阅读说明：本技术 一种基于和差协同阵构建的平面互质阵列设计方法 (planar co-prime array design method based on sum-difference cooperative array construction ) 是由 任仕伟 王贵愚 高巍 于 2019-10-25 设计创作，主要内容包括：本发明公开了一种基于和差协同阵构建的平面互质阵列设计方法,主要解决现有技术中平面互质阵列自由度受限于仅利用差分协同阵的问题,以及和差协同阵的研究局限于一维线性阵列的问题,通过压缩平面互质阵列其中一个子阵的阵元间距,并重新设置两个子阵的相对位置,使其纵向排布且呈左右对称并相隔一定距离。以本发明的方法构建的平面互质阵列,最终形成的差分协同阵与和协同阵能够拼接成一个和差协同阵,该和差协同阵包含一个大面积的均匀间距虚拟矩形面阵。与传统平面互质阵列的差分协同阵相比,本发明的方法大幅度提高了阵列的自由度。(The invention discloses a planar co-prime array design method based on sum-difference co-prime arrays, which mainly solves the problems that the degree of freedom of the planar co-prime array in the prior art is limited to only utilizing a differential co-prime array and the research of the sum-difference co-prime array is limited to a -dimensional linear array, the planar co-prime array is formed by compressing the array element spacing of sub-arrays and resetting the relative positions of two sub-arrays to be longitudinally arranged and be bilaterally symmetrical and spaced apart by fixed distance.)

1, planar co-prime array design method based on sum and difference cooperative array construction, characterized in that, it includes the following steps:

step 1, determining basic parameters of a planar co-prime array, selecting pairs of co-prime natural numbers M₁，M₂Require M therein₁Can be decomposed into two natural numbers

step 2, respectively constructing two sub-arrays of the planar co-prime array on an xCy coordinate plane, wherein sub-arrays are formed by M₂×M₂A uniform square array formed by array elements, the spacing between adjacent array elements isIs marked as

step 3, sub-array

Step 4, the sub-array is processed

Step 5, the sub-array is processedThe ld distance is translated along the negative direction of the y axis integrally, and l meets the condition

Step 6, resetting an x ' O ' y ' coordinate system; in sub-arrays

Step 7, forming subarrays

first, from sub-array

Secondly, from the sub-arrayAnd sub-arrayThe position coordinates of the array elements are summed pairwise to obtain series sum value coordinates, and negative values of the coordinates are grouped together to form a set, a composition and a cooperation array which is recorded as

Finally, byAnd

Step 8, utilizing sum and difference cooperative array

2. The design method of planar co-prime arrays constructed based on sum-difference co-arrays according to claim 1, wherein the finally generated difference co-arrays uniform rectangular area arrays are respectively arranged at the upper side and the lower side of the x' axis, and the mathematical expression of the position of the virtual array element is as follows:

3. kinds of bases and sums according to claim 1The design method of the planar co-prime array constructed by the difference co-ordination array is characterized in that the finally generated sum co-ordination array

4. the design method of planar co-prime arrays constructed based on sum-difference co-arrays according to claim 1, wherein the sum-difference co-arrays generated in step 7

The technical field is as follows:

the invention belongs to the technical field of array signal processing, and particularly relates to a construction method of planar co-prime arrays, which can be used for generating sum-difference cooperative arrays with high degree of freedom.

Technical background:

the DOA estimation is important research branches in the array signal processing field, which utilizes array antennas with specific structures to receive spatial domain signals, and estimates the DOA of the received signals through the modern signal processing theory technology and related optimization methods thereof, and is widely applied to the military and civil fields by .

The Vaidyanathan and the like further step forward a multi-dimensional co-prime sampling theory, push the co-prime array structure to a two-dimensional plane, and combine the concept of a differential cooperative array to develop series research on the planar co-prime array.

The current research on the sum and difference cooperative arrays is limited to linear sparse arrays, and has a larger research space for the combination of a two-dimensional plane sparse array and a sum and difference cooperative array.

The invention content is as follows:

the invention aims to provide an optimized array arrangement scheme of planar co-prime arrays aiming at the defects of the prior art, so that a finally generated differential cooperative array and a sum cooperative array can be combined into a differential cooperative array with a larger virtual aperture, and the degree of freedom of the array is effectively improved.

