Conformal digital-analog hybrid array multi-beam forming method

Abstract

The invention belongs to the technical field of antenna engineering, and particularly provides a conformal digital-analog hybrid array multi-beam forming method, which is used for solving the problem of multi-beam forming optimization of a conformal array under a digital-analog hybrid array architecture. According to the method, firstly, accurate modeling is carried out on the conformal digital-analog hybrid array, then, a far-field radiation model is established for the multi-beam forming problem, finally, the initial optimization problem which is difficult to solve is converted into a plurality of sub-problems with closed-form solutions to carry out distributed iteration solving, the solving speed is high, and the method is suitable for large-scale popularization and application. And the analog weight and the digital weight can be converged to optimal values at the same time, so that conformal digital-analog hybrid array multi-beam forming is completed. Moreover, the invention can realize the functions of controllable dynamic range of array element level simulation weight amplitude, controllable main lobe shape and width, controllable multi-beam quantity, free configuration of analog-digital mixing ratio and the like, has extremely high flexibility, and can adapt to the requirements of different application scenes.

Description

Technical Field

[0001] The present invention belongs to the field of antenna engineering technology, and relates to a multi-beam pattern forming method under a conformal antenna array digital-analog hybrid architecture, and specifically to a conformal digital-analog hybrid array multi-beam forming method. Background Art

[0002] Conformal multi-beam arrays can achieve multi-beam coverage in a wide angle range. On the one hand, due to factors such as impedance mismatch, beam broadening deformation, and beam gain reduction, the scanning range of traditional planar arrays is limited to within 120°. By bending the antenna array conformally in the scanning dimension, the array switches the active radiation aperture through switch control when the scanning angle changes, which can overcome the various shortcomings of planar arrays when scanning at large angles and achieve large-angle scanning. On the other hand, multi-beam antennas can achieve functions such as rapid scanning detection and simultaneous tracking of multiple targets by forming multiple independent beams, and are widely used in radar, satellite communications and other fields. The all-digital array architecture can achieve flexible multi-beam scanning, but it is expensive and difficult to use for large-scale arrays; the analog architecture antenna array needs to switch analog channels to achieve multi-beam functions, which lacks flexibility; the digital-analog hybrid architecture array is a compromise between cost and performance, but it is necessary to study specific beamforming methods to achieve multi-beam shaping optimization.

[0003] The special geometric structure of conformal arrays brings great difficulty to beamforming design. Planar phased array beamforming technology is relatively mature, but for conformal arrays, since array factors cannot be extracted, beamforming technology applicable to planar arrays is mostly ineffective. In addition, the digital-analog hybrid architecture puts forward new constraints on multi-beam optimization, requiring multiple beams to share the unit-level analog weight amplitude and phase, and to achieve multi-beamforming by adjusting the amplitude and phase of the sub-array-level digital channel, which further increases the difficulty of beamforming. The document "Haupt RL, "Thinned arrays using genetic algorithms", IEEE transactions on antennas and propagation, 1994, 42 (7): 993-999" uses genetic algorithms to shape the side lobes of the directional pattern. In theory, it is applicable to any antenna array, but this type of algorithm is slow. When dealing with large conformal arrays, its search optimization process is very slow, or even unacceptable. The document "Li M, Wang X, Dong J, "Optimal difference pattern synthesis with polarization control for arbitrary arrays", IEEE Antennas and Wireless Propagation Letters, 2012, 11: 1358-1361" optimizes the polarization problem of conformal arrays. The main method is to construct the low cross-polarization optimization problem as a convex optimization constraint and use a convex optimization algorithm to solve it. However, its optimization speed is slow and it cannot optimize non-convex problems such as dynamic range constraints. It can be seen that the existing technology basically does not involve the multi-beamforming optimization problem of conformal arrays under the digital-analog hybrid array architecture. Summary of the invention

[0004] The object of the present invention is to provide a conformal digital-analog hybrid array multi-beamforming method to solve the multi-beamforming optimization problem of the conformal array under the digital-analog hybrid array architecture.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A conformal digital-analog hybrid array multi-beamforming method comprises the following steps:

[0007] Step 1. Determine the conformal digital-analog hybrid array configuration according to the known conformal array architecture, and determine the pattern index constraint according to the set optimization goal;

[0008] Step 2. Establish a far-field radiation model of the conformal digital-analog hybrid array according to the conformal array configuration;

[0009] Step 3. According to the pattern index constraints and far-field radiation model of the conformal digital-analog hybrid array, the conformal digital-analog hybrid array multi-beamforming is completed based on the alternating direction multiplier method.

