阅读说明：本技术 一种余弦频偏频控阵波束合成方法 (Cosine frequency offset frequency control array beam synthesis method ) 是由 马秀荣 单云龙 达新宇 于 2021-09-06 设计创作，主要内容包括：本申请公开了一种余弦频偏频控阵波束合成方法,该方法包括：步骤1,根据阵元编号,确认频控阵的余弦频偏系数,并根据预设序号与余弦频偏系数进行累加求和,将累加求和结果记作余弦频偏；步骤2,根据参考编号,对余弦频偏进行移位运算,将移位运算结果记作斜率可控余弦频偏,并根据斜率可控余弦频偏和阵元位置,计算频控阵的余弦频率和相参相位,其中,参考编号由预计方向图斜率确定；步骤3,根据余弦频率和相参相位,确定频控阵的余弦频偏频控阵波束。通过本申请中的技术方案,降低了频偏频控阵波束宽度,有助于提高波束可控性和探测精度。(The application discloses a cosine frequency offset frequency control array beam synthesis method, which comprises the following steps: step 1, confirming a cosine frequency offset coefficient of a frequency control array according to an array element number, performing accumulation summation according to a preset serial number and the cosine frequency offset coefficient, and recording an accumulation summation result as cosine frequency offset; step 2, carrying out shift operation on the cosine frequency offset according to the reference number, recording the shift operation result as slope controllable cosine frequency offset, and calculating the cosine frequency and the coherent phase of the frequency control array according to the slope controllable cosine frequency offset and the array element position, wherein the reference number is determined by the slope of a predicted directional diagram; and step 3, determining a cosine frequency offset frequency control array wave beam of the frequency control array according to the cosine frequency and the coherent phase. By the technical scheme, the beam width of the frequency offset frequency control array is reduced, and the beam controllability and the detection precision are improved.)

1. A cosine frequency offset frequency control array beam synthesis method is characterized by comprising the following steps:

step 1, confirming a cosine frequency offset coefficient of a frequency control array according to an array element number, performing accumulation summation with the cosine frequency offset coefficient according to a preset serial number, and recording the accumulation summation result as the cosine frequency offset;

step 2, carrying out shift operation on the cosine frequency offset according to a reference number, recording a shift operation result as slope controllable cosine frequency offset, and calculating the cosine frequency and the coherent phase of the frequency controlled array according to the slope controllable cosine frequency offset and the array element position, wherein the reference number is determined by the slope of a predicted directional diagram;

and 3, determining a cosine frequency offset frequency control array wave beam of the frequency control array according to the cosine frequency and the coherent phase.

2. The method according to claim 1, wherein the step 1 of performing summation accumulation according to a preset sequence number and the cosine frequency offset coefficient specifically comprises:

step 11, selecting a sequence number which is a preset value with the greatest common divisor of the beam width adjusting parameter alpha in the preset sequence numbers, and recording the sequence number as a summation sequence number;

and step 12, performing multiplication transformation on the cosine frequency offset coefficient according to the summation serial number and the frequency offset step length, and calculating the cosine frequency offset according to the result of the multiplication transformation by adopting an accumulation summation mode.

3. The cosine frequency offset frequency control array beam forming method of claim 2, wherein the preset value is 1, and the calculation formula of the cosine frequency offset is as follows:

in the formula,. DELTA.f_bAnd (M) is the cosine frequency offset, M is an array element number, M is 0,1, …, M-1, M is the number of array elements in the frequency control array, n is a preset serial number, α is the beam width adjusting parameter, gcd (n, α) is 1 which is a greatest common divisor filtering function, and Δ f is a frequency offset step length.

