Signal/noise separation using FrFT rotational parameter obtained in relation to Wigner Distribution

Patent metadata

Field	Value
Publication number	US-9804999-B2
Application number	US-201514963329-A
Country	US
Kind code	B2
Filing date	Dec 9, 2015
Priority date	Dec 9, 2015
Publication date	Oct 31, 2017
Grant date	Oct 31, 2017

Abstract

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 t a 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.

First claim

The invention claimed is:

1. A computer-implemented method, comprising:
determining, by a computing system, a value of a rotational parameter a for a Fractional Fourier Transform (FrFT) for which a projection of a product of a Wigner Distribution (WD) reduces interference, noise, a complex, time-varying channel, or any combination thereof, in a received signal so that a signal-of-interest (SOI) can be separated;
filtering out the interference, noise, complex, time-varying channel, or any combination thereof, by the computing system; and
separating out the SOI from the interference, noise, complex, time-varying channel, or any combination thereof, by the computing system.

2. The computer-implemented method of claim 1 , wherein the value of the rotational parameter a corresponds to a value for which a product of energies of the SOI and the interference, noise, complex, time-varying channel, or any combination thereof, is minimized in the FrFT domain.

3. The computer-implemented method of claim 1 , wherein the SOI comprises a cellular communication signal, a satellite communication signal, a radar signal, an image signal, a speech signal, or any combination thereof.

4. The computer-implemented method of claim 1 , wherein a transmitter of the received signal is non-stationary due to movement, Doppler shift, time-varying signals, drifting frequencies, or any combination thereof.

5. The computer-implemented method of claim 1 , wherein the received signal cannot be separated in both a time domain and a frequency domain.

6. The computer-implemented method of claim 1 , wherein the filtering further comprises employing a reduced rank multistage Wiener filter (MWF) to remove non-stationary interference along an optimum FrFT axis t a of the WD.

7. The computer-implemented method of claim 1 , wherein a number of samples used for the determination is four or eight samples per bit.

8. The computer-implemented method of claim 1 , wherein the rotational parameter a is selected such that the SOI and the interference, noise, complex, time-varying channel, or any combination thereof, overlap as little as possible.

9. The computer-implemented method of claim 1 , wherein the computing of the parameter a comprises:
computing, by the computing system, energies of the FrFTs of both the SOI and the interference, noise, complex, time-varying channel, or any combination thereof;
computing a summation of values of a product of the energies of the SOI and the interference, noise, complex, time-varying channel, or any combination thereof, by the computing system, over a new time-frequency axis t a defined by the rotational parameter a; and
selecting a value of a, by the computing system, for which a result is minimum as an optimum a.

10. The computer-implemented method of claim 1 , wherein the computing of the rotational parameter a comprises:
initializing a to 0, by the computing system;
computing an energy of a FrFT of the SOI a using |X a (i)| 2 =|F a x(i)| 2 , by the computing system;
computing an energy of a FrFT of the interference, noise, or both, using |X I a (i)| 2 =|F a x I (i)| 2 , by the computing system;
computing a summation of values of the product of the energies, by the computing system, over a new time-frequency axis t a defined by the rotational parameter a, using XX l (a)=Σ i=1 N |X a (i)| 2 |X l a (i)| 2 ;
incrementing a, by the computing system;
repeating the computing steps above, by the computing system, until a=2; and
when a=2, selecting a based on a value where, XX I (a) is minimum, by the computing system.

11. The computer-implemented method of claim 1 , wherein the computing of the rotational parameter a comprises:
initializing a to 0, by the computing system;
computing an energy of a FrFT of the SOI as |X a (i)| 2 =|F a x(i)| 2 , by the computing system;
computing an energy of a FrFT of the complex, time-varying channel as |H a (i)| 2 =|F a h(i)| 2 , by the computing system;
computing a summation of values of the product of the energies, by the computing system, over a new time-frequency axis t a defined by the rotational parameter a, using XH (a)=Σ i=1 N |X a (i)| 2 |H a (i)| 2 ;
incrementing a, by the computing system;
repeating the computing steps above, by the computing system, until a=2; and
when a=2, selecting a based on a value where XH (a) is minimum, by the computing system.

12. The computer-implemented method of claim 1 , wherein the filtering further comprises:
computing filter coefficients g 0 , by the computing system, using a correlations subtraction architecture of a reduced rank multistage Wiener filter (CSA-MWF).

13. The computer-implemented method of claim 12 , wherein recursion equations for the CSA-MWF are given by

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Assignees

• Aerospace Corp

Inventors

• Sud Seema

Classifications

• G06F17/141 Primary

  Discrete Fourier transforms · CPC title

• G06F17/14 Primary

  Fourier, Walsh or analogous domain transformations {, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms (for correlation function computation G06F17/156; spectrum analysers G01R23/16)} · CPC title