Interference suppression using repeated reduced rank adaptive filtering in Fractional Fourier Transform domains

The Fractional Fourier Transform (FrFT) is a powerful tool that cancels interference and noise in non-stationary, real-world, environments to pull out a signal-of-interest (SOI). This requires estimation of the best rotational parameter ‘a’ to rotate the signal to a new domain along an axis ‘ta’ for filtering. The value of ‘a’ is usually chosen to give the minimum mean-square error (MMSE) between the desired SOI and its estimate. Recently, a technique was presented that uses repeated MMSE-FrFT filtering. This is done with a training sequence using mean-square error (MSE) as the metric by which to compute ‘a’ at each stage. This simple approach improves performance over conventional single stage MMSE-FrFT methods or methods based solely on filtering in frequency using an FFT. In this paper we apply repeated reduced rank adaptive filtering using a multistage Wiener filter (MWF). We show that the proposed MMSE-MWF-FrFT repeated filtering method significantly reduces the MSE over the repeated MMSE-FrFT method typically with just L = 1 or 2 stages and a nominal filter rank, D = 5, vs. L = 3 for MMSE. This is demonstrated by simulation using non-stationary channels as well as two types of non-stationary interference: chirp and Gaussian signals, at signal-to-noise ratios (SNRs) as low as 0 dB and carrier-to-noise ratios (CIRs) also down to 0 dB. Reduction in MSE from 0.001 to 10−4 or 10−5, or lower, is observed.