4. The method of claim 2, wherein the process of calculating the beamwidth adjustment parameter α specifically comprises:

step 111, calculating a reference cosine frequency offset corresponding to each adjusting parameter in a parameter range and a reference beam width corresponding to each reference cosine frequency offset in a traversal mode, wherein the reference beam width is 3dB beam width;

step 112, selecting the largest monotonous interval in the monotonous intervals of the reference beam widths, selecting the reference beam width closest to the target beam width in the largest monotonous interval, and recording the adjustment parameter corresponding to the selected reference beam width as the beam width adjustment parameter.

5. The method of claim 4, wherein the maximum monotonic interval of the monotonic intervals of the reference beam width is selected, and the reference beam width closest to the target beam width is selected in the maximum monotonic interval, and further comprising:

selecting the maximum monotonous interval in the monotonous intervals of the reference beam width;

adjusting the maximum monotone interval according to a preset protection parameter to reduce the maximum monotone interval;

and selecting the reference beam width closest to the target beam width in the reduced maximum monotone interval.

6. The cosine frequency offset frequency control array beam forming method of claim 1, wherein in said step 2, said slope controllable cosine frequency offset is calculated by the formula:

Δf_c(m)＝circshift[Δf_b(m),i]

in the formula,. DELTA.f_c(m) is the slope-controllable cosine frequency offset, circshift [ solution ]]As a right cyclic shift function, Δ f_bAnd (m) is the cosine frequency offset, m is an array element number, and i is a reference number.

7. The method of claim 6 wherein in step 2, said cosine frequency f is frequency-offset frequency-controlled array beam forming_cThe calculation formula of (m) is:

f_c(m)＝f₀+Δf_c(m)

the phase of the phase differenceThe calculation formula of (2) is as follows:

in the formula, r₀Is the coherent distance of the coherent point, c is the speed of light, x_mNumbering the array elements in m array element positions, x₀For reference to the position of the array element, theta₀Is the coherent angle of the coherent point,f₀is the reference frequency of the frequency control array.

8. The method of any of claims 1 to 7, wherein the method further comprises:

according to the slope controllable cosine frequency deviation, calculating a wave speed directional diagram of the frequency control array and a wave speed width corresponding to the wave speed directional diagram, wherein the wave speed directional diagram P_cThe formula for calculating (θ, r) is:

where θ is the observation angle, r is the observation distance, M is the number of array elements, M is 0,1, …, M-1, M is the number of array elements in the frequency control array, c is the speed of light, Δ f is the speed of light, and_c(m) is the slope-controllable cosine frequency offset, f₀Is the reference frequency, x, of the frequency-controlled array_mNumbering the array elements in m array element positions, x₀In order to refer to the array element position of the array element,is the coherent phase.

Technical Field

The application relates to the technical field of beam synthesis, in particular to a cosine frequency offset frequency control array beam synthesis method.

Background

In the field of antenna beam velocity synthesis, for beam synthesis of phased array antennas, the angular pointing of a beam can be freely controlled, but the beam is independent of distance. The beam synthesis technology of the frequency control array antenna can synthesize the beam related to the distance, and has certain application prospect in the aspects of distance-related interference suppression, distance fuzzy suppression, directional communication and the like. And the beam width of the frequency control array is reduced, which is beneficial to improving the beam detection precision.

The classical frequency control array antenna comprises a constant frequency offset frequency control array proposed by Paul Antonik et al, an air force laboratory in 2006, and can obtain a beam related to distance, but the beam has obvious periodicity in distance, which can cause distance ambiguity, and the beam width is only related to the distance of array elements of the frequency control array antenna and the number of the array elements, and the beam width is not controllable.

To solve the problem of obvious beam periodicity, Waseem Khan et al propose a log-frequency offset frequency control array, the frequency control array antenna can also obtain a beam related to distance, and the beam has no periodic structure in a certain distance spatial domain range, so that the distance ambiguity problem is solved, but the beam has the main problems of high side lobe level, large beam main lobe width and poor beam controllability.

