Distributed beamforming method and apparatus

Abstract

The embodiment of the present disclosure relates to the technical field of distributed beamforming, and provides a distributed beamforming method and device, the method comprising: constructing an antenna array model satisfying a specific condition according to the positions and excitation phases of each antenna unit in the antenna array; constructing an objective function according to an optimization target; performing discrete processing on the objective function to obtain an objective function satisfying a quadratic unconstrained binary optimization problem form; using a coherent Ising machine and a simulated annealing algorithm respectively to solve the objective function satisfying the quadratic unconstrained binary optimization problem form to obtain corresponding coherent Ising machine solving results and simulated annealing solving results; comparing the coherent Ising machine solving results and the simulated annealing solving results to select the most suitable solving result; and converting the selected most suitable solving result into a phase parameter of the antenna array and optimizing the antenna array according to the phase parameter. The embodiment of the present disclosure can greatly improve the optimization effect and improve the optimization efficiency.

Description

Technical Field

[0001] This disclosure relates to the field of distributed beamforming technology, and in particular to a distributed beamforming method and apparatus. Background Technology

[0002] Distributed beamforming is a technique that concentrates signal energy in a specific direction through the collaborative work of multiple nodes, and it is widely used in wireless communication, radar, and other fields. Relying on the special design of the antenna, its radiation field can be concentrated in a certain spatial direction. Antenna directivity refers to the relationship between the relative value of the antenna's radiation field and its spatial direction at the same distance in the far field. Antenna directivity can be represented by the antenna pattern. An antenna pattern typically includes at least two lobes, where the lobe with the highest radiation intensity is called the main lobe, and the remaining lobes are called side lobes. The more concentrated the radiation is on the main lobe, the better the directivity and the stronger the anti-interference capability. Side lobes cause energy diffusion and increased attenuation, so they need to be reduced.

[0003] In existing technologies, there are various distributed beamforming methods, each with its own advantages and disadvantages. For example, feedback-based methods, such as 1-bit feedback mechanisms, are suitable for dynamic environments but have high communication overhead. Coherent continuous wave signal transmission and frequency-phase synchronization methods can improve beamforming accuracy, but have high requirements for hardware precision and synchronization. Location-based methods are suitable for static scenarios but have strict requirements for location accuracy. Array antenna beamforming methods can flexibly adjust beam direction and width, but have high system complexity. In practical applications, the most suitable beamforming method should be selected comprehensively based on the specific scenario and system requirements to achieve the best signal transmission effect. Summary of the Invention

[0004] This disclosure aims to address at least one of the problems existing in the prior art by providing a distributed beamforming method and apparatus.

[0005] One aspect of this disclosure provides a distributed beamforming method, the distributed beamforming method comprising:

[0006] Based on the position and excitation phase of each antenna element in the antenna array, construct an antenna array model that satisfies specific conditions;

[0007] Based on the optimization objective, construct the objective function;

[0008] Discretize the objective function to obtain an objective function that satisfies the form of a quadratic unconstrained binary optimization problem;

[0009] The objective function satisfying the form of a quadratic unconstrained binary optimization problem was solved using the coherent Ising machine and the simulated annealing algorithm, respectively, and the corresponding coherent Ising machine solution and simulated annealing solution results were obtained.

[0010] By comparing the coherent Ising machine solution results with the simulated annealing solution results, the most suitable solution result is selected.

[0011] The most suitable solution is selected and converted into the phase parameters of the antenna array, and the antenna array is optimized based on the phase parameters.

[0012] Optionally, the step of constructing an antenna array model that satisfies specific conditions based on the position and excitation phase of each antenna element in the antenna array includes:

[0013] Let the antenna array be symmetrically distributed about the origin, and let the position vector of antenna element i in the antenna array be... Recorded as Where λ is the wavelength of the electromagnetic wave, d is the distance between two adjacent antenna elements, and N is the total number of antenna elements included in the antenna array.

