Determining the angle of arrival of a target signal received by an array of antenna elements

• US 8,031,119 B1
• Filed: 07/29/2009
• Issued: 10/04/2011
• Est. Priority Date: 07/29/2009
• Status: Active Grant

• Current Assignee: Engility LLC (Science Applications International Corporation)
• Original Assignee: L-3 Services Incorporated (L3Harris Technologies, Inc.)
• Inventors: McGann, David Delaney, Francis, James Covosso
• Primary Examiner(s): Liu; Harry
• Application Number:
  US12/511,783
• Time in Patent Office: 797 Days
• Field of Search: 342/444
• US Class Current: 342/444
• CPC Class Codes: G01S 3/74 Multi-channel systems specially adapted for direction-finding, i.e. having a single antenna system capable of giving simultaneous indications of the directions of different signals systems in which the directions of different signals are determined sequentially and displayed simultaneously G01S3/04, G01S3/14

Abstract

In a system for determining the angle of arrival of a target signal received by an array of antenna elements, a pair of receivers simultaneously obtain observations of a received target signal from multiple elements of an array of antenna elements; and a computer processes the simultaneously obtained samples of the target signal to determine a maximum likelihood estimation (MLE) of the angle of arrival φ of the target signal by using the following equation: φ_MLE=argmax_φRe(α*β). The value of β is determined in accordance with whether the target signal is known or unknown. When the target signal is unknown, the computer also processes the simultaneously obtained samples of the target signal to estimate the bandwidth of the received target signal by using binary hypotheses and a generalized log likelihood ratio test (GLLRT) or by using multiple hypotheses and pair-wise generalized log likelihood ratio tests. The value of a bandwidth constraint M that is associated with the estimated bandwidth is used to derive the value of β that is used to determine the MLE of φ.

Claims

1. A method of estimating the angle of arrival of a target signal received by an array of antenna elements, comprising the steps of:

(a) with a pair of receivers, simultaneously obtaining samples of a received target signal from multiple elements of an array of antenna elements; and

(b) with a computer, processing the simultaneously obtained samples of the target signal to determine a maximum likelihood estimation (MLE) of the angle of arrival φ

of the target signal by using the following equation;

φ

_MLE=argmax_φ

Re(α

*β

)

wherein α

is a complex vector that represents a phase difference associated with the angle of arrival that should be observed upon receipt of the signal by two particular antenna elements from which the samples are obtained; and

β

represents the phase difference that is observed upon receipt of the signal by the two particular antenna elements from which the samples are obtained;

wherein when the target signal is unknown,

β

_n=y*<sub>2n−

1</sub>y_2n in the time domain and β

_n=Y*<sub>2n−

1</sub>Y_2n in the frequency domain,

wherein y<sub>2n−

1</sub> and y_2n are complex N-tuple vectors representing the samples obtained from the nth simultaneously sampled pair of antenna elements and Y is a Fourier transform of y.

2. A method according to claim 1, wherein for a phased array of said antenna elements, α

_n=e<sup>i(μ

2n(Φ

)−

μ

2n−

1(φ

))</sup>, wherein μ

is a function of the angle of arrival that depends upon the geometry of the array of antenna elements.

3. A method according to claim 1, further comprising the steps of:

(c) estimating the bandwidth of the received target signal by using binary hypotheses and a generalized log likelihood ratio test (GLLRT);

4. A method according to claim 1, further comprising the steps of:

(c) estimating the bandwidth of the received target signal by using multiple hypotheses and pair wise generalized log likelihood ratio tests in accordance with;

5. A method of estimating the angle of arrival of a target signal received by an array of antenna elements, comprising the steps of:

(a) with a pair of receivers, simultaneously obtaining samples of a received target signal from multiple elements of an array of antenna elements; and

(b) with a computer, processing the simultaneously obtained samples of the target signal to determine a maximum likelihood estimation (MLE) of the angle of arrival φ

of the target signal by using the following equation;

φ

_MLE=argmax_φ

Re(α

*β

)

wherein α

is a complex vector that represents a phase difference associated with the angle of arrival that should be observed upon receipt of the signal by two particular antenna elements from which the samples are obtained; and

β

represents the phase difference that is observed upon receipt of the signal by the two particular antenna elements from which the samples are obtained;

wherein when the target signal is known,

6. A method according to claim 5, wherein for a phased array of said antenna elements, α

_n=e<sup>i(μ

2n(φ

)−

μ

2n−

1(φ

)),</sup>

wherein μ

is a function of the angle of arrival that depends upon the geometry of the array of antenna elements.

