Method and apparatus for random array beamforming

• US 4,559,605 A
• Filed: 09/16/1983
• Issued: 12/17/1985
• Est. Priority Date: 09/16/1983
• Status: Expired due to Fees

• Current Assignee: The Boeing Co.
• Original Assignee: The Boeing Co.
• Inventors: Norsworthy, Keith
• Primary Examiner(s): Harkcom, Gary V.
• Application Number:
  US06/532,854
• Time in Patent Office: 823 Days
• Field of Search: 364/600-602, 364/604, 364/715, 364/728, 364/726, 364/819, 364/821, 364/827, 367/3-5, 367/20-21, 367/99-103, 367/118-119, 367/122-126, 367/138, 367/141, 250/265-267, 250/269, 73/861.25, 73/861.26, 73/861.27
• US Class Current: 708/403
• CPC Class Codes: G01S 3/802 Systems for determining direction or deviation from predetermined direction
• CPC Class Codes: G01V 1/20 Arrangements of receiving elements, e.g. geophone pattern

Abstract

A beamforming method and apparatus utilizing a plurality of sensing elements which are free to take up random positions. Each sensing element generates output signals in response to sensed radiation. The signals are fed to a data process or which generates Fourier frequency components of each output signal and selects a Fourier frequency component for each given radiation frequency to form a group of frequency components. The data processor performs a spatial convolution, interpolation and spatial Fourier transform followed by an averaging procedure in order to obtain an output signal which is indicative of the far field radiation power as a function of angle thus providing the desired beamforming information.

Claims

1. Beamforming apparatus comprising:

(a) a plurality of transducers randomly distributed for receiving radiant energy, said transducers generating analog output signals indicative of the received radiant energy,

(b) means for converting said analog transducer output signals at a predetermined sampling rate into digital signals,

(c) means for storing a group of said digital signals for each transducer,

(d) means for performing a discrete Fourier transformation of each group of digital signals to obtain Fourier frequency coefficients F.sub.ω

(k) where ω

identifies the frequency and k is an integer having values 1,2 . . . N identifying the transducer, N being the total number of distributed transducers,

(e) means for spatially convolving said coefficients F.sub.ω

(k) of equal ω

to obtain a set of coefficients G.sub.ω

"(D) where D is the spacing between pairs of transducers,

(f) means for generating additional values of G.sub.ω

"(D) by interpolation to obtain a substantially continuous function I₁₀₇ "(D),

(g) means for performing a spatial Fourier transformation of I₁₀₇ "(D) to obtain a transform function T.sub.∫

(F) where F is a parameter representing the different spatial frequencies in I₁₀₇ "(D)

(h) means for averaging a plurality of values of at least one of G.sub.ω

"(D), I.sub.ω

"(D) and T.sub.ω

(F) from a plurality of said output signal groups, and

(i) means, responsive to the averaged or average-derived value of T.sub.ω

(F) for generating an output representative of the far field power of said radiant energy as a function of angle.

2. Apparatus as recited in claim 1 wherein said transducers are responsive to acoustic radiant energy and are distributed in water for sensing acoustic energy radiated from submerged or surface vessels.

3. Apparatus as recited in claim 1 further comprising means for periodically determining the relative position of each of said transducers.

4. Apparatus as recited in claim 1 wherein said means for converting comprises means for sampling the output signal of said transducer at a sampling rate at least twice that of the maximum radiation frequency ω

and for generating the discrete Fourier transform component of said sampled output signals.

5. A method of beamforming comprising the steps of:

(a) deploying a plurality of sensing elements, said sensing elements free to take up random positions and each sensing element generating output signals in response to sensed radiation,

(b) detecting output signals from each of the sensing elements,

(c) determining the relative positions of said sensing elements,

(d) generating Fourier frequency components of each output signal,

(e) selecting a Fourier frequency component F.sub.ω

(k) for a given radiation frequency ω

from said output signals of each of said sensed elements thereby forming a group of frequency components F.sub.ω

(k) where k is an integer identifying a sensing element and having values k=1,2 . . . N, where N is the integer number of deployed sensing elements,

(f) spatially convolving said group of frequency components to obtain a set of coefficients G.sub.ω

"(D) where D is the spacing between pairs of sensing elements,

(g) interpolating additional values of G.sub.ω

"(D) between said set of coefficients to obtain a substantially continuous function I.sub.ω

"(D),

(h) spatially Fourier transforming I.sub.ω

"(D) to obtain the transform function T.sub.ω

"(F), where F is a parameter representing the different spatial frequencies in the I.sub.ω

"(D) function,

(i) time averaging a plurality of values of at least one of G.sub.ω

"(D), I.sub.ω

"(D) and T.sub.ω

"(F) from a plurality of said output signal groups, and

(j) after step i, providing an output of said averaged or average-derived transform function T.sub.ω

"(F) indicative of the far field power of said radiation as a function of angle.

