Low-redundancy-rate sparse array configuration design method
阅读说明：本技术 一种低冗余率的稀疏阵列构型设计方法 (Low-redundancy-rate sparse array configuration design method ) 是由 赵嫔姣 胡国兵 陈正宇 王利伟 陈恺 蒋凌瑕 于 2021-07-13 设计创作，主要内容包括：本发明涉及一种低冗余率的稀疏阵列构型设计方法,包括以下步骤：(1)确定两级稀疏子阵列的阵元数目及阵元间距；(2)设计稀疏阵列构型并推导阵元位置分布的解析表达式；(3)推导稀疏阵列在差分共阵域、求和共阵域及求和差分共阵域的连续区间；(4)基于步骤3中的连续区间,计算求和差分虚拟阵的连续自由度；(5)推导求和共阵与差分共阵重叠度的表达式；(6)计算该稀疏阵列构型的共阵冗余率。本发明通过减少求和虚拟阵与差分虚拟阵之间的阵元重叠率,解决了现有同类阵列设计方法存在的共阵冗余度过高的问题,在相同阵元数的情况下,具有更高的阵列利用率与自由度,从设计层面提升了角度估计性能。(The invention relates to a sparse array configuration design method with low redundancy rate, which comprises the following steps: (1) determining the number of array elements and the spacing of the array elements of the two-stage sparse subarray; (2) designing a sparse array configuration and deducing an analytical expression of array element position distribution; (3) deducing continuous intervals of the sparse array in a differential common array domain, a summation common array domain and a summation differential common array domain; (4) calculating the continuous freedom degree of the summation difference virtual array based on the continuous interval in the step 3; (5) deducing an expression of the overlapping degree of the summation common array and the difference common array; (6) and calculating the common array redundancy rate of the sparse array configuration. The method solves the problem of overhigh common array redundancy degree of the existing similar array design method by reducing the array element overlapping rate between the summation virtual array and the difference virtual array, has higher array utilization rate and freedom degree under the condition of the same array element number, and improves the angle estimation performance from the design level.)
1. A sparse array configuration design method with low redundancy rate is characterized by comprising the following steps:
step 1: determining the number of array elements and the spacing of the array elements of the two-stage sparse subarray;
step 2: designing a sparse array configuration and deducing an analytical expression of array element position distribution based on the parameters set in the step 1;
and step 3: deducing continuous intervals of the sparse array in a differential common array domain, a summation common array domain and a summation differential common array domain according to the analytic expressions of the sparse array configuration and the array element position distribution designed in the step 2;
and 4, step 4: calculating the continuous freedom degree and the optimal solution of the summation difference virtual array based on the continuous interval deduced in the step 3;
and 5: deriving an expression of the overlapping degree of the summation common array and the difference common array based on the continuous interval derived in the step 3;
step 6: and calculating the common array redundancy rate of the sparse array configuration according to the results of the step 4and the step 5.