[0010] Furthermore, in step 1, the conformal array configuration is specifically the array shape parameters; the pattern index constraints include: the number of beams I, the upper limit constraint of the main lobe of each beam U i mi and the main lobe lower bound constraint L i mi , the main lobe area of ​​each beam The sidelobe level index SLL of each beam i , the sidelobe area of ​​each beam Simulation weight amplitude dynamic range ratio DRR, iteration number T0, θ and represents the coordinate component of the spherical coordinate system, i represents the beam number, i = 1, 2, ..., I, the subscripts mi and si represent the angle numbers of the main lobe area and the side lobe area of ​​the i-th beam after the angle is sampled at equal intervals, and the corresponding total number of sampling points is M i With S i .

[0011] Furthermore, in step 1, the conformal digital-analog hybrid array adopts a circular linear array, and the array shape parameters include: array radius R, array element spacing d, number of array elements K, and a global spherical coordinate system O0 is established with the center of the array as the coordinate origin.

[0012] Furthermore, in step 2, the far-field radiation model of the conformal digital-analog hybrid array is expressed as:

[0013]

[0014] in, represents the total electric field radiated by the conformal array, θ and represents the coordinate component of the global spherical coordinate system O0; k represents the array element number, K is the number of array elements; ω k represents the weight of the kth array element, represents the radiated electric field after the kth array element superimposes the spatial phase, represents the kth array element pattern in the global spherical coordinate system O0, j is an imaginary unit, λ is the operating wavelength of the electromagnetic wave in free space, R is the array radius, θ k The local spherical coordinate system O represents the kth array element k The coordinate components of .

[0015] Furthermore, in step 3, the specific process of the alternating direction multiplier method is:

[0016] The multi-beamforming problem of conformal mode-digital hybrid array is mathematically modeled, and the optimization objective is obtained as follows:

[0017]

[0018] 1≤|ω Ak |≤DRR,k=1,2...K

[0019] Where i represents the beam number, k represents the array element number, I represents the number of beams, and K represents the number of array elements; SLL i represents the sidelobe level index of the i-th beam, σ i is the scaling factor of the ith beam, ω i represents the element weight vector of the i-th beam, ω A represents the simulation weight vector, ω Ak ω A The kth element of , and represents the simulation weight of the kth array element, ω i D represents the digital weight vector of the i-th beam; represents the main lobe area and side lobe area of ​​the i-th beam, They represent the sampling sets of the array far-field radiation electric field in the main lobe area and side lobe area of ​​the i-th beam, respectively. mi and si represent the angle numbers after the main lobe area and side lobe area of ​​the i-th beam are sampled at equal intervals. The corresponding total number of sampling points is M i With S i ; χ is the iteration weight, B i is the auxiliary variable introduced, express The mi-th element of express The si-th element of is the Lagrangian weight, express The mi-th element of express The si-th element of AD represents the transformation matrix, R i represents the switch matrix of the i-th beam; U i mi and represents the upper and lower mainlobe constraints of the i-th beam, DRR is the dynamic range ratio of the simulated weight amplitude; the superscript H represents the conjugate transpose symbol, ⊙ represents element-wise multiplication, and ||·||2 represents the 2-norm of the vector;

[0020] According to the alternating direction multiplier method, the optimized simulation weight vector ω is obtained. A With the numerical weight vector ω i D .

[0021] 6. The conformal digital-analog hybrid array multi-beamforming method according to claim 5, characterized in that in step 3, the variable is updated according to the alternating direction multiplier method until a preset convergence judgment condition is met. Taking the tth variable update as an example, the specific process of the variable update is:

[0022] Step 3-1. Update the scaling factor σ i(t) , the update result is expressed as σ i(t+1) , the update expression is:

[0023]

[0024]

[0025] Wherein, the superscript (t+1) indicates the new value of the variable obtained at the tth iteration, and the superscript (t) indicates the initial value of the variable at the tth iteration. In subsequent steps, the superscripts (t+1) and (t) have the same meaning.