In order to solve the technical problems, the invention is realized by the following technical scheme, which comprises the following steps:

step 1, determining basic parameters of a planar co-prime array, selecting pairs of co-prime natural numbers M₁，M₂Require M therein₁Can be decomposed into two natural numbers

And p, i.e.:

step 2, respectively constructing two sub-arrays of the planar co-prime array on the xOy coordinate plane, wherein sub-arrays are formed by M₂×M₂A uniform square array formed by array elements, the spacing between adjacent array elements is

Is marked as

Wherein [ r₁：s：r₂]Represents from r₁To r₂Step-by-step range of s, and sub-arrays consisting of M₁×M₁Uniform square array composed of array elements with M space between adjacent array elements₂d, is marked as

Where d is the half wavelength of the incident signal, and the incident signal wavelength λ is known; the bottom left corner array elements of the two sub-arrays coincide with the origin of coordinates O; the bottom edges of the two sub-arrays are coincided with the x axis in the positive direction; the left longitudinal edges of the two sub-arrays are both aligned with the y-axisDirection superposition;

step 3, sub-arrayIntegral negative translation along y axisDistance of sub-array

Is coincident with the positive direction of the x-axis, at this time

Step 4, the sub-array is processed

Integral translation along positive x-axis direction

Distance from the sub-arrayAnd sub-array

The formed planar coprime array is bilaterally symmetrical, and the symmetry axis is that x is 0.5M₂(M₁-1) at this time

Step 5, the sub-array is processed

The ld distance is translated along the negative direction of the y axis integrally, and l meets the conditionThe larger the value of l is, the higher the degree of freedom of the finally obtained sum-difference synergistic array is, and at the moment

Step 6, resetting an x ' O ' y ' coordinate system; in sub-arraysThe straight line of the bottom edge of (A) is the x' axis, in sub-array

And sub-array

The common left-right symmetrical axis is a new y 'axis, and a new origin of coordinates O' is located in the subarray

At the midpoint of the bottom line of (1), i.e., (0.5M) in the original xOy coordinate system₂(M₁-1), 0) points; the final sub-array element position is expressed as

Step 7, forming subarrays

And sub-array

Generating a sum and difference cooperative array by the array elements;

first, from sub-array

And sub-array

The position coordinates of the array elements are subjected to pairwise difference, and the obtained series difference coordinate set forms a difference cooperative array which is recorded as

Secondly, from the sub-array

And sub-array

The position coordinates of the array elements are summed pairwise to obtain series sum value coordinates, and negative values of the coordinates are grouped together to form a set, a composition and a cooperation array which is recorded as

Finally, by

And

union of constituents constitutes a sum and difference synergistic array, denoted

Step 8, utilizing sum and difference cooperative array

The uniform rectangular area array with the maximum continuous virtual array elements can implement various wave arrival direction estimation algorithms to accurately estimate the incoming wave direction of the space signal.

, the final generated difference cooperative array uniform rectangular arrays are respectively arranged on the upper and lower sides of the x' axisThe mathematical expression of the position of the quasi-array element is as follows:

Final generation and collaboration array

There are uniform rectangular area arrays in the center of the x ' O ' y ' plane, and the mathematical expression of the virtual array element position is:

further , the sum and difference synergy array generated in step 7

There are uniform rectangular area arrays in the center of the x ' O ' y ' plane, and the mathematical expression of the virtual array element position is:

the continuous range provides an array of degrees of freedom of

The invention has the following beneficial effects:

(1) the planar co-prime array constructed by the invention is a two-dimensional planar sparse array, the antenna array element spacing is integral multiple of the traditional unit array element spacing (half wavelength of received signals), and the influence of the mutual coupling effect between the array elements on the received signals can be effectively reduced;

(2) compared with a directly laid planar co-prime array and a traditional method of only constructing a differential cooperative array, the sum-difference cooperative array constructed by the planar co-prime array can provide higher array freedom degree under the same array element number; on the contrary, under the condition of providing the same array freedom degree, the design method of the invention can greatly reduce the requirement on the number of array elements.

Description of the drawings:

FIG. 1 is a block diagram of the overall flow of the method of the present invention;

FIG. 2 is an exemplary diagram of two subarrays of an initial planar co-prime array constructed in step 2 of the present invention, wherein M is₁＝4，M₂＝3，

In the figure, "○" denotes a subarray"◇" denotes a subarray

The array element of (2);

FIG. 3 is an exemplary diagram of two subarrays after step 3 of the present invention, where M is₁＝4，M₂＝3，In the figure, "○" denotes a subarray

"◇" denotes a subarray

The array element of (2);

FIG. 4 is an exemplary diagram of two subarrays after step 4 of the present invention, where M is₁＝4，M₂＝3，

In the figure, "○" denotes a subarray"◇" denotes a subarrayThe array element of (2);

