Interference Cancellation by Repeated Filtering in the Fractional Fourier Transform Domain Using Mean-Square Error Convergence

摘要

The Fractional Fourier Transform (FrFT) is a useful tool that separates signals-of-interest (SOIs) from interference and noise in non-stationary environments. This requires estimation of the rotational parameter "a? to rotate the signal to a new domain along an axis "ta?, in which the interference can best be filtered out. The value of "a? is typically chosen as that which minimizes the mean-square error (MSE) between the desired SOI and its estimate or that minimizes the overlap between the signal and noise, projected onto the axis "ta?. In this paper, we extend this concept to perform repeated filtering, in multiple FrFT domains to reduce the MSE further than can be done with a single FrFT. We perform this solely using MSE as the metric by which to compute "a? at each stage, thereby simplifying the approach and improving performance over conventional single stage FrFT methods or methods based solely on the frequency domain filtering, such as the Fast Fourier transform (FFT). We show that the proposed method improves the MSE two or three orders of magnitude over the conventional methods using L ≤ 3 stages of FrFT filtering.