Abstract:
A class of planar arrays having broad frequency range applications for source location, source imaging or target illumination with projected beams is described in this disclosure. The non-redundant arrays are circularly symmetric and made up of a plurality of sensing and/or transmitting elements arranged so as to substantially eliminate grating lobes for a broad range of frequencies. Signals received from or transmitted to the elements are appropriately phased to control the beam of the array.

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to planar arrays having broad frequency range applications for source location, source imaging or target illumination with projected beams. Prior attempts to address planar array design where the number of array elements is restricted focus on single frequency application, don&#39;t address the issue of circular symmetry, and/or are for far-field application and thus do not comprehensively address near-field, circularly symmetric, and broad band application for source mapping or target illumination with projected beams. 
     Regular arrays are known in the state of the art whereby array elements are placed in a periodic arrangement such as a square, triangle, or hexagonal grid. In these arrangements, adjacent elements are required to be spaced within one-half wavelength of each other to prevent the array pattern from having multiple mainlobes in other than the steered direction, a phenomenon commonly referred to as spatial aliasing or grating lobes. This half-wavelength requirement can be cost prohibitive from the standpoint of the number of array elements required in broad frequency range applications because the lowest frequency for intended use drives the array aperture size larger (to achieve adequate array resolution), while the highest frequency drives the element spacing smaller (to avoid spatial aliasing). 
     Irregular arrays are known in the state of the art for providing a way to address grating lobe problems inherent in regular arrays because irregular arrays eliminate periodicities in the element locations. Random arrays are known in the state of the art as one form of irregular array. Random arrays are limited in ability to predictably control worst case sidelobes. When array element location can be controlled, an algorithm may be used to determine element placement that will guarantee irregular spacing and allow for more predictable control of worst case sidelobes. Prior art contains many examples of irregularly spaced linear arrays many of which are non-redundant, that is, no spacing between any given pair of elements is repeated. Non-redundancy provides a degree of optimality in array design with respect to controlling grating lobes. 
     Prior art for designing irregular planar arrays is largely ad-hoc. Only a few simple examples of non-redundant planar arrays—where there is either a relatively small number of elements or a simplistic element distribution such as around the perimeter of a circle—appear to exist in prior art. Prior art appears void of non-redundant planar array design techniques for locating an arbitrary number of elements distributed throughout the array aperture (as opposed to just around the perimeter) in a controlled manner to ensure non-redundancy and circular symmetry. 
     It is one object of the present invention to provide a planar array design substantially absent of grating lobes across a broad range of frequencies where the available number of elements is substantially less than that required to construct a regular (i.e., equally spaced element) array with inter-element spacing meeting the half-wavelength criteria typically required to avoid grating lobe contamination in source maps or projected beams. 
     Another objective of the present invention is to provide a planar array design that provides circular symmetry so that the source map resolution or projected beamwidth is not substantially array-dimension (i.e., azimuthal angle) dependent. 
     A further object of the invention is to provide a planar array design that makes optimal use of a fixed number of array elements in the sense that the array is non-redundant. 
     Still another object of the invention is to provide space density tapering flexibility in the array design to allow for trade-offs in the array design between array beamwidth and sidelobe levels. 
     Yet another object of the present invention is to provide a general method for distributing an arbitrary number of elements on an arbitrary diameter circular planar aperture in a manner that guarantees circular symmetry and non-redundancy in the spatial sampling space. 