FIG. 5 is an exemplary diagram of two subarrays after step 5 and step 6 of the present invention, where M is₁＝4，M₂＝3，

In the figure, "○" denotes a subarray

"◇" denotes a subarray

The array element of (2);

FIG. 6 is an exemplary diagram of array element positions of a differential cooperative array generated by a planar co-prime array constructed according to the present invention, where "□" denotes the array elements of the differential cooperative array;

FIG. 7 is a diagram of an example of the positions of array elements of a planar co-prime array and a co-ordinated array, where "□" indicates the array elements of the co-ordinated array;

fig. 8 is an exemplary diagram of the array element positions of the sum and difference cooperative arrays generated by the planar co-prime array constructed by the present invention, and "□" in the diagram indicates the array elements of the sum and difference cooperative arrays.

The specific implementation mode is as follows:

the technical solution and effects of the present invention will be described in detail below with reference to the accompanying drawings.

Step 1, determining basic parameters of a planar co-prime array; selecting a pair of coprime natural numbers M₁＝4，M₂3 where M ₁2 × 2, i.e

Step 2, respectively constructing two sub-arrays of a planar co-prime array on an xCy coordinate plane; wherein the sub-arrayIs composed of 9 array elements (3X 3) with the distance between adjacent array elements

The array element positions are

As indicated by "○" in fig. 2 for sub-arrays

The position of the array element; sub-array

Is composed of 16 array elements (4 × 4), and the distance between adjacent array elements is M₂d is 3d, and the array element position is

As indicated by "◇" in fig. 2 for sub-arrays

The position of the array element; the bottom left corner array elements of the two sub-arrays coincide with the origin of coordinates O;

step 3, sub-array

The whole body is translated along the negative direction of the y axis for a distance of 4d, so that the subarray is formedIs coincident with the x-axis in the forward direction, as shown in fig. 3, at which timeThe array element position is

Step 4, the sub-array is processed

The whole body is translated along the positive direction of the x axis by a distance delta x which is 2.5d, so that the sub array is formed

And sub-array

The formed planar coprime array is bilaterally symmetrical, and the symmetry axis is x ═ 4.5d, in this caseThe array element position is

As shown in fig. 4;

step 5, the sub-array is processed

The whole body is translated along the y-axis in the negative direction by a distance of l-2 d

The array element position is

Step 6, resetting an x ' O ' y ' coordinate system; in sub-arrays

The straight line of the bottom edge of (A) is the x' axis, in sub-array

And sub-array

The common left-right symmetrical axis is a new y 'axis, namely x under the original xCy coordinate system is 4.5d, and a new coordinate origin O' is positioned in the sub-array

The middle point of the bottom edge of the two sub-arrays is (4.5d, 0) point under the original xCy coordinate system, and finally the array element positions of the two sub-arrays are

As shown in fig. 5;

thus, the construction of the planar co-prime array designed by the invention is finished. According to the arrangement of the planar co-prime array, a sum-difference synergistic array is generated:

first, two sub-arrays are formed

And

the two-dimensional coordinates of the respective array elements are differed pairwise, the obtained difference two-dimensional coordinates form a set, namely, the difference cooperative array of the planar co-prime array of the invention is formed, the distribution of the array elements is shown as □ in figure 6, uniform rectangular area arrays are respectively arranged on the upper side and the lower side of an x' axis of the difference cooperative array, and the positions of virtual array elements are uniform rectangular area arrays

Secondly, two sub-arrays are arrangedAndthe two-dimensional coordinates of the respective array elements are summed pairwise with each other, the two-dimensional coordinates of the obtained sum values and the union formed by the negative values of the sums form the sumThe array element distribution of the planar co-prime array and the cooperative array of the invention is shown as □ in figure 7, thus the co-prime array and the cooperative array form uniform rectangular area arrays in the center of an x ' O ' y ' coordinate plane, and the virtual array element position is

Finally, the difference cooperative array and the sum cooperative array are combined together at to form the sum-difference cooperative array of the planar co-prime array of the present invention, the array elements are distributed as shown in "□" in fig. 8, and the virtual array elements are located at positions of

The array freedom degree provided by the continuous array elements of the sum and difference cooperative array is 9d multiplied by 26d to 234d²(ii) a It can be seen that the missing array elements in the center of the difference cooperative array in fig. 6 are just filled by the array elements of the sum cooperative array in fig. 7, and finally the sum and difference cooperative array forms a larger uniform rectangular area array, so that the sum and difference cooperative array constructed by the planar co-prime array designed by the invention greatly improves the array degree of freedom.