Hole-free sparse array antenna with even maximum array element spacing and design method thereof

Abstract

The invention provides a nonporous sparse array antenna with even maximum array element spacing and a design method thereof. The design method comprises the following implementation steps: designing an array element internal spacing distribution set; designing a corresponding array element position distribution set; it is proved that the sparse array has a non-porous differential common array, and the continuous degree of freedom of the array is calculated; and calculating weighting functions omega (1), omega (2) and omega (3) of the array configuration. According to the method, the non-porous sparse array design under the maximum array element spacing criterion is provided, and the direction finding performance is improved from the array design level while the continuous array freedom degree is ensured to be increased.

Description

Technical Field

[0001] The invention belongs to the technical field of array antenna design, and in particular relates to a non-aperture sparse array antenna with an even maximum array element spacing and a design method thereof. Background Art

[0002] Among the existing sparse array configuration designs, the most typical ones are coprime arrays and their derivative arrays and nested arrays and their derivative arrays. This type of sparse array configuration is explained from the perspective of sensor array. The Maximum Inter-Element Spacing (IES) Constraint (MISC) provides a new perspective for sparse array design, with the advantages of simple structure and easy capture of array element distribution patterns. However, some existing sparse array designs based on the MISC principle have holes (such as EMISC and IMISC), and the array degrees of freedom need to be further improved. Summary of the invention

[0003] The present invention aims at the deficiencies in the prior art and provides a non-aperture sparse array antenna with an even maximum array element spacing.

[0004] In order to achieve the above purpose, the present invention adopts the following technical solutions:

[0005] In a first aspect, the present invention provides a non-aperture sparse array antenna with an even maximum array element spacing, wherein the maximum array element spacing of the array configuration is M is an even number, N is the number of array elements, N ≥ 10, and the internal spacing distribution of the array elements is for:

[0006]

[0007] Where M s =M / 2,M q =M / 4, r = NM, the array configuration consists of 7 uniform linear arrays ULA, the array element spacing of each ULA is 1, 2, M respectively s +1, M, M s -1, 1 and 2, superscript M q -1, M q , r-1, M q and M q -1 is the number of repetitions corresponding to the array element spacing.

[0008] Optionally, the array element position distribution set of the array configuration is for:

[0009]

[0010] Wherein, ULA1 to ULA7 represent seven uniform linear arrays, and IES represents the array element spacing.

[0011] Optionally, the maximum continuous degree of freedom of the array configuration uDOF = -1.5M 2 +2MN-3.

[0012] Optionally, three weight functions ω(1), ω(2) and ω(3) used to characterize the mutual coupling effect between array elements in the array configuration are respectively:

[0013] ω(1)=2;

[0014] ω(2)=0.5M-2;

[0015]

[0016] Wherein, the weight function ω(l) represents the number of sensor pairs corresponding to the common array index, and the above formula shows that in this array configuration, the number of sensor pairs with a common array index of 1 is only 1; the number of sensor pairs with a common array index of 2 is 0.5M-2; when the number of array elements is 10≤N≤16, the number of sensor pairs with a common array index of 3 is 0.25M+2; when the number of array elements is N≥17, the number of sensor pairs with a common array index of 3 is 2.

[0017] In a first aspect, the present invention provides a method for designing a non-aperture sparse array antenna with an even maximum array element spacing, comprising the following steps:

[0018] Step 1: Design the internal spacing distribution set of array elements;

[0019] Step 2: Determine the corresponding array element position distribution set according to the array element internal spacing distribution set designed in step 1;

[0020] Step 3: Based on the array configuration obtained in step 2, verify that it has a hole-free differential common array, and calculate the maximum continuous degree of freedom of the array configuration;

[0021] Step 4: Based on the array configuration obtained in step 2, calculate the weight function ω(l) representing the number of sensor pairs corresponding to the common array index .

[0022] Optionally, in step 1, the design of the internal spacing distribution set of the array elements is specifically:

[0023] For an array configuration with N array elements, N ≥ 10, the maximum array element spacing is defined as And M is an even number, define M s =M / 2,M q =M / 4, r = NM, then the internal spacing distribution set of the array element is It is expressed as:

[0024]

[0025] In the formula, the array configuration consists of 7 uniform linear arrays ULA, and the array element spacing of each ULA is 1, 2, M respectively. s +1, M, M s -1, 1 and 2, superscript M q -1, M q , r-1, M q and M q -1 is the number of repetitions corresponding to the array element spacing.