[0014] Let the excitation phase of antenna element i and its origin-symmetric antenna element i′ both be α. i And satisfy in, Let i be the position vector of antenna element i′. The vector from the origin to the field point n and r is the distance from the origin to the field point, θ n Let be the zenith angle between the line connecting the origin to the field point n and the positive z-axis. Let be the azimuth angle between the projection of the line connecting the origin to the field point onto the xy plane and the positive x-axis. Let be the wave vector in the direction of electromagnetic wave propagation and its magnitude be the wave number. And ensure that the excitation amplitude of each antenna element is the same;

[0015] The antenna array model is constructed according to the following formula: in, Let n be the electric field at point n. The direction of the electric field component of the antenna element and

[0016] Optionally, constructing the objective function based on the optimization objective includes:

[0017] The optimization objective is to minimize sidelobe levels and control the main beam pointing to concentrate energy in a specific direction. The objective function H is constructed according to the following formula: Where, δ n It is a weighting factor that takes a negative value at the main lobe position and a positive value at the side lobe position.

[0018] Optionally, constructing the objective function based on the optimization objective further includes:

[0019] Let the weighting factor and The objective function H is expressed as H = ∑ i,j A ij cosα i cosα j , where coefficient A ij for Let be the position vector of antenna element j in the antenna array.

[0020] Optionally, the discretization of the objective function to obtain an objective function satisfying the form of a quadratic unconstrained binary optimization problem includes:

[0021] The decision variable cosα i Performing a binary expansion, we get Where k is cosα i The corresponding binary expansion term number, where k = 1, 2, ..., kmax; kmax is cosα i The total number of terms in the corresponding binary expansion; x ik1 x ik2 cosα i The two binary variables corresponding to the binary expansion both take values ​​in the range of ±1.

[0022] The decision variable cosα after binary expansion i Substituting into the expression of the objective function H, H = ∑ i,j A ij cosα i cosα j We obtain the objective function that initially satisfies the form of a quadratic unconstrained binary optimization problem. Where l is cosα j The corresponding binary expansion term number; x jl1 x jl2 cosα j The corresponding binary variables in their binary expansion all take values ​​in the range of ±1;

[0023] x ik1 and x ik2 These are respectively used as the (2kmax(i-1)+2(k-1)+1)th and (2kmax(i-1)+2(k-1)+2)th spins in the Ising model, and the objective function is... Let H = xQx be the objective function that satisfies the standard form of a quadratic unconstrained binary optimization problem. T Where x is based on x ik1 x ik2 x jl1 xjl2 The size of the creation is The matrix Q is a quadratic unconstrained binary optimization matrix, where each element takes values ​​in the range of ±1; Q is the (ik,jl)-th element of Q, which is represented as... T represents transpose.

[0024] Optionally, the step of solving the objective function satisfying the form of a quadratic unconstrained binary optimization problem using a coherent Ising machine and a simulated annealing algorithm respectively, to obtain the corresponding coherent Ising machine solution and simulated annealing solution, includes:

[0025] The expression for the Ising model is determined as follows: Among them, H is For the Ising-Hamiltonian, J mm′ σ is the coupling coefficient between the m-th spin and the m′-th spin; m σ represents whether the m-th spin is up or down. m′ σ represents whether the m′-th spin is spinning up or down. m or σ m′ The value σ is 1 when it rotates upwards. m or σ m′ The value is -1 when rotating downwards;

[0026] Let Isin Hamidon quantity H is Equal to the objective function H, Q ik,jl The value of is used as the Ising Hamiltonian H is The coupling coefficient J in mm′ The value of will be used to solve the objective function H = xQx, which satisfies the standard form of a quadratic unconstrained binary optimization problem. T The problem is transformed into the problem of finding the ground state of the corresponding Ising problem;

[0027] Based on formula The dynamic evolution of the coherent Ising machine was numerically simulated using the Euler method, and the Ising Hamiltonian H was calculated. is The spin state corresponding to the minimum value of μ is taken as the solution result of the coherent Ising machine; where μ m μ represents the amplitude of the m-th degenerate optical parametric oscillator, used to simulate the spin state of the m-th spin in the Ising model; m′ denoted by , m′, represents the amplitude of the m′-th degenerate optical parametric oscillator, used to simulate the spin state of the m′-th spin in the Ising model; t represents time, p represents the pump coefficient, and c represents the coupling strength between the degenerate optical parametric oscillator pulses.