Later, researchers have proposed a sine frequency offset frequency control array, and the wave beam is converged in a small angle-distance range, so that a spherical wave beam is realized, the wave beam also solves the problem of periodicity in distance, and the wave beam distance dimension wave beam width and the angle dimension wave beam width are both greatly reduced, but the wave beam controllability of the sine frequency offset frequency control array is poor, and the angle pointing of the wave beam cannot be freely controlled.

Disclosure of Invention

The purpose of this application lies in: the beam width of the frequency deviation frequency control array is reduced, and the beam controllability and the detection precision are improved.

The technical scheme of the application is as follows: a cosine frequency offset frequency control array beam synthesis method is provided, which comprises the following steps: step 1, confirming a cosine frequency offset coefficient of a frequency control array according to an array element number, performing accumulation summation according to a preset serial number and the cosine frequency offset coefficient, and recording an accumulation summation result as cosine frequency offset; step 2, carrying out shift operation on the cosine frequency offset according to the reference number, recording the shift operation result as slope controllable cosine frequency offset, and calculating the cosine frequency and the coherent phase of the frequency control array according to the slope controllable cosine frequency offset and the array element position, wherein the reference number is determined by the slope of a predicted directional diagram; and step 3, determining a cosine frequency offset frequency control array wave beam of the frequency control array according to the cosine frequency and the coherent phase.

In any one of the above technical solutions, further, in step 1, performing accumulation summation according to a preset sequence number and a cosine frequency offset coefficient, specifically including: step 11, selecting a sequence number which is the maximum common divisor of the preset sequence numbers and the beam width adjusting parameter alpha and recording the sequence number as a summation sequence number; and step 12, performing multiplication transformation on the cosine frequency offset coefficient according to the summation sequence number and the frequency offset step length, and calculating the cosine frequency offset according to the result of the multiplication transformation by adopting an accumulation summation mode.

In any of the above technical solutions, further, the preset value is 1, and the calculation formula of the cosine frequency offset is as follows:

in the formula,. DELTA.f_bAnd (M) is cosine frequency offset, M is an array element number, M is 0,1, and M-1, M is the number of array elements in the frequency control array, n is a preset serial number, alpha is a beam width adjusting parameter, gcd (n, alpha) 1 is a greatest common divisor screening function, and delta f is a frequency offset step length.

In any of the above technical solutions, further, the calculation process of the beam width adjustment parameter α specifically includes: step 111, calculating reference cosine frequency offsets corresponding to all adjustment parameters in a parameter range and reference beam widths corresponding to all the reference cosine frequency offsets in a traversal mode, wherein the reference beam width is 3dB beam width; step 112, selecting the largest monotonous interval in the monotonous intervals of the reference beam widths, selecting the reference beam width closest to the target beam width in the largest monotonous interval, and recording the adjustment parameter corresponding to the selected reference beam width as the beam width adjustment parameter.

In any of the above technical solutions, further, selecting a largest monotonic interval of the monotonic intervals of the reference beam width, and selecting a reference beam width closest to the target beam width in the largest monotonic interval, specifically, the method further includes: selecting a maximum monotonous interval in the monotonous intervals of the reference beam width; adjusting the maximum monotonous interval according to preset protection parameters to reduce the maximum monotonous interval; and selecting the reference beam width closest to the target beam width in the reduced maximum monotone interval.

In any of the above technical solutions, further, in step 2, a calculation formula of the slope-controllable cosine frequency offset is as follows:

Δf_c(m)＝circshift[Δf_b(m)，i]

in the formula,. DELTA.f_c(m) is a slope-controllable cosine frequency offset, circshift [ solution ]]As a right cyclic shift function, Δ f_bAnd (m) is cosine frequency deviation, m is an array element number, and i is a reference number.

In any of the above technical solutions, further, in step 2, the cosine frequency f_cThe calculation formula of (m) is:

f_c(m)＝f₀+Δf_c(m)

phase of phase differenceThe calculation formula of (2) is as follows:

in the formula, r₀Is the coherent distance of the coherent point, c is the speed of light, x_mNumbering the array elements in m array element positions, x₀For reference to the position of the array element, theta₀Is the coherent angle of the coherent point, f₀Is the reference frequency of the frequency controlled array.