[0026] Optionally, in step 2, the array element position distribution set is:

[0027]

[0028] Wherein, ULA1 to ULA7 represent 7 uniform linear arrays respectively, and IES represents the array element spacing.

[0029] Optionally, in step 3, the verification that it has a differential common matrix without holes is specifically as follows:

[0030] Define 0≤z≤1, 1≤l1≤M / 4-1, 1≤l2≤M / 4, 1≤r0≤NM-1, z, l1, l2, r0 are positive integers;

[0031] When 10≤N≤15, the continuous interval in [1, M] is and Joint decision, where

[0032]

[0033] The set [M+1, -7M 2 / 8-5M / 4+NM] is caused by the difference set as well as To fill,

[0034]

[0035] Collection [-7M 2 / 8-5M / 4+NM+1, -3M 2 / 4+NM-2] is composed of the difference set and Fill, where

[0036]

[0037] When N ≥ 16, the difference set and Jointly construct a continuous interval [1, 3M / 2-2]; difference set and The union of generates a continuous interval [3M / 2-1, -7M 2 / 8-5M / 4+NM]; differential set and The holes are filled in between and a continuous interval is generated [-7M 2 / 8-5M / 4+NM+1, -3M 2 / 4+NM-2];

[0038] Therefore, the array configuration is [3M 2 / 4-NM+2,-3M 2 / 4+NM-2] has a differential common matrix without holes.

[0039] Optionally, in step 3, the maximum continuous degree of freedom of the array configuration uDOF = -1.5M 2 +2MN-3.

[0040] Optionally, in step 4, three weight functions ω(1), ω(2) and ω(3) used to characterize the mutual coupling effect between array elements in the array configuration are respectively:

[0041] ω(1)=2;

[0042] ω(2)=0.5M-2;

[0043]

[0044] The above formula shows that in this array configuration, the number of sensor pairs with a common array index of 1 is only 1; the number of sensor pairs with a common array index of 2 is 0.5M-2; when the number of array elements is 10≤N≤16, the number of sensor pairs with a common array index of 3 is 0.25M+2; when the number of array elements N≥17, the number of sensor pairs with a common array index of 3 is 2.

[0045] The beneficial effects of the present invention are as follows: the present invention discloses a hole-free sparse array antenna with an even maximum array element spacing and a design method thereof, designs an array configuration with a hole-free differential common array based on the maximum internal array element spacing restriction principle, and all virtual array elements are used for degree of freedom expansion, thereby improving the array degree of freedom and improving the angle measurement performance from the array design level. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 The invention discloses a flow chart of a method for designing a non-aperture sparse array antenna with an even maximum array element spacing.

[0047] Figure 2 The present invention discloses a method for designing a non-perforated sparse array with an even maximum array element spacing (GEMISC E) and the comparison arrays (MISC, EMISC, IMISC, xMISC) as the signal-to-noise ratio changes. DETAILED DESCRIPTION

[0048] The present invention will now be described in further detail with reference to the accompanying drawings.

[0049] In one embodiment, the present invention proposes a design method for a non-aperture sparse array antenna with an even maximum array element spacing, such as Figure 1 As shown, the specific steps include:

[0050] Step 1: Design the internal spacing distribution set of array elements.

[0051] For an array configuration with N array elements (N ≥ 10), the maximum array element spacing is defined as And M is an even number, define M s =M / 2,M q =M / 4, r=NM, then the inter-element spacing distribution set (Inter-Element Spacing, IES) is expressed as:

[0052]

[0053] Among them, g n It represents the n-times repetition of the array element spacing g. According to the above array element internal spacing distribution set, the array configuration consists of seven uniform linear arrays (ULA), and the array element spacing of each sub-array is 1, 2, M, respectively. s +1, M, M s -1, 1 and 2.

[0054] Step 2: Based on the results in step 1, design the corresponding array element position distribution set:

[0055]

[0056] Wherein, ULA1 to ULA7 represent seven uniform linear arrays, and IES represents the array element spacing.