6. A beamforming method as recited in claim 5 wherein said plurality of sensing elements form an array and said method further comprising the step of multiplying the continuous function I.sub.ω

"(D) with a shading function for weighting outer sensing elements of said array less than inner sensing elements of said array.

7. A beamforming method as recited in claim 5 wherein said deployment step includes randomly distributing said plurality of sensing elements in water for sensing submerged or surface vessels, said detecting step including detecting acoustic radiation from said vessels.

8. A beamforming method as recited in claim 5 wherein said step of providing an output includes generating a plot of the far field power as a function of angle.

9. A beamforming method as recited in claim 8 wherein said step of generating a plot includes displaying said plot on a CRT device.

10. A beamforming method as recited in claim 5 further comprising the step of periodically determining the relative position of each of said plurality of sensing elements.

11. A beamforming method as recited in claim 5 further comprising the steps of sampling the output signals at a sampling rate at least twice that of the given radiation frequency ω

and generating the discrete Fourier frequency component of said sampled output signals.

12. A beamforming method as recited in claim 5 wherein said time averaging step includes time averaging I.sub.ω

"(D).

13. A beamforming method as recited in claim 5 wherein said plurality of sensing elements form an array and said method further comprising the step of multiplying the convolution coefficients G.sub.ω

"(D) with a shading function for weighting outer sensing elements of said array less than inner sensing elements of said array.

14. A method of beamforming comprising the steps of:

(a) deploying a plurality of sensing elements, said sensing elements free to take up random positions, each sensing element generating output signals in response to sensed radiation,

(b) detecting output signals from each of the sensing elements,

(c) generating Fourier frequency components of each output signal,

(d) selecting a Fourier frequency component F.sub.ω

(k) for a given radiation frequency ω

from said output signals of each of said sensed elements thereby forming a group of frequency components F.sub.ω

(k) where k is an integer identifying a sensing element having values k=1,2 . . . N, where N is the integer number of deployed sensing elements,

(e) spatially convolving said group of frequency components to obtain a set of coefficients G.sub.ω

"(D) where D is the spacing between pairs of sensing elements,

(f) multiplying the set of coefficients G.sub.ω

"(D) by applying a shading function thereto, said shading function weighting smaller values of D more heavily than larger values of D,

(g) taking an average value of the shading multiplied coefficients Gω

"(D) to obtain G.sub.ω

"(D),

(h) solving a set of simultaneous equations for the unknown spatial frequency coefficients X_p, ##EQU9## where 1/λ

_p is the spatial frequency of the p^th unknown,

θ

_p is the direction angle to the p^th unknown,

D_j is the j^th cross sensor separation,

α

_j is the J^th cross sensor angle,

W_j is the weighting factor,

Re[G.sub.ω

"(D)] is the real part of G.sub.ω

"(D), and

M is the number of orthogonal frequency components; and

(i) providing an output of said spatial frequency coefficients X_p as a function of θ

_p.

15. A method as recited in claim 14 wherein said deployment step includes randomly distributing said plurality of sensing elements in water for sensing submerged or surface vessels, said detecting step including detecting acoustic radiation from said vessels.

16. A method as recited in claim 14 wherein said step of providing an output includes generating a plot of the far field power as a function of angle.

17. A method as recited in claim 14 wherein said step of generating a plot includes displaying said plot on a CRT device.

18. A method as recited in claim 14 further comprising the step of periodically determining the relative position of each of said plurality of sensing elements.

19. A method as recited in claim 14 further comprising the steps of sampling the output signals at a sampling rate at least twice that of the given radiation frequency ω

and generating the discrete Fourier frequency component of said sampled output signals.

