Classical Channel Estimation for OFDM based on Delay-Doppler Response

In an Orthogonal Frequency Division Multiplexing (OFDM) system, the channel is often modeled as a two-dimensional zero-mean Gaussian random process in time and frequency with known second order statistics. With pilot symbols placed across the time-frequency plane, the channel´s response at a particular time-frequency point can be derived from its correlation with the nearby pilot locations. However, this a priori channel statistics may not always be available or the channel may not even be stationary to be adequately characterized by a correlation function. In this paper, we introduce a model of time-varying channel based on its delay-Doppler response. We show that a widely adopted time-frequency correlation model, upon which popular channel estimators for OFDM are often based, can be viewed as a special case of such a model with separable statistical profiles imposed on the delay-Doppler plane. Without using any statistical assumption on the channel, we derive a classical estimator based on the two-dimensional delay- Doppler correlator, which can be implemented using Discrete Fourier Transforms (DFT) of the pilot symbol measurements. Simulation results show promising performance even when the pilot symbols´ insertion rate is at the channel´s maximum delay-Doppler spread.