[0028] Optionally, the step of solving the objective function satisfying the form of a quadratic unconstrained binary optimization problem using a coherent Ising machine and a simulated annealing algorithm respectively, to obtain the corresponding coherent Ising machine solution and simulated annealing solution, includes:

[0029] Let the temperature start from the set initial temperature T max The evolution begins. At each temperature, the spin in the Ising model corresponding to the objective function is flipped N·kmax times, and the current temperature is multiplied by the annealing factor to obtain the next temperature, until the temperature evolution reaches the set minimum temperature T. min The lowest temperature T min The spin state of the Ising model corresponding to the lower objective function is used as the solution result of the simulated annealing;

[0030] In each flip, a spin from the Ising model corresponding to the objective function is randomly selected for flipping. If the value of the objective function after the flip is less than the value of the objective function before the flip, the flip is accepted; otherwise, it is performed with probability. Accept this flip, where ΔH represents the difference between the objective function value after the spin flip and the objective function value before the spin flip, e represents the base of the natural logarithm, and T′ represents the current temperature.

[0031] Optionally, converting the selected most suitable solution result into the phase parameters of the antenna array includes:

[0032] The most suitable solution result corresponding to x ik1 and x ik2 Substitute the value In this process, we obtain the decision variable cosα. i The value of .

[0033] Optionally, optimizing the antenna array based on the phase parameters includes:

[0034] Based on decision variable cosα i The value of α is obtained by calculating the excitation phase α using the inverse cosine function. i The value of α depends on the excitation phase α. i The value of is used to optimize the antenna array.

[0035] Another aspect of this disclosure provides a distributed beamforming device, the distributed beamforming device comprising:

[0036] The model building module is used to build an antenna array model that meets specific conditions based on the position and excitation phase of each antenna element in the antenna array.

[0037] The objective function construction module is used to construct the objective function based on the optimization objective.

[0038] The discretization module is used to discretize the objective function to obtain an objective function that satisfies the form of a quadratic unconstrained binary optimization problem.

[0039] The solution module is used to solve the objective function that satisfies the form of a quadratic unconstrained binary optimization problem using the coherent Ising machine and the simulated annealing algorithm, respectively, and obtain the corresponding coherent Ising machine solution and simulated annealing solution.

[0040] The comparison module is used to compare the solution results of the coherent Ising machine with the solution results of the simulated annealing and select the most suitable solution result;

[0041] The optimization module is used to convert the most suitable solution result into the phase parameters of the antenna array, and optimize the antenna array based on the phase parameters.

[0042] Compared with the prior art, this disclosure transforms the optimization problem of the excitation phase of each antenna element in the antenna array into a corresponding QUBO problem, solves the QUBO problem using a coherent Ising machine and a simulated annealing algorithm respectively, and optimizes the antenna element using the most suitable solution, which greatly improves the optimization effect and efficiency. Attached Figure Description

[0043] One or more embodiments are illustrated by way of example with the corresponding pictures in the accompanying drawings. These illustrations do not constitute a limitation on the embodiments. Elements with the same reference numerals in the drawings are denoted as similar elements. Unless otherwise stated, the figures in the drawings are not to be limited by scale.

[0044] Figure 1 A flowchart of a distributed beamforming method provided in one embodiment of this disclosure;

[0045] Figure 2 This is a flowchart illustrating a distributed beamforming method provided for another embodiment of this disclosure. Detailed Implementation

[0046] In the field of antenna array optimization, traditional methods such as gradient descent and convex optimization are widely used, but they often face challenges such as convergence to local optima and high computational complexity when dealing with complex nonlinear and multi-peak problems. To overcome these limitations, various intelligent optimization algorithms have been introduced, including Genetic Algorithm (GA), Simulated Annealing (SA), and Coherent Ising Machine (CIM), which have shown unique advantages in antenna design optimization.

[0047] Genetic algorithms (GALs) are global optimization methods based on natural selection and genetic mechanisms, particularly suitable for complex search spaces. By simulating biological evolution, GALs have been used in antenna design to optimize parameters such as the spacing, amplitude, and phase of array elements to achieve specific radiation characteristics. For example, researchers have used GALs to optimize the element spacing and feed current amplitude of linear antenna arrays, successfully reducing sidelobe levels and pointing the main beam in a specific direction. Furthermore, GALs have been applied to the design optimization of microstrip patch antennas, demonstrating their wide applicability in the field of antenna design.

