# US 5,790,475 A · Process and apparatus for improved interference suppression in echo-location and imaging systems

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- Number: US 5,790,475 A
- Document ID: US5790475A
- Status: Granted
- Kind: A
- Application number: 08/738,874
- Filed: 1996-10-28
- Granted: 1998-08-04
- Earliest claimed: 1996-10-28
- Assignees: Multispec Corporation
- Inventors: Vasilis Z. Marmarelis; Chrysostomos L. Nikias; David Sheby
- Web page: https://patentgrep.com/patent/US5790475A

## CPC

- G01S 13/284: {using coded pulses}
- G01S 7/2883: {using FFT processing}
- G01S 7/2921: {based on data belonging to one radar period}
- G01S: RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES

## Abstract

In echo-location and imaging systems, interference suppression is accomplished by shaping the transmitted signal waveform. Interference suppression permits more accurate range estimates or image formation, respectively. These specially shaped waveforms can also be used in communication systems to secure more accurate message transmission in the presence of interference. Shaping of the transmitted signal may be accomplished in two ways: (1) by convolving an elemental waveform with a multi-level pseudorandom sequence (i.e., binary, ternary, Poisson, etc.); or (2) by transforming nonlinearly the amplitude of the elemental waveform to give it high skewness. Interference suppression in the former case is achieved through matched filtering (replica correlation or pulse compression), and in the latter case it is accomplished by bispectrum-bicoherence processing.

## Claims

### Claim 1

In an echo location or imaging system, generating target range estimates an apparatus providing improved interference suppression, comprising:
means for generating an elemental waveform w(k);
means for generating a pseudorandom sequence p(n);
a convolution processor receiving the elemental waveform w(k) and pseudorandom sequence p(n) for generating a pseudorandomly convoluted waveform s(n);
means for transmitting the convoluted waveform s(n) through a medium containing interference .epsilon.(n); and
means for recovering the target range estimates f(m).

### Claim 2 (depends on 1)

The apparatus of claim 1 wherein the elemental waveform may be any of the following: sinusoidal pulse, linear FM pulse (chirp), hyperbolic FM pulse, or impulse.

### Claim 3 (depends on 1)

The apparatus of claim 1 wherein the pseudorandom sequence p(n) has impulsive autocorrelation characteristics.

### Claim 4 (depends on 1)

The apparatus of claim 1 wherein said pseudorandom sequence p(n) is multi-level.

### Claim 5 (depends on 1)

The apparatus of claim 1 wherein said pseudorandom sequence p(n) is binary.

### Claim 6 (depends on 1)

The apparatus of claim 1 wherein said convolution processor generates the convoluted waveform according to the relationship: ##EQU13## where: w(o) is the elemental waveform, with k=0, 1, 2, . . . K, and
p(n) is the pseudorandom sequence, with n=1, . . . (N+K).

### Claim 7

In an echo location or imaging system, generating target range estimates an apparatus providing an improved signal-to-noise ratio, comprising:
means for generating an elemental waveform w(k);
means for receiving the elemental waveform w(k) and producing a highly skewed waveform w.sub.s (k) by nonlinear transformation;
means for transmitting the skewed waveform w.sub.s (k) through a medium containing interference .epsilon.(n); and
means for recovering the target range estimates f(m).

### Claim 8 (depends on 7)

The apparatus of claim 7 wherein the elemental waveform may be any of the following: sinusoidal pulse, linear FM pulse (chirp), hyperbolic FM pulse, or impulse.

### Claim 9 (depends on 7)

The apparatus of claim 7 wherein said nonlinear transformation means comprises non-odd static nonlinear transformation.

### Claim 10

In an echo location or imaging system, generating target range estimates an apparatus providing improved interference suppression and an improved signal-to-noise ratio, comprising:
means for generating an elemental waveform w(k);
means for generating a pseudorandom sequence p(n);
a convolution processor for receiving the elemental waveform w(k) and pseudorandom sequence p(n) and generating a pseudorandomly convoluted waveform s(n);
means for receiving the convoluted waveform s(n) and generating a skewed convoluted waveform s.sub.s (n) by nonlinear transformation;
means for transmitting the skewed convoluted waveform s.sub.s (n) through a medium containing interference .epsilon.(n); and
means for recovering the target range estimates f(m).

