CN111025236A - Non-uniform area array design method based on improved nested linear array - Google Patents

Non-uniform area array design method based on improved nested linear array Download PDF

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CN111025236A
CN111025236A CN201911359728.2A CN201911359728A CN111025236A CN 111025236 A CN111025236 A CN 111025236A CN 201911359728 A CN201911359728 A CN 201911359728A CN 111025236 A CN111025236 A CN 111025236A
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array
uniform area
area array
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abscissa
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杨明磊
王晓冉
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Kunshan Innovation Institute of Xidian University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
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Abstract

The invention discloses an inhomogeneous area array design method based on an improved nested linear array, which comprises the following steps: determining array element number A contained in a radar antenna, and determining the size of a non-uniform area array according to the array element number A contained in the radar antenna, wherein the horizontal axis of the non-uniform area array comprises B array elements, and the vertical axis of the non-uniform area array comprises C array elements; determining the horizontal coordinates of all array elements in the non-uniform area array according to the array element number B on the horizontal axis of the non-uniform area array; determining the vertical coordinates of all array elements in the non-uniform area array according to the array element number C on the longitudinal axis of the non-uniform area array; and determining the positions of all array elements of the final non-uniform area array according to the abscissa and the ordinate of all array elements of the non-uniform area array. The invention provides an inhomogeneous area array design method based on an improved nested linear array, which can improve the degree of freedom and the aperture of the array, and the array element position has a closed expression, thereby being beneficial to the deployment of the array.

Description

Non-uniform area array design method based on improved nested linear array
Technical Field
The invention belongs to the technical field of radars, and particularly relates to an inhomogeneous area array design method based on an improved nested linear array.
Background
In the field of array signal processing, the planar array can estimate the two-dimensional angle of a target signal, so that compared with a linear array, the planar array can provide more target direction information and has greater detection advantages. Therefore, the area array has wide application in the aspects of beam forming, radar imaging, communication and the like. From the perspective of array design, it is generally required that the aperture of an area array is as large as possible, the degree of freedom is as large as possible, a differential synthesis array is completely filled, and the position of an array element can be described by a closed expression or a simple rule.
A Piya Pal research team and the like propose a nested area array, the array has larger degree of freedom, a differential synthesis array is completely filled, and the position of an array element of the array has a closed expression; a Van Trees research team provides a uniform rectangular array, and the degree of freedom and the aperture of the array are small; the Sunli research and development team provides a minimum redundant array, the array is designed based on the minimum redundant linear array, the differential synthesis array is completely filled, the degree of freedom is larger than that of a nested area array, but the position of the minimum redundant linear array element can only be obtained in a computer searching mode and cannot be obtained through a closed expression.
In summary, the existing non-uniform area array, for example: although the nested area array, the uniform rectangular array and the minimum redundant area array can all obtain the degree of freedom which is more than the number of array elements, the nested area array, the uniform rectangular array and the minimum redundant area array have certain defects: the requirements that the aperture is as large as possible, the differential synthesis array is completely filled, and the array element position can be obtained through a closed expression cannot be simultaneously realized.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides an improved nested linear array-based non-uniform area array design method, which can improve the degree of freedom and the array aperture of the array, and the array element position has a closed expression, thereby being beneficial to the deployment of the array.
In order to achieve the aim, the invention provides a non-uniform area array design method based on an improved nested linear array, which comprises the following steps:
s1, determining array element number A contained in the radar antenna, and determining the size of the non-uniform area array according to the array element number contained in the radar antenna, wherein the horizontal axis of the non-uniform area array comprises B array elements, and the vertical axis of the non-uniform area array comprises C array elements; A. b and C are positive integers greater than 0, respectively, and satisfy A ═ B × C;
s2, determining the abscissa X of the non-uniform area array according to the array element number B on the transverse axis of the non-uniform area array;
s3, determining the vertical coordinate Y of the non-uniform area array according to the array element number C on the longitudinal axis of the non-uniform area array;
and S4, determining the final non-uniform area array Z according to the abscissa X of the non-uniform area array and the ordinate Y of the non-uniform area array.