In any of the above technical solutions, further, the method further includes: according to the slope controllable cosine frequency deviation, calculating the wave speed directional diagram of the frequency control array and the wave speed width and wave speed directional diagram P corresponding to the wave speed directional diagram_cThe formula for calculating (θ, r) is:

where θ is an observation angle, r is an observation distance, M is an array element number, M is 0,1, M-1, M is the number of array elements in the frequency control array, c is a light velocity, and Δ f is an angular velocity_c(m) is the slope-controllable cosine frequency offset, f₀Is a reference frequency, x, of the frequency-controlled array_mNumbering the array elements in m array element positions, x₀In order to refer to the array element position of the array element,are coherent phases.

The beneficial effect of this application is:

according to the technical scheme, a cosine frequency deviation coefficient is introduced, accumulated summation is carried out according to a preset serial number and the cosine frequency deviation coefficient to obtain the cosine frequency deviation, frequency deviation among array elements is set to be an agreed cosine function summation form by using a number theory, and strong irrelevance of the frequency deviation among the array elements can be guaranteed. Then, calculating slope controllable cosine frequency deviation by adopting a shift operation mode to obtain cosine frequency and phase-coherent phase of the frequency control array, further determining cosine frequency deviation frequency control array wave beams of the frequency control array, and forming spherical wave beams by frequency design combining cosine frequency deviation and number theory, thereby not only eliminating periodic structures in the cosine frequency deviation frequency control array wave beams, but also further reducing the distance dimensional width of the wave beams

In a preferred implementation manner of the present application, a corresponding beam width adjustment parameter is selected in a maximum monotonic section of monotonic sections of a reference beam width to ensure a cosine frequency offset calculated in a cosine function summation form, and a slope-controllable cosine frequency offset is obtained through shift operation according to a selected reference number, so that the purpose of freely controlling the pointing direction of a beam angle-distance dimensional directional diagram of a frequency control array is achieved, and beam controllability and detection accuracy are further improved.

Drawings

The advantages of the above and/or additional aspects of the present application will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:

fig. 1 is a schematic flow diagram of a cosine frequency offset frequency controlled array beam forming method according to an embodiment of the present application;

FIG. 2 is a graph of correspondence between tuning parameters and reference beamwidths according to one embodiment of the present application;

FIG. 3 is a plot of expected pattern slope versus reference number according to one embodiment of the present application;

FIG. 4 is a frequency offset simulation of cosine frequency offset coefficients according to an embodiment of the present application;

FIG. 5 is a wave velocity pattern simulation of cosine frequency offset coefficients in accordance with an embodiment of the present application;

FIG. 6 is a frequency offset simulation of cosine frequency offset according to an embodiment of the present application;

FIG. 7 is a plot of a wave velocity pattern simulation of a cosine frequency offset in accordance with an embodiment of the present application;

FIG. 8 is a frequency offset simulation of slope controlled cosine frequency offset according to an embodiment of the present application;

FIG. 9 is a graph of a wave velocity pattern simulation of a slope controllable cosine frequency offset in accordance with an embodiment of the present application;

FIG. 10 is an enlarged view of the main lobe corresponding to reference numeral 3 according to one embodiment of the present application;

FIG. 11 is an enlarged view of the main lobe corresponding to reference numeral 6 according to one embodiment of the present application.

Detailed Description

In order that the above objects, features and advantages of the present application can be more clearly understood, the present application will be described in further detail with reference to the accompanying drawings and detailed description. It should be noted that the embodiments and features of the embodiments of the present application may be combined with each other without conflict.

In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application, however, the present application may be practiced in other ways than those described herein, and therefore the scope of the present application is not limited by the specific embodiments disclosed below.

