Almost Linear Complexity Methods for Delay-Doppler Channel Estimation

TL;DR

This paper introduces the incidence and cross methods for delay-Doppler channel estimation, achieving near-linear complexity with improved efficiency over previous algorithms by using chirp sequences.

Contribution

It presents novel incidence and cross methods utilizing chirp sequences, reducing computational complexity for delay-Doppler channel estimation.

Findings

Incidence method has complexity O(NlogN + r^3).

Cross method has complexity O(NlogN + r^2).

Both methods outperform previous algorithms in efficiency.

Abstract

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 delay-Doppler parameters is the pseudo-random method. 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(N^2logN) arithmetic operations. In [1] the flag method was introduced to provide a faster algorithm for delay-Doppler channel estimation. It uses specially designed flag sequences and its complexity is O(rNlogN) for channels of sparsity r. In these notes, we introduce the incidence and cross methods for channel estimation. They use triple-chirp and double-chirp sequences of length N, correspondingly. These sequences 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.