### Claim 11 (depends on 10)

The apparatus of claim 10 wherein the elemental waveform may be any of the following: sinusoidal pulse, linear FM pulse (chirp), hyperbolic FM pulse, or impulse.

### Claim 12 (depends on 10)

The apparatus of claim 10 wherein the pseudorandom sequence p(n) has impulsive autocorrelation characteristics.

### Claim 13 (depends on 10)

The apparatus of claim 10 wherein said pseudorandom sequence p(n) is multilevel.

### Claim 14 (depends on 10)

The apparatus of claim 10 w herein said pseudorandom sequence p(n) is binary.

### Claim 15 (depends on 10)

The apparatus of claim 10 wherein said convolution processor generates convoluted waveforms according to the relationship: ##EQU14## where: w(k) is the elemental waveform, with k=0, 1, 2, . . . K, and
p(n) is the pseudorandom sequence, with n=1, . . . (N+K).

### Claim 16 (depends on 10)

The apparatus of claim 10 wherein said nonlinear transformation means comprises non-odd static nonlinear transformation.

### Claim 17 (depends on 10)

The apparatus of claim 10 wherein said means for recovering the transmitted waveform s.sub.s (s) comprises:
means for receiving the elemental waveform, w(k) and generating a skewed waveform w.sub.s (k);
a bispectrum processor receiving a signal transmitted through an interference medium and the skewed waveform w.sub.s (k), said processor generating the bispectrum for the received signal and the skewed waveform;
a spectrum processor simultaneously receiving the signal transmitted through an interference medium and the skewed waveform w.sub.s (k) said spectrum processor generating the spectrum for the received signal and the skewed waveform;
means for forming a ratio between the bispectrum for the received signal and the bispectrum for the skewed waveform; and
a bispectral bicoherence signal reconstruction processor receiving the bispectrum ratio from said ratio forming means, the spectrum of the received signal and the spectrum of the skewed waveform from said spectrum processor, said processor recovering the estimate of target ranges.

### Claim 18 (depends on 17)

The apparatus of claim 17 wherein said bispectral bicoherence signal reconstruction processor comprises:
means for forming a ratio between the spectrum of the received signal and the spectrum of the skewed waveform;
a bicoherence processor receiving the spectrum ratio from the spectrum ratio forming means, and receiving the bispectrum ratio from the bispectrum ratio forming means, said bicoherence processor generating a bicoherence signal;
means for receiving the bicoherence signal and generating a weighting factor; and
a reconstruction processor receiving the weighting factor from said weighting factor generating means and the bispectrum ratio from said ratio forming means for generating the target range estimates f(m).

### Claim 19

In an echo-location system wherein a transmitted signal s(n) encounters interference .epsilon.(n), is reflected by a target, and received as a signal r(n), an apparatus for improving the range estimates to the target for any given interference .epsilon.(n), said apparatus comprising:
means for generating an elemental waveform w(k);
means for generating a pseudorandom sequence p(n);
a convolution processor receiving the elemental waveform w(k) and pseudorandom sequence p(n) for generating a pseudorandomly convoluted waveform s(n);
means for transmitting the convoluted waveform s(n) to a target that reflects the waveform; and
means for receiving the reflected convoluted waveform r(n) which contains an interference component .epsilon.(n) and correlating the reflected signal r(n) with the convoluted waveform s(n) to generate a target range estimate f(m).

### Claim 20 (depends on 19)

The apparatus of claim 19 wherein the elemental waveform may be any of the following: sinusoidal pulse, linear FM pulse (chirp), hyperbolic FM pulse, or impulse.

### Claim 21 (depends on 19)

The apparatus of claim 19 wherein the pseudorandom sequence p(n) has impulsive autocorrelation characteristics.

### Claim 22 (depends on 19)

The apparatus of claim 19 wherein said pseudorandom sequence p(n) is multi-level.

