Design method for non-uniform array without ambiguity in direction finding

Abstract

The present invention provides a method for designing a non-uniform array without ambiguity in direction finding, which is a method for rationally traversing by computer to design a non-uniform direction-finding array with high precision and no ambiguity. First, all possible reasonable non-uniform array forms in the actual situation are calculated; these non-uniform arrays are tested using the MUSIC algorithm at high-frequency ambiguous frequency points, and factors that may cause angle measurement ambiguity, such as channel inconsistency, etc., can be added during the test. Multiple Monte Carlo experiments are carried out for each array form, the root mean square error of angle measurement is calculated, and the array form with a smaller root mean square error is selected according to the test results; after the selected form is determined, it is verified whether non-ambiguous high-precision angle measurement can be achieved within the required angle measurement range. If the first selection does not meet the requirements, other array forms with a small root mean square error are selected again and tested again until the design requirements are met. The present invention can consider the factors affecting angle measurement ambiguity in the array design, the design method is reliable, and it has good application prospects.

Description

Technical Field

[0001] The present invention provides a non-uniform array design method for achieving unambiguous one-dimensional direction finding and two-dimensional direction finding in the field of direction of arrival (DOA) estimation when the signal frequency band spans a relatively wide range, and can achieve a better direction finding effect. Background Art

[0002] Direction finding systems play an important role in many application fields. For example, they have very special significance for radar systems, sonar systems, communication systems, navigation, geolocation, military weapon fields, etc. Some direction finding systems need to span a very wide frequency band range, such as the radar signal reconnaissance frequency band of 2 GHz - 18 GHz. The high frequency band can ensure the direction finding accuracy, but there may be ambiguity problems. The low frequency band may not have ambiguity problems, but it is difficult to ensure the direction finding accuracy. Therefore, a large number of de-ambiguity algorithms have been proposed in early interferometric direction finding, such as the long and short baseline method, the virtual baseline method, etc. When there are the influences of array element mutual coupling and channel inconsistency, the effectiveness of these algorithms is greatly reduced or even fails. When the array aperture is limited, these problems are directly related to the array placement and the element spacing. The element spacing of a uniform array has a greater impact on direction finding ambiguity. When its spacing is greater than half the wavelength, it will lead to direction finding ambiguity problems. Therefore, studying how to adjust the positions of antenna elements and reasonably arrange the positions of antenna elements in the antenna disk with limited element placement space, so as to solve the direction finding ambiguity problem of the uniform array when the aperture-wavelength ratio is large, is of great significance for a high-precision broadband direction finding system. For non-uniform arrays, experts and scholars have proposed many classical non-uniform arrays, such as the minimum redundancy linear array proposed by Moffet, A, and the generalized minimum redundancy array derived from it, as well as the maximum continuous delay array, the minimum gap array, etc. In recent years, the concept of nested arrays has been jointly proposed by Professor Piya Pal and P.P. Vaidyanathan, but its minimum spacing still needs to be less than half the signal wavelength, and when the frequency is high, the mutual coupling effect is obvious. Although a series of derived array forms such as super nested arrays have been derived later. Subsequently, the concept of co-prime arrays was proposed by the two scholars Piya Pal and P.P. Vaidyanathan, but the above problems still exist. In view of the above problems, the present invention proposes a method for finding a better array layout form to overcome the influences of factors such as channel inconsistency and mutual coupling effect on direction finding, and achieve the purpose of high angle measurement accuracy and no ambiguity value. Summary of the Invention

[0003] With the array aperture of D mm, assuming the antenna diameter is d mm and the number of antennas is N, under this condition, the placement positions of the array elements can be roughly traversed to seek an array placement form with no direction finding ambiguity, small direction finding error, and good effect within the angle measurement range and within the direction finding frequency range of (2 GHz to 18 GHz).