[0048] The goal of the quadratic unconstrained binary optimization (QUBO) problem is to minimize the following quadratic function: f(x) = x T Qx, where x is a vector of binary variables (taking values ​​of 0, 1, 1, or -1), and Q is a symmetric weight matrix. The QUBO model aims to find the combination of binary variables that minimizes the objective function. In antenna array optimization problems, design objectives (such as minimizing sidelobe levels, beam direction control, etc.) can be represented by constructing an appropriate QUBO model. By defining a suitable weight matrix Q and binary variables x (e.g., x can represent the switching state or phase setting of antenna elements), the antenna array optimization problem can be transformed into solving the corresponding QUBO problem. This modeling approach facilitates the use of optimization techniques such as quantum annealing and coherent Ising machines to find the optimal antenna configuration.

[0049] Simulated annealing is a stochastic search algorithm that mimics the physical annealing process and is suitable for global optimization problems. Simulated annealing avoids getting trapped in local optima by allowing for poor solutions in the initial stage, and then gradually reduces the "temperature" to converge to the global optimum. In antenna design, simulated annealing is used to optimize the excitation amplitude and element spacing of circular antenna arrays to achieve desired sidelobe levels and minimum beamwidth. Furthermore, simulated annealing has been applied to detect faulty antenna elements in linear arrays, demonstrating its effectiveness in complex optimization problems.

[0050] A coherent Ising machine is a computational device based on optical nonlinear effects. It utilizes optical parametric oscillators (OPOs), particularly degenerate optical parametric oscillators (DOPOs), to simulate the evolution of the Ising model, thereby solving combinatorial optimization problems. An OPO is a nonlinear optical process that, through the interaction of a nonlinear crystal and a pump laser, converts a high-energy photon into two low-energy photons. A DOPO is a special case of an OPO, where the output signal photon and idler photon have the same frequency. Upon reaching a certain threshold, a phase transition occurs, resulting in a bistable characteristic in the output light pulse. When the pump intensity increases beyond a certain threshold, collective symmetry breaking occurs, at which point the DOPO output can choose between two possible phase states. In a coherent Ising machine, the spin state can be represented by the phase of the DOPO output light; in-phase represents one spin state, while out-of-phase represents another. Multiple DOPOs can be connected to form a network to simulate a multi-spin Ising model. By adjusting the coupling between DOPOs, spin-spin interactions in the Ising model can be simulated.

[0051] In recent years, the coherent Ising machine has attracted attention in antenna system optimization. Researchers have transformed the configuration selection problem of reconfigurable antenna multiple-input multiple-output (MIMO) systems into an Ising model and solved it using CIM to maximize the signal-to-noise ratio of the received signal. Results show that the coherent Ising machine outperforms traditional methods in terms of computational complexity and performance, approaching the optimal performance of exhaustive search. Furthermore, the superior performance of the coherent Ising machine in solving combinatorial optimization problems offers new application prospects for fields such as neural computing and optical computing.

[0052] This disclosure provides a distributed beamforming method and apparatus suitable for coherent Ising machines and simulated annealing. To make the objectives, technical solutions, and advantages of the embodiments of this disclosure clearer, the various embodiments of this disclosure will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details are presented in the various embodiments of this disclosure to facilitate a better understanding of the disclosure. However, the technical solutions claimed in this disclosure can be implemented even without these technical details and with various variations and modifications based on the following embodiments. The division of the various embodiments below is for descriptive convenience and should not constitute any limitation on the specific implementation of this disclosure. The various embodiments can be combined and referenced with each other without contradiction.

[0053] One embodiment of this disclosure relates to a distributed beamforming method, the process of which is as follows: Figure 1 As shown, it includes steps S110 to S160. The following is in conjunction with... Figure 2 Steps S110 to S160 are described in detail.

[0054] Step S110: Based on the position and excitation phase of each antenna element in the antenna array, construct an antenna array model that meets specific conditions.

[0055] Specifically, after starting the antenna array directivity optimization process, step S110 is mainly used to construct an antenna array model that meets specific conditions, and the excitation phase of each antenna element in the antenna array is used as the optimization variable.

