Estimation of the Optimum Rotational Parameter for the Fractional Fourier Transform Using Domain Decomposition

The Fractional Fourier Transform (FrFT) provides significant interference suppression over the Fast Fourier Transform (FFT) when the signal-of-interest (SOI) or interference is non-stationary. Its main limitation is estimating the optimum rotational parameter ‘a’. Current techniques choose ‘a’ that gives the minimum mean-square error (MMSE) between an SOI and its estimate. Such techniques are computational, and they do not provide good estimates when signal-to-noise ratio (SNR) or sample support is kept low, as is required in nonstationary environments. In this paper, we propose to estimate ‘a’ using Fractional Fourier domain decomposition (FFDD). We project the interference onto the FFDD basis vectors and choose ‘a’ that maximizes the projection. We show by simulation, using a non-stationary chirp channel function, that we estimate ‘a’ better than MMSE methods with just N = 4 samples down to Eb/N0 = 3 dB. Averaging over M = 10 trials improves accuracy to Eb/N0 = 0 dB. Keywords—Fractional Fourier Transform, Domain Decomposition, Singular Valued Decomposition.