Step 5, calculating to obtain a differential synthesis array { v } according to the final non-uniform area array ZDCA}。
Further, in S1, the expression of B is:
Figure BDA0002336864150000021
represents a round-down operation; the expression of C is, C ═ A ÷ B.
Further, in S2, the expression of X is:
X＝{b1,b2,…,bm}×d
wherein, bmThe abscissa of the array element of the m-th column of the non-uniform area array is expressed, m is more than or equal to 1 and less than or equal to B, BmX d denotes the position of the array element of the m-th column of the non-uniform area array, and b1And d is 0, and represents the unit array element interval in the non-uniform area array, and takes the value of half wavelength of a radar transmission signal.
Further, in S3, the expression of the ordinate Y is:
Y＝{c1,c2,…,cn}×d
wherein, cnThe vertical coordinate of the array element of the nth row of the non-uniform area array is expressed, n is more than or equal to 1 and less than or equal to C, CnX d denotes the position of the array element of the n-th row of the non-uniform area array, and c1And d is 0 and represents the unit array element interval in the non-uniform area array.
Further, in S4, the expression of the non-uniform area array Z is:
Z＝{(bm,cn)1≤m≤B,1≤n≤C}×d
wherein, bmRepresents the abscissa of the m-th array element in the abscissa X of the non-uniform area array, cnThe ordinate of the nth array element in the ordinate Y of the non-uniform area array is shown, (b)m,cn) The coordinates of the array element of the mth column and the nth row of the non-uniform area array are shown, (b)m,cn) And x d represents the position of the array element of the nth row of the mth column of the non-uniform area array, and d represents the unit array element interval in the non-uniform area array.
Further, in the step 5, the differential synthesis array { v }DCAThe expression is:
{vDCA}＝{(bm-bm',cn-cn')1≤m≤B,1≤m'≤B,1≤n≤C,1≤n'≤C}
when m is 1, respectively enabling m' to be 1 to B; and when n is 1, let n' take 1 to C respectively; and further respectively obtain (b)1-b1,c1-c1) To (b)1-bM,c1-cN)；
Then let m take 2 to B respectively and let n take 2 to C respectively to obtain (B)2-b1,c2-c1) To (b)B-bB,cC-cC)；
Wherein, bmRepresents the abscissa of the m-th array element in the abscissa X of the non-uniform area array, bm'Represents the abscissa of the m' th array element in the abscissa X of the non-uniform area array, cnThe ordinate of the nth array element in the ordinate Y of the non-uniform area array, cn'And the ordinate of the n' th array element in the ordinate Y of the non-uniform area array is shown.
Further, the differential synthesis array { v }DCAThe array element is of a complete filling type, and the degree of freedom of the array element is the number of array elements of the differential synthesis array; the differential synthesis array { v }DCAThe degree of freedom is DOF, which is expressed as:
DOF＝(2bB+1)×(2cC+1)
wherein, bBRepresents the abscissa of the B-th array element in the abscissa X of the non-uniform area array, cCExpressing the ordinate of the C array element in the ordinate Y of the non-uniform area array; the differential synthesis array is a uniform area array without holes.
Further, the differential synthesis array further includes the following steps:
the preset conditions are as follows: setting K targets in the differential synthesis array, wherein the K targets are respectively non-correlated targets, the distances between the K targets and the non-uniform area array respectively meet preset requirements, and the radar transmitting signals are parallel waves and narrow-band signals when reaching the non-uniform area array; the noise and the radar emission signal are independent from each other and are additive, independent and equally distributed Gaussian processes; when multi-target detection is performed for K targets, KThe number of array elements A included in the radar is larger than that of the array elements A included in the radar, and the pitch angle corresponding to the kth target is thetakThe azimuth angle corresponding to the kth target is phikAnd theta is not less than-90 degreesk≤90°，0°≤φkLess than or equal to 360 degrees, and K is a positive integer greater than 0.
