Delay-doppler channel estimation in almost linear complexity

Alexander Fish, Shamgar Gurevich, Ronny Hadani, Akbar M. Sayeed, Oded Schwartz

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


A fundamental task in wireless communication is channel estimation: Compute the channel parameters a signal undergoes while traveling from a transmitter to a receiver. In the case of delay-Doppler channel, i.e., a signal undergoes only delay and Doppler shifts, a widely used method to compute the delay-Doppler parameters is the matched filter algorithm. It uses a pseudo-random sequence of length $N$, and, in case of non-trivial relative velocity between transmitter and receiver, its computational complexity is O(N2N). In this paper we introduce a novel approach of designing sequences that allow faster channel estimation. Using group representation techniques we construct sequences, which enable us to introduce a new algorithm, called the flag method, that significantly improves the matched filter algorithm. The flag method finds m delay-Doppler parameters in O(mNN) operations. We discuss applications of the flag method to GPS, and radar systems.

Original languageAmerican English
Article number6563167
Pages (from-to)7632-7644
Number of pages13
JournalIEEE Transactions on Information Theory
Issue number11
StatePublished - 2013
Externally publishedYes


  • Channel estimation
  • GPS
  • Heisenberg-Weil sequences
  • fast matched filter
  • fast moving users
  • flag method
  • high-frequency communication
  • radar
  • sequence design
  • time-frequency shift problem


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