Channel Estimation Using a Chirp Signal and the Fractional Fourier Transform

The Fractional Fourier Transform (FrFT) is a useful tool that has many applications, such as interference mitigation for communications and radar target echo separation. In this paper, we present a new use, which is estimating an unknown multipath channel, by sending a short chirp signal through the channel. The multiple received chirps in multipath are rotated to the proper FrFT dimension where they become high power tones, whose amplitudes and delays are easily estimated by determining which values in the rotated spectrum exceed a given threshold $\gamma$, which is also easily computed. These are then mapped back to the original time domain. This method is enabled because of the nature of the FrFT and its ability to pull signals, especially chirp signals, out of noise. We present the signal and multipath model, and then describe how the FrFT is used to obtain the channel estimates. Through simulations, we show that this is a very accurate method, providing root mean-square error (RMSE) estimates of both channel coefficients and delays at least an order magnitude below that of existing methods, even at signal-to-noise ratios (SNRs) as low as 0dB. It is also very low in complexity, because all coefficient amplitude and delays are estimated simultaneously with few computations; it therefore offers a promising channel estimation solution for existing and future terrestrial communications systems, including 4G/5G cellular systems requiring high data rate applications.