[0057] Step 3: Based on the array configuration in step 2, prove that it has a hole-free differential common array and calculate the maximum continuous degree of freedom of the array, including:

[0058] (1) Prove that it has a hole-free differential matrix:

[0059] Distribute the set according to the internal spacing of the array elements Definition, define 0≤z≤1, 1≤l1≤M / 4-1, 1≤l2≤M / 4, 1≤r0≤NM-1, where z, l1, l2, r0 are positive integers.

[0060] When 10≤N≤15, the continuous interval in [1, M] is and Joint decision, where

[0061]

[0062] The set [M+1, -7M 2 / 8-5M / 4+NM] can be represented by the differential set as well as To fill,

[0063]

[0064] Collection [-7M 2 / 8-5M / 4+NM+1, -3M 2 / 4+NM-2] can be represented by the difference set and Fill, where

[0065]

[0066] When N ≥ 16, the difference set and Jointly construct a continuous interval [1, 3M / 2-2]; difference set and The union of generates a continuous interval [3M / 2-1, -7M 2 / 8-5M / 4+NM]; differential set and The holes are filled in between and a continuous interval is generated [-7M 2 / 8-5M / 4+NM+1, -3M 2 / 4+NM-2].

[0067] Therefore, the array configuration is [3M 2 / 4-NM+2,-3M 2 / 4+NM-2] has a differential common matrix without holes.

[0068] (2) Calculate the maximum continuous degree of freedom: uDOF = -1.5M 2 +2MN-3.

[0069] Step 4: Based on the array configuration in step 2, calculate the weight functions ω(1), ω(2), and ω(3), including:

[0070] Define the weight function ω(l) to represent the number of sensor pairs corresponding to the common array index l. According to the array element position distribution given in step 2, calculate the three weight functions ω(1), ω(2), and ω(3) used to characterize the mutual coupling effect between array elements in the array configuration, which are ω(1) = 2, ω(2) = 0.5M-2, and The above results show that in this array configuration, the number of sensor pairs with a common array index of 1 is only 1; the number of sensor pairs with a common array index of 2 is 0.5M-2; when the number of array elements is 10≤N≤16, the number of sensor pairs with a common array index of 3 is 0.25M+2; when the number of array elements is N≥17, the number of sensor pairs with a common array index of 3 is 2.

[0071] In another embodiment, the present invention proposes a non-aperture sparse array antenna with an even maximum element spacing, which is obtained by adopting the design method of the above embodiment. The element internal spacing distribution set, element position distribution set, continuous degrees of freedom and weight function of the array configuration are the same as those of the above embodiment, so they will not be repeated here.

[0072] Figure 2 The present invention discloses a method for designing a non-perforated sparse array with an even maximum array element spacing (GEMISC E ) and the comparison arrays (MISC, EMISC, IMISC, xMISC) with the change of signal-to-noise ratio, the number of snapshots is 600, and the mutual coupling coefficient is 0.3. Figure 2 It can be seen that the root mean square error of all arrays decreases with the increase of signal-to-noise ratio. Under the same signal-to-noise ratio, GEMISC E There is minimal angle measurement error.

[0073] In summary, the present invention discloses a hole-free sparse array antenna with an even maximum array element spacing and a design method thereof, which is an array configuration with a hole-free differential co-array designed based on the maximum internal array element spacing limitation principle. It improves the array degree of freedom while ensuring the "hole-free" differential co-array, thereby improving the angle measurement performance from the array design level.

[0074] The above are only preferred embodiments of the present invention. The protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A non-aperture sparse array antenna with an even maximum element spacing, characterized in that: The maximum element spacing of the array configuration is M is an even number, N is the number of array elements, N ≥ 10, and the internal spacing distribution of the array elements is for: Where M s =M / 2,M q =M / 4, r = NM, the array configuration consists of 7 uniform linear arrays ULA, the array element spacing of each ULA is 1, 2, M respectively s +1, M, M s -1, 1 and 2, superscript M q -1, M q , r-1, M q and M q -1 is the number of repetitions corresponding to the array element spacing.

2. The non-aperture sparse array antenna with an even maximum array element spacing as claimed in claim 1, characterized in that: The array element position distribution set of the array configuration for: Wherein, ULA1 to ULA7 represent seven uniform linear arrays, and IES represents the array element spacing.