     SUMMARY OF THE INVENTION 
     A planar array of sensing or transmitting elements (e.g., microphones or antennas) spaced on a variety of arc lengths and radii along a set of identical logarithmic spirals, where members of the set of spirals are uniformly spaced in angle about an origin point, having lower worst-case sidelobes and better grating lobe reduction across a broad range of frequencies than arrays with uniformly distributed elements (e.g., square or rectangular grid) or random arrays. The array is circularly symmetric and when there are an odd number of spirals, the array is non-redundant. A preferred spiral specification embodiment combines the location of array elements on concentric circles forming the geometric radial center of equal-area annuli with locations on an innermost concentric circle whose radius is independently selected to enhance the performance of the array for the highest frequencies at which it will be used. This result applies over a broad wavelength band, e.g. 10:1 ratio, making it useful for phased acoustic microphone or speaker arrays, or for phased electromagnetic antenna arrays. For small numbers of array elements, it is superior to a random array. Alternate spiral specification embodiments provide array space density tapering alternatives allowing for flexibility in array design and for array performance trade-offs between array beamwidth and sidelobe levels. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The aforementioned and other objects and features of the present invention will become clear from the following description taken in conjunction with the preferred embodiments thereof with reference to the accompanying drawings throughout which like parts are designated by like reference numerals, and in which: 
     FIG. 1 is a diagrammatic view of a circular planar array made up of multiple logarithmic spiral shaped arrays with equi-annular area spaced elements in accordance with an embodiment of the invention wherein array elements from one of the spirals are highlighted; 
     FIG. 2 is a diagrammatic view of a coarray representing the set of all vector spacings between elements in the array aperture in accordance with an embodiment of the invention; 
     FIG. 3 is a diagrammatic view of a circular planar array made up of multiple logarithmic spiral shaped arrays with equal radial increment spaced elements in accordance with an embodiment of the invention wherein elements from one of the spirals are highlighted; 
     FIG. 4 is a diagrammatic view of a circular planar array made up of multiple logarithmic spiral shaped arrays with outside-in logarithmic radial increment spaced elements in accordance with an embodiment of the invention wherein elements from one of the spirals are highlighted; 
     FIG. 5 is an exemplary array pattern for single frequency operation using the FIG. 1 array at 1 kHz focused at a point 54 inches off broadside; 
     FIG. 6 is an exemplary array pattern for single frequency operation using the FIG. 1 array at 5 kHz focused at a point 54 inches off broadside; 
     FIG. 7 is an exemplary array pattern for single frequency operation using the FIG. 1 array at 10 kHz focused at a point 54 inches off broadside; 
     FIG. 8 is a plot of worst-case sidelobe characteristics for single frequency operation using the FIG. 1 array at 1 kHz focused at a point 54 inches off broadside; 
     FIG. 9 is a plot of worst-case sidelobe characteristics for single frequency operation using the FIG. 1 array at 5 kHz focused at a point 54 inches off broadside; 
     FIG. 10 is a plot of worst-case sidelobe characteristics for single frequency operation using the FIG. 1 array at 10 kHz focused at a point 54 inches off broadside; and, 
     FIG. 11 is a block diagram illustrative showing microphone input, signal conditioning, signal processing, and display from the planar array of FIG. 1 for noise source location mapping. 
    
    
     DESCRIPTION OF THE INVENTION 
     The present planar array design  15  shown in FIG. 1 shows array elements  12  represented by circles. A subset of the elements  14  are highlighted to emphasize their distribution along a logarithmic spiral  16 . The highlighted elements  14  may be located along the spiral according to any of a number of methods. One preferred method, as shown in FIG. 1, is equi-annular area sampling where the M- 1  outermost elements of the M-element spiral are located coincident with the geometric radial centers of concentric equal-area annuli. The Mth element is located independently at some radius less than that of the innermost of the aforementioned M- 1  elements to enhance the performance of the array at the highest frequencies for its intended use. Circular symmetry is achieved by clocking N-element circular arrays of equally spaced elements  17  off of each of the spiral elements  14  as shown in FIG.  1 . If the number of elements in the circular arrays is odd, the resulting array has zero redundancy in its spatial sampling space. This is represented by the coarray shown in FIG. 2 which represents the set of all vector spacings between elements  12  in the array aperture of FIG.  1 . Each point  18  in the coarray represents a vector difference between the locations of two elements in the array. For the present planar array design  15 , none of these vector differences is repeated. 
