WO2007063298A1

WO2007063298A1 - Spatial array

Info

Publication number: WO2007063298A1
Application number: PCT/GB2006/004457
Authority: WO
Inventors: Ronald Mchugh; Mark Joseph Wilson
Original assignee: Heriot-Watt University
Priority date: 2005-11-29
Filing date: 2006-11-29
Publication date: 2007-06-07
Also published as: GB0524252D0

Abstract

A non-periodic spatial array that includes a periodic sub-array.

Description

Spatial Array

The present invention relates to a spatial array and a method for generating a spatial array beam pattern. In particular, the present invention relates to a non-periodic spatial array that includes a periodic sub-array.

Background

Spatial array beam patterns are typically generated using a phased array of elements distributed in space. The elements are preferably transducers suited to the particular application, for example acoustic or electromagnetic transducers. When the array acts as a receiver, a 'beamforming' process is applied to the data received by each of the elements. 'Beamforming' effectively involves delaying and summing the received signals to produce an output. The set of delays applied to the received signals controls the direction in which the array is steered. The magnitude of the output in each direction relates to the received signal strength and the array geometry. Repeating this process for a series of delays allows the incoming signal strength over a range of directions to be established and hence a spatial radiation or beampattern for the array to be determined. When the phased array is used as a transmitter, the delaying of data occurs prior to transmission rather than after reception.

In transmission and reception modes, beamforming techniques are used to provide an output. Many beamforming algorithms exist but all effectively delay and sum the received data in the time domain, as shown in Figure 1. For a detailed discussion on some known beamforming algorithms, see for example "Efficient digital signal processing algorithm for sonar imaging", [McHugh, R.; Shaw, S.; Taylor, N.; Radar, Sonar and Navigation, IEE Proceedings - Volume 143, Issue 3, June 1996 Page(s):149] and "Underwater Acoustic System Analysis", [S.W. Burdic,. Prentice- Hall, 1984, pp. 303-338], the contents of which are incorporated herein by reference. Often within array-based beamforming, a weighting function is used. This treats the data received by some elements with greater significance than others, thereby to manipulate the beam pattern. Whilst array weighting is often incorporated into the beamforming algorithm, it may be applied elsewhere in the system.

i Weighting functions are often applied to periodic arrays, since they can offer significantly reduced sidelobes. Reduced sidelobes are desirable as this gives greater rejection to signals from directions other than the direction the array is steered to. A periodic array with a flat weighting function has a peak sidelobe of around -13.5dB, but a weighting function may reduce this to around —50dB without needing to increase the number of elements. However, the consequence is that the main lobe width increases, and so resolution falls. Further discussion of these points can be found in "On the use of windows for harmonic analysis with the discrete Fourier transform", [Harris, F.J.; Proceedings of the IEEE Volume 66, Issue 1, Jan. 1978 Page(s): 51-83], the contents of which are incorporated herein by reference

The geometry of the array is a key factor in determining its beampattem. For two- dimensional imaging, the array elements are arranged linearly, whilst in the case of three-dimensional imaging, a planar arrangement is required. Currently, most arrays are designed with the array elements spaced periodically. Periodic array design is well researched and beampatterns with recognised sidelobe structures are easily implemented. This is the preferred design method for most spatial arrays. This area of the technology is discussed in more detail in "Digital beamforming in ultrasound", [Steinberg, B.D.; Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on Volume 39, Issue 6, Nov. 1992 Page(s): 716 - 721], "Underwater Acoustic System Analysis" [S.W. Burdic, Prentice-Hall, 1984], "Sonar Signal Processing", [R.O. Nielsen, Artech House, 1991], and "Principles Of Aperture And Array System Design", [B. Steinberg, Wiley, New York, 1976], the contents of which are incorporated herein by reference.

Periodic arrays suffer from a number of problems, one of which arises from spatial aliasing. This occurs when insufficient periodic samples are taken and it is impossible to uniquely determine the direction of the incoming signals, resulting in grating lobes forming in the array beampattem. The maximum spacing of array elements at which spatial aliasing can be avoided is around half the wavelength of the incoming signal. In some circumstances, the effects of aliasing may be tolerated and the periodic spacing increased, although this is not ideal for all applications. In spatial filtering and beamforming, the effective length of the employed aperture is the principle factor in determining the spatial resolution, where the resolution is defined as the width of the main lobe. The higher the spatial resolution that is required, the longer the aperture has to be, and hence the more elements that are needed to fully populate the array. For planar arrays, improved resolution requires that the array length must be increased in both dimensions. Thus, for periodically spaced arrays, resolution varies proportionally to number of elements for linear arrays and as the square of number of elements for planar arrays, hi practice, the cost of a spatial array is directly linked to the number of elements used, and so it is generally desirable to minimize the number required.