[0026] Step 3-2: Update parameters The update result is expressed as Update the expression to:

[0027]

[0028] Step 3-3: Update parameters With SLL i(t) , solve the following optimization problem:

[0029]

[0030] and SLL i# For the variables to be solved, SLL i# The value of S i +1 interval, calculate S of the above optimization problem for all intervals i +1 potential optimal solution, and by comparing the sizes of these potential optimal solutions, select the potential optimal solution that minimizes the objective function value as the optimal solution to the above optimization problem;

[0031] According to the SLL corresponding to the optimal solution i# Solve the above optimization problem by taking the value range of and SLL i# The optimal value of is the updated With SLL i(t+1) ;

[0032] Step 3-4: Update parameter ω i(t) , the update result is expressed as ω i(t+1) , the update expression is:

[0033] ω i(t+1) =(Q i (Q i ) H ) -1 (Q i ) H y i(t+1) ,

[0034] Q i =[σ i(t+1) P i ,I K×K ],

[0035]

[0036] Among them, I K×K represents the identity matrix of order K×K;

[0037] Step 3-5: Update parameters The update result is expressed as Update the expression to:

[0038]

[0039] in, represents the Lagrangian weight The kth element of Represents auxiliary variable B i(t) The kth element of , j represents the imaginary unit, arg(·) represents the phase of the complex number, and the superscript * represents the conjugate;

[0040] Step 3-6: Update parameters The update result is expressed as Update the expression to:

[0041]

[0042] in, Represents the array element weight vector ω i(t) The kth element of represents the Lagrangian weight The kth element of R ADk Represents the transformation matrix R AD The k-th row vector of ;

[0043] Step 3-7: Update parameters The update result is expressed as Update the expression to:

[0044]

[0045] Step 3-8: Update the Lagrangian weights. The update expression is:

[0046]

[0047] Step 3-9: After each iteration, determine whether the penalty term meets the preset convergence criteria. If so, stop the iteration and return the optimized simulation weight vector ω A With the numerical weight vector ω i D , otherwise, continue iterating.

[0048] Furthermore, in step 3-9, the preset convergence judgment condition is: the penalty term value is less than ξ or the number of iterations reaches the number of iterations T0.

[0049] Furthermore, in steps 3-9, the penalty term c (t+1) It is expressed as:

[0050]

[0051] where ||·|| ∞ Represents the infinity norm of a vector.

[0052] In terms of working principle:

[0053] The present invention rotates the radiation patterns of different array elements from the local spherical coordinate system to the global spherical coordinate system based on the unit radiation patterns of the array elements and the prior conditions such as the array face shape, array element position, and array element orientation, using mathematical methods such as rotation matrices. On this basis, the far-field radiation model of the conformal array is established using the principle of radiation pattern superposition, laying the foundation for subsequent beamforming problems.

[0054] According to the conformal digital-analog hybrid array architecture configuration method, each array element is connected to an analog channel to realize independent adjustment of analog weights, and multiple array elements are connected to a digital subarray channel. Therefore, digital weight amplitude and phase adjustment can only be realized at the subarray level; according to the multi-beam forming principle, multiple beams share a set of array element-level analog weights, and different digital weights corresponding to different beams can be superimposed on the same digital channel, which is the working principle of the digital-analog hybrid multi-beam array; based on this, the present invention establishes a digital-analog hybrid conformal array multi-beam forming optimization problem; and, for this strongly non-convex problem, the present invention converts it into the corresponding augmented Lagrangian problem, and decomposes it into multiple sub-problems for solving, and finally relies on the good convergence of the alternating direction multiplier method to converge to the local optimal value and complete the conformal digital-analog hybrid array multi-beam forming.