     Alternative spiral element spacing methods are shown in FIGS. 3 and 4. In FIG. 3 the spiral elements  14  are spaced on equal radial increments along the spiral  16  between an inner and outer radial specification. In FIG. 4 the spiral elements  14  are spaced in logarithmically increasing radial increments along the spiral  16  between an outer and inner radial specification (i.e., the radial increment between spiral elements increases as the spiral is traversed from the outermost to the innermost element). This is referred to as logarithmic radial spacing outside-in. Another method, referred to as logarithmic radial spacing inside-out locates the spiral elements on logarithmically increasing radial increments along the spiral between an inner and outer radial specification. These and other spiral element spacing methods exhibit trade-offs between array mainlobe width (i.e., array resolution) and sidelobe levels. Arrays with the elements concentrated near the perimeter such as the array  18  of FIG. 3 have a narrower mainlobe and correspondingly higher average sidelobe levels. Arrays with the elements concentrated near the center such as the array  19  of FIG. 4 have a broader mainlobe and correspondingly lower average sidelobe levels. The embodiments of FIGS. 1,  3 , and  4  and the embodiment comprising logarithmic radial spacing inside-out are exemplary only of radial spacing configurations in accordance with the invention. 
     The general design parameters for the present arrays are as follows: (1) logarithmic spiral angle; (2) inner radius; (3) outer radius; (4) number of elements per spiral; (5) number of elements per circle (i.e., number of spirals); and (6) spiral element spacing method. These parameters form a broad class of circularly symmetric non-redundant planar arrays (provided the number of elements per circle is odd) that have exceptionally low worst-case sidelobe characteristics across a broad range of frequencies compared to what can be achieved with regular or random arrays. 
     Array patterns for the embodiment of FIG. 1 are shown for 1 kHz in FIG. 5, for 5 kHz in FIG. 6, and for 10 kHz in FIG. 7, with the array focused at a point 54 in. off broadside demonstrating the absence of grating lobes over a broad frequency range and broad scan region, and showing the circularly symmetric characteristics of the array. These exemplary array patterns were determined for frequencies corresponding to atmospheric propagation of acoustic waves using a propagation speed of 1125 ft./s. Worst-case sidelobe characteristics for the embodiment of FIG. 1 are shown for 1 kHz in FIG. 8, for 5 kHz in FIG. 9, and for 10 kHz in FIG. 10, demonstrating strong grating lobe suppression over a broad frequency range for−90 13  to+90 13  elevation angle with the array focused at a point 54 in. off broadside. FIGS. 8,  9 , and  10  show the array pattern envelope that is formed by taking the largest value from 45 azimuthal angle cuts through the array pattern at each of 91 elevation angles. 
     FIG. 11 shows a block diagram for the instrumentation, signal conditioning, data acquisition, signal processing, and display system for an acoustic application of the array of FIG.  1 . The N-channel array design  1  is implemented by positioning N microphones at appropriate spatial locations such that the positions of the centers of the microphone diaphragms relative to each other match the array design specification (i.e., the spatial coordinates). The N microphone systems consisting of microphone button (array element)  12 , pre-amplifier  3 , and transmission line  4  are fed into N corresponding input modules  5 . Each input channel contains programmable gain  6 , analog anti-alias filter  7 , and sample and hold analog-to-digital conversion  8 . Input channels share a common trigger bus  9  so that sample and hold is simultaneous. A common system bus  10  hosts the input modules and channels the simultaneously acquired time series data to the beamformer  11 . The beamformer may be one or more of a number of conventional time and/or frequency domain beamforming processes which provide data for readout means comprising a graphical display device  13 . 
     As an example, a frequency domain beamformer  11  provides signal processing from the planar array of N microphone elements  12  and  14  of FIGS. 1 and 11 performing the following steps: 
     1. Fourier Transform to produce a narrowband signal for each channel. 
     2. Integrate the pairwise products of the narrowband signals in time to give the N×N correlation matrix. 
     3. Find the N-dimensional complex steering vector for each potential direction of arrival (plane wave beamforming case) or source location (spherical beamforming case). 
     4. Multiply the correlation matrix by the steering vectors to produce the estimated source power for each direction of arrival or source location. 
     The graphical device  13  then presents a contour plot of the estimated source distribution. 
     While a certain specific apparatus has been described, it is to be understood that this description is made only by way of example and not as a limitation to the scope of the invention as set forth in the objects and in the accompanying claims.