7. A method of estimating the bandwidth of a target signal received by an array of antenna elements, comprising the steps of:

(a) with a pair of receivers, simultaneously obtaining samples of a received target signal from multiple elements of an array of antenna elements; and

(b) with a computer, processing the simultaneously obtained samples of the target signal to estimate the bandwidth of the received target signal by using binary hypotheses and a generalized log likelihood ratio test (GLLRT).

8. A method according to claim 7, wherein the GLLRT is:

9. A method according to claim 8, wherein λ

(M₁, M₂)=argmin V ar{φ

_MLE}.

10. A method of estimating the bandwidth of a target signal received by an array of antenna elements, comprising the steps of:

(a) with a pair of receivers, simultaneously obtaining samples of a received target signal from multiple elements of an array of antenna elements; and

(b) with a computer, processing the simultaneously obtained samples of the target signal to estimate the bandwidth of the received target signal by using multiple hypotheses and pair wise generalized log likelihood ratio tests in accordance with;

11. A system for estimating the angle of arrival of a target signal received by an array of antenna elements, comprising:

a pair of receivers adapted for simultaneously obtaining samples of a received target signal from multiple elements of an array of antenna elements; and

a computer adapted for processing the simultaneously obtained samples of the target signal to determine a maximum likelihood estimation (MLE) of the angle of arrival φ

of the target signal by using the following equation;

φ

_MLE=argmax_φ

Re(α

*β

)

wherein α

is a complex vector that represents a phase difference associated with the angle of arrival that should be observed upon receipt of the signal by two particular antenna elements from which the samples are obtained; and

β

represents the phase difference that is observed upon receipt of the signal by the two particular antenna elements from which the samples are obtained;

wherein when the target signal is unknown, β

_n=y*<sub>2n−

1</sub>y_2n in the time domain and β

_n=Y*<sub>2n−

1</sub>Y_2n in the frequency domain,

wherein y<sub>2n−

1</sub> and y_2n are complex N-tuple vectors representing the samples obtained from the nth simultaneously sampled pair of antenna elements and Y is a Fourier transform of y.

12. A system according to claim 11, further comprising:

means for estimating the bandwidth of the received target signal by using binary hypotheses and a generalized log likelihood ratio test (GLLRT); and

means for deriving the value of β

_n=<

Y<sub>2n−

1</sub>, Y_2n>

_M in the frequency domain or the value of β

_n=<

y<sub>2n−

1</sub>, y_2n>

_M in the time domain by using the respective value of M that is associated with the estimated bandwidth pursuant to said GLLRT.

13. A system according to claim 11, further comprising the steps of:

means for estimating the bandwidth of the received target signal by using multiple hypotheses and pair wise generalized log likelihood ratio tests in accordance with;

14. A system for estimating the angle of arrival of a target signal received by an array of antenna elements, comprising the steps of:

a pair of receivers adapted for simultaneously obtaining samples of a received target signal from multiple elements of an array of antenna elements; and

a computer adapted for processing the simultaneously obtained samples of the target signal to determine a maximum likelihood estimation (MLE) of the angle of arrival φ

of the target signal by using the following equation;

φ

_MLE=argmax_φ

Re(α

*β

)

wherein α

is a complex vector that represents a phase difference associated with the angle of arrival that should be observed upon receipt of the signal by two particular antenna elements from which the samples are obtained; and

β

represents the phase difference that is observed upon receipt of the signal by the two particular antenna elements from which the samples are obtained;

wherein when the target signal is known,

15. A system for estimating the bandwidth of a target signal received by an array of antenna elements, comprising the steps of:

a pair of receivers adapted for simultaneously obtaining samples of a received target signal from multiple elements of an array of antenna elements; and

a computer adapted for processing the simultaneously obtained samples of the target signal to estimate the bandwidth of the received target signal by using binary hypotheses and a generalized log likelihood ratio test (GLLRT).

16. A system according to claim 15, wherein the GLLRT is:

17. A system according to claim 16, wherein λ

(M₁, M₂)=argmin V ar{φ

_MLE}.

