Abstract:
This invention relates to the use of a sufficiently-sampled auxiliary array in combination with one or more under-sampled sub-arrays. The sufficiently-sampled auxiliary array is used to create a signal-free reference (SFR) beam that contains grating lobe interference. The SFR may be used to cancel the interfering grating lobe in an under-sampled main beam by coherently eliminating or subtracting the SFR from the main beam. Exemplary aspects of the invention thus support significant under population of the full aperture and avoid the problems and limitations of previous solution, with consequent savings in sensor hardware cost and weight.

Description:
FIELD OF INVENTION 
     This invention relates generally to the field of line array sensors and specifically to isolating and reducing grating lobe interference. 
     BACKGROUND 
     When beamforming a line array having uniformly spaced elements, grating lobes can appear if the element spacing exceeds one-half (½) of a wavelength. This effect is analogous to the aliasing that occurs when sampling time data at less than the Nyquist rate. In a narrowband sense, grating lobes introduce ambiguity. When wideband beamforming, these narrowband grating lobes smear out across bearing and raise the overall background level. This invention serves to cancel grating lobes, thus enabling operation of line arrays in a band above the ½ wavelength design frequency. 
     Referring to  FIG. 1 , a graph illustrating an exemplary beam pattern  100  associated with a line array having an under-sampled uniform element spacing, a spacing that exceeds half the wavelength associated with the design frequency of the array. As shown in  FIG. 1 , the beam pattern  100  comprises a main lobe  110  and an undesirable grating lobe  120 . The occurrence of grating lobes such as grating lobe  120  is a well known problem in the art. Grating lobes are artifacts or a form of aliasing that result when a uniformly spaced array is operated above its half-wavelength design frequency. 
     Referring now to  FIG. 2 , graphs are shown that illustrate the problems encountered with grating lobes when broadband beamforming is carried out. Graph  200  illustrates the introduction of the grating lobe  210  as frequency increases. As can be seen in  FIG. 2  the angle at which the grating lobe appears also varies as a function of frequency. Integration of this beam pattern  200  over frequency results in a broadband beam  250  with a smeared grating lobe  260  that appears as a background plateau. This smeared grating lobe  260  can mask desired signals. 
     Several approaches currently seek to address the grating lobe problem. The most basic approach simply involves raising the design frequency by decreasing channel-spacing over the entire array thereby raising sensor costs and processing requirements. 
     In another approach grating lobes are avoided by limiting the field of view and the operating frequency range.  FIG. 3  illustrates beam patterns  310 ,  320  and  330  associated with three different steering angles of 90, 75 and 70 degrees respectively. The beam patterns  310  and  320  associated with 90 or 75 degrees shows minimal to no grating lobe interference, however when the main lobe is steered to 70 degrees a grating lobe  332  appears. The approach in this situation is simply to avoid steering beyond 70 degrees, which limits operational effectiveness in certain cases. 
     Referring now to  FIGS. 4   a  and  4   b , another approach for preventing grating lobes involves the use of an array with non-uniform element spacing.  FIG. 4   a  illustrates a beam pattern  410  resulting from an array  420  with logarithmically-spaced array elements  430   a - n . Grating lobe interference is avoided, however as can be higher side lobe levels are introduced. 
     Current methods for reducing grating lobe interference either require significant sensor hardware costs, merely attempt to avoid the problem, or introduce a host of additional problems. Improvements are thus needed to resolve these problems. 
     SUMMARY OF THE INVENTION 
     An exemplary embodiment of the invention contemplates use of a sufficiently sampled auxiliary array in combination with one or more under-sampled sub-arrays to reject grating lobe interference. The exemplary embodiment uses the smaller but sufficiently-sampled auxiliary array to create a signal-free reference (SFR) beam that only contains information from a grating lobe. In another aspect of an exemplary embodiment of the invention the SFR is used to cancel the interfering grating lobe in the under-sampled main beam by applying an estimate of the phase shift between the two and coherently eliminating or subtracting the phase-shifted signal-free reference from the main beam. Exemplary aspects of the invention thus support significant under population of the full aperture and avoid the problems and limitations of previous solutions, with consequent savings in sensor hardware cost and weight. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a graph illustrating an exemplary beam pattern  100  associated with a line array having an under-sampled uniform element spacing. 
         FIG. 2  is a set of graphs that illustrate the effect of grating lobe interference when broadband beamforming is carried out. 
         FIG. 3  is a set of graphs showing beam patterns used in a prior art solution. 
         FIG. 4   a  is a graph showing a beam-pattern resulting from a prior art solution. 
         FIG. 4   b  is diagram of the prior art solution that generates the beam pattern of  FIG. 4   a.    
         FIG. 5  is a diagram of a line array in accordance with an exemplary embodiment of the invention. 
         FIG. 6  is a block diagram illustrating a grating lobe rejection (GLR) process processing in accordance with an exemplary embodiment of the invention. 
         FIG. 7  is a set of diagrams illustrating a conventional nested line array. 
         FIG. 8  is a graph illustrating directivity vs. frequency using GLR for a nested array in accordance with an exemplary embodiment of the invention compared with conventional beam forming (CBF). 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to the present exemplary embodiments of the invention, examples of which are illustrated in the accompanying drawings. 
