Interference reduction by step function removal

US 20030125912A1
Filed: 12/28/2001
Published: 07/03/2003
Est. Priority Date: 12/28/2001
Status: Active Grant

First Claim

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1. A method comprising:

observing a finite duration signal y_nthat comprises a representation of a mixture of a desired signal and an undesired signal, the undesired signal comprising an offset component;

modeling the offset component of the undesired signal as comprising a step function u defined by unknown step function parameters;

estimating the unknown step function parameters; and

adjusting y_nbased on the estimated step function parameters.

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Abstract

Correcting a signal offset may include observing a finite duration signal y_nthat comprises a representation of a mixture of a desired signal and an undesired signal. The undesired signal may include an offset component which may be modeled as comprising a step function u defined by unknown step function parameters. The unknown step function parameters may be estimated using, for example, a maximum likelihood method. Thereafter, y_nmay be corrected based on the estimated step function parameters.

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39 Claims

1. A method comprising:
- observing a finite duration signal y_nthat comprises a representation of a mixture of a desired signal and an undesired signal, the undesired signal comprising an offset component;
  
  modeling the offset component of the undesired signal as comprising a step function u defined by unknown step function parameters;
  
  estimating the unknown step function parameters; and
  
  adjusting y_nbased on the estimated step function parameters.
- View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11)
- - 2. The method of claim 1 in which y_ncomprises a continuous signal.
  - 3. The method of claim 1 in which y_ncomprises a discrete signal.
  - 4. The method of claim 3 in which:
    - y_nincludes N samples and comprises a discrete representation of a mixture of the desired signal, the undesired signal, and a second signal including a generally sinusoidal waveform and an attenuated version of the desired signal; and
      
      y_nis modeled as including a discrete representation of the desired signal and a discrete representation of an offset component related to a square of the undesired signal, in which the offset component is modeled as comprising a step function u defined by unknown step function parameters.
  - 5. The method of claim 1 in which the step function parameters include a first parameter c1 indicative of a first amplitude of the step function, a second parameter c2 indicative of a second amplitude of the step function, and a third parameter a indicative of a point at which the step function transitions from the first amplitude to the second amplitude, and in which the desired signal is a function of at least one unknown signal parameter θ
    - .
  - 6. The method of claim 5 in which y_nincludes N samples and estimating the step function parameters includes jointly estimating θ
    - , c1, c2, and α
      
      (0≦
      
      α
      
      <
      
      N) based on a non-linear optimization method.
  - 7. The method of claim 5 in which y_nincludes N samples and estimating the step function parameters includes estimating c1, c2, and a (0≦
    - α
      
      <
      
      N) based on a maximum likelihood method.
  - 8. The method of claim 7 in which the estimates of the step function parameters comprise:
    - a first estimate □
      
      1 of c1 where $\hat{c} 1 \approx \frac{1}{\hat{α}} \sum_{n = 0}^{\hat{α} - 1} y_{n};$ a second estimate □
      
      2 of c2 where $\hat{c} 2 \approx \frac{1}{N - \hat{α}} \sum_{n = \hat{α}}^{N - 1} y_{n}; and$ a third estimate {circumflex over (a )} of α
      
      where $\hat{α} \approx \arg \max_{α_{Test}} \frac{1}{α_{Test}} {\langle \sum_{n = 0}^{α_{Test} - 1} y_{n} \rangle}^{2} + \frac{1}{N - α_{Test}} {\langle \sum_{n = α_{Test}}^{N - 1} y_{n} \rangle}^{2}, 0 \leq α_{Test} < N - 1.$
  - 9. The method of claim 8 in which determining {circumflex over (a )} comprises:
    - selecting more than one value of α
      
      _Test;
      
      determining a value g for each selected value of α
      
      _Testwhere $g \approx \frac{1}{α_{Test}} {\langle \sum_{n = 0}^{α_{Test} - 1} y_{n} \rangle}^{2} + \frac{1}{N - α_{Test}} {\langle \sum_{n = α_{Test}}^{N - 1} y_{n} \rangle}^{2};$ selecting from among the determined values of g one or more maximum values of g; and
      
      selecting {circumflex over (a )} based on the one or more maximum values of g.
  - 10. The method of claim 9 in which less than N values of α
    - _Testare selected.
  - 11. The method of claim 7 in which estimating the step function parameters further comprises jointly estimating θ
    - , c1, c2, and α
      
      based on a non-linear minimization of a function comprising

12. A system comprising:
- an observation circuit structured and arranged to observe a finite duration signal y_nthat comprises a discrete representation of a mixture of a desired signal and an undesired signal, the undesired signal comprising an offset component;
  
  a modeling circuit structured and arranged to model the offset component of the undesired signal as comprising a step function u defined by unknown step function parameters;
  
  an estimating circuit structured and arranged to determine estimated step function parameters representative of the unknown step function parameters; and
  