[0004] The design method of this invention includes the following steps:

[0005] (1) Calculate the minimum and maximum spacings that can be achieved between adjacent antenna elements according to the array aperture and the number of array elements;

[0006] (2) Determine the moving step size of the array elements according to the adjacent spacing range obtained in step (1) to ensure compliance with the actual situation;

[0007] (3) For the moving step size of the array elements in step (2), determine all possible forms of array element placement;

[0008] (4) Determine the highest frequency according to the required angular frequency range, and determine the angular step interval according to the angular measurement accuracy to meet the angular measurement accuracy requirements. Influencing factors such as channel inconsistency can be set in this step;

[0009] (5) Use the parameters obtained in step (4) to conduct a Monte Carlo experiment. Use the MUSIC algorithm to test all array forms in step (3) at the highest frequency. Conduct 100 Monte Carlo experiments at a certain angle to obtain the root mean square error of angle measurement for all arrays;

[0010] (6) For the angle measurement results in step (5), select one of the array forms with a smaller root mean square error of angle measurement among all the array placement forms in step (3);

[0011] (7) According to the array placement form obtained in step (6), verify whether there is angle measurement ambiguity within the angle measurement range for this array form and whether the accuracy requirements can be met. If the requirements are met, the array obtained in step (6) is the non-uniform array that meets the direction finding requirements. If not, repeat steps (6) and (7) until an array that meets the requirements is found;

[0012] This invention also includes the following features:

[0013] 1. Step (1) is specifically as follows:

[0014] In the one-dimensional case, the array aperture is D mm, the antenna diameter is assumed to be d mm, element 1 is at the coordinate origin O, element N is at the coordinate (D, 0), and the other (N - 2) elements change their positions continuously between the two elements. The minimum spacing between elements is 1 mm, and the maximum spacing is (D - (N - 1)*d) mm.

[0015] In the two-dimensional case, the array aperture is D mm, the antenna diameter is assumed to be d mm, the minimum interval between elements is ψ°. The maximum angular interval is (360 - (N - 1)*ψ°).

[0016] 2. Step (2) is specifically as follows:

[0017] Considering the actual situation, the placement error of array antenna elements can reach more than 1 mm. Therefore, the positions of the elements can be traversed with a step of 1 mm, which is in line with the actual situation. In the case of a two-dimensional circular array, the error can reach 3°. Traversing the positions of the elements with a step of 3° is in line with the actual situation.

[0018] 3. Step (3) is specifically as follows:

[0019] In the one-dimensional case, the positions of the elements are traversed with a step of 1 mm. Element 1 is at the coordinate origin O, element N is at the coordinate (D, 0), and the other (N - 2) elements continuously change their positions between the two elements. The swing range of element 2 is ((d + 1) to (2 * d + 2)) mm, the swing range of element 3 is the position of element 2 plus d + 1 mm, up to (3 * d + 2) mm, and the swing range of the position of element 4 is the position of element 3 plus 31 mm to (4 * d + 2), and so on.

[0020] In the case of a two-dimensional circular array, the positions of the elements are traversed with a step of β°. Element 1 is at the X coordinate (-D / 2, 0), and the other N - 1 elements are arranged clockwise. According to the minimum angular interval in step (1), element 2 is at (ψ° to 360° - (N - 2) * ψ°), element 3 is at (2 * ψ° to 360° - (N - 3) * ψ°), and so on.

[0021] 4. Step (4) is specifically as follows:

[0022] According to the angular frequency range, the highest frequency is f (GHz), and the angular measurement accuracy is δ°. Therefore, the angular step δ° and the channel inconsistency ε° can be set. Other influencing factors, such as mutual coupling effect, can be added in this step to increase the reliability of the designed array.

[0023] 5. Step (5) is specifically as follows: Test according to all the array placement forms obtained in step (3).

[0024] In the one-dimensional case, after fixing the array form, using the MUSIC algorithm, when the incident signal is at the highest frequency f (GHz), the incident angle is α°, the channel inconsistency is ε°, and the signal-to-noise ratio is relatively low, perform angle measurement for all the array placement forms obtained in step (3). Conduct 100 Monte Carlo experiments for each array form, calculate its root mean square error, and find the array placement form with a relatively small root mean square error of angle measurement.