3. The non-aperture sparse array antenna with an even maximum element spacing as claimed in claim 2, characterized in that: The maximum continuous degree of freedom of the array configuration uDOF = -1.5M 2 +2MN-3.

4. The non-aperture sparse array antenna with an even maximum array element spacing as claimed in claim 2, characterized in that: The three weight functions ω(1), ω(2) and ω(3) used to characterize the mutual coupling effect between array elements in the array configuration are: ω(1)=2; ω(2)=0.5M-2; Wherein, the weight function ω(l) represents the number of sensor pairs corresponding to the common array index, and the above formula shows that in this array configuration, the number of sensor pairs with a common array index of 1 is only 1; the number of sensor pairs with a common array index of 2 is 0.5M-2; when the number of array elements is 10≤N≤16, the number of sensor pairs with a common array index of 3 is 0.25M+2; when the number of array elements is N≥17, the number of sensor pairs with a common array index of 3 is 2.

5. A method for designing a non-aperture sparse array antenna with an even maximum array element spacing, characterized in that: The steps include: Step 1: Design the internal spacing distribution set of array elements; Step 2: Determine the corresponding array element position distribution set according to the array element internal spacing distribution set designed in step 1; Step 3: Based on the array configuration obtained in step 2, verify that it has a hole-free differential common array, and calculate the maximum continuous degree of freedom of the array configuration; Step 4: Based on the array configuration obtained in step 2, calculate the weight function ω(l) representing the number of sensor pairs corresponding to the common array index .

6. The design method according to claim 5, characterized in that: In step 1, the design of the internal spacing distribution set of the array elements is specifically: For an array configuration with N array elements, N ≥ 10, the maximum array element spacing is defined as And M is an even number, define M s =M / 2,M q =M / 4, r = NM, then the internal spacing distribution set of the array element is It is expressed as: In the formula, the array configuration consists of 7 uniform linear arrays ULA, and the array element spacing of each ULA is 1, 2, M respectively. s +1, M, M s -1, 1 and 2, superscript M q -1, M q , r-1, M q and M q -1 is the number of repetitions corresponding to the array element spacing.

7. The design method according to claim 6, characterized in that: In step 2, the array element position distribution set is: Wherein, ULA1 to ULA7 represent seven uniform linear arrays, and IES represents the array element spacing.

8. The design method according to claim 7, characterized in that: In step 3, the verification that it has a differential common matrix without holes is as follows: Define 0≤z≤1, 1≤l1≤M / 4-1, 1≤l2≤M / 4, 1≤r0≤NM-1, z, l1, l2, r0 are positive integers; When 10≤N≤15, the continuous interval in [1, M] is and Joint decision, where The set [M+1, -7M 2 / 8-5M / 4+NM] is caused by the difference set as well as To fill, Collection [-7M 2 / 8-5M / 4+NM+1, -3M 2 / 4+NM-2] is composed of the difference set and Fill, where When N ≥ 16, the difference set and Jointly construct a continuous interval [1, 3M / 2-2]; difference set and The union of generates a continuous interval [3M / 2-1, -7M 2 / 8-5M / 4+NM]; differential set and The holes are filled in between and a continuous interval is generated [-7M 2 / 8-5M / 4+NM+1, -3M 2 / 4+NM-2]; Therefore, the array configuration is [3M 2 / 4-NM+2,-3M 2 / 4+NM-2] has a differential common matrix without holes.

9. The design method according to claim 7, characterized in that: In step 3, the maximum continuous degree of freedom of the array configuration uDOF = -1.5M 2 +2MN-3.

10. The design method according to claim 7, characterized in that: In step 4, the three weight functions ω(1), ω(2) and ω(3) used to characterize the mutual coupling effect between array elements in the array configuration are respectively: ω(1)=2; ω(2)=0.5M-2; The above formula shows that in this array configuration, the number of sensor pairs with a common array index of 1 is only 1; the number of sensor pairs with a common array index of 2 is 0.5M-2; when the number of array elements is 10≤N≤16, the number of sensor pairs with a common array index of 3 is 0.25M+2; when the number of array elements N≥17, the number of sensor pairs with a common array index of 3 is 2.

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