S11, calculating the array manifold A of the non-uniform area array horizontal axis B array elementsxCalculating a direction matrix A of C array elements included in a longitudinal axis of the non-uniform area arrayyThe differential synthesis arrays are sequentially arranged along the direction of the transverse axis of the differential synthesis arrays, so that C sub-arrays are obtained; wherein
The 1 st sub-array is A1，A1＝AxD1(Ay)；
The 2 nd sub-array is A2，A2＝AxD2(Ay)；
Until the C-th sub-array is AC，AC＝AxDC(Ay)；
Wherein
Figure BDA0002336864150000031
Figure BDA0002336864150000041
Dm(.) is a direction matrix A of C array elements which is composed of the longitudinal axis of the non-uniform area arrayyA diagonal matrix constructed in the m-th row of (c); c,. m ═ 1, 2; d represents unit array element interval in the non-uniform area array, lambda is the wavelength of electromagnetic waves, j is an imaginary number unit, and e is an exponential function;
s12, calculating signal data x (t) received by the differential synthesis array, where the expression is:
Figure BDA0002336864150000042
where s (t) is a narrow-band signal corresponding to K targets, and s (t) ═ s1(t),s2(t),…,sn(t),…,sK(t)]T，sn(t) denotes the nthIncident signals corresponding to targets, the incident signals corresponding to each target are independent and uncorrelated in time and are in complex Gaussian distribution
Figure BDA0002336864150000043
Representing the incident signal s corresponding to the nth targetn(t) power;
n (t) represents a mean of 0 and a variance of σ2White gaussian noise satisfying independent equal distribution and being uncorrelated with an incident signal corresponding to each target, respectively;
t represents the sampling time, t is 1,2, …, and N represents the fast beat number;
CN represents gaussian distribution.
S13, according to the signal data x (t) received by the differential synthesis array, decoherence is carried out by using a space smoothing algorithm, and then the arrival direction estimation is carried out by using a unitary ESPRIT algorithm, so that the arrival direction estimation values of the K targets are respectively obtained.
Compared with the prior art, the invention has the following advantages and beneficial effects:
firstly, the technical scheme provided by the invention is simple, the differential synthesis array is a completely filled rectangular area array, the parameter estimation can be carried out by utilizing the traditional uniform array-based processing method, the angle ambiguity problem is effectively avoided, and meanwhile, the beam forming capability is better;
secondly, the array element position in the technical scheme provided by the invention can be described by a closed expression or a simple rule, so that the array deployment and related research are greatly facilitated;
thirdly, the technical scheme provided by the invention has higher degree of freedom, aperture and resolution, and can realize underdetermined direction estimation on the target with a plurality of array elements.
Drawings
Fig. 1 is a flow chart of a non-uniform area array design method based on improved nested linear arrays in the embodiment of the invention;
FIG. 2 is a diagram of a non-uniform area array structure obtained by using the method of the present embodiment when the number of elements of a given radar array is 49;
FIG. 3 is a diagram of a differential synthesis array structure obtained by using the method of the present embodiment when the number of elements of a radar array is 49;
FIG. 4 is a diagram illustrating the estimation of the direction of arrival for 66 targets using the present invention given a radar array element number of 49;
FIG. 5 is a non-uniform area array structure diagram obtained by using the method of the present embodiment when the number of elements of a given radar array is 36;
FIG. 6 is a non-uniform area array structure diagram obtained by using a nested area array when the number of elements of a given radar array is 36;
FIG. 7 is a diagram of a differential synthesis array structure obtained by using the method of the present embodiment when the number of elements of a radar array is given as 36;
FIG. 8 is a diagram of a differential synthesis array structure obtained using nested area arrays given a radar array element number of 36;
FIG. 9 is a diagram illustrating the result obtained by estimating the direction of arrival of the target using the method of the present embodiment when the number of elements of the radar array is 36;
FIG. 10 is a diagram illustrating the results obtained by using a nested area array for estimation of the direction of arrival of a target given that the number of elements of a radar array is 36;
FIG. 11 is a schematic diagram showing the comparison of the mean square error of each of the nested area arrays and the method of this embodiment with the signal-to-noise ratio when the number of elements of the radar array is 365;
FIG. 12 is a diagram showing the respective degree of freedom of a differential synthesis array and a nested area array obtained by the method of the present embodiment, given several different sets of radar array elements;
fig. 13 is a structural schematic diagram of an improved nested linear array in the embodiment.