[0055] In summary, the beneficial effect of the present invention is that it provides a conformal digital-analog hybrid array multi-beam forming method, firstly, the conformal digital-analog hybrid array is accurately modeled, then a far-field radiation model is established for the multi-beam forming problem, and finally the difficult-to-solve initial optimization problem is converted into multiple sub-problems with closed-form solutions for distributed iterative solution. The solution speed is fast, and the analog weights and digital weights can converge to the optimal value at the same time, thereby completing the conformal digital-analog hybrid array multi-beam forming; and the present invention can realize the functions of controllable dynamic range of analog weight amplitude at the array element level, controllable main lobe shape and width, controllable number of multi-beams, free configuration of analog-to-digital mixing ratio, etc., with extremely strong flexibility, which can adapt to the needs of different application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 The figure is a flow chart of the conformal digital-analog hybrid array multi-beamforming method of the present invention.

[0057] Figure 2 Schematic diagram of the structure of a conformal digital-analog hybrid array in an embodiment of the present invention.

[0058] Figure 3 Schematic diagram of the multi-beam conformal digital-analog hybrid array in an embodiment of the present invention.

[0059] Figure 4 4 is a diagram showing the distribution of simulation weight amplitudes of a conformal digital-analog hybrid array in an embodiment of the present invention.

[0060] Figure 5 4 is a digital weight amplitude distribution diagram of a conformal digital-analog hybrid array in an embodiment of the present invention. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical solution and beneficial effects of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0062] This embodiment provides a conformal digital-analog hybrid array multi-beamforming method, the process of which is as follows: Figure 1 As shown, the specific steps include:

[0063] Step 1. Determine the pattern index constraints and array shape parameters of the conformal array;

[0064] The pattern index constraints include: the number of beams I, the upper limit constraint of the main lobe of each beam U i mi and the main lobe lower bound constraint L i mi , the main lobe area of ​​each beam The sidelobe level index SLL of each beam i , the sidelobe area of ​​each beam The simulated weight amplitude dynamic range ratio DRR, the number of iterations T0, the superscript i represents the beam number, i = 1, 2, ..., I, the subscripts mi and si represent the angle numbers of the main lobe area and the side lobe area of ​​the i-th beam after the angles are sampled at equal intervals, and the total number of sampling points is M i With S i ; Conformal array configuration refers to the array shape parameters. Taking a typical circular array as an example, the array shape parameters include: array radius R, array element spacing d, number of array elements K, and establish a global spherical coordinate system O0 with the center of the array as the coordinate origin to determine the coordinate position of the kth array element (α k ,β k ), k = 1, 2, ..., K;

[0065] Step 2. Establish the far-field radiation model of the conformal array;

[0066] The radiation pattern of each array element is obtained by full-wave simulation or ideal radiation pattern factor substitution, and a local spherical coordinate system O is established with the center of the array element as the coordinate origin and the direction of the array element as the axis. k , then the kth array element pattern is expressed as Among them, θ k and represents the local spherical coordinate system O k The coordinate components in the global spherical coordinate system O0; while in the global spherical coordinate system O0, the kth array element pattern is expressed as θ and represents the coordinate components in the global spherical coordinate system O0; since the position and orientation of each array element are different, the expression of the directional pattern of each array element in the global spherical coordinate system O0 is different, so it is necessary to convert the local spherical coordinate system O k The array element pattern is rotated to the global spherical coordinate system O0, and the calculation process is expressed as:

[0067] e rk =N k e r ,

[0068] e r =e x sinθcosφ+e y sinθsinφ+e z cosθ,

[0069] e rk =e xk sinθ k cosφ k +e yk sinθ k sinφ k +e zk cosθ k ,

[0070]

[0071] Among them, e r represents the unit vector in the global spherical coordinate system O0, e rk Represents the spherical coordinate system O k The unit vector in N k represents the transformation matrix of the kth array element; e x 、e y 、e z are the unit vectors e r The components in the x, y, and z directions are similar, e xk 、e yk 、e kz are the unit vectors e rk Components in the x, y, and z directions;

[0072] According to the above formula, we can get the global spherical coordinate system O0 and the local spherical coordinate system O k The corresponding relationship between the angle coordinates in the local spherical coordinate system is used to convert the array element pattern expression of each array element in the local spherical coordinate system into the array element pattern expression in the global spherical coordinate system, and the kth array element pattern in the global spherical coordinate system O0 is obtained. Therefore, the far-field radiation model of the conformal array is established and expressed as:

[0073]

[0074] in, represents the total electric field radiated by the conformal array, ω k represents the weight of the kth array element, λ is the working wavelength of the electromagnetic wave in free space, represents the radiated electric field after the kth array element superimposes the spatial phase;

[0075] So far, the far-field radiation model of the conformal array has been established, and the weight ω of each array element is set k , which can control the total electric field radiated by the conformal array Achieve beamforming;

[0076] Step 3. Perform conformal mode-digital hybrid array multi-beamforming based on the alternating direction multiplier method;

[0077] The alternating direction multiplier method transforms the optimization problem into an augmented Lagrangian problem and solves it step by step, solving only one or more variables at a time. First, the multi-beamforming problem of the conformal mode-digital hybrid array is mathematically modeled, and the optimization goal is to minimize the sidelobe levels of multiple beams, that is, to minimize the SLL i , expressed as:

[0078]

[0079] 1≤|ω Ak |≤DRR,k=1,2...K

[0080]

[0081] ω A =[ω A1 ω A2 ... AK ] H ,

[0082]

[0083] in, They represent the sampling sets of the array far-field radiation electric field in the main lobe area and side lobe area of ​​the i-th beam, respectively. It represents the sampling of the radiated electric field in the main lobe area of ​​the i-th beam after the k-th array element superimposes the spatial phase. represents the sampling of the radiated electric field in the sidelobe area of ​​the i-th beam after the k-th array element superimposes the spatial phase; σ i is the scaling factor of the i-th beam, which is introduced to avoid the problem of reducing the feasible solution area due to improper optimization target setting; ω i represents the element weight vector of the i-th beam, which is composed of the simulated weight vector ω A With the numerical weight vector ω i D constitute, represents the weight of the kth element of the ith beam, ω Ak represents the simulation weight of the kth array element, represents the weight of the vth digital channel of the ith beam, v = 1, 2, ..., V, V represents the number of digital channels; R AD Represents the conversion matrix, which is used to represent the connection relationship between analog channels and digital channels; R i The switch matrix of the i-th beam is used to indicate which digital channels the i-th beam is synthesized from. A matrix element of 1 indicates that the digital channel is on, and a matrix element of 0 indicates that the digital channel is off. The superscript H indicates conjugate transpose, and the superscript T indicates transpose. Multiple beams share one analog weight vector, so ω A It has nothing to do with i; multiple beams can be configured with different digital weight vectors, and one digital channel is connected to multiple analog channels, so ω i D Related to i, and the number of digital channels V is less than the total number of array elements K; ω i With ω A ,ω i D The relationship is shown in the above formula, which is represented by the transformation matrix RAD and the switch matrix R i Decide;

[0084] At this point, the optimization objective in step 1 is described as a non-convex optimization problem, which is transformed into an augmented Lagrangian problem:

[0085]

[0086] 1≤|ω Ak |≤DRR,k=1,2...K

[0087] Among them, χ is the iteration weight, B i is the auxiliary variable introduced, express The mi-th element of express The si-th element of is the Lagrangian weight, express The mi-th element of express The si-th element of AD represents the transformation matrix, R i represents the switch matrix of the i-th beam; U i mi With L i mi represents the upper and lower mainlobe constraints of the i-th beam, DRR is the dynamic range ratio of the simulated weight amplitude; the superscript H represents the conjugate transpose symbol, ⊙ represents element-wise multiplication, and ||·||2 represents the 2-norm of the vector;

[0088] According to the alternating direction multiplier method, the above problem is decomposed into 8 sub-problems for alternating solution, and the parameters are updated by solving the 8 sub-problems; the superscript (t+1) represents the new value of the variable obtained in the t-th iteration, and the superscript (t) represents the initial value of the variable in the t-th iteration. The specific process is:

[0089] Step 3-1. Update the scaling factor σ i(t) , the update result is expressed as σ i(t+1) , the update expression is:

[0090]

[0091] Step 3-2: Update parameters The update result is expressed as Update the expression to:

[0092]