As shown in fig. 1, this embodiment provides a cosine frequency offset frequency controlled array beam forming method, which is applicable to a frequency controlled array antenna, where a plurality of array elements are arranged in the frequency controlled array, and the method includes:

step 1, confirming a cosine frequency offset coefficient of a frequency control array according to an array element number, performing accumulation summation according to a preset serial number and the cosine frequency offset coefficient, and recording an accumulation summation result as cosine frequency offset;

specifically, the cosine frequency offset coefficient in this embodiment is set as follows:

in the formula, M is an array element number, M is 0,1, and M-1, and M is the number of array elements in the frequency control array.

As will be understood by those skilled in the art, the above-mentioned cosine frequency offset coefficient Δ f_a(m) is characterized in that: the frequency deviation is alternately increased and decreased twice, and the corresponding cosine frequency deviation is periodically increased and decreased along with the increase of the array element serial number.

According to the rule of frequency control array frequency offset design, alternate frequency offset is lifted, the distance dimension beam width can be reduced, the characteristic can be enhanced through periodic lifting frequency offset, and the problem caused by the periodic lifting frequency offset is that the directional diagram of the beam is periodic.

Therefore, in order to solve the problem of periodicity of the beam pattern, the embodiment selects a specific cosine frequency offset coefficient for summation, and because the periods of the selected cosine frequency offset coefficients participating in summation are different, the obtained cosine frequency offset is ensured to be alternately ascending and descending, the obtained cosine frequency offset is ensured to be non-periodic frequency offset, and the problem of periodicity of the beam pattern is solved.

Further, performing accumulation summation according to a preset sequence number and a cosine frequency offset coefficient, specifically including:

step 11, selecting a sequence number which is the maximum common divisor of the preset sequence numbers and the beam width adjusting parameter alpha and recording the sequence number as a summation sequence number; the preset value may be set according to actual requirements, and in order to highlight the non-periodicity of the cosine frequency offset, the preset value is set to be 1 in this embodiment.

Preferably, the embodiment further provides a process for calculating the beam width adjustment parameter α, which specifically includes:

step 111, calculating reference cosine frequency offsets corresponding to all adjustment parameters in a parameter range and reference beam widths corresponding to all the reference cosine frequency offsets in a traversal mode, wherein the reference beam width is 3dB beam width;

specifically, a parameter range is set to [12, 53], and a cosine frequency offset corresponding to each adjustment parameter and a corresponding reference beam width are calculated in a traversal mode.

It should be noted that, the method for calculating the reference beam width is not limited in this embodiment, and a conventional manner for calculating the 3dB beam width may be adopted, and the calculated 3dB beam width is taken as the reference beam width, and the calculation result is shown in table 1.

TABLE 1

Therefore, a corresponding relation curve between the adjustment parameter and the reference beam width can be obtained, and as shown in fig. 2, each monotone interval in the corresponding relation curve can be obtained by analyzing the corresponding relation curve, including a monotone increasing interval and a monotone decreasing interval.

And 112, selecting the maximum monotonic interval in the monotonic intervals of the reference beam width, selecting the reference beam width closest to the target beam width in the maximum monotonic interval, and recording the adjustment parameter corresponding to the selected reference beam width as the beam width adjustment parameter, wherein the target beam width is a set value and can be set according to actual requirements.

Specifically, in each obtained monotone interval, a maximum monotone interval including a maximum adjustment parameter value range is selected, and the interval may be a monotone increasing interval or a monotone decreasing interval.

In a preferred implementation manner of this embodiment, in order to ensure validity of each beam width value in the selected maximum monotonic interval, the cosine frequency offset corresponding to the selected beam width adjustment parameter is necessarily located in the monotonic interval, so a preset protection parameter is set, and a value of the preset protection parameter may be 1₁+1，α₂-1]Therefore, the finally selected interval is the reduced maximum monotone interval [ α ]₁，α₂]＝[28，33]。

It should be noted that, if there is a case that the two monotone intervals have the same range size, the interval with the smaller value of the adjustment parameter is selected as the selected maximum monotone interval.