Detailed Description
The following describes the embodiments and effects of the present invention with reference to the accompanying drawings.
Referring to fig. 1, the implementation steps of the invention are as follows:
s1, determining array element number A contained in the radar antenna, and determining the size of the non-uniform area array according to the array element number A contained in the radar antenna, wherein the horizontal axis of the non-uniform area array comprises B array elements, and the vertical axis of the non-uniform area array comprises C array elements; A. b and C are each a positive integer greater than 0, and satisfy a ═ B × C.
1a) Determining array element number B on the horizontal axis of the non-uniform area array:
Figure BDA0002336864150000051
represents a round-down operation;
1b) and determining the array element number C on the vertical axis of the non-uniform area array, wherein C is A/B.
S2, determining the abscissa X of the non-uniform area array according to the array element number B on the horizontal axis of the non-uniform area array, wherein the expression is as follows:
X＝{b1,b2,…,bm}×d
wherein, bmThe abscissa of the array element of the m-th column of the non-uniform area array is expressed, m is more than or equal to 1 and less than or equal to B, BmX d denotes the position of the array element of the m-th column of the non-uniform area array, and b1And d is 0, and represents unit array element interval in the non-uniform area array, and generally takes the value of half wavelength of a radar transmission signal.
The abscissa X of the non-uniform area array corresponds to the array element position of the improved nested linear array of B array elements. The structure of the improved nested linear array is shown in figure 13.
As can be seen from fig. 13, the improved nested linear array is composed of the nested array and an additional array element, and the total number M of the array elements is M1+M2+1. Wherein, the nested array comprises two uniform linear arrays, the array element position v of the 1 st level uniform linear array1＝{md,m＝0,1,…,M1-1} and array element position v of 2 nd level uniform linear array2＝{n(M1+2)d+M1d,n＝0,…,M2-1}. The last additional array element is placed furthest to the right (M) from the 2 nd uniform line array1+1) d.
In order to maximize the degree of freedom of the improved nested linear arrays, the number M of array elements of two uniform linear arrays can be distributed through arithmetic geometric mean inequality1And M2When the total array element number is B, the optimal array configuration parameters can be obtained as shown in the following table.
Improved nested linear array optimal array configuration
Total array element number B Optimum M1And M2 DOF
Even number of M1＝B2-1,M2＝B2 B 22+2B-3
Is odd number M1＝(B-1)2-1,M2＝(B+1)2 B 22+2B-72
By the optimal array configuration parameters and the array structure of the improved nested linear arrays, the position of each array element of the improved nested linear arrays can be obtained when the number of the array elements is B, and the abscissa X of the non-uniform area array can be obtained.
S3, determining the vertical coordinate Y of the non-uniform area array according to the array element number C on the vertical axis of the non-uniform area array, wherein the expression is as follows:
Y＝{c1,c2,…,cn}×d
wherein, cnThe vertical coordinate of the array element of the nth row of the non-uniform area array is expressed, n is more than or equal to 1 and less than or equal to C, CnX d denotes the position of the array element of the n-th row of the non-uniform area array, and c1And d is 0 and represents the unit array element interval in the non-uniform area array.
The abscissa Y of the non-uniform area array corresponds to the array element position of the improved nested linear array of C array elements. And the acquisition mode of the positions of the improved nested linear array elements of the C array elements is the same as the acquisition mode of the positions of the improved nested linear array elements of the B array elements in S2.
S4, determining the final non-uniform area array Z according to the abscissa X of the non-uniform area array and the ordinate Y of the non-uniform area array, wherein the expression is as follows:
Z＝{(bm,cn)1≤m≤B,1≤n≤C}×d
wherein, bmRepresents the abscissa of the m-th array element in the abscissa X of the non-uniform area array, cnThe ordinate of the nth array element in the ordinate Y of the non-uniform area array is shown, (b)m,cn) The coordinates of the array element of the mth column and the nth row of the non-uniform area array are shown, (b)m,cn) And x d represents the position of the array element of the nth row of the mth column of the non-uniform area array, and d represents the unit array element interval in the non-uniform area array.