[0093] Step 3-3: Update parameters With SLL i(t) , solve the following optimization problem:

[0094]

[0095] and SLL i# For the variables to be solved, SLL i# The value of S i +1 interval, calculate S of the above optimization problem for all intervals i +1 potential optimal solution, and by comparing the sizes of these potential optimal solutions, select the potential optimal solution that minimizes the objective function value as the optimal solution to the above optimization problem;

[0096] According to the SLL corresponding to the optimal solution i# Solve the above optimization problem by taking the value range of and SLL i# The optimal value of is the updated With SLL i(t+1) ;

[0097] Step 3-4: Update parameter ω i(t) , the update result is expressed as ω i(t+1) , the update expression is:

[0098] ω i(t+1) =(Q i (Q i ) H ) -1 (Q i ) H y i(t+1) ,

[0099] Q i =[σ i(t+1) P i ,I K×K ],

[0100]

[0101] Among them, I K×K represents the identity matrix of order K×K;

[0102] Step 3-5: Update parameters The update result is expressed as Update the expression to:

[0103]

[0104] in, represents the Lagrangian weight The kth element of Represents auxiliary variable B i(t) The kth element of , j represents the imaginary unit, arg(·) represents the phase of the complex number, and the superscript * represents the conjugate;

[0105] Step 3-6: Update parameters The update result is expressed as Update the expression to:

[0106]

[0107] in, Represents the array element weight vector ω i(t) The kth element of represents the Lagrangian weight The kth element of R ADk Represents the transformation matrix R AD The k-th row vector of ;

[0108] Step 3-7: Update parameters The update result is expressed as Update the expression to:

[0109]

[0110] Step 3-8: Update the Lagrangian weights. The update expression is:

[0111]

[0112] Step 3-9: After each iteration, determine whether the penalty term meets the preset convergence criteria. If so, stop the iteration and return the optimized simulation weight vector ω A With the numerical weight vector ω i D , otherwise, continue iterating.

[0113] When the penalty term c (t+1) When the preset convergence judgment condition is met, that is, when the penalty term value is less than ξ, or when the number of iterations reaches the maximum number of iterations T0, the iteration is stopped and the optimized simulation weight vector ω is returned. A With the numerical weight vector ω i D , otherwise continue iterating.

[0114] Specifically, the conformal digital-analog hybrid array in this embodiment is as follows: Figure 2 As shown in the figure, the conformal digital-analog hybrid array is arranged in a ring, with a radius R of 3λ, λ is the working wavelength in free space, and each array element is distributed on the ring with equal arc spacing, and the arc spacing d is 0.5λ. The global spherical coordinate system O0 is established with the center of the circle as the coordinate origin. The number of array elements K and the array element position parameter (α k ,βk ) is specifically expressed as:

[0115]

[0116] There are 28 array elements distributed on the ring. Every 7 adjacent array elements form a digital sub-array, which is represented by corresponding symbols. * represents the first digital sub-array, ○ represents the second digital sub-array, + represents the third digital sub-array, △ represents the fourth digital sub-array, and floor(·) represents rounding down.

[0117] Regarding the multi-beam pattern constraint, the number of beams I is set to 2 beams, the first beam points to -40°, and the second beam points to +40°. Since the multiple beams are pencil beams, the main lobe area only includes a single angle sampling point at the beam pointing, that is, -40° and +40°. Then M i Both are 1, U i mi and L i mi All are set to 1; the dynamic range of the simulated weight amplitude DRR at the array element level is 3, and the sidelobe area of ​​the two beams is and They are [-90°, -52°] ∪ [-28°, 90°] and [-90°, 28°] ∪ [52°, 90°] respectively; the open channels corresponding to the first beam are digital channels 1, 2, and 3, and the open digital channels corresponding to the second beam are 2, 3, and 4; according to the above constraint parameters, the conversion matrix R can be determined AD With the switch matrix R i for:

[0118] R 1 =

[1110] T ,R 2 =

[0111] T ,

[0119]

[0120] E1=[1 1 1 1 1 1 1],E0=[0 0 0 0 0 0 0]

[0121] According to the above parameter configuration, the far-field radiation model of the conformal array is established; and η1, η2, η3, η4 are initialized to zero vectors. and B i The vector is initialized to zero, the upper limit of the number of iterations T0 is set to 20000 times, and the convergence judgment parameter ξ is set to 1×10 -7 , the iteration weight χ is set to 10, and the multi-beam optimization problem is solved iteratively.