     Referring to  FIG. 5 , a graph is shown illustrating an exemplary embodiment of the invention. A line array  500  is shown separated into an auxiliary-array  510 , a first sub-array  520   a , and a second sub-array  520   b . While only two sub-arrays are shown it is to be understood that any number of sub-arrays may be used. The sub-arrays  520   a  and  520   b  each comprise M elements  522   a - n . The auxiliary array  510  comprises 2M elements  512   a - n . It is to be understood however that auxiliary array  510  may have any integer multiple of elements of the sub-arrays, depending on the desired maximum operating frequency, also known as the design frequency, of the line array  500 . As shown, the first and second sub-arrays  520   a  and  520   b  have been under-sampled, meaning that their element spacing is greater that ½ the operating wavelength associated with the desired design frequency of the array  500 . At certain azimuths, an under-sampled uniformly-spaced array will see grating lobes. As previously discussed, one solution is to simply sufficiently populate the entire array to increase the design frequency of the array. However, as shown in the exemplary embodiment of  FIG. 5 , only auxiliary sub-array  510  is sufficiently populated. This sole auxiliary array  510  will be sufficiently sampled with twice the number of elements of sub-array  520   a  or  520   b . As a result, when the auxiliary sub-array  510  is beamformed it will not have the grating lobes that are introduced when sub-arrays  520   a  or  520   b  are beamformed at the same higher frequency. The grating lobe can then be isolated as a signal free reference (SFR) by coherently eliminating or subtracting the auxiliary-array  510  beam from the sub-array  520   a  beam in accordance with equation  550 . This SFR can then be used to cancel the grating lobe interference seen when any of the additional under-sampled arrays are beamformed. This process will now be discussed in greater detail. 
     Referring now to  FIG. 6 , a block diagram illustrating a grating lobe rejection (GLR) process of an exemplary embodiment of the invention is shown. As shown, a parallel process is performed for each sub-array  520   a - n . For each sub-array  520   a - n  a conventional beamforming (CBF) module  610   a - n  carries out a beamforming process. The output generated from each of the processes  610   a - n  is then used as input to a Phase Matching module  620   a - n  in order adjust the phase of SFR  550 . Phase matching module  620   a - n  is necessary in order to perform processing to account for the phase shift introduced as a result of the spacing of the elements of the linear array  500 . Each of the phase-matching modules takes as input the same SFR signal  550  and after shifting its phase for each sub-array  520   a - n  passes the output to a combining module  630   a - n . The phase shifting performed by the phase-matching function varies linearly from sub-array to sub-array. The phase shift is a function of the location of the grating lobe which can be determined by a number of methods including performing cross-correlation between the auxiliary array  510  and each of the sub-arrays  520   a - n . The combining module  630   a - n  will in turn coherently eliminate or subtract the phase-matched SFR from the output of each of CBF modules  610   a - n . The result is that the grating lobe interference introduced as a result of beamforming each of the under-sampled sub-arrays  520   a - n  will be completely cancelled or rejected. This output is shown as  632   a - n . Each of the outputs  630   a - n  are then passed through another CBF module  640  to generate the full GLR beam pattern output  642 . The net effect is that the entire under-sampled array can be operated at a higher frequency without suffering from grating lobe interference and without having to increase the density of the elements. 
     Referring now to  FIG. 7 , a conventional nested array  700  is shown. As shown in  FIG. 7 , a nested array  700  may comprise a set of array elements  702   a - n  spaced with a base spacing  710  or an interval multiple thereof. The elements  702   a - n  are selectively activated to achieve a uniform spacing with one of three different intervals. Each of the three intervals corresponds to one of three different frequency range configurations, a low frequency (LF) range configuration  720 , a medium frequency range (MF) configuration  730 , and a high frequency (HF) range configuration  740 . As the operating frequency approaches the upper edge of a given frequency range, grating lobe interference will begin to occur and therefore the activation of the elements  702   a - n  of the nested array  700  must be reconfigured such that the spacing is stepped down to jump to a higher design frequency. Each time the spacing is stepped down a subset of elements must be deactivated. As an example when stepping down from LF to MF the two outermost elements (shown as white dots) will be deactivated (shown as black dots). The design frequency increases, however an undesirable drop in gain also occurs. In an alternate embodiment of the present invention the GLR processing may be applied to nested arrays to improve the array gain or Directivity Index of the array at higher frequency ranges. Instead of deactivating certain elements the same SFR processing described above can be applied to allow the outer under-sampled portions of the array to remain active without seeing the grating lobe interference that would normally occur. 
     Referring now to  FIG. 8 , a graph  800  of the directivity versus frequency is shown which illustrates the improvement seen when applying GLR to nested arrays. As shown in  FIG. 8 , traditional nested array CBF  810  results in a directivity gain that drops at frequencies  812  and  814  which correspond to reconfiguration of the nested array  700  to jump to a higher design frequency. The benefit of applying GLR processing to a nested array  700  is seen in the GLR curve which realizes improved gain since all of the array elements can be utilized. 
     Exemplary embodiments of the present invention may be implemented using sonar or radar array elements as well as both line arrays and two dimensional arrays. In the case of a two-dimensional array a two-dimensional auxiliary sub-matrix would be overpopulated to sufficiently populate the sub-matrix in similar manner to the auxiliary array of the line array described above. 
     While the foregoing invention has been described with reference to the above-described embodiment, various modifications and changes can be made without departing from the spirit of the invention. Accordingly, all such modifications and changes are considered to be within the scope of the appended claims.