses exactly M <K QAM unitary matrices each having at least one non-unit-norm entry. Greatest common divisor of Gaussian integers plays a key role in ensuring that the algorithm generates a set of unique sequences and, consequently, in deriving their enumeration formula. Our 1Qum and 2Qum algorithms generate generalized Case I, II and III, as well as, generalized Case IV and V sequences given by Liu et al. in 2013, respectively, in addition to many other sequences. The ratio of the total number to Case I-V sequences grows with the constellation size and the sequence length. As an example, for 1024-QAM and length 1024, our algorithm generates 340% additional sequences.

Original languageEnglish (US)
Title of host publicationConference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017
EditorsMichael B. Matthews
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Electronic)9781538618233
StatePublished - Apr 10 2018
Event51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017 - Pacific Grove, United States
Duration: Oct 29 2017Nov 1 2017

Publication series

NameConference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017


Other51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017
Country/TerritoryUnited States
CityPacific Grove

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Computer Networks and Communications
  • Hardware and Architecture
  • Signal Processing
  • Biomedical Engineering
  • Instrumentation


  • Boolean functions
  • Complementary sequences
  • Gaussian integers
  • QAM constellation
  • paraunitary matrices
  • unitary matrices


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