  a correction circuit structured and arranged to correct y_nbased on the estimated step function parameters.
- View Dependent Claims (13, 14, 15, 16, 17, 18, 19, 20, 21, 22)
- - 13. The system of claim 12 in which y_ncomprises a continuous signal.
  - 14. The system of claim 12 in which y_ncomprises a discrete signal.
  - 15. The system of claim 14 in which:
    - y_nincludes N samples and comprises a discrete representation of a mixture of the desired signal, the undesired signal, and a second signal including a generally sinusoidal waveform and an attenuated version of the desired signal; and
      
      the modeling circuit is further configured to model y_nas comprising a discrete representation of the desired signal and also a discrete representation of an offset component related to a square of the undesired signal.
  - 16. The system of claim 12 in which the unknown step function parameters include a first parameter c1 indicative of a first amplitude of the step function, a second parameter c2 indicative of a second amplitude of the step function, and a third parameter α
    - indicative of a point at which the step function transitions from the first amplitude to the second amplitude, and in which the desired signal is a function of at least one unknown signal parameter θ
      
      .
  - 17. The system of claim 16 in which y_nincludes N samples and the estimating circuit is further configured to estimate jointly the unknown step function parameters θ
    - , c1, c2, and α
      
      (0≦
      
      α
      
      <
      
      N) based on a non-linear optimization method.
  - 18. The system of claim 16 in which y_nincludes N samples and the estimating circuit is further configured to estimate the unknown step function parameters c1, c2, and α
    - (0≦
      
      α
      
      <
      
      N) based on a maximum likelihood method.
  - 19. The system of claim 18 in which the estimating circuit is further configured to estimate the unknown step function parameters as comprising:
    - a first estimate □
      
      1 of c1 where $\hat{c} 1 \approx \frac{1}{\hat{α}} \sum_{n = 0}^{\hat{α} - 1} y_{n};$ a second estimate □
      
      2 of c2 where $\hat{c} 2 \approx \frac{1}{N - \hat{α}} \sum_{n = \hat{α}}^{N - 1} y_{n}; and$ a third estimate {circumflex over (a )} of α
      
      where $\hat{α} \approx \arg \max_{α_{Test}} \frac{1}{α_{Test}} {\langle \sum_{n = 0}^{α_{Test} - 1} y_{n} \rangle}^{2} + \frac{1}{N - α_{Test}} {\langle \sum_{n = α_{Test}}^{N - 1} y_{n} \rangle}^{2}, 0 \leq α_{Test} < N .$
  - 20. The system of claim 19 in which the estimating circuit is further configured to determine {circumflex over (a )} based on the following:
    - selecting more than one value of α
      
      _Test;
      
      determining a value g for each selected value of α
      
      _Testwhere $g \approx \frac{1}{α_{Test}} {\langle \sum_{n = 0}^{α_{Test} - 1} y_{n} \rangle}^{2} + \frac{1}{N - α_{Test}} {\langle \sum_{n = α_{Test}}^{N - 1} y_{n} \rangle}^{2};$ selecting from among the determined values of g one or more maximum values of g; and
      
      selecting {circumflex over (a )} based on the one or more maximum values of g.
  - 21. The system of claim 20 in which less than N values of α
    - _Testare selected by the estimating circuit.
  - 22. The system of claim 18 in which the estimating circuit is further configured to estimate jointly the unknown step function parameters θ
    - , c1, c2, and α
      
      based on non-linear minimization of a function comprising

23. A computer program stored on a computer readable medium or a propagated signal, the computer program comprising:
- an observation code segment configured to cause a computer to observe a finite duration signal y_nthat comprises a representation of a mixture of a desired signal and an undesired signal, the undesired signal comprising an offset component;
  
  a modeling code segment configured to cause the computer to model the offset component of the undesired signal as comprising a step function u defined by unknown step function parameters;
  
  an estimating code segment configured to cause the computer to determine estimated step function parameters representative of the unknown step function parameters; and
  
  a correcting code segment configured to cause the computer to correct y_nbased on the estimated step function parameters.
- View Dependent Claims (24, 25, 26, 27, 28, 29, 30, 31, 32, 33)
- - 24. The computer program of claim 23 in which y_ncomprises a continuous signal.
  - 25. The computer program of claim 23 in which y_ncomprises a discrete signal.
  - 26. The computer program of claim 25 in which:
    - y_nincludes N samples and comprises a discrete representation of a mixture of the desired signal, the undesired signal, and a second signal including a generally sinusoidal waveform and an attenuated version of the desired signal;
      
      a modeling code segment configured to cause the computer to model y_nas comprised of s_n, a discrete representation of the desired signal and also a discrete representation of an offset component related to a square of the undesired signal, in which the modeling code segment also is configured to cause the computer to model the offset component as comprising a step function u defined by unknown step function parameters.
  - 27. The computer program of claim 23 in which the unknown step function parameters include a first parameter c1 indicative of a first amplitude of the step function, a second parameter c2 indicative of a second amplitude of the step function, and a third parameter α
    - indicative of a point at which the step function transitions from the first amplitude to the second amplitude, and in which the desired signal is a function of at least one unknown signal parameter θ
      
      .
  - 28. The computer program of claim 27 in which y_nincludes N samples and the estimating code segment further comprises a non-linear optimization code segment configured to cause the computer program to estimate jointly the unknown step function parameters θ
    - , c1, c2, and α
      