[0122] like Figure 3The multi-beam pattern of this embodiment is shown. It can be seen from the figure that the first beam points to -40° and the side lobe level SLL 1 =-28.5dB; the second beam points to +40°, sidelobe level SLL 2 =-28.5dB. Further, Figure 4 The simulated weight amplitude distribution diagram of this embodiment is shown as follows: Figure 5 The figure shows the digital weight amplitude distribution diagram of the present embodiment. It can be seen from the figure that the optimized array element-level analog weight amplitude meets the requirement of dynamic range DRR=3, and all beams use the same analog weight; the digital weight of the first beam obtained by optimization shows that digital channels 1, 2, and 3 are not 0, channel 4 is 0, and the weights of the 7 array elements in each digital channel subarray are completely consistent, which meets the preset conditions; similarly, the digital weight of the second beam also meets the preset conditions.

[0123] The above description is only a specific implementation mode of the present invention. Any feature disclosed in this specification, unless otherwise stated, can be replaced by other alternative features that are equivalent or have similar purposes; all the disclosed features, or all the steps in the methods or processes, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A conformal digital-analog hybrid array multi-beamforming method, characterized in that: The following steps are involved: Step 1. Determine the conformal digital-analog hybrid array configuration according to the prior conformal array architecture, and determine the pattern index constraint according to the set optimization goal; Step 2. Establish a far-field radiation model of the conformal digital-analog hybrid array according to the conformal array configuration; Step 3. According to the pattern index constraints and far-field radiation model of the conformal digital-analog hybrid array, the conformal digital-analog hybrid array multi-beamforming is completed based on the alternating direction multiplier method.

2. The conformal digital-analog hybrid array multi-beamforming method according to claim 1, characterized in that: In step 1, the conformal array configuration is specifically the array shape parameters; the pattern index constraints include: the number of beams I, the upper limit constraint of the main lobe of each beam U i mi and the main lobe lower bound constraint L i mi , the main lobe area of ​​each beam The sidelobe level index SLL of each beam i , the sidelobe area of ​​each beam Simulation weight amplitude dynamic range ratio DRR, iteration number T0, θ and represents the coordinate component of the spherical coordinate system, i represents the beam number, i = 1, 2, ..., I, the subscripts mi and si represent the angle numbers of the main lobe area and the side lobe area of ​​the i-th beam after the angle is sampled at equal intervals, and the corresponding total number of sampling points is M i With S i .

3. The conformal digital-analog hybrid array multi-beamforming method according to claim 2, characterized in that: In step 1, the conformal digital-analog hybrid array adopts a circular linear array, and the array shape parameters include: array radius R, array element spacing d, number of array elements K, and a global spherical coordinate system O0 is established with the array center as the coordinate origin.

4. The conformal digital-analog hybrid array multi-beamforming method according to claim 1, characterized in that: In step 2, the far-field radiation model of the conformal digital-analog hybrid array is expressed as: in, represents the total electric field radiated by the conformal array, θ and represents the coordinate component of the global spherical coordinate system O0; k represents the array element number, K is the number of array elements; ω k represents the weight of the kth array element, represents the radiated electric field after the kth array element superimposes the spatial phase difference, represents the kth array element pattern in the global spherical coordinate system O0, j is an imaginary unit, λ is the operating wavelength of the electromagnetic wave in free space, R is the array radius, θ k The local spherical coordinate system O represents the kth array element k The coordinate components of .