### Claim 23 (depends on 19)

The apparatus of claim 19 wherein said pseudorandom sequence p(n) is binary.

### Claim 24 (depends on 19)

The apparatus of claim 19 wherein said convolution processor generates the convoluted waveforms according to the relationship: ##EQU15## where: w(k) is the elemental waveform, with k=0, 1, 2, . . . K, and
p(n) is the pseudorandom sequence, with n=1, . . . (N+K).

### Claim 25

In an echo-location system wherein a transmitted signal encounters interference .epsilon.(n), is reflected by a target, and received as a signal r(n), an apparatus for improving the range estimates to the target for any given interference .epsilon.(n), said apparatus comprising:
means for generating an elemental waveform w(k);
means for receiving the elemental waveform w(k) and producing a highly skewed waveform w.sub.s (k) by nonlinear transformation;
means for transmitting the skewed waveform w.sub.s (k) to a target that reflects the waveform w.sub.s (k): and
means for receiving the reflected waveform w.sub.s (k) which contains an interference component .epsilon.(n) and generating a target range estimate f(m) .

### Claim 26 (depends on 25)

The apparatus of claim 25 wherein the elemental waveform may be any of the following: sinusoidal pulse, linear FM pulse (chirp), hyperbolic FM pulse, or impulse.

### Claim 27 (depends on 25)

The apparatus of claim 25 wherein said nonlinear transformation means comprises non-odd static nonlinear transformation.

### Claim 28

In an echo-location system wherein a transmitted signal encounters interference .epsilon.(n), is reflected by a target, and received as a signal r(n), an apparatus for improving the range estimates to the target for any given interference .epsilon.(n), said apparatus comprising:
means for generating an elemental waveform w(k);
means for generating a pseudorandom sequence p(n);
a convolution processor for receiving the elemental waveform w(k) and pseudorandom sequence p(n) and generating a pseudorandom convoluted waveform s(n);
means for generating an amplitude skewed convoluted waveform s.sub.s (n) by nonlinear transformation;
means for transmitting the skewed convoluted waveform s.sub.s (n) to a target that reflects the waveform; and
means for receiving the reflected skewed convoluted waveform r.sub.s (n) which contains an interference component .epsilon.(n) and generating a target range estimate f(m).

### Claim 29 (depends on 28)

The apparatus of claim 28 wherein the elemental waveform may be any of the following: sinusoidal pulse, linear FM pulse (chirp), hyperbolic FM pulse, or impulse.

### Claim 30 (depends on 28)

The apparatus of claim 28 wherein the pseudorandom sequence p(n) has impulsive autocorrelation characteristics.

### Claim 31 (depends on 28)

The apparatus of claim 28 wherein said pseudorandom sequence p(n) is multi-level.

### Claim 32 (depends on 28)

The apparatus of claim 28 wherein said pseudorandom p(n) sequence p(n) is binary.

### Claim 33 (depends on 28)

The apparatus of claim 28 wherein said convolution processor generates the convoluted waveforms according to the relationship: ##EQU16## where: w(k) is the elemental waveform, with k=0, 1, 2, . . . K, and
p(n) is the pseudorandom sequence, with n=1, . . . (N+K).

### Claim 34 (depends on 28)

The apparatus of claim 28 wherein said nonlinear transformation means comprises non-odd static nonlinear transformation.

### Claim 35 (depends on 28)

The apparatus of claim 28 wherein said means for receiving the reflected waveform r.sub.s (n) and generating a target range estimate f(m) comprises:
means for receiving the elemental waveform w(k) and generating an amplitude skewed waveform w.sub.s (k);
a bispectrum processor for receiving the reflected waveform r.sub.s (n) and the skewed waveform w.sub.s (k) and generating the bispectrum B.sub.r (.omega..sub.1, .omega..sub.2) for r.sub.s (n) and the bispectrum B.sub.W (.omega..sub.1, .omega..sub.2) for w.sub.s (k);
a spectrum processor for receiving the reflected waveform r.sub.s (n) and the skewed waveform w.sub.s (k) and generating the spectrum S.sub.r (.omega.) for r.sub.s (n) and the spectrum S.sub.w (.omega.) for w.sub.s (k);
means for generating the bispectral ratio R.sub.1 (.omega..sub.1, .omega..sub.2) by taking B.sub.r (.omega..sub.1, .omega..sub.2) over B.sub.w (.omega..sub.1, .omega..sub.2); and
a bispectral bicoherence signal reconstruction processor receiving the bispectral ratio R.sub.1 (.omega..sub.1, .omega..sub.2), the spectrum S.sub.r (.omega.), and the spectrum S.sub.w (o) and generating the target range estimate f(m).