[0025] In the two-dimensional case, select the azimuth angle and the elevation angle. At the highest frequency, with the channel inconsistency of ε° and a relatively low signal-to-noise ratio, conduct 10 or 20 Monte Carlo experiments for each array form, calculate the root mean square errors of the azimuth angle and the elevation angle measurement, and find the array placement form with relatively small root mean square errors of both the azimuth angle and the elevation angle measurement.

[0026] 6. Step (7) is specifically as follows: According to the array obtained in step (6):

[0027] In the one-dimensional case, traverse the angle measurement range in steps of δ° to verify whether there is no ambiguity within the angle measurement range and whether the angle measurement root mean square error is small. If it meets the requirements of no ambiguity and accuracy, it is the final design form of the non-uniform array. Otherwise, repeat steps (6) (7).

[0028] In the two-dimensional case, the azimuth and elevation angles need to be combined according to the angle step, and all possible angle combinations need to be tested. Each array form needs to be tested 10 or 20 times. The root mean square error of the azimuth and elevation angles is calculated. If all angle combinations are unambiguous and have high accuracy within the measurement range, then the final non-uniform array design is selected. Otherwise, repeat steps (6) and (7).

[0029] Compared with the prior art, the beneficial effects of the present invention are: 1. The non-uniform array design method proposed in the present invention is more flexible and more in line with actual conditions. 2. The present invention is applicable to both one-dimensional and two-dimensional direction finding situations. 3. When looking for a better array arrangement, influencing factors such as channel inconsistency and mutual coupling effect can be added to eliminate arrays with obvious mutual coupling effect or arrays that are greatly affected by channel inconsistency, thereby solving the influence of channel inconsistency and mutual coupling effect on angle measurement. 4. Compared with the interferometer deambiguation algorithm, this method uses the MUSIC algorithm to screen the array form, which can obtain higher angle measurement accuracy and better robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flow chart of the design method;

[0031] Figure 2 This is a schematic diagram of the placement of one-dimensional direction-finding array elements;

[0032] Figure 3 This is a schematic diagram of the placement of two-dimensional direction-finding array elements;

[0033] Figure 4 is the root mean square error of angle measurement for all array forms of one-dimensional array;

[0034] Figure 5 is the root mean square error of angle measurement for all array forms of two-dimensional array;

[0035] Figure 6 It is to verify the root mean square error of the designed one-dimensional array within the angle measurement range;

[0036] Figure 7 It is used to verify the root mean square error of the designed two-dimensional array within the angle measurement range. DETAILED DESCRIPTION

[0037] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0038] In this embodiment, the array aperture is 160 mm, the array model is a one-dimensional non-uniform linear array, the number of array elements is 5, the incident signal is a narrowband signal at 18 GHz. To avoid the observation angle falling on the grid, the signal incident angle is set to 29.3°, the search step is set to 0.5°, the signal-to-noise ratios are set to two conditions of 0 dB and 5 dB respectively, the number of snapshots is 100, the channel inconsistency is 10°, and 100 Monte Carlo experiments are carried out for each array form. Assume the antenna diameter is 30 mm, and the positions of the array elements are traversed with a step of 1 mm. Array element 1 is at the coordinate origin O, array element 5 is at the coordinate (160, 0), and the other three array elements continuously change their positions between the two array elements. The swing range of array element 2 is (31 mm to 62 mm), the swing range of array element 3 is 31 mm plus the position of array element 2, up to 62 mm minus the position of array element 5, and the swing range of the position of array element 4 is 31 mm plus the position of array element 3 to 31 mm minus the position of array element 5. The specific placement form is as shown in the appendix Figure 2 shown. Calculate the root mean square error of direction finding for each array. If the root mean square error is greater than 5°, it is considered that the position of this array may be ambiguous, discard this position, and find the position with a smaller mean square error of the array position, as shown in the appendix Figure 4 shown. In the direction finding range (-30° to 30°), traverse with a step of 0.1°, calculate the root mean square error of each angle. If the mean square error can meet the requirements within the direction finding range and there is no large error situation, it is considered that there is no ambiguity, and this array can be selected as the final array. The results are as shown in the appendix Figure 6 shown.