      (0≦
      
      α
      
      <
      
      N) based on a non-linear optimization method.
  - 29. The computer program of claim 27 in which y_nincludes N samples and the estimating code segment further comprises a maximum likelihood code segment configured to cause the computer to estimate the unknown step function parameters c1, c2, and α
    - (0≦
      
      α
      
      <
      
      N) based on a maximum likelihood method.
  - 30. The computer program of claim 29 in which the maximum likelihood code segment is further configured to cause the computer to estimate the unknown step function parameters as comprising:
    - a first estimate □
      
      1 of c1 where $\hat{c} 1 \approx \frac{1}{\hat{α}} \sum_{n = 0}^{\hat{α} - 1} y_{n};$ a second estimate □
      
      2 of c2 where $\hat{c} 2 \approx \frac{1}{N - \hat{α}} \sum_{n = \hat{α}}^{N - 1} y_{n}; and$ a third estimate {circumflex over (a )} of α
      
      where $\hat{α} \approx \arg \max_{α_{Test}} \frac{1}{α_{Test}} {\langle \sum_{n = 0}^{α_{Test} - 1} y_{n} \rangle}^{2} + \frac{1}{N - α_{Test}} {\langle \sum_{n = α_{Test}}^{N - 1} y_{n} \rangle}^{2}, 0 \leq α_{Test} < N .$
  - 31. The computer program of claim 30 in which the maximum likelihood code segment further comprises:
    - a selecting code segment configured to cause the computer to select more than one value of α
      
      _Test;
      
      a calculating code segment configured to cause the computer to determine a value g for each selected value of α
      
      _Testwhere $g \approx \frac{1}{α_{Test}} {\langle \sum_{n = 0}^{α_{Test} - 1} y_{n} \rangle}^{2} + \frac{1}{N - α_{Test}} {\langle \sum_{n = α_{Test}}^{N - 1} y_{n} \rangle}^{2};$ a g_max code segment configured to cause the computer to select from among the determined values of g one or more maximum values of g; and
      
      an {circumflex over (a )}_max code segment configured to cause the computer to select {circumflex over (a )} based on the one or more maximum values of g.
  - 32. The computer program of claim 31 in which the selecting code segment is further configured to cause the computer to select less than N values of α
    - _Test.
  - 33. The computer program of claim 29 in which the maximum likelihood code segment is further configured to cause the computer to estimate jointly the unknown step function parameters θ
    - , c1, c2, and α
      
      based on non-linear minimization of a function comprising

34. A processor which:
- observes a finite duration signal y_nthat comprises a representation of a mixture of a desired signal and an undesired signal, the undesired signal comprising an offset component;
  
  models the offset component of the undesired signal as a step function u defined by unknown step function parameters;
  
  determines estimated step function parameters; and
  
  corrects the signal y_nbased on the estimated step function parameters.
- View Dependent Claims (35, 36, 37, 38, 39)
- - 35. The processor of claim 34 in which y_ncomprises a continuous signal.
  - 36. The processor of claim 34 in which y_ncomprises a discrete signal.
  - 37. The processor of claim 36 in which:
    - y_nincludes N samples and comprises a discrete representation of a mixture of the desired signal, the undesired signal, and a second signal including a generally sinusoidal waveform and an attenuated version of the desired signal; and
      
      y_nis modeled as including a discrete representation of the desired signal and also a discrete representation of an offset component related to a square of the undesired signal, and models the offset component as a step function u defined by unknown step function parameters.
  - 38. The processor of claim 34 in which y_nincludes N samples and the unknown step function parameters include a first parameter c1 indicative of a first amplitude of the step function, a second parameter c2 indicative of a second amplitude of the step function, and a third parameter α
    - (0≦
      
      α
      
      <
      
      N) indicative of a point at which the step function transitions from the first amplitude to the second amplitude.
  - 39. The processor of claim 38 in which the processor estimates the unknown step function parameters as comprising:
    - a first estimate □
      
      1 of c1 where $\hat{c} 1 \approx \frac{1}{\hat{α}} \sum_{n = 0}^{\hat{α} - 1} y_{n};$ a second estimate □
      
      2 of c2 where $\hat{c} 2 \approx \frac{1}{N - \hat{α}} \sum_{n = \hat{α}}^{N - 1} y_{n};$ and a third estimate {circumflex over (a )} of α
      
      where $\hat{α} \approx \arg \max_{α_{Test}} \frac{1}{α_{Test}} {\langle \sum_{n = 0}^{α_{Test} - 1} y_{n} \rangle}^{2} + \frac{1}{N - α_{Test}} {\langle \sum_{n = α_{Test}}^{N - 1} y_{n} \rangle}^{2} .$

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Current Assignee
Intel Corporation
Original Assignee
Intel Corporation
Inventors
Golden, Stuart A., Askar, Naiel K.

Granted Patent

US 6,834,260 B2
Time in Patent Office

Days
Field of Search
US Class Current

703/2
CPC Class Codes

H04L 25/061 providing hard decisions on...

Interference reduction by step function removal

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Interference reduction by step function removal

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Abstract

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39 Claims

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