Then, the reference beam width corresponding to each adjustment parameter in the selected maximum monotonic interval is determined, as shown in table 2.

TABLE 2

In this embodiment, the target beam width is set to 1.00km, and is in the interval [ α [ ]₁，α₂]＝[28，33]In the above embodiments, the reference beam widths closest thereto are 0.94km and 1.06km, respectively, and the corresponding adjustment parameters are 29 and 30, and therefore, the value of the beam width adjustment parameter may be set to either one of 29 and 30, that is, α is 29 or α is 30.

Step 12, performing multiplication transformation on the cosine frequency offset coefficient according to the summation sequence number and the frequency offset step length, and calculating the cosine frequency offset according to the result of the multiplication transformation by adopting an accumulation summation mode, wherein a preset value is set to be 1, and the calculation formula of the cosine frequency offset is as follows:

in the formula,. DELTA.f_bAnd (M) is cosine frequency offset, M is an array element number, M is 0,1, and M-1, M is the number of array elements in the frequency control array, n is a preset serial number, alpha is a beam width adjusting parameter, gcd (n, alpha) 1 is a greatest common divisor screening function, and delta f is a frequency offset step length.

It should be noted that the sum of the algebras of the Lamarcoujin is calculatedThe method is a number theory function, and is characterized in that a summation result has orthogonality, so that the cosine frequency offset can be ensured to have strong irrelevance, and further, a synthetic beam does not have a periodic structure.

And 2, performing shift operation on the cosine frequency offset according to the reference number, recording the shift operation result as slope controllable cosine frequency offset, and calculating the cosine frequency and the coherent phase of the frequency control array according to the slope controllable cosine frequency offset and the array element position.

It should be noted that the reference number in this embodiment is determined by the expected directional diagram slope, and the specific process is not limited. The closest expected pattern slope may be selected from the look-up table of the beam pattern slope and the reference number according to the desired beam pattern slope, and the corresponding reference number may be looked up as the reference number in step 2, wherein the look-up table of the beam pattern slope and the reference number may be determined according to historical experience, array element number, accuracy requirement, and the like.

The lookup table of the beam pattern slope and the reference number in this embodiment is shown in table 3.

TABLE 3

Reference numerals	Beam pattern slope k
		i＝1	-15.0°/5km
i＝2	-12.0°/5km
		i＝3	-8.0°/5km
i＝4	-7.5°/5km
		i＝5	-1.5°/5km
i＝6	0.0°/5km
		i＝7	2.5°/5km
i＝8	4.5°/5km
		i＝9	8.0°/5km
i＝10	11.5°/5km
		i＝11	12.0°/5km
i＝12	15.0°/5km

That is, when the desired beam pattern slope is 3 °/5km, the beam pattern slope 2.5 °/5km is selected as the expected pattern slope in table 3, and the corresponding number i ═ 7 is used as the reference number.

When the reference number is determined according to the expected directional diagram slope, the reference number may also be determined according to a corresponding relationship curve, as shown in fig. 3, the corresponding relationship curve is a monotonically increasing curve, the curve may be formed by interpolation fitting according to the rule of the slope and the reference number, and then the reference number is determined according to the expected directional diagram slope.

It should be noted that the value of reference number i is related to the positive and negative of the beam pattern slope, and the corresponding relationship is as follows:

reference numeralsWhen the frequency control array beam pattern slope of cosine frequency deviation is positive, the beam pointing direction is the positive direction angle direction, wherein,is rounding up the symbol.

Reference numeralsAnd in time, the slope of the cosine frequency offset frequency control array beam directional diagram is zero, and the beam pointing direction does not change along with the distance.