### Claim 36 (depends on 35)

The apparatus of claim 35 wherein said bispectral bicoherence signal reconstruction processor comprises:
means for generating the spectral ratio S(.omega.) by taking S.sub.r (.omega.) over S.sub.w (.omega.);
a bicoherence processor for receiving the spectral ratio S(.omega.) and the bispectral ratio R(.omega..sub.1, .omega..sub.2) and generating a bicoherence Q(.omega..sub.1, .omega..sub.2);
means for generating a weighting factor A(.omega..sub.1, .omega..sub.2) in response to said bicoherence Q(.omega..sub.1, .omega..sub.2); and
a complex auto-recursive reconstruction processor receiving the bispectral ratio R(.omega..sub.1, .omega..sub.2) and the weighting factor A(.omega..sub.1, .omega..sub.2) and generating an estimate of the FFT of the target range F(.omega.).

### Claim 37 (depends on 36)

The apparatus of claim 36 further comprising:
means for generating the conjugate of F(.omega.) and supplying it to said reconstruction processor; and
an Inverse Fast Fourier Transform generating means for receiving the F(.omega.) and generating the target range.

### Claim 38

In a telemetric system exhibiting interference .epsilon.(n), a process for providing interference suppression, the steps of the process comprising:
generating a pseudorandom convoluted waveform s(n) by convoluting an elemental waveform w(k) with a pseudorandom sequence p(n);
transmitting the convoluted waveform s(n) through a medium having interference .epsilon.(n); and
recovering the waveform s(n) at a receiving end.

### Claim 39 (depends on 38)

The process of claim 38 wherein the elemental waveform may be any of the following: sinusoidal pulse, linear FM pulse (chirp), hyperbolic FM pulse, or impulse.

### Claim 40 (depends on 39)

The process of claim 39 wherein said pseudorandom sequence p(n) is multi-level.

### Claim 41 (depends on 40)

The process of claim 40 wherein said multi-level pseudorandom sequence is binary.

### Claim 42

In a telemetric system exhibiting interference .epsilon.(n), a process for providing improved signal-to-noise ratio, the steps of the process comprising:
generating a highly skewed waveform w.sub.s (k) by nonlinear transformation of an elemental waveform w(k);
transmitting the skewed waveform w.sub.s (k) through a medium having interference .epsilon.(n); and
recovering the waveform w(k) at a receiving end.

### Claim 43 (depends on 42)

The process of claim 42 wherein the elemental waveform may be any of the following: sinusoidal pulse, linear FM pulse (chirp), hyperbolic FM pulse, or impulse.

### Claim 44 (depends on 42)

The process of claim 42 wherein said generating step further comprises non-odd static nonlinear transformation.

### Claim 45

In a telemetric system exhibiting interference .epsilon.(n), a process for providing interference suppression and an improved signal-to-noise ratio, the steps of the process comprising:
generating a pseudorandom convoluted waveform s(n) by convoluting an elemental waveform w(k) with a pseudorandom sequence p(n);
generating a skewed convoluted waveform s.sub.s (n) by nonlinear transformation of the convoluted waveform s(n);
transmitting the skewed convoluted waveform s.sub.s (n) through a medium having interference .epsilon.(n); and
recovering the transmitted waveform s.sub.s (n) at a receiving end.

### Claim 46 (depends on 45)

The process of claim 45 wherein the elemental waveform may be any of the following: sinusoidal pulse, linear FM pulse (chirp), hyperbolic FM pulse, or impulse.