[0039] A two-dimensional non-uniform circular array with 5 array elements, and the placement positions are as shown in the appendix Figure 3As shown in the figure. The incident signal is a narrowband signal with a frequency of 18 GHz. The signal incident angle is set to an azimuth angle of 20° and an elevation angle of 55°, that is, a course angle of 33.3° and an elevation angle of 13.4°. The search step is set to 0.5°, the signal-to-noise ratio is set to 13 dB, the number of snapshots is 100, the channel non-uniformity is 10°, and 10 Monte Carlo experiments are carried out for each array form. Assume the antenna diameter is 50 mm, and the array elements are traversed with a step of 3°. Element 1 is at an azimuth angle of 0°, and the other four array elements are constantly changing positions. The swing azimuth angle range of element 2 is 60° to (360° - 4×60°), the swing azimuth angle range of element 3 is element 2 + 60° to (360° - 3×60°), the swing azimuth angle range of element 4 is element 3 + 60° to (360° - 2×60°), and the swing azimuth angle range of element 5 is element 4 + 60° to (360° - 1×60°). Calculate the root mean square error of direction finding for each array. If the root mean square error is greater than 5°, it is considered that the array position may be ambiguous, and this array is discarded. Find the position with a smaller root mean square error of direction finding for the array position. The traversal results are as attached Figure 5 As shown. After selecting the array, verify whether there is no ambiguity within the direction finding range. The results are as attached Figure 7 As shown.

[0040] Table 1 Simulation parameter table

[0041]

[0042] Figure 6 , Figure 7 shows the direction finding accuracy of one-dimensional and two-dimensional direction finding within the direction finding range of the present invention;

[0043] This shows that the non-uniform array design method is effective and can achieve unambiguous and accurate direction finding within a wide frequency range under low signal-to-noise ratio and high channel non-uniformity conditions.

[0044] Other step details and functions of the non-uniform array design in the embodiments of the present invention are known to those skilled in the art. To reduce redundancy, they are not described herein.

[0045] In summary, the present invention discloses a method for designing a non-uniform direction-finding array with no ambiguity and high precision based on reasonable computer traversal. The invention first calculates all possible reasonable non-uniform array forms in actual situations; then tests these non-uniform arrays using the MUSIC algorithm at high-frequency ambiguous frequency points, and factors that may cause angle measurement ambiguity, such as channel inconsistency, etc., can be added during the test. Multiple Monte Carlo experiments are carried out for each array form, the root mean square error of angle measurement is calculated, and then the array form with a smaller root mean square error is selected according to the test results; after the selected form, finally verify whether it is possible to achieve non-ambiguous and high-precision angle measurement within the required angle measurement range. If the first selection does not meet the requirements, other array forms with a small root mean square error can be selected again and tested again until the design requirements are met. The present invention can consider the factors affecting angle measurement ambiguity in the array design, and this non-uniform array design method is reliable and has good application prospects.

Claims

1. A method for designing a non-uniform array without ambiguity in direction finding, characterized in that The steps are as follows: Step (1): Calculate the minimum and maximum spacings that can be achieved between adjacent antenna elements based on the array aperture and the number of array elements; Step (2): Determine the element movement step size according to the adjacent spacing range obtained in Step (1) to ensure compliance with the actual situation; Step (3): Determine all possible element placement forms for the element movement step size in Step (2); Step (4): Determine the highest frequency according to the required angular measurement frequency range, and determine the angular step interval according to the angular measurement accuracy to meet the angular measurement accuracy requirements; Step (5): Conduct Monte Carlo experiments using the parameters obtained in Step (4). Use the MUSIC algorithm to test all the array forms in Step (3) at the highest frequency. Conduct 100 Monte Carlo experiments at a certain angle to obtain the root mean square error of the angular measurement for all arrays; Step (6): For the angular measurement results in Step (5), select one of the array forms with a relatively small root mean square error of angular measurement among all the array placement forms in Step (3); Step (7): According to the array placement form obtained in Step (6), verify whether there is angular measurement ambiguity within the angular measurement range for this array form and whether the accuracy requirements can be met. If the requirements are met, the array obtained in Step (6) is the non-uniform array that meets the direction finding requirements. If not, repeat Steps (6) and (7) until an array that meets the requirements is found.