S5, calculating to obtain a differential synthesis array { v } according to the final non-uniform area array ZDCAThe expression is as follows:
{vDCA}＝{(bm-bm',cn-cn')1≤m≤B,1≤m'≤B,1≤n≤C,1≤n'≤C}
when m is 1, respectively enabling m' to be 1 to B; and when n is 1, let n' take 1 to C respectively; and further respectively obtain (b)1-b1,c1-c1) To (b)1-bM,c1-cN)。
Then let m take 2 to B respectively and let n take 2 to C respectively to obtain (B)2-b1,c2-c1) To (b)B-bB,cC-cC)。
Wherein, bmRepresents the abscissa of the m-th array element in the abscissa X of the non-uniform area array, bm'Represents the abscissa of the m' th array element in the abscissa X of the non-uniform area array, cnThe ordinate of the nth array element in the ordinate Y of the non-uniform area array, cn'And the ordinate of the n' th array element in the ordinate Y of the non-uniform area array is shown.
The differential synthesis array { v }DCAIs of the fully filled type with a degree of freedom ofThe number of array elements of the differential synthesis array; computing a differentially synthesized array { v }DCAThe degree of freedom is DOF, which is expressed as:
DOF＝(2bB+1)×(2cC+1)
wherein, bBRepresents the abscissa of the B-th array element in the abscissa X of the non-uniform area array, cCExpressing the ordinate of the C array element in the ordinate Y of the non-uniform area array; the differential synthesis array is a uniform area array without holes.
S6, considering far-field signals, and setting K targets, wherein the K targets are respectively non-correlated targets, the K targets are respectively far enough away from the non-uniform area array, and radar emission signals are regarded as parallel waves and narrow-band signals when reaching the non-uniform area array; assuming that noise and signals transmitted by the radar are mutually independent and are additive, independent and identically distributed Gaussian processes, when multi-target detection is carried out on K targets, K is required to be greater than the number A of array elements included by the radar, and the pitch angle corresponding to the kth target is thetakThe azimuth angle corresponding to the kth target is phikAnd theta is not less than-90 degreesk≤90°，0°≤φkLess than or equal to 360 degrees, and K is a positive integer greater than 0.
Firstly, respectively calculating array manifold A of B array elements included by the horizontal axis of the non-uniform area arrayxAnd the longitudinal axis of the non-uniform area array comprises a direction matrix A of C array elementsySequentially arranging the differential synthesis arrays along the direction of the transverse axis of the differential synthesis arrays to obtain C sub-arrays; wherein
The 1 st sub-array is A1，A1＝AxD1(Ay)；
The 2 nd sub-array is A2，A2＝AxD2(Ay)；
Until the C-th sub-array is AC，AC＝AxDC(Ay)；
Wherein
Figure BDA0002336864150000081
Figure BDA0002336864150000082
Dm(.) is a direction matrix A of C array elements which is composed of the longitudinal axis of the non-uniform area arrayyA diagonal matrix constructed in the m-th row of (c); c,. m ═ 1, 2; d represents unit array element interval in the non-uniform area array, lambda is the wavelength of electromagnetic waves, j is an imaginary number unit, and e is an exponential function;
then, the signal data received by the differential synthesis array is calculated to be x (t), and the expression is as follows:
Figure BDA0002336864150000083
where s (t) is a narrow-band signal corresponding to K targets, and s (t) ═ s1(t),s2(t),…,sn(t),…,sK(t)]T，sn(t) represents the incident signals corresponding to the nth target, and the incident signals corresponding to each target are independent and uncorrelated in time and all obey the complex Gaussian distribution
Figure BDA0002336864150000084
Representing the incident signal s corresponding to the nth targetn(t) power; n (t) represents a mean of 0 and a variance of σ2White gaussian noise satisfying independent equal distribution and being uncorrelated with an incident signal corresponding to each target, respectively; t represents the sampling time, t is 1,2, …, and N represents the fast beat number; CN represents gaussian distribution.
Finally, according to the signal data x (t) received by the differential synthesis array, firstly carrying out decoherence by using a space smoothing algorithm, and then carrying out direction-of-arrival estimation by using a unitary ESPRIT algorithm to respectively obtain the direction-of-arrival estimation values of the K targets; wherein K is a positive integer greater than 0.
