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A fundamental task in wireless communication is channel estimation: Computethe channel parameters a signal undergoes while traveling from a transmitter toa receiver. In the case of delay-Doppler channel, i.e., a signal undergoes onlydelay and Doppler shifts, a widely used method to compute delay-Dopplerparameters is the pseudo-random method. It uses a pseudo-random sequence oflength N; and, in case of non-trivial relative velocity between transmitter andreceiver, its computational complexity is O(N^2logN) arithmetic operations. In[1] the flag method was introduced to provide a faster algorithm fordelay-Doppler channel estimation. It uses specially designed flag sequences andits complexity is O(rNlogN) for channels of sparsity r. In these notes, weintroduce the incidence and cross methods for channel estimation. They usetriple-chirp and double-chirp sequences of length N, correspondingly. Thesesequences are closely related to chirp sequences widely used in radar systems.The arithmetic complexity of the incidence and cross methods is O(NlogN + r^3),and O(NlogN + r^2), respectively.

Almost Linear Complexity Methods for Delay-Doppler Channel Estimation