Interference suppression using repeated reduced rank adaptive filtering in fractional fourier transform (FrFT) domains

Patent metadata

Field	Value
Publication number	US-10437664-B2
Application number	US-201715698697-A
Country	US
Kind code	B2
Filing date	Sep 8, 2017
Priority date	Sep 8, 2017
Publication date	Oct 8, 2019
Grant date	Oct 8, 2019

Abstract

A signal-of-interest (SOI) may be separated from interference and/or noise using repeated reduced rank minimum mean-square error Fractional Fourier Transform (MMSE-FrFT) filtering and a low rank adaptive multistage Wiener filter (MWF). A number of stages in the MWF, L, may be chosen such that at the L th stage, the MSE between the SIM estimate and the true SW is less than or equal to an error threshold ∈ (e.g., ∈=0.001). By combining these filtering techniques, significant improvement in reducing the mean-square error (MSE) may be realized over single stage MMSE-FrFT, repeated MMSE-FrFT, and MMSE-FFT algorithms—indeed, by an order of magnitude or more.

First claim

The invention claimed is:

1. A computer-implemented method of performing repeated reduced rank MMSE-MWF-FrFT filtering, comprising:
computing, by a computing system, minimum mean-square error (MMSE) filter coefficients over all a for a current optimum filter to be applied to a received signal, where a is a rotational parameter;
computing, by the computing system, a best a for the current filter and a current smallest MMSE;
updating the received signal, by the computing system, using the current smallest MMSE;
when the current smallest MMSE is not less than or equal to an error threshold, repeating, by the computing system, the computation of the MMSE filter coefficients, the computation of the best a and the current smallest MMSE, and the updating of the received signal using the current smallest MMSE until the current smallest MMSE is less than or equal to the error threshold; and
when the current smallest MMSE is less than or equal to the error threshold, extracting a signal-of-interest (SOI), by the computing system, from the updated received signal.

2. The computer-implemented method of claim 1 , wherein
a number of iterations L of computing the MMSE filter coefficients, computing the best a and the current smallest MMSE, and updating the received signal using the current smallest MMSE is at least two.

3. The computer-implemented method of claim 1 , wherein
when the error threshold is reached or exceeded, L sets of a values and filter weights are provided to be applied to data in the received signal following a training sequence, where L is a number of iterations, and
the SOI is extracted from the updated received signal using the L sets of a values and filter weights.

4. The computer-implemented method of claim 1 , wherein the computing of the MMSE filter coefficients further comprises setting a number of filter stages D to a number sufficiently smaller than a number of samples per block N that rank reduction is achieved.

5. The computer-implemented method of claim 1 , wherein the computing of the MMSE filter coefficients further comprises transforming all variables to a fractional Fourier transformation (FrFT) domain.

6. The computer-implemented method of claim 1 , wherein the error threshold is 0.001 or less.

7. The computer-implemented method of claim 1 , wherein the repeated reduced rank adaptive filtering is performed using a correlations subtraction architecture of a multistage Wiener filter (CSA-MWF) in the fractional Fourier transformation (FrFT) domain.

8. The computer-implemented method of claim 7 , wherein the CSA-MWF computes the D scalar weights w j , j=1, 2, . . . , D, from which the current optimum filter is formed, and the current optimum filter is given by:
g 0,MMSE-MWF-FrFT ( l )= w 1 ( l ) h 1 ( l )− w 1 ( l ) w 2 ( l ) h 2 ( l )+ . . . −(−1) D w 1 ( l ) w 2 ( l ) . . . w D ( l ) h D ( l ).

9. The computer-implemented method of claim 8 , wherein forward recursion for the filter coefficients for j=1, 2, . . . , D is determined by:
h j ( l )=(Σ Ω {d* j-1 ( i,l ) x j-1 ( i,l )})/(∥Σ Ω {d* j-1 ( i,l ) x j-1 ( i,l )}∥)

d j ( i,l )= h j H ( l ) x j-1 ( i,l )
x j ( i,l )= x j-1 ( i,l )− h j ( l ) d j ( i,l )

and backward recursion for the filter coefficients for j=D, D−1, . . . , 1 is determined by
∈ D ( l )= d D ( i )

w j ( l )=(Σ Ω {d* j-1 ( i,l )∈ j ( i,l )})/(Σ Ω {|∈ j ( i,l )| 2 })

∈ j-1 ( i,l )= d j-1 ( i,l )− w* j ( l )∈ j ( i,l ).

10. The computer-implemented method of claim 1 , wherein the repeated reduced rank MMSE-MWF-FrFT filtering realizes improved signal demodulation over single stage MMSE-FrFT, repeated MMSE-FrFT, and MMSE-FFT algorithms by at least on order of magnitude.

11. 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.

12. 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, time-varying channels, drifting frequencies, or any combination thereof.

13. The computer-implemented method of claim 1 , wherein the received signal cannot be separated in either a time domain or a frequency domain alone.

14. The computer-implemented method of claim 1 , wherein the current smallest MMSE is computed by:

MMSE
⁢

⁢

FrFT
⁡

(
l
)

=

arg
⁢

min

a
⁡

(
l
)

⁢

1
M

⁢

∑

i
=
1

M

⁢

⁢



x
^

MWF

⁡

(

i
,
l

)

-

x
⁡

(
i
)

⁢


2

where
{circumflex over (x)} MWF ( i,l ) F −a(l) G 0,MMSE-MWF-FrFT ( i,l ) F a(l) y ( i,l )
and
g 0,MMSE-MWF-FrFT ( l )= w 1 ( l ) h 1 ( l )− w 1 ( l ) w 2 ( l ) h 2 ( l )+ . . . −(−1) D w 1 ( l ) w 2 ( l ) . . . w D ( l ) h D ( l ).

15. A computer program configured to perform repeated reduced rank MMSE-MWF-FrFT filtering embodied on a non-transitory computer-readab

Assignees

• Aerospace Corp

Inventors

• Sud Seema

Classifications

• G06F7/48

  using non-contact-making devices, e.g. tube, solid state device; using unspecified devices · CPC title

• H03H17/0213

  Frequency domain filters using Fourier transforms · CPC title

• H03H2021/0094

  Interference Cancelling · CPC title

• G06F11/0793 Primary

  Remedial or corrective actions (recovery from an exception in an instruction pipeline G06F9/3861; by retry G06F11/1402; for recovering from a failure of a protocol instance or entity H04L69/40) · CPC title

• H03H21/0043

  Adaptive algorithms · CPC title