Robust, Efficient Estimation of the Optimal Rotation Parameter of the Fractional Fourier Transform using its Relation to the Wigner Distribution

A novel approach provides accurate estimation of the parameter a of a Fractional Fourier Transform (FrFT). A value of a may be selected for which the Wigner Distributions (WDs) of a signal-of-interest (SOI) and interference overlap as little as possible. However, instead of computing the WD for each signal, the FrFT may be computed for each WD, recognizing that the projection of the WD of a signal onto an axis ta is the energy of the FrFT along the same axis. Since the technique computes a using the SOI and a measure of the interference separately, significant improvements can be made in the estimate, especially at low signal-to-noise ratio (SNR). Once the estimate is obtained, a reduced rank filter may be applied to remove the interference, since minimum mean-square error (MMSE) approaches will again fail when using the low sample support required of non-stationary environments. The technique is not only computationally more efficient than MMSE, but far more robust as well.