In an attempt to improve efficiency, much research has been conducted to design arrays in which the element spacing is deliberately made irregular or random. Since resolution depends on array length, if array elements are spaced non-periodically the resolution is independent of element number. Additionally, removal of the periodicity means that aliasing does not occur. Hence, in theory, a large aperture can be constructed using fewer elements than for a periodic array design. This is discussed in more detail in "Principles Of Aperture And Array System Design", [B. Steinberg, Wiley, New York, 1976] and "The peak sidelobe of the phased array having randomly located elements", [B. Steinberg, IEEE Transactions on Antennas and Propagation, vol 20, Issue 2, pp. 129 — 136, Mar 1972.], the contents of which are incorporated herein by reference.

Common approaches to the design of non-periodic or 'sparse' arrays use search techniques such as genetic algorithms, simulated annealing or linear programming. Such techniques search for the optimum design using a given performance parameter. Further examination of sparse arrays and their design can be found in "Element placement in thinned arrays using genetic algorithms" [DJ. O'Neill, Oceans Engineering for Today's Technology and Tomorrow's Preservation.' Proceedings Volume 2, 13-16 Sept. 1994 Page(s): 11/301 - 11/306 vol.2], "Thinned arrays using genetic algorithms", [R.L. Flaupt, IEEE Transactions on Antennas and Propagation, Volume 42, Issue 7, July 1994 Page(s): 993 - 999], "Properties of the beampattern of weight- and layout-optimized sparse arrays"and [S. Holm, B. Elgetun, and G. Dahl, in IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 44, no. 5, pp. 983-991, Sept. 1997], and "Sidelobe Reduction in Array-Pattern Synthesis Using Genetic Algorithm", Keen-Keong Yan and Yilong Lu, IEEE Trans. Antennas And Propagation, Vol. 45, No. 7, pp. 1117-1122, July 1997], the contents of which are incorporated herein by reference.

Statistically, the average sidelobe level of a sparse array is around 101og₁₀(l/N) , where N = number of elements. An optimised array may have a peak sidelobe level not much higher than this. This indicates that the non-periodic array requires many elements to achieve a low peak sidelobe level whilst periodic arrays can achieve such sidelobe levels through weighting, regardless of element number. However, array weighting has been found to be largely ineffective when applied to sparse arrays, as standard weighting functions are only effective when periodicity exists. In an attempt to remedy this problem, random algorithmically optimised weighting functions have been applied to sparse arrays, but these have been found only to reduce the peak sidelobe level by a few dBs, which is insufficient to resolve the high peak sidelobe problem. This is the primary reason that sparse array designs have never been seen as a rival to periodic array designs.

Summary of the Invention According to the present invention, there is provided a spatial array having a plurality of elements in a non-periodic array and a plurality of elements in at least one periodic sub-array.

The non-periodic array may comprise all of the elements of the entire array. The elements of the non-periodic and periodic arrays may be intermixed/interspersed. The non-periodic and the periodic arrays may share one or more elements. In some cases, the array may include two or more periodic sub-arrays.

By using periodic and non-periodic arrays of elements, good sidelobe and resolution performance are provided, whilst utilizing a comparatively low number of elements.

The proportion of elements in the periodic portion of the array may vary depending on the performance specifications of the array. For example, the elements in the periodic portion may comprise fifty percent or more of the elements in the array, and in some circumstances seventy five percent or more of the elements in the array.

Each periodic portion may include three or more elements. Each array may include five or more elements. Preferably, the array includes ten or more elements, for example sixteen or more elements.

Preferably, the array is a receiver. One or more parts of the array could be used in transmission mode.

The array may have any suitable shape, for example, it may be linear or planar or conformal or circular.

According to another aspect of the invention, there is provided a method for processing data received by plurality of elements in an non-periodic array that has a periodic portion or sub-array, the method comprising processing data from the non- periodic portion using a first beamforming process; processing data from the periodic portion using a second beamforming process and using data from both processes to create a fused image.