The effects of the present invention are further verified and explained by the following computational simulation.
Simulation 1: the multi-target direction of arrival estimation of the array of the invention is simulated.
1.1) simulation conditions: assuming that the number of array elements is 49, the number of targets is 66, the target elevation angles [24 °,36 °,48 °,59 °,69 °,80 ° ] are provided, 11 targets exist at each elevation angle, and the 11 targets at each elevation angle are uniformly distributed at 32 ° intervals in the azimuth [ -160 °,160 ° ], (uniformly distributed, the distribution interval is 160 [ -2/(11-1) × 32 °) signal-to-noise ratio is 0, and the fast beat number is 1000.
1.2) simulation content and result:
under the above 1.1) simulation conditions, the array structure is shown in fig. 2, and the structure diagram of the differential synthesis array is shown in fig. 3; then, estimating the direction of arrival of the 66 targets, wherein the simulation result is shown in fig. 4, and referring to fig. 4, the simulation result is a result schematic diagram obtained by estimating the direction of arrival of the 66 targets by using the method when the number of the given radar array elements is 49; as can be seen from FIG. 4, the method can realize the estimation of the direction of arrival of the target with more than array elements, and has better underdetermined estimation capability.
Simulation 2: and carrying out simulation comparison on the array target direction of arrival estimation of the invention and the nested area array.
2.1) simulation conditions: assuming an array element number of 36, a target number of 20, target elevation angles [25 °,37 °,48 °,58 °,67 °,4 targets exist at each elevation angle, and 4 targets at each elevation angle are evenly distributed at about 93 ° intervals in azimuth [ -140 °,140 ° ] with signal-to-noise ratios (SNR) from-20 to 10, 500 snapshots, 200 repeat trials.
2.2) simulation content and results:
under the simulation conditions of 2.1) above, the array structure of the present invention and the nested area array is, as shown in fig. 5 and 6, fig. 7 is a structure diagram of a differential synthesis array obtained by using the method of the present embodiment when the number of radar array elements is given as 36, and fig. 8 is a structure diagram of a differential synthesis array obtained by using the nested area array when the number of radar array elements is given as 36.
Under the simulation conditions of 2.1) above, simulation comparison is performed on the estimation of the direction of arrival of the array target of the present invention and the nested area array, and the result is shown in fig. 9 and 10, where fig. 9 is a schematic diagram of the result obtained by using the method of the present embodiment to estimate the direction of arrival of the target when the given number of radar array elements is 36, and fig. 10 is a schematic diagram of the result obtained by using the nested area array to estimate the direction of arrival of the target when the given number of radar array elements is 36.
As can be seen from fig. 7 and 8, the degrees of freedom obtained using the present invention are:
[13+(13+1)]×[13+(13+1)]＝729。
the degrees of freedom obtained using the nested area array are: [11+ (11+1) ] × [11+ (11+1) ], 529.
Compared with a nested array, the differential synthesis array obtained by the method has larger array aperture and higher degree of freedom, and can realize estimation of more target directions of arrival.
Under the above 2.1) simulation conditions, a comparison graph of the root mean square error of the two arrays as a function of the signal-to-noise ratio is given, and the result is shown in fig. 11. FIG. 11 is a schematic diagram showing the comparison of the mean square error of each of the nested area arrays and the method of this embodiment with the change of the signal-to-noise ratio when the number of elements of the radar array is 36; as can be seen from fig. 6, the estimation error of the differential synthesis array and the estimation error of the nested area array obtained by the method of the present embodiment are respectively reduced with the increase of the signal-to-noise ratio, and when the signal-to-noise ratio is above 0dB, the mean square error of the estimation value obtained by the method of the present embodiment and the mean square error of the estimation value of the nested area array both gradually tend to be stable, but the method of the present embodiment has higher estimation accuracy.
Simulation 3: the method is compared with the nested area array in simulation of different array element number freedom degrees.
3.1) simulation conditions: the number of array elements is: a ═ 16,20,25,30,36,42,49,56,64,72,81,90,100,110, 121;
3.2) simulation content and results:
under the above simulation conditions of 3.1), the degree of freedom of the present invention and the nested area array given different array element numbers is as shown in fig. 12.