5. The conformal digital-analog hybrid array multi-beamforming method according to claim 1, characterized in that: In step 3, the specific process of the alternating direction multiplier method is: The multi-beamforming problem of conformal mode-digital hybrid array is mathematically modeled, and the optimization objective is obtained as follows: Where i represents the beam number, k represents the array element number, I represents the number of beams, and K represents the number of array elements; SLL i represents the sidelobe level index of the i-th beam, σ i is the scaling factor of the ith beam, ω i represents the element weight vector of the i-th beam, ω A represents the simulation weight vector, ω Ak is the vector ω A The kth element of , and represents the simulation weight of the kth array element, ω i D represents the digital weight vector of the i-th beam; represents the main lobe area and side lobe area of ​​the i-th beam, They represent the sampling sets of the array far-field radiation electric field in the main lobe area and side lobe area of ​​the i-th beam, respectively. mi and si represent the angle numbers after the main lobe area and side lobe area of ​​the i-th beam are sampled at equal intervals. The corresponding total number of sampling points is M i With S i ; χ is the iteration weight, B i is the auxiliary variable introduced, Representation vector The mi-th element of Representation vector The si-th element of is the Lagrangian weight, Representation vector The mi-th element of Representation vector The si-th element of AD represents the transformation matrix, R i represents the switch matrix of the i-th beam; U i mi With L i mi represents the upper and lower mainlobe constraints of the i-th beam, DRR is the dynamic range ratio of the simulated weight amplitude; the superscript H represents the conjugate transpose symbol, ⊙ represents element-wise multiplication, and ||·||2 represents the 2-norm of the vector; According to the alternating direction multiplier method, the optimized simulation weight vector ω is obtained. A With the numerical weight vector ω i D .

6. The conformal digital-analog hybrid array multi-beamforming method according to claim 5, characterized in that: In step 3, the variable is updated according to the alternating direction multiplier method until the preset convergence judgment condition is met. Taking the tth variable update as an example, the specific process of variable update is: Step 3-1. Update the scaling factor σ i(t) , the update result is expressed as σ i(t+1) , the update expression is: Wherein, the superscript (t+1) indicates the new value of the variable obtained at the tth iteration, and the superscript (t) indicates the initial value of the variable at the tth iteration. In subsequent steps, the superscripts (t+1) and (t) have the same meaning. Step 3-2: Update parameters The update result is expressed as Update the expression to: Step 3-3: Update parameters With SLL i(t) , solve the following optimization problem: and SLL i# For the variables to be solved, SLL i# The value of S i +1 interval, calculate S of the above optimization problem for all intervals i +1 potential optimal solution, and by comparing the sizes of these potential optimal solutions, select the potential optimal solution that minimizes the objective function value as the optimal solution to the above optimization problem; According to the SLL corresponding to the optimal solution i# Solve the above optimization problem by taking the value range of and SLL i# The optimal value of is the updated With SLL i(t+1) ; Step 3-4: Update parameter ω i(t) , the update result is expressed as ω i(t+1) , the update expression is: ω i(t+1) =(Q i (Q i ) H ) -1 (Q i ) H y i(t+1) , Q i =[σ i(t+1) P i ,I K×K ], Among them, I K×K represents the identity matrix of order K×K; Step 3-5: Update parameters The update result is expressed as Update the expression to: in, represents the Lagrangian weight The kth element of Represents auxiliary variable B i(t) The kth element of , j represents the imaginary unit, arg(·) represents the phase of the complex number, and the superscript * represents the conjugate; Step 3-6: Update parameters The update result is expressed as Update the expression to: in, Represents the array element weight vector ω i(t) The kth element of represents the Lagrangian weight The kth element of R ADk Represents the transformation matrix R AD The k-th row vector of ; Step 3-7: Update parameters The update result is expressed as Update the expression to: Step 3-8: Update the Lagrangian weights. The update expression is: Step 3-9: After each iteration, determine whether the penalty term meets the preset convergence criteria. If so, stop the iteration and return the optimized simulation weight vector ω A With the numerical weight vector ω i D , otherwise, continue iterating.

7. The conformal digital-analog hybrid array multi-beamforming method according to claim 6, characterized in that: In step 3-9, the preset convergence judgment condition is: the penalty term value is less than ξ or the number of iterations reaches the maximum number of iterations T0.

8. The conformal digital-analog hybrid array multi-beamforming method according to claim 6, characterized in that: In steps 3-9, the penalty term c (t+1) It is expressed as: Among them, ||·|| ∞ Represents the infinity norm of a vector.

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