2. The non-uniform array design method for ambiguity-free direction finding according to claim 1, wherein Specifically, Step (1) is as follows: In the one-dimensional case, the array aperture is D mm, the antenna diameter is d mm, element 1 is at the coordinate origin O, element N is at the coordinate (D, 0), and the other (N - 2) elements continuously change their positions between the two elements. The minimum spacing between elements is 1 mm, and the maximum spacing is (D - (N - 1)*d) mm; in the two-dimensional case, the array aperture is D mm, the antenna diameter is d mm, the minimum element interval is ψ°; the maximum angular interval is (360 - (N - 1)*ψ°).

3. The non-fuzzy direction finding non-uniform array design method according to claim 1, characterized in that, Specifically, Step (2) is as follows: Traverse the positions of the element placement with a step of 1 mm, and traverse the positions of the element placement with a step of 3°.

4. The non-fuzzy direction finding non-uniform array design method according to claim 1, characterized in that Specifically, Step (3) is as follows: In the one-dimensional case, traverse the positions of the element placement with a step of 1 mm. Element 1 is at the coordinate origin O, element N is at the coordinate (D, 0), and the other (N - 2) elements continuously change their positions between the two elements. The swing range of element 2 is ((d + 1)~(2*d + 2)) mm, the swing range of element 3 is the position of element 2 plus d + 1 mm to (3*d + 2) mm, the swing range of the position of element 4 is the position of element 3 plus 31 mm to (4*d + 2), and so on; In the two-dimensional circular array case, traverse the positions of the element placement with a step of β°. Element 1 is at the X coordinate (-D / 2, 0), and the other N - 1 elements are placed clockwise. According to the minimum angular interval in Step (1), element 2 is at (ψ°~360°-(N - 2)*ψ°), element 3 is at (2*ψ°~360°-(N - 3)*ψ°), and so on.

5. The method for designing a non-uniform array for unambiguous direction finding according to claim 1, wherein Step (4) is specifically as follows: According to the angular frequency range, with the highest frequency being f (GHz), the angular measurement accuracy being δ°, set the angular step as δ°, and the channel non-uniformity as ε°. In this step, other influencing factors are added, such as the mutual coupling effect, to increase the reliability of the designed array.

6. The non-uniform array design method for ambiguity-free direction finding according to claim 1, characterized in that Step (5) is specifically as follows: In the one-dimensional case, after fixing the array form, using the MUSIC algorithm, when the incident signal is at the highest frequency f (GHz), the incident angle is α°, and the channel non-uniformity is ε°, and the signal-to-noise ratio is relatively low, perform angle measurement for all the array placement forms obtained in step (3). Conduct 100 Monte Carlo experiments for each array form, calculate its root mean square error, and find the array placement form with a relatively small root mean square error of angle measurement. In the two-dimensional case, select the azimuth angle and the elevation angle. At the highest frequency, with the channel non-uniformity being ε° and the signal-to-noise ratio being relatively low, conduct 10 or 20 Monte Carlo experiments for each array form, calculate the root mean square error of angle measurement for the azimuth angle and the elevation angle, and find the array placement form with relatively small root mean square errors of angle measurement for both the azimuth angle and the elevation angle.

7. The non-uniform array design method for unambiguous direction finding according to claim 1, characterized in that Step (7) is specifically as follows: In the one-dimensional case, traverse at a step of δ° within the angle measurement range to verify whether there is no ambiguity within the angle measurement range and the root mean square error of angle measurement is relatively small. If it meets the requirements of angle measurement without ambiguity and accuracy, it is the final design form of the non-uniform array; otherwise, repeat steps (6) and (7). In the two-dimensional case, combine the azimuth angle and the elevation angle according to the angular step, test all possible angle combinations, conduct 10 or 20 Monte Carlo experiments for each array form, calculate the root mean square error of angle measurement for the azimuth angle and the elevation angle. If within the angle measurement range, all angle combinations have no ambiguity and high accuracy, it is the final design form of the non-uniform array; otherwise, repeat steps (6) and (7).

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