[0056] The electric field of a plane electromagnetic wave in a homogeneous medium magnetic field wave vector in the direction of propagation The following relationship must be satisfied:

[0057] Where v is the electromagnetic wave speed in the medium, and ω is the angular frequency of the electromagnetic wave. Let be the wave vector in the direction of electromagnetic wave propagation and its magnitude be the wave number. λ is the wavelength of the electromagnetic wave. Let be the amplitude of the electromagnetic wave, j be the imaginary unit, and e be the base of the natural logarithm. Millimeter waves typically operate in the 30 GHz to 300 GHz frequency band, corresponding to wavelengths of 1 mm to 10 mm. In practice, because the magnetic field component of electromagnetic waves is relatively weak, only the electric field component is generally considered. This is the vector from the source point (i.e., the antenna element that generates the electromagnetic wave) to the field point (i.e., the observation point). The antenna's directivity is independent of time t, so we can focus solely on this vector. Space section Its size is determined by its real part Decide.

[0058] Let the antenna array be distributed near the origin O, and the measured field points be located on a semicircular arc far from the antenna, then we have:

[0059]

[0060] in, Let θ be the vector from the origin to the field point n, r be the distance from the origin to the field point, and θ be the distance from the origin to the field point. n Let be the zenith angle between the line connecting the origin to the field point n and the positive z-axis. The azimuth angle between the projection of the line connecting the origin to the field point onto the xy plane and the positive x-axis.

[0061] make Let r be the position vector of antenna element i, and let r >> R be the position vector of antenna element i. i Approximately, the electric field generated by antenna element i at field point n is obtained. for:

[0062]

[0063] Where, α i Let i be the excitation phase of antenna element i. The excitation amplitude E of antenna element i i The corresponding vector.

[0064] electric field at point n Since the electric fields generated by all the wire units at that point are superimposed, we have:

[0065]

[0066] In r >> R i Under these conditions, the beam directions of each antenna element at the same field point are approximately the same. Therefore, we assume that the electric field components of each antenna element are all along the same direction. and That is, the electric field direction of each antenna element is perpendicular to the plane where the field point is located, and E is taken as... i =1, meaning that the excitation amplitude of each antenna element is the same. Also, to facilitate the generalization of the problem, (α) i +kr) is denoted as the new α i Then we have:

[0067]

[0068] It should be noted that, This method is applicable to all antenna arrays that satisfy a centrally symmetrical distribution. The following example illustrates an antenna array that satisfies a centrally symmetrical distribution.

[0069] By selecting a suitable origin O and antenna arrangement, the antenna array is symmetrically distributed about the origin O, and antenna element i and its symmetrical antenna element i′ about the origin satisfy the following conditions:

[0070]

[0071] Let the antenna array be a uniform linear array of N antenna elements arranged at equal intervals on both sides of the origin O along the x-axis, with the distance between any two adjacent antenna elements being half a wavelength. Then we have:

[0072]

[0073] Where d is the distance between two adjacent antenna elements.

[0074] Let λ = 0.3m, then for the measurement area, we have:

[0075] Let the excitation phase of antenna element i and its symmetrical antenna element i′ about the origin be α. i Then we have:

[0076]

[0077] This successfully separates the contribution of the excitation phase, greatly facilitating subsequent optimization, and allows for the direct conversion of cosα. i As a decision variable.

[0078] After setting the decision variable cosα i Then, the corresponding antenna array model can be constructed based on the decision variable as an optimization model, and the corresponding objective function can be determined.

[0079] In summary, step S110 may include:

[0080] Let the antenna array be symmetrically distributed about the origin, and let the position vector of antenna element i in the antenna array be... Recorded as Where λ is the wavelength of the electromagnetic wave, d is the distance between two adjacent antenna elements, and N is the total number of antenna elements included in the antenna array.

[0081] Let the excitation phase of antenna element i and its origin-symmetric antenna element i′ both be α. i And satisfy in, Let i′ be the position vector of antenna element i′. The vector from the origin to the field point n and r is the distance from the origin to the field point, θ n Let be the zenith angle between the line connecting the origin to the field point n and the positive z-axis. Let be the azimuth angle between the projection of the line connecting the origin to the field point onto the xy plane and the positive x-axis. Let be the wave vector in the direction of electromagnetic wave propagation and its magnitude be the wave number. And ensure that the excitation amplitude of each antenna element is the same;

[0082] Construct an antenna array model based on the following formula: in, Let n be the electric field at point n. The direction of the electric field component of the antenna element and

[0083] Step S120: Construct the objective function based on the optimization objective.

[0084] Specifically, step S120 mainly involves constructing a suitable objective function expression based on the optