Sparse array design method with high DOA estimation precision

Abstract

The invention discloses a design method of a sparse array with high DOA (direction of arrival) estimation precision, the sparse array is composed of five uniform linear arrays, a closed expression can uniquely determine the positions of all sensors according to the given number of the sensors, high uniform degree of freedom and low mutual coupling effect can be realized, and the sparse array has high DOA estimation precision. The method comprises the following implementation steps: calculating basic unit length between sensors, determining array parameters, calculating sensor positions of five uniform linear arrays, and determining positions of all sensors of the sparse array. Under the condition that the number of the sensors is the same, a larger uniform degree of freedom and lower mutual coupling can be obtained, and the DOA estimation precision can be improved.

Description

Technical Field

[0001] The present invention relates to the field of sensor array design, and more specifically, to a sparse array design method with high DOA estimation accuracy. Background Art

[0002] Sparse arrays can use fewer sensors to achieve the same or greater uniform degrees of freedom (uDOF) than traditional uniform linear arrays (ULA), and can effectively reduce the mutual coupling (MC) effect between sensors, with higher accuracy of direction of arrival (DOA) estimation. Sparse arrays vectorize the received signal matrix to obtain an equivalent differential array. The virtual sensors in the differential array are located at the differential positions of the physical sensors. The number of maximum continuous segments in the differential array is usually much larger than the number of physical sensors. Therefore, sparse arrays can achieve uDOF far exceeding the number of physical sensors with fewer physical sensors. At the same time, the sparsity of the array increases the distance between sensors, thereby reducing the MC effect between sensors.

[0003] In recent years, many novel sparse array structures have been proposed, which can achieve higher uDOF than traditional ULA and effectively reduce the MC effect. For example, MISC (Z. Zheng, W. Wang, Y. Kong, and Y. D. Zhang, "MISC array: A new sparse array design achieving increased degrees of freedom and reduced mutual coupling effect," IEEE Trans. Signal Process., vol. 67, no. 7, pp. 1728–1741, April 2019.), UF-4BL (W. Shi, S. A. Vorobyov, and Y. Li, "ULA fitting for sparse array design," IEEE Trans. Signal Process., vol. 69, pp. 6431–6447, 2021.), ICNA (Z. Peng, Y. Ding, S. Ren, H. Wu, and W. Wang, "Coprime nested arrays for DOA estimation: Exploiting the nesting property of coprime array," IEEE Signal Process. Lett., vol. 29, pp. 444–448, Dec. 2021.), ANAII-2 (J. Liu, Y. Zhang, Y. Lu, S. Ren, and S. Cao, "Augmented nested arrays with enhanced DOF and reduced mutual coupling," IEEETrans.Signal Process., vol.65, no.21, pp.5549–5563, Nov.2017.), IMISC (W.Shi, Y.Li, and RCde Lamare, “Novel sparse array design based on the maximum inter-elementspacing criterion,” IEEE Signal Process. Lett., vol. 29, pp. 1754–1758, Jul. 2022.), ATLI-1BL (W. Shi and Y.Li, "Improved uniform linear array fitting scheme within created lower bound on uniform degrees of freedom for DOA estimation," IEEE Trans. Instrum. Meas., vol. 71, pp. 1–14, Sep. 2022.), EMISC (X. Sheng, D. Lu, Y. Li, and R. C. de Lamare, "Enhanced MISC-based sparse array with high uDOFs and low mutual coupling," IEEE Trans. Circuits Syst. II, Exp. Briefs, Aug. 2023.), SANA (X. Wang, L. Zhao, and Y. Jiang, "Super augmented nested arrays: A new sparse array for improved DOA estimation accuracy," IEEE Signal Processing Letters, Dec. 2023.), and other sparse array design methods have further improved the uDOF of the array and reduced the MC effect between sensors. . Summary of the invention

[0004] The present invention provides a sparse array design method with high DOA estimation accuracy, which is named Enhanced Multi-ULA Sparse Array (EMUSA). EMUSA consists of 5 ULAs and has a closed-form expression that can uniquely determine the positions of all sensors. It can achieve high uDOF and low MC effect and has high DOA estimation accuracy.

[0005] The technical solution adopted by the present invention is as follows: The present invention provides a sparse array design method with high DOA estimation accuracy, comprising the following steps:

[0006] (1) Determine the basic unit length between sensors. The basic unit length d between sensors must satisfy d≤λ / 2, where λ is the wavelength of the incident signal. The minimum spacing d between sensors is 1 unit length.

[0007] (2) Determine array parameters. Based on the given number of sensors N (N ≥ 12), determine the maximum sensor spacing of EMUSA as Determine the sensor spacing and number of sensors for the 5 ULAs based on N and P;

[0008] (3) Determine the positions of all sensors based on array parameters. EMUSA can be represented by five ULAs: The sensor locations of the 5 ULAs are:

[0009]

[0010] The signal model of the method of the present invention is: assuming that M unrelated far-field narrowband signals at different angles are received by the EMUSA proposed by the present invention, and considering the mutual coupling effect, the received signal vector of the EMUSA at the t-th snapshot can be expressed as:

[0011] x(t)=CBs(t)+n(t)

[0012] Where s(t)=[s1(t),s2(t),...,s M (t)] T is the signal vector, n(t) is the power The zero-mean additive white Gaussian noise array manifold B = [b(θ1), b(θ2), ..., b(θ M )] T ,b(θ m ) is the steering vector of the mth source, and C is the mutual coupling matrix, which is expressed as:

[0013]

[0014] Where |n1-n2| represents the distance between two sensors in EMUSA.

[0015] Furthermore, the total MC effect of EMUSA can be expressed by the coupling leakage E:

[0016]

[0017] Generally, the larger the coupling leakage, the more severe the mutual coupling effect.

[0018] The weight function w(j) is defined as the number of sensor pairs with sensor spacing j. The first three weight functions w(1), w(2), and w(3) are the main factors affecting the MC effect of sparse arrays. The smaller the weight function, the smaller the MC effect of the sparse array. The first three weight functions of EMUSA are

[0019] w(1)=1,w(2)=1,w(3)=5,12≤N≤17

[0020] w(1)=1,w(2)=1,w(3)=1,N≥18

[0021] Among them, the sparse array The maximum number of consecutive virtual sensors in the resulting differential array is uDOF, which includes the following steps:

[0022] (1) Calculation The differential array of is used to obtain the virtual sensor;

[0023] (2) Calculate the maximum number of consecutive virtual sensors in the differential array.

[0024] Furthermore, the uDOF of EMUSA can be calculated by the following formula:

[0025]

[0026] Where N is the total number of physical sensors in EMUSA.

[0027] Furthermore, the uDOF ratio of EMUSA is calculated according to the following formula:

[0028]

[0029] Where R(N)=(uDOF-1) / 2 is the maximum number of continuous positive virtual sensors. The smaller the uDOF ratio, the higher the uDOF of the array. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a structural diagram of the EMUSA proposed in the present invention, which is composed of 5 ULAs;

[0031] Figure 2 It is a comparison chart of the relationship between the uDOF ratio and the number of sensors of the EMUSA proposed by the present invention and eight other sparse arrays;

[0032] Figure 3 This is a comparison chart of the relationship between coupling leakage and the number of sensors between the EMUSA proposed in the present invention and eight other sparse arrays;

[0033] Figure 4 It is the curve of DOA estimation error changing with signal-to-noise ratio of EMUSA proposed in the present invention and other 8 sparse arrays under the same conditions;

[0034] Figure 5 It is the curve of the DOA estimation error of EMUSA proposed by the present invention and other 8 sparse arrays changing with the mutual coupling coefficient under the same conditions;

[0035] Figure 6 It is the curve of the DOA estimation error of EMUSA proposed in the present invention and other 8 sparse arrays changing with the number of snapshots under the same conditions; DETAILED DESCRIPTION

[0036] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0037] Example 1

[0038] This embodiment shows that given the number of sensors, according to Figure 1 The process of obtaining the array structure.

[0039] The EMUSA structure proposed by the present invention is as follows Figure 1 As shown, we only need to give a certain number of sensors, and can Figure 1 Calculate the positions of all sensors of EMUSA, including the following steps:

[0040] (1) Determine the basic unit length between sensors. The basic unit length d between sensors must satisfy d≤λ / 2. Set d to 1 unit length.

[0041] (2) Determine array parameters. Assuming that the number of sensors N = 13, the maximum sensor spacing of EMUSA is P = 10. Based on N and P, the sensor spacing and number of sensors for the five ULAs can be determined.

[0042] (3) Determine the positions of all sensors based on the array parameters. Figure 1 The sensor locations of the five ULAs can be determined as follows:

[0043]

[0044] Therefore, the array structure of EMUSA Among them, the uDOF of EMUSA is calculated according to the following formula:

[0045]

[0046] Among them, input N=13 and obtain uDOF=115.

[0047] Example 1 shows that the EMUSA proposed in the present invention can obtain a corresponding sparse array structure according to the given number of sensors. Its structure is simple and easy to derive, and a closed-form expression for the positions of all sensors is given. The maximum uDOF of the obtained EMUSA can reach

[0048] Example 2

[0049] This embodiment conducts a simulation experiment on the proposed EMUSA.

[0050] Figure 2It is a comparison of the uDOF ratio of the proposed EMUSA and other 8 sparse arrays with the number of sensors ranging from 20 to 80. As can be seen from the figure, the proposed EMUSA has a higher uDOF with the same number of sensors.

[0051] Figure 3 It is a comparison of the coupling leakage between the proposed EMUSA and other 8 sparse arrays when the number of sensors ranges from 20 to 80. As can be seen from the figure, under the same number of sensors, EMUSA has lower MC effect than most sparse arrays.

[0052] Figure 4 It is the curve of the error of angle estimation of the proposed EMUSA and other 8 sparse arrays under the same conditions as the signal-to-noise ratio changes. It can be seen from the figure that under the same signal-to-noise ratio, the proposed EMUSA has a higher DOA estimation accuracy.

[0053] Figure 5 It is a curve showing the variation of the angle estimation error of the proposed EMUSA and the other 8 sparse arrays under the same conditions with the mutual coupling coefficient. It can be seen from the figure that under the same mutual coupling coefficient, the proposed EMUSA has a higher DOA estimation accuracy.

[0054] Figure 6 It is the curve of the angle estimation error of the proposed EMUSA and other 8 sparse arrays under the same conditions as the number of snapshots. It can be seen from the figure that under the same number of snapshots, the proposed EMUSA has higher DOA estimation accuracy.

[0055] Example 2 shows that, compared with other sparse array solutions, the method of the present invention has obvious advantages in uDOF, MC, and DOA estimation accuracy.

Claims

1. A sparse array design method with high DOA estimation accuracy is named Enhanced Multi-ULA Sparse Array (EMUSA). EMUSA consists of 5 ULAs and has a closed-form expression that can uniquely determine the positions of all sensors.

2. The sparse array design method with high DOA estimation accuracy according to claim 1, characterized in that: The following steps are involved: (1) Determine the basic unit length between sensors. The basic unit length d between sensors must satisfy d≤λ / 2, where λ is the wavelength of the incident signal. The minimum spacing between sensors, λ / 2, is assumed to be 1 unit length. (2) Determine the array parameters. Based on the given number of sensors N (N ≥ 12), determine the maximum sensor spacing of EMUSA as Determine the sensor spacing and number of sensors for the 5 ULAs based on N and P; (3) Determine the positions of all sensors according to the array parameters. EMUSA can be represented by five ULAs: The sensor locations of the 5 ULAs are: The sensor position is represented by the sensor interval.

3. The sparse array design method with high DOA estimation accuracy according to claim 2, characterized in that: The sparse array contains five ULAs: the first ULA starts at position 0, ends at position P-6, and has a sensor interval of 4; the second ULA starts at position End position is The sensor spacing is The starting position of the third ULA is End position is The sensor spacing is P; the starting position of the fourth ULA is End position is The sensor spacing is The starting position of the fifth ULA is End position is The sensor interval is 4.

4. The sparse array design method with high DOA estimation accuracy according to claim 2, characterized in that: From sparse array The maximum number of continuous virtual sensors in the resulting differential array is continuous degrees of freedom, which includes the following steps: (1) Calculation The differential array of is used to obtain the virtual sensor; (2) Calculate the maximum number of continuous virtual sensors in the differential array. The maximum continuous segment is the continuous degree of freedom of the array.

5. The sparse array design method with high DOA estimation accuracy according to claim 2, characterized in that: The continuous degrees of freedom of this sparse array can be calculated by the following formula: Where N is the total number of sensors in the sparse array EMUSA.

6. The sparse array design method with high DOA estimation accuracy according to claim 2, characterized in that: The first three weight functions w(1), w(2), w(3) of the sparse array are: w(1)=1,w(2)=1,w(3)=5,12≤N≤17 w(1)=1,w(2)=1,w(3)=1,N≥18 Where N is the total number of sensors in the sparse array EMUSA.

Images