The non-periodic portion may comprise the entire array or a sub-set thereof and the periodic portion may be a sub-array within the entire, non-periodic array.

To create an image, one of the beamforming algorithms is applied to the elements that are in the non-periodically spaced part of the array, typically the entire array, to produce a beam pattern with a narrow main lobe width and a high-resolution image, but a high peak sidelobe level. The other is applied to the periodic portion of the array only. The separate images are then fused. This involves forming an overall image on the basis of some optimisation criteria. This criteria may be as simple as selecting the pixel with the lowest magnitude normalised to the other pixel values.

The beam forming algorithms may be of any suitable form, for example those described the referenced prior art. Both beamforming algorithms may be the same or substantially the same. Preferably, a weighting is applied to the periodic portion, so that the beam pattern has a very low peak sidelobe level. The weighting may be incorporated into the beamforming algorithm.

According to another aspect of the invention, there is provided a method for designing an array that has a plurality of elements in positioned non-periodically overall, but at least some elements positioned periodically, the method comprising selecting one or more performance criteria and optimizing the geometry of the array to meet the selected criteria.

Preferably, optimizing the geometry of the array involves using random searches or a computational search technique for searching through many possible array configurations to identify the array that most closely matches the specification. The search process is operable to optimise the positions of the elements and/or the number of elements and/or proportion of periodic elements to sparse elements weighting and/or array size.

Various aspects of the invention will now be described by way of example only and with reference to the accompanying drawings, of which:

Figure 2 is a schematic view of a receiver that has a hybrid sparse periodic array;

Figure 3 is a flow diagram for designing a specific implementation of the receiver of Figure 2; Figure 4a shows 40 hybrid element positions and weights for an implementation of the device of Figure 2;

Figure 4b shows a 32 element periodic sub-array for the device of Figure 4a;

Figure 5 shows the beam patterns for the sparse array and periodic sub-array for the device of Figures 4a and 4b; Figure 6 shows the hybrid array beam pattern that a fused version of the beam patterns of Figure 5;

Figure 7 shows beam patterns for each of a conventional periodic array and a hybrid array in accordance with the invention, and Figure 8 shows an alternative hybrid sparse periodic array that can be used in the receiver of Figure 2.

Figure 2 shows a linear spatial hybrid sparse periodic array 10. Overall the array 10 is non-periodic, because the spacing of the elements 11 is not the same along the entire length. However, it has a periodic sub-array or portion 12 along its length, in which the element spacing is the same. Elements in the non-periodic part of the array are spaced further apart than elements in the periodic portion of the array. Because of this the number of elements in the array of Figure 2 is less than would be required for a conventional periodic array of the same length.

To form an image using the non-periodic array 10 of Figure 2, data from all of the elements is captured and processed using a first beamforming algorithm. This can be of any suitable type, such as described in the referenced prior art. The first beamforming algorithm provides the non-periodic or sparse array output. At the same time, data from elements in the periodic portion of the array 12 is captured and processed using a second beamforming algorithm. Again, this can be of any suitable type, such as described in the referenced prior art. The second beamforming algorithm provides the periodic array output. Typically, a weighting is applied to the periodic portion, so that the beam pattern has a very low peak sidelobe level. This may be incorporated into the beamforming algorithm.

Data from both algorithms is used to generate two separate images. From Figure 2 it can be seen that the image from the beamforming algorithm applied to the non- periodic array has a narrow main lobe, but relatively high sidelobe. hi contrast, the output from the beamforming algorithm applied to the periodic array has a low peak sidelobe, but relatively wide main lobe. The two images are fused to provide a final image. This can be done by forming an overall image on the basis of optimisation criteria that may be as simple as selecting the pixel with the lowest magnitude normalised to the other pixel values. Of course, other more complex techniques could be used if desired. Advantageously, the fused image contains a narrow peak sidelobe obtained from the long, non-periodic array, and also a low peak sidelobe level from the short, periodically spaced sub-array. By splitting the array into non-periodic and periodic components, processing each received signal separately and then combining the results, a hybrid sparse periodic array is provided having a high resolution and low peak sidelobe output. Thus, there is provided a spatial filter that has a similar sidelobe performance and spatial resolution as state of the art periodic arrays, but with a much reduced element count.