### Claim 47 (depends on 45)

The process of claim 45 wherein said skewed convoluted waveform generating step further comprises non-odd static nonlinear transformation.

### Claim 48 (depends on 45)

The process of claim 45 wherein said pseudorandom sequence p(n) is multi-level.

### Claim 49 (depends on 45)

The process of claim 45 wherein said pseudorandom sequence p(n) is binary.

### Claim 50

In an echo-location system wherein a transmitted signal encounters interference .epsilon.(n), is reflected by a target, and received as a signal r(n), a process for providing improved range estimates f(m) to the target for any given interference .epsilon.(n), said apparatus comprising:
generating a pseudorandom convoluted waveform s(n) by convoluting an elemental waveform w(k) with a pseudorandom sequence p(n);
generating an amplitude skewed convoluted waveform s.sub.s (n) by nonlinear transformation of s(n);
transmitting the skewed convoluted waveform s.sub.s (n) to a target that reflects the waveform; and
generating target range estimates f(m) from the reflected received waveform r.sub.s (n).

### Claim 51 (depends on 50)

The apparatus of claim 50 wherein the elemental waveform may be any of the following: sinusoidal pulse, linear FM pulse (chirp), hyperbolic FM pulse, or impulse.

### Claim 52 (depends on 50)

The apparatus of claim 50 wherein the pseudorandom sequence p(n) has impulsive autocorrelation characteristics.

### Claim 53 (depends on 50)

The apparatus of claim 50 wherein said pseudorandom sequence p(n) is multi-level.

### Claim 54 (depends on 50)

The apparatus of claim 50 wherein said pseudorandom sequence p(n) is binary.

### Claim 55 (depends on 50)

The apparatus of claim 50 wherein the amplitude skewed convoluted waveform generating step further comprises non-odd static nonlinear transformation.

### Claim 56 (depends on 50)

The apparatus of claim 50 wherein said generating target range estimate f(m) step comprises the steps of:
generating an amplitude skewed waveform w.sub.s (k) by nonlinear transformation of w(k);
generating a bispectrum B.sub.r (.omega..sub.1, .omega..sub.2) from the received signal r.sub.s (n);
generating a bispectrum B.sub.w (.omega..sub.1, .omega..sub.2) from the waveform w.sub.s (k);
generating a spectrum S.sub.r (.omega.) from the received waveform r.sub.s (n);
generating a spectrum S.sub.w (.omega.) from the waveform w.sub.s (k);
generating a bispectral ratio R.sub.1 (.omega..sub.1, .omega..sub.2) from bispectrum B.sub.r (.omega..sub.1, .omega..sub.2) and B.sub.w (.omega..sub.1, .omega..sub.2); and
generating a target range estimate f(m) from the bispectral ratio R.sub.1 (.omega..sub.1, .omega..sub.2), the spectrum S.sub.r (O), and the spectrum S.sub.w (.omega.).

### Claim 57 (depends on 56)

The process of claim 56 wherein said target range estimate generating step comprises the steps of:
generating a spectral ratio S(.omega.) from the spectrum S.sub.r (.omega.) and the spectrum S.sub.w (.omega.);
generating a bicoherence signal Q(.omega..sub.1, .omega..sub.2) from the spectral ratio S.sub.w (.omega.) and the bispectral ratio R.sub.1 (.omega..sub.1, .omega..sub.2);
generating a weighting factor A(.omega..sub.1, .omega..sub.2) from the bicoherence signal Q(.omega..sub.1, .omega..sub.2); and
generating the target range estimates f(m) from the bispectral ratio R.sub.1 (.omega..sub.1, .omega..sub.2) and the weighting factor A(.omega..sub.1, .omega..sub.2).

### Claim 58 (depends on 57)

The process of claim 57 wherein said target range estimate f(m) generating step comprises the steps of:
generating a bispectrum F(.omega.);
generating the conjugate F(.omega.) of the bispectrum; and
generating the target range estimates f(m) from the bispectrum F(.omega.) by an Inverse Fast Fourier Transform.