As can be seen from fig. 12, the degree of freedom of the present invention is greater than that of the nested area array within a given array element number range; meanwhile, it can be seen that with the increase of the number of array elements, the difference between the degree of freedom of the nested planar array and the degree of freedom of the nested planar array is larger and larger, that is, the number of array elements is more, and the effect of the nested planar array in the aspect of improving the degree of freedom is more obvious.
In conclusion, the differential synthesis array obtained by the non-uniform area array design method provided by the invention has higher DOF (degree of freedom) and larger array aperture, can realize the estimation of DOA (direction of arrival) of more targets, simultaneously improves the direction finding precision, and the position of an array element can be obtained by a closed expression, thereby verifying the correctness, the effectiveness and the reliability of the method.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention; thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (8)

1. A non-uniform area array design method based on an improved nested linear array is characterized by comprising the following steps:
s1, determining array element number A contained in the radar antenna, and determining the size of the non-uniform area array according to the array element number contained in the radar antenna, wherein the horizontal axis of the non-uniform area array comprises B array elements, and the vertical axis of the non-uniform area array comprises C array elements; A. b and C are each a positive integer greater than 0, and satisfy a ═ B × C.
And S2, determining the abscissa X of the non-uniform area array according to the array element number B on the horizontal axis of the non-uniform area array.
And S3, determining the vertical coordinate Y of the non-uniform area array according to the array element number C on the vertical axis of the non-uniform area array.
And S4, determining the final non-uniform area array Z according to the abscissa X of the non-uniform area array and the ordinate Y of the non-uniform area array.
S5, calculating to obtain a differential synthesis array { v } according to the final non-uniform area array ZDCA}。
2. The method for designing the non-uniform area array based on the improved nested linear arrays as claimed in claim 1, wherein in S1, the expression of B is:
Figure FDA0002336864140000011
Figure FDA0002336864140000012
represents a round-down operation; the expression of C is, C ═ A ÷ B.
3. The method for designing the non-uniform area array based on the improved nested linear arrays as claimed in claim 1, wherein in S2, the expression of X is:
X＝{b1,b2,…,bm}×d
wherein, bmThe abscissa of the array element of the m-th column of the non-uniform area array is expressed, m is more than or equal to 1 and less than or equal to B, BmX d denotes the position of the array element of the m-th column of the non-uniform area array, and b1And d is 0, and represents the unit array element interval in the non-uniform area array, and takes the value of half wavelength of a radar transmission signal.
4. The non-uniform area array design method based on improved nested linear arrays as claimed in claim 1, wherein in S3, the expression of the ordinate Y is:
Y＝{c1,c2,…,cn}×d
wherein, cnThe vertical coordinate of the array element of the nth row of the non-uniform area array is expressed, n is more than or equal to 1 and less than or equal to C, CnX d denotes the position of the array element of the n-th row of the non-uniform area array, and c1And d is 0 and represents the unit array element interval in the non-uniform area array.
5. The method as claimed in claim 1, wherein in S4, the expression of the non-uniform area Z is:
Z＝{(bm,cn)|1≤m≤B,1≤n≤C}×d
wherein, bmRepresents the abscissa of the m-th array element in the abscissa X of the non-uniform area array, cnThe ordinate of the nth array element in the ordinate Y of the non-uniform area array is shown, (b)m,cn) Representing non-uniform area arrays(ii) m column and n row of (b)m,cn) And x d represents the position of the array element of the nth row of the mth column of the non-uniform area array, and d represents the unit array element interval in the non-uniform area array.