2. The method for designing the sparse array configuration with low redundancy rate as claimed in claim 1, wherein in step 1, two levels of sparse subarrays are definedAndsub-arrayIn the array element number is N1And the array element interval is N1d, sub-arrayIn the array element number is N2And the array element interval is N2d, wherein N1≤N2D is lambda/2, lambda is the wavelength of incident signal, and the total number of array elements N is N1+N2+1。
3. The method as claimed in claim 2, wherein in step 2, the array element positions in the sparse array configuration are distributedSatisfy the requirement ofWherein
4. The method as claimed in claim 3, wherein in the step 3, the sparse array has a continuous and continuous interval (-S) in the whole differential common array region1,S1) WhereinThe continuous interval of the sparse array in the summation common array domain is (-S)2,S3) WhereinN2-N1＝ε，
When the epsilon is more than or equal to 0 and less than 3,
when the epsilon is 3, the process is carried out,
when the epsilon is 4, the process is carried out,
when ε > 4and ε ≠ 6,
when the epsilon is 6, the process is carried out,
the sparse array is continuous in the whole summation difference common array domain and has continuous intervals (-S)3,S3)。
5. The method as claimed in claim 4, wherein in step 4, the continuous DOF of the said virtual matrix is DOFConverting the optimal solution problem of the DOF into an optimization problem of the following formula:
wherein DOFmaxRepresenting the optimal solution of DOF, N0The solution to the above equation optimization problem is, according to the AM-GM inequality, N-1:
6. the method as claimed in claim 4, wherein in step 5, the expression of the overlap degree Ω of the sum and difference common arrays is Ω -2 (S)1-S2+1), according to step 3,
when the epsilon is more than or equal to 0 and less than 3,
when the epsilon is 3, the process is carried out,
when the epsilon is 4, the process is carried out,
when ε > 4and ε ≠ 6,
when the epsilon is 6, the process is carried out,
7. the method as claimed in claim 5 or 6, wherein the common matrix redundancy rate η in step 6 is defined as
When the epsilon is more than or equal to 0 and less than 3,
when the epsilon is 3, the process is carried out,
when the epsilon is 4, the process is carried out,
when ε > 4and ε ≠ 6,
when the epsilon is 6, the process is carried out,
when the continuous degree of freedom is optimal, according to step 4,
when in useWhen η is 0.16;
when in useWhen the value of epsilon is 0,eta to N0First derivative ofAnd maximum redundancy rate Andrespectively represent N08 and N0The corresponding co-array redundancy rate is 10;
when N is present1＝2,N2When 3, η is 0.2424;
when in useWhen the value of epsilon is 1,and maximum redundancy rate Represents N0The corresponding co-array redundancy rate is 7;
satisfy 2 < N1≤N2Under the conditions ofWhen the array redundancy rate eta is less than or equal to 0.0496, whenAnd the common array redundancy rate eta is less than or equal to 0.105.
Technical Field
The invention belongs to the field of array antenna design, and particularly relates to a sparse array configuration design method with low redundancy rate.
Background
The sparse array is an array configuration formed by sparsely arranging array elements in the antenna receiving array according to a certain rule, compared with a traditional uniform array, the sparse array breaks through the limitation of the space Nyquist sampling theorem, has the advantages of array aperture expansion, freedom improvement, reduction of mutual coupling effect among the array elements and the like, and is favorable for improving the angle measurement performance from the array design level.
The configuration design of the sparse array can be mainly divided into a differential common array class and a summation differential common array class. The differential common array type represents an array comprising: the limitation of the minimum redundant array, the minimum hole array, the coprime array, the nested array and the derivative array of the arrays is that the number of freedom degrees in the constructed virtual array can not exceed twice of the physical aperture. At present, few researches are carried out on the sparse array design method based on the sum and difference common array, the array element overlapping rate between the constructed sum virtual array and the difference virtual array is large, the common array redundancy is high, and the common array freedom degree is limited.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a sparse array configuration design method with low redundancy rate, which reduces the array element overlapping rate of a differential common array and a summation common array from the array configuration design level so as to reduce the common array redundancy rate, improve the array freedom degree and further improve the angle measurement performance.
In order to achieve the purpose, the invention adopts the following technical scheme:
a low-redundancy-rate sparse array configuration design method comprises the following steps:
step 1: determining the number of array elements and the spacing of the array elements of the two-stage sparse subarray;
step 2: designing a sparse array configuration and deducing an analytical expression of array element position distribution based on the parameters set in the step 1;
and step 3: deducing continuous intervals of the sparse array in a differential common array domain, a summation common array domain and a summation differential common array domain according to the analytic expressions of the sparse array configuration and the array element position distribution designed in the step 2;
and 4, step 4: calculating the continuous freedom degree and the optimal solution of the summation difference virtual array based on the continuous interval deduced in the step 3;
and 5: deriving an expression of the overlapping degree of the summation common array and the difference common array based on the continuous interval derived in the step 3;
step 6: and calculating the common array redundancy rate of the sparse array configuration according to the results of the step 4and the step 5.