20. A beamforming apparatus comprising:

(a) a plurality of transducers randomly distributed for receiving radiant energy, said transducers generating analog output signals indicative of the received radiant energy,

(b) means for converting said analog transducer output signals at a predetermined sampling rate into digital signals,

(c) means for storing a group of said digital signals for each transducer,

(d) means for performing a discrete Fourier transformation of each group of digital signals to obtain Fourier frequency coefficients F.sub.ω

(k) where ω

identifies the frequency and k is an integer having values 1,2 . . . N identifying the transducer, N being the total number of distributed transducers,

(e) means for spatially convolving said coefficients F.sub.ω

(k) for a given ω

value to obtain a set of coefficients G.sub.ω

"(D) where D is the spacing between pairs of transducers,

(f) means for multiplying the set of coefficients G.sub.ω

"(D) by applying a shading function thereto, said shading function weighting smaller values of D more heavily than larger values of D,

(g) means for taking an average value of the shading multiplied coefficients G.sub.ω

"(D) over a plurality of said groups of digital signals G.sub.ω

"(D),

(h) means for solving a set of simultaneous equations for the unknown spatial frequency coefficients X_p, ##EQU10## where 1/λ

_p is the spatial frequency of the p^th unknown,

θ

_p is the direction angle to the p^th unknown,

D_j is the j^th cross sensor separation,

α

_j is the j^th cross sensor angle,

W_j is the weighting factor,

Re[G.sub.ω

"(D)] is the real part of G.sub.ω

"(D), and

M is the number of orthogonal frequency components; and

(i) means for providing an output of said spatial frequency coefficients X_p as a function of θ

_p.

21. A beamforming apparatus as recited in claim 20 wherein said transducers are responsive to acoustic radiant energy and are distributed in water for sensing acoustic energy radiated from submerged or surface vessels.

22. A beamforming apparatus as recited in claim 20 further comprising means for periodically determining the relative position of each of said transducers.

23. A beamforming apparatus as recited in claim 20 wherein said means for converting comprises means for sampling the output signal of said transducer at a sampling rate at least twice that of the maximum radiation frequency ω

and for generating the discrete Fourier transform component of said sampled output signals.

24. A method of beamforming comprising the steps of:

(a) deploying a plurality of sensing elements, said sensing elements free to take up random positions, each sensing element generating output signals in response to sensed radiation,

(b) detecting output signals from each of the sensing elements,

(c) generating Fourier frequency components of each output signal,

(d) selecting a Fourier frequency component F.sub.ω

(k) for a given radiation frequency ω

from said output signals of each of said sensed elements thereby forming a group of frequency components F.sub.ω

(k) where k is an integer identifying a sensing element and having values k=1,2 . . . N, where N is the integer number of deployed sensing elements,

(e) spatially convolving said group of frequency components to obtain a set of coefficients G.sub.ω

"(D) where D is the spacing between pairs of sensing elements,

(f) if the number of said plurality of sensing elements is larger than 2A/λ

for a one-dimensional array or 4(Ax,Ay/λ

²) for a two-dimensional array where A is the aperture of said plurality of sensing elements for said one-dimensional array and (Ax,Ay) is the aperture of said two-dimensional array and λ

=1/2π

ω

, then

(i) interpolating additional values of G.sub.ω

"(D) between said set of coefficients to obtain a substantially continuous function I.sub.ω

"(D),

(ii) spatially Fourier transforming I.sub.ω

"(D) to obtain the transform function T.sub.ω

"(F), where F is a parameter representing the different spatial frequencies in I.sub.ω

"(D),

(iii) averaging a plurality of values of at least one of G.sub.ω

"(D), I.sub.ω

"(D) and T.sub.ω

"(F) over a plurality of said groups of frequency components, and

(iv) after step (f) (iii), providing an output of said averaged or average-derived transform function T.sub.ω

"(F) indicative of the far field power of said radiation as a function of angle, and

(g) if the number of said plurality of sensing elements is smaller than in step (f) then

(i) multiplying the set of coefficients G.sub.ω

"(D) by applying a shading function thereto, said shading function weighting smaller values of D more heavily than larger values of D,

(ii) taking an average value of the shading multiplied coefficients G.sub.ω

"(D) over a plurality of said groups of frequency components to obtain G.sub.ω

"(D),

(iii) solving a set of simultaneous equations for the unknown spatial frequency coefficients X_p, ##EQU11## where 1/λ

_p is the spatial frequency of the p^th unknown,

θ

_p is the direction angle to the p^th unknown,

D_j is the j^th cross sensor separation,

α

_j is the j^th cross sensor angle,

W_j is the weighting factor,

Re[G.sub.ω

"(D)] is the real part of G.sub.ω

"(D), and

M is the number of orthogonal frequency components and

(iv) providing an output of said spatial frequency codfficients X_p as a function of θ

_p.

25. A method as recited in claim 24 wherein said deployment step includes randomly distributing said plurality of sensing elements in water for sensing submerged or surface vessels, said detecting step including detecting acoustic radiation from said vessels.

26. A method as recited in claim 24 wherein said detecting step comprises the steps of sampling the output signals at a sampling rate at least twice that of the given radiation frequency ω

and generating the discrete Fourier frequency component of said output signals.