Delay-Doppler Channel Estimation with Almost Linear Complexity

TL;DR

This paper introduces the flag method, a novel algorithm for delay-Doppler channel estimation that significantly reduces computational complexity from quadratic to nearly linear, benefiting GPS, radar, and mobile systems.

Contribution

The paper presents a new sequence design and the flag method, achieving almost linear complexity for delay-Doppler channel estimation, improving over traditional matched filter algorithms.

Findings

The flag method reduces complexity to O(mNlog(N))

Sequences enable faster delay-Doppler channel estimation

Applicable to GPS, radar, and mobile communication systems

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, a widely used method 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(N^{2}log(N)). 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 the channel parameters in O(mNlog(N)) operations, for channel of sparsity m. We discuss applications of the flag method to GPS, radar system, and mobile communication as well.