Further, in the step 1, two-level sparse sub-arrays are definedAndsub-arrayIn the array element number is N1And the array element interval is N1d, sub-arrayIn the array element number is N2And the array element interval is N2d, wherein N1≤N2D is lambda/2, lambda is the wavelength of incident signal, and the total number of array elements N is N1+N2+1。
Further, in step 2, the array element positions in the sparse array configuration are distributedSatisfy the requirement ofWherein
Further, in the step 3, the sparse array is continuous in the whole differential common array domain and has a continuous interval (-S)1,S1) WhereinThe continuous interval of the sparse array in the summation common array domain is (-S)2,S3) WhereinN2-N1＝ε，
When the epsilon is more than or equal to 0 and less than 3,
when the epsilon is 3, the process is carried out,
when the epsilon is 4, the process is carried out,
when ε > 4and ε ≠ 6,
when the epsilon is 6, the process is carried out,
the sparse array is continuous in the whole summation difference common array domain and has continuous intervals (-S)3,S3)。
Further, in step 4, the continuous degree of freedom DOF of the summed-differential virtual array isAnd the optimal solution solving problem of DOF can be converted into an optimization problem of the following formula:
wherein DOFmaxRepresenting the optimal solution of DOF, N0The solution to the above equation optimization problem is, according to the AM-GM inequality, N-1:
further, the expression of the overlap degree Ω of the summation common matrix and the differential common matrix in step 5 is Ω -2 (S)1-S2+1), according to step 3,
when the epsilon is more than or equal to 0 and less than 3,
when the epsilon is 3, the process is carried out,
when the epsilon is 4, the process is carried out,
when ε > 4and ε ≠ 6,
when the epsilon is 6, the process is carried out,
further, the co-array redundancy rate η in step 6 is defined as
When the epsilon is more than or equal to 0 and less than 3,
when the epsilon is 3, the process is carried out,
when the epsilon is 4, the process is carried out,
when ε > 4and ε ≠ 6,
when the epsilon is 6, the process is carried out,
when the continuous degree of freedom is optimal, according to step 4,
when in useWhen η is 0.16;
when in useWhen the value of epsilon is 0,eta to N0First derivative ofAnd maximum redundancy rate Andrespectively represent N08 and N0The corresponding co-array redundancy rate is 10;
when N is present1＝2,N2When 3, η is 0.2424;
when in useWhen the value of epsilon is 1,and maximum redundancy rate Represents N0The corresponding co-array redundancy rate is 7;
satisfy 2 < N1≤N2Under the conditions ofWhen the array redundancy rate eta is less than or equal to 0.0496, whenAnd the common array redundancy rate eta is less than or equal to 0.105.
Different from the traditional sparse array design method based on difference common array and the traditional sparse array design method based on sum difference common array, the sparse array configuration design method with low redundancy rate disclosed by the invention reduces the array element overlapping rate between the sum virtual array and the difference virtual array in the implementation process to reduce the common array redundancy rate, has higher array utilization rate and array freedom under the condition of the same array element number, and improves the angle estimation performance of the sparse array from the design level.
Drawings
FIG. 1 is a schematic flow chart of the present invention.
FIG. 2 shows the redundancy of the common array with N under different epsilon1A graph of the change in value.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings.
Referring to fig. 1, the method for designing a low redundancy rate sparse array configuration of the present invention includes:
step 1: determining the number of array elements and the array element spacing of two-stage sparse subarrays, specifically as follows:
defining two-level sparse subarraysAndsub-arrayIn each array element interval is N1d and the number of array elements is N1Array of sub-arraysThe space between the middle array elements is N2d and the number of array elements is N2，N1≤N2The total array element number is N1+N2+1, where d ═ λ/2, λ denotes the incident signal wavelength.
