Delay-doppler channel estimation in almost linear complexity

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.