6. The method as claimed in claim 1, wherein in S5, the differential synthesis array { v } isDCAThe expression is:
{vDCA}＝{(bm-bm',cn-cn')|1≤m≤B,1≤m'≤B,1≤n≤C,1≤n'≤C}
when m is 1, respectively enabling m' to be 1 to B; and when n is 1, let n' take 1 to C respectively; and further respectively obtain (b)1-b1,c1-c1) To (b)1-bM,c1-cN)；
Then let m take 2 to B respectively and let n take 2 to C respectively to obtain (B)2-b1,c2-c1) To (b)B-bB,cC-cC)；
Wherein, bmRepresents the abscissa of the m-th array element in the abscissa X of the non-uniform area array, bm'Represents the abscissa of the m' th array element in the abscissa X of the non-uniform area array, cnThe ordinate of the nth array element in the ordinate Y of the non-uniform area array, cn'And the ordinate of the n' th array element in the ordinate Y of the non-uniform area array is shown.
7. The method as claimed in claim 6, wherein said array { v } is formed by differential synthesisDCAThe array element is of a complete filling type, and the degree of freedom of the array element is the number of array elements of the differential synthesis array; the differential synthesis array { v }DCAThe degree of freedom is DOF, which is expressed as:
DOF＝(2bB+1)×(2cC+1)
wherein, bBRepresents the abscissa of the B-th array element in the abscissa X of the non-uniform area array, cCRepresenting non-uniform area arraysThe ordinate of the C array element in the ordinate Y; the differential synthesis array is a uniform area array without holes.
8. The method for designing the non-uniform area array based on the improved nested linear arrays as claimed in claim 1, wherein the differential synthesis array further comprises the following steps:
the preset conditions are as follows: setting K targets in the differential synthesis array, wherein the K targets are respectively non-correlated targets, the distances between the K targets and the non-uniform area array respectively meet preset requirements, and the radar transmitting signals are parallel waves and narrow-band signals when reaching the non-uniform area array; the noise and the radar emission signal are independent from each other and are additive, independent and equally distributed Gaussian processes; when multi-target detection is carried out on K targets, K is larger than array element number A included by the radar, and the pitch angle corresponding to the kth target is thetakThe azimuth angle corresponding to the kth target is phikAnd theta is not less than-90 degreesk≤90°，0°≤φkLess than or equal to 360 degrees, and K is a positive integer greater than 0;
s11, calculating the array manifold A of the non-uniform area array horizontal axis B array elementsxCalculating a direction matrix A of C array elements included in a longitudinal axis of the non-uniform area arrayyThe differential synthesis arrays are sequentially arranged along the direction of the transverse axis of the differential synthesis arrays, so that C sub-arrays are obtained; wherein
The 1 st sub-array is A1，A1＝AxD1(Ay)；
The 2 nd sub-array is A2，A2＝AxD2(Ay)；
Until the C-th sub-array is AC，AC＝AxDC(Ay)；
Wherein
Figure FDA0002336864140000031
Figure FDA0002336864140000032
Dm(.) is a direction matrix A of C array elements which is composed of the longitudinal axis of the non-uniform area arrayyA diagonal matrix constructed in the m-th row of (c); c,. m ═ 1, 2; d represents unit array element interval in the non-uniform area array, lambda is the wavelength of electromagnetic waves, j is an imaginary number unit, and e is an exponential function;
s12, calculating signal data x (t) received by the differential synthesis array, where the expression is:
Figure FDA0002336864140000033
where s (t) is a narrow-band signal corresponding to K targets, and s (t) ═ s1(t),s2(t),…,sn(t),…,sK(t)]T，sn(t) represents the incident signals corresponding to the nth target, and the incident signals corresponding to each target are independent and uncorrelated in time and obey complex Gaussian distribution
Figure FDA0002336864140000034
Figure FDA0002336864140000035
Representing the incident signal s corresponding to the nth targetn(t) power;
n (t) represents a mean of 0 and a variance of σ2White gaussian noise satisfying independent equal distribution and being uncorrelated with an incident signal corresponding to each target, respectively;
t represents the sampling time, t is 1,2, …, and N represents the fast beat number;
CN represents a Gaussian distribution;
s13, according to the signal data x (t) received by the differential synthesis array, decoherence is carried out by using a space smoothing algorithm, and then the arrival direction estimation is carried out by using a unitary ESPRIT algorithm, so that the arrival direction estimation values of the K targets are respectively obtained.
CN201911359728.2A 2019-12-25 2019-12-25 Non-uniform area array design method based on improved nested linear array Withdrawn CN111025236A (en)

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