Reference numeralsAnd in the time, the slope of the cosine frequency offset frequency control array beam directional diagram is negative, and the beam pointing direction is a negative direction angle direction.

In this embodiment, the calculation formula of the slope-controllable cosine frequency offset is as follows:

Δf_c(m)＝circshift[Δf_b(m)，i]

in the formula,. DELTA.f_c(m)Is a slope-controlled cosine frequency deviation, Δ f_b(m) is a cosine frequency offset, m is an array element number, circshift [ m ]]As a right circular shift function, i.e. circshift [ Δ f ]_b(m)，i]Denotes the frequency deviation of cosine Δ f_b(m) cyclically shifted to the right by i bits, i being the reference number.

Further, the cosine frequency f_cThe calculation formula of (m) is:

f_c(m)＝f₀+Δf_c(m)

phase of phase differenceThe calculation formula of (2) is as follows:

in the formula, r₀Is the coherent distance of the coherent point, c is the speed of light, x_mNumbering the array elements in m array element positions, x₀For reference to the position of the array element, theta₀Is the coherent angle of the coherent point, f₀Is the reference frequency of the frequency controlled array.

And step 3, determining a cosine frequency offset frequency control array wave beam of the frequency control array according to the cosine frequency and the coherent phase.

Specifically, according to the array signal processing theory and the position of the array element in the frequency control array, the corresponding cosine frequency offset frequency control array beam can be derived from the calculated cosine frequency and coherent phase, and the detailed process is not repeated.

On the basis of the above embodiment, the method further includes: according to the slope controllable cosine frequency deviation, calculating the wave speed directional diagram of the frequency control array and the wave speed width and wave speed directional diagram P corresponding to the wave speed directional diagram_cThe formula for calculating (θ, r) is:

in the formula, θ is an observation angle, r is an observation distance, m is an array element number, and m is 0, 1.M-1, M is the number of array elements in the frequency control array, c is the speed of light, Δ f_c(m) is the slope-controllable cosine frequency offset, f₀Is a reference frequency, x, of the frequency-controlled array_mNumbering the array elements in m array element positions, x₀In order to refer to the array element position of the array element,are coherent phases.

To verify the above method in this embodiment, the number of array elements M is set to 12, and the reference frequency f is set to₀2GHz, coherent distance r of coherent points₀30km, coherent angle θ₀The array element position with the array element number m is as follows:

x_m＝m×0.5λ₀

in the formula, the reference wavelength λ₀＝0.15m。

The observation airspace is as follows: the range of the observation distance r is more than 0km and less than 100km, and the range of the observation angle theta is more than minus 90 degrees and less than theta 90 degrees.

As shown in fig. 4 and 5, the cosine frequency offset coefficient Δ f_aThe calculation results for (m) are shown in table 4.

TABLE 4

At this time, the corresponding wave velocity directional diagram expression is:

where θ is the observation angle, r is the observation distance, and x_mIs the position of the array element, and c is the speed of light.

Corresponding beam coherent phaseComprises the following steps:

in the formula, r₀Is the coherent distance, θ₀Are coherent angles.

Wave velocity directional diagram P according to cosine frequency deviation coefficient_a(theta, r) and calculating the corresponding cosine frequency offset coefficient frequency control array beam width r_a。

It should be noted that the beam width in this embodiment is a width corresponding to a maximum decrease of 3dB in the main beam amplitude of the beam pattern in the distance dimension, and the calculation process is as follows:

cosine frequency deviation coefficient frequency control array beam directional diagram P_a(theta, r) the maximum value of the main lobe is A_pFrom the distance dimension, main lobe maximum A_pAt the position, respectively searching the first A in the positive direction and the negative direction of the distance dimension_pPosition of value/2, where A is positive in the distance dimension_pThe position of the value/2 is denoted A₁Negative A_pThe position of the value/2 is denoted A₂Thus, the cosine frequency offset coefficient frequency control array beam width r_a＝A₂-A₁。

Through calculation, the cosine frequency deviation coefficient frequency control array beam width r_aThe result of the calculation is r_a＝7.95km。

Similarly, in the present embodiment, the beam width adjustment parameter α is taken as an example 29, and as shown in fig. 6 and 7, the cosine frequency offset Δ f is obtained_bThe calculation results for (m) are shown in table 5.