Step 2: designing a sparse array configuration and calculating an analytical expression of array element position distribution based on the parameters set in the step 1, wherein the array element position distribution in the sparse array configurationSatisfies the following conditions:wherein the content of the first and second substances,
and step 3: deducing continuous intervals of the sparse array in a differential common array domain, a summation common array domain and a summation differential common array domain according to the analytical expression of array configuration and array element position distribution designed in the step 2, wherein the continuous intervals are as follows:
(1) continuous interval of differential common matrix:
the sparse array disclosed by the invention is continuous in the whole differential common array domain, and the continuous interval is as follows: (-S)1,S1) Wherein, in the step (A),
(2) successive intervals of the summation co-matrix:
the invention discloses a sparse array, which has the following continuous intervals in a summation common array domain: (-S)2,S3) Wherein N is defined2-N1＝ε，
1) Solving for S2Value of
When the epsilon is more than or equal to 0 and less than 3,
when the epsilon is 3, the reaction time is as low as,
when the epsilon is 4, the process is carried out,
when epsilon is more than 4and epsilon is not equal to 6,
when the epsilon is 6, the reaction time is as short as 6,
2) solving for S3Value of
(3) Successive intervals of the sum-difference common matrix:
the sparse array disclosed by the invention is continuous in the whole summation difference common array domain, and the continuous interval is as follows: (-S)3,S3) Wherein, in the step (A),
and 4, step 4: based on the continuous interval expression derived in the step 3, calculating the continuous freedom degree and the optimal solution of the summation difference virtual array, which are specifically as follows:
(1) calculating the continuous freedom of the summation difference virtual array:
(2) optimal solution for DOF:
the optimal solution solving problem for DOF can be converted to an optimization problem of the following formula:
according to the AM-GM inequality, the solution of the optimization problem is as follows:
and 5: deriving an expression of the overlapping degree of the summation common array and the difference common array, which is as follows:
according to the step 3, the superposition degree omega of the virtual array elements in the summation common array and the difference common array is deduced to be 2 (S)1-S2The expression of +1) is given,
when the epsilon is more than or equal to 0 and less than 3,
when the epsilon is 3, the reaction time is as low as,
when the epsilon is 4, the process is carried out,
when epsilon is more than 4and epsilon is not equal to 6,
when the epsilon is 6, the reaction time is as short as 6,
step 6: calculating the common array redundancy rate of the array configuration, specifically as follows:
(1) defining co-array redundancy rateDeducing the common array redundancy rate of the array configuration of the invention:
when the epsilon is more than or equal to 0 and less than 3,
when the epsilon is 3, the reaction time is as low as,
when the epsilon is 4, the process is carried out,
when epsilon is more than 4and epsilon is not equal to 6,
when the epsilon is 6, the reaction time is as short as 6,
(2) the co-array redundancy rate when the degree of freedom reaches the optimum:
according to the step 4, deducing the corresponding co-array redundancy when the continuous freedom degree obtains the maximum value:
1) when in useWhen the sum of η is 0.16,
when in useWhen the value of epsilon is equal to 0,
2) when N is present1＝2,N2When equal to 3, η is 0.2424
When in useWhen the value of epsilon is 1,
in conclusion, 2 < N is satisfied1≤N2Under the conditions ofThe common array redundancy rate eta of the sparse array configuration disclosed by the invention is less than or equal to 0.0496, and when the common array redundancy rate eta is less than or equal to 0.0496In time, the invention discloses that the common array redundancy rate eta of the sparse array configuration is less than or equal to 0.105.
FIG. 2 shows the co-array redundancy with N of the low-redundancy sparse array under different values of epsilon1It can be seen from the graph that under the same other conditions, the co-array redundancy is minimized when epsilon is 0,
in summary, the sparse array configuration design method with low redundancy rate disclosed by the invention solves the problem of overhigh co-array redundancy degree of the existing similar array design method by reducing the array element overlapping rate between the summation virtual array and the differential virtual array in the implementation process, has higher array utilization rate and freedom degree under the condition of the same array element number, and improves the angle estimation performance from the array design level.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.
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