It should be noted that a region of distortion generally exists between the main lobe and sidelobes. As the design is a combination of a periodic array and a sparse array, an image change occurs when crossing from one array to the other. Because the final image is a compound of two arrays, there is a crossover point in the beam pattern where the overlap of the periodic and sparse functions interacts. The magnitude of this distortion is generally around -2OdB and so its effect is likely to be insignificant.

The design of the array depends on the application for which it is to be used. Typically, its geometry is optimized to achieve a particular spatial filter performance, for example a compounded beampattern that has a narrow main lobe and low peak sidelobe, and where the distortion caused by the crossover between arrays is minimised. This may be achieved using random searches or by a computational search technique, for example using a genetic algorithm for searching through many possible array configurations to identify the array that most closely matches the specification.

Figure 3 shows the steps in a typical design process, in which the position of the elements is being optimized. This involves identifying optimization set up parameters, such as the total number of elements, the number of elements in the periodic array, the periodic weighting function and the array length. Then a search is done to generate a set of possible element positions. To do this, firstly, the. array response is simulated and the beampatterns of sparse and periodic arrays calculated. Then the beampatterns are fused to create the hybrid response, as described above. The fitness of the array is established with regard to predetermined selection criteria (usually main lobe width, peak sidelobe level and distortion). The fitness and array geometry are then recorded and the process repeated until an appropriate solution is found.

In order to test the effectiveness of the invention, a hybrid sparse linear array was simulated. The design specification was to provide a 3dB beam width of 2° and a peak sidelobe level of -35dB. A genetic algorithm was used. The search indicated that this specification could be achieved with 40 elements, 32 periodically arranged and spaced at half wavelengths and the remaining arranged non-periodically, but also at multiples of half wavelengths. The positions are shown below in meters, with the wavelength set to Im. Since these positions are simply scaled by the wavelength, multiplying them by another wavelength would produce an identical beampattern.

0 1.0000 2.5000 3.5000 6.5000 7.0000 7.5000 8.0000 8.5000 9.0000

9.5000 10.0000 10.5000 11.0000 11.5000 12.0000 12.5000 13.0000 13.5000 14.0000 14.5000 15.0000 15.5000 16.0000 16.5000 17.0000 17.5000

18.0000 18.5000 19.0000 19.5000 20.0000 20.5000 21.0000 21.5000 22.0000 27.0000 28.5000 29.0000 29.5000

The 32 elements positioned from 6.5λ to 22λ form the periodic sub-array. The weighting function applied to the entire array was a unity (or rectangular) weighting, whilst a chebychev, -35dB weighting function was applied to the periodic sub-array. The weights for the chebychev function are given by:

0.2503 0.1774 0.2341 0.2976 0.3669 0.4406 0.5170 0.5943 0.6703 0.7431 0.8103 0.8700 0.9202 0.9594 0.9863 1.0000 1.0000 0.9863

0.9594 0.9202 0.8700 0.8103 0.7431 0.6703 0.5943 0.5170 0.4406

0.3669 0.2976 0.2341 0.1774 0.2503

The element positions and weights are shown graphically in Figures 4a and 4b. The beam patterns for the 40 element sparse array and the 32 element periodic sub-array are shown in Figure 5. The images from the entire 40 element array and the 32 element sub-array are compounded to produce a final image, as shown in Figure 6.

From this, it can be seen that the distortion in the beampattern is minimal and the 3dB beam width is around 2.06° broadening to 4.06° when steered to the edge of the scanning sector. The peak sidelobe is also -35dB.

In order to estimate the savings of the hybrid array, a standard periodic array was designed to the same specification. The optimized periodic array had 60 elements spaced at half wavelength intervals, with a chebyshev -35dB weighting function. This is the same type of weighting function as used in the hybrid array, although the specific numbers used were different because of the different number of elements. Figure 7 shows the beam pattern for both the periodic array and the hybrid array. From this it can be seen that the periodic design has a 3dB beamwidth of around 2.2°, approximately the same as the 2.06° offered by the hybrid array. The peak sidelobe of both arrays is around -35dB. Hence, the array of the present invention closely matches the performance of the periodic array for this design specification. However, the hybrid array of the present invention has 40 elements, whilst the periodic array has 60 elements. Therefore, the hybrid array requires 33% fewer elements than the periodic array.