TABLE 5

Cosine frequency deviation	Value taking
		Δfb(0)	8.7kHz
Δfb(1)	5.0kHz
		Δfb(2)	-10.0kHz
Δfb(3)	5.0kHz
		Δfb(4)	-8.7kHz
Δfb(5)	20.0kHz
		Δfb(6)	-10.0kHz
Δfb(7)	-5.0kHz
		Δfb(8)	10.0kHz
Δfb(9)	-10.0kHz
		Δfb(10)	-18.7kHz
Δfb(11)	40.0kHz

At this time, the corresponding wave velocity directional diagram expression is:

corresponding beam coherent phaseComprises the following steps:

calculated beam width r_b＝9.81km。

As shown in fig. 8 and 9, two sets of reference numbers, i-3 and i-6, respectively, are selected. Slope controllable cosine frequency deviation delta f_cThe calculation results of (m) are shown in table 6.

TABLE 6

At this time, the corresponding wave velocity directional diagram expression is:

corresponding beam coherent phaseComprises the following steps:

since the value of the reference number i is related to the positive and negative of the beam pattern slope, for the reference number i being 3, the reference number is satisfiedIn fig. 9(a), it can be seen that the slope of the beam pattern of the cosine frequency offset frequency-controlled array is positive, the beam pointing direction is the positive direction angle direction, and the corresponding beam width r_c＝9.81km。

As shown in fig. 10, the slope of the main lobe of the beam is marked by the dashed line, the slope of the beam pattern of the cosine frequency offset frequency-controlled array is negative, the beam pointing direction is a negative direction angle direction, and the slope of the beam pointing direction is-8 °/5 km.

For reference number i-6, the reference number is satisfiedIn fig. 9(b), it can be seen that the slope of the beam pattern of the cosine frequency offset frequency-controlled array is zero, the beam pointing direction does not change with the distance, and the corresponding beam width r_c＝9.81km。

As shown in fig. 11, the slope of the main lobe of the beam is marked by the dashed line, the slope of the cosine frequency offset frequency controlled array beam pattern is zero, and the beam pointing direction does not change with the distance. The beam slope is 0 °/5 km.

The technical scheme of the present application is described in detail above with reference to the accompanying drawings, and the present application provides a cosine frequency offset frequency control array beam forming method, which includes: step 1, confirming a cosine frequency offset coefficient of a frequency control array according to an array element number, performing accumulation summation according to a preset serial number and the cosine frequency offset coefficient, and recording an accumulation summation result as cosine frequency offset; step 2, carrying out shift operation on the cosine frequency offset according to the reference number, recording the shift operation result as slope controllable cosine frequency offset, and calculating the cosine frequency and the coherent phase of the frequency control array according to the slope controllable cosine frequency offset and the array element position, wherein the reference number is determined by the slope of a predicted directional diagram; and step 3, determining a cosine frequency offset frequency control array wave beam of the frequency control array according to the cosine frequency and the coherent phase. By the technical scheme, the beam width of the frequency offset frequency control array is reduced, and the beam controllability and the detection precision are improved.

The steps in the present application may be sequentially adjusted, combined, and subtracted according to actual requirements.

The units in the device can be merged, divided and deleted according to actual requirements.

Although the present application has been disclosed in detail with reference to the accompanying drawings, it is to be understood that such description is merely illustrative and not restrictive of the application of the present application. The scope of the present application is defined by the appended claims and may include various modifications, adaptations, and equivalents of the invention without departing from the scope and spirit of the application.