18. A system for estimating the bandwidth of a target signal received by an array of antenna elements, comprising the steps of:

a pair of receivers adapted for simultaneously obtaining samples of a received target signal from multiple elements of an array of antenna elements; and

a computer adapted for processing the simultaneously obtained samples of the target signal to estimate the bandwidth of the received target signal by using multiple hypotheses and pair wise generalized log likelihood ratio tests in accordance with;

19. A computer readable storage medium for use with a computer in a system for determining the angle of arrival of a target signal received by an array of antenna elements, wherein the system comprises:

a pair of receivers adapted for simultaneously obtaining samples of a received target signal from multiple elements of an array of antenna elements; and

a computer,

wherein the computer readable storage medium contains computer executable program instructions for causing the computer to process the simultaneously obtained samples of the target signal to determine a maximum likelihood estimation (MLE) of the angle of arrival φ

of the target signal by using the following equation;

φ

_MLE=argmax_φ

Re(α

*β

)

wherein α

is a complex vector that represents a phase difference associated with the angle of arrival that should be observed upon receipt of the signal by two particular antenna elements from which the samples are obtained; and

β

represents the phase difference that is observed upon receipt of the signal by the two particular antenna elements from which the samples are obtained;

wherein when the target signal is unknown, β

_n=y*<sub>2n−

1</sub>y_2n in the time domain and β

_n=Y*<sub>2n−

1</sub>Y_2n in the frequency domain,

wherein y<sub>2n−

1</sub> and y_2n are complex N-tuple vectors representing the samples obtained from the nth simultaneously sampled pair of antenna elements and Y is a Fourier transform of y.

20. A computer readable storage medium according to claim 19, wherein for a phased array of said antenna elements, α

_n=e<sup>i(μ

2n(φ

)−

μ

2n−

1(φ

))</sup>, wherein μ

is a function of the angle of arrival that depends upon the geometry of the array of antenna elements.

21. A computer readable storage medium according to claim 19, further comprising the steps of:

(c) estimating the bandwidth of the received target signal by using binary hypotheses and a generalized log likelihood ratio test (GLLRT);

22. A computer readable storage medium according to claim 19, further comprising the steps of:

(c) estimating the bandwidth of the received target signal by using multiple hypotheses and pair wise generalized log likelihood ratio tests in accordance with;

23. A computer readable storage medium for use with a computer in a system for determining the angle of arrival of a target signal received by an array of antenna elements, wherein the system comprises:

a pair of receivers adapted for simultaneously obtaining samples of a received target signal from multiple elements of an array of antenna elements; and

a computer,

wherein the computer readable storage medium contains computer executable program instructions for causing the computer to process the simultaneously obtained samples of the target signal to determine a maximum likelihood estimation (MLE) of the angle of arrival φ

of the target signal by using the following equation;

φ

_MLE=argmax_φ

Re(α

*β

)

wherein α

is a complex vector that represents a phase difference associated with the angle of arrival that should be observed upon receipt of the signal by two particular antenna elements from which the samples are obtained; and

β

represents the phase difference that is observed upon receipt of the signal by the two particular antenna elements from which the samples are obtained;

wherein when the target signal is known,

24. A computer readable storage medium according to claim 23, wherein for a phased array of said antenna elements, α

_n=e<sup>i(μ

2n(φ

)−

μ

2n−

1(φ

))</sup>, wherein μ

is a function of the angle of arrival that depends upon the geometry of the array of antenna elements.

25. A computer readable storage medium for use with a computer in a system for estimating the bandwidth of a target signal received by an array of antenna elements, wherein the system comprises:

a pair of receivers adapted for simultaneously obtaining samples of a received target signal from multiple elements of an array of antenna elements; and

a computer,

wherein the computer readable storage medium contains computer executable program instructions for causing the computer to process the simultaneously obtained samples of the target signal to estimate the bandwidth of the received target signal by using binary hypotheses and a generalized log likelihood ratio test (GLLRT).

26. A computer readable storage medium according to claim 25, wherein the GLLRT is:

27. A computer readable storage medium according to claim 26, wherein λ

(M₁, M₂)=argmin V ar{φ

_MLE}.

28. A computer readable storage medium for use with a computer in a system for estimating the bandwidth of a target signal received by an array of antenna elements, wherein the system comprises:

a pair of receivers adapted for simultaneously obtaining samples of a received target signal from multiple elements of an array of antenna elements; and

a computer,

wherein the computer readable storage medium contains computer executable program instructions for causing the computer to process the simultaneously obtained samples of the target signal to estimate the bandwidth of the received target signal by using multiple hypotheses and pair wise generalized log likelihood ratio tests in accordance with;