The present invention utilizes a novel hybrid sparse-periodic design technique that can be used in any scenario employing waveform reception, including all electromagnetic and acoustical applications, whilst providing significant savings in the number of elements needed. The exact savings over conventional periodic spaced arrays depends on practical requirements, but is generally of the order of 30% to 50%. Although the invention requires a minor degree of image processing in order to construct the waveform image, the saving in cost due to the reduction in element numbers vastly exceeds any image-processing overhead.

The invention is of particular applicability to the fields of sonar, radar, mobile communications and medical ultrasound. It can also be applied to synthetic aperture techniques, commonly used in sonar and radar, where the aperture is created through the physical movement of the antenna.

A skilled person will appreciate that variations of the disclosed arrangements are possible without departing from the invention. For example although the invention is described with reference to a linear array, it is applicable to any geometrical array arrangement, such as planar, conformal, circular etc. Equally, whilst the invention is described generally with reference to time domain processing, it could also be used in the frequency domain. Also whilst in the search process of Figure 3 the positions of the elements are optimized and factors such as the number of elements, proportion of periodic elements to sparse elements, weighting function and array length are set or pre-determined, in some circumstances, these factors may also have to be incorporated into the optimisation process, for example, through a random weighting function. Furthermore, although the hybrid sparse periodic array of Figure 2 has a distinct periodic array in which the elements are adjacent one another, at least some, if not all, of the periodically spaced elements may be non-adjacent and interspersed with non-periodically spaced elements, as shown in Figure 8. Accordingly the above description of the specific embodiment is made by way of example only and not for the purposes of limitation. It will be clear to the skilled person that minor modifications may be made without significant changes to the operation described.

Claims

1. A non-periodic spatial array having a plurality of elements, some of which are arranged in at least one periodic portion or sub-array.

2. An array as claimed in claim 1 that includes two or more periodic portions or sub-arrays.

3. An array as claimed in claim 1 or claim 2 wherein the elements in the periodic portion or sub-array comprise fifty percent or more of the elements in the array.

4. An array as claimed in claim 3 wherein the elements in the periodic portion or sub-array comprise seventy five percent or more than the elements in the array.

5. An array as claimed in any of the preceding claims wherein each periodic portion or sub-array includes three or more elements.

6. An array as claimed in any of the preceding claims including five or more elements.

7. An array as claimed in claim 6 including ten or more elements, for example sixteen or more elements.

8. An array as claimed in any of the preceding claims, wherein elements in the or each periodic portion are interspersed with non-periodically spaced elements.

9. An array as claimed in any of the preceding claims, wherein elements in the or each periodic portion are non-adjacent.

10. An array as claimed in any of the preceding claims, wherein at least one of the elements in the or each periodic portion is included in the non-periodic array.

11. An array as claimed in any of the preceding claims, wherein the array is linear or planar or conformal or circular.

12. A spatial array as claimed in any of the preceding claims in which the elements are electromagnetic.

13. A spatial array as claimed in any of the preceding claims in which the elements are acoustic.

14. A spatial array as claimed in any of the preceding claims in which the elements are optical.

15. A spatial array as claimed in any of the preceding claims in which the elements are receiver elements.

16. A spatial array as claimed in claim 15 wherein the receivers are operable to transmit data.

17. A method comprising receiving data at an array as claimed in any of the preceding claims; processing data from the non-periodic array using a first beamforming process; processing data from the periodic portion or sub-array using a second beamforming process and using data from both processes to create a fused image.

18. A method as claimed in claim 17 comprising applying a weighting function to data received from the non-periodic array.

19. A method as claimed in claim 18 wherein the weighting function is included in the first process.

20. A method as claimed in any of claims 17 to 19 comprising applying a weighting to data received from the periodic portion of the array.

21. A method as claimed in claim 20 wherein the weighting function is included in the second process.

22. A method as claimed in any of claims 17 to 21 wherein the first and second beamforming processes are substantially the same.

23. A method for designing an array as claimed in any of claims 1 to 16 comprising selecting one or more performance criteria and optimizing the geometry of the array to meet the selected criteria.

24. A method as claimed in claim 23 wherein optimizing the geometry of the array involves using random searches or a computational search technique for searching through many possible array configurations to identify the array that most closely matches the specification.

25. A method as claimed in claim 24 wherein the search process is operable to optimise the positions of the elements and/or the number of elements and/or proportion of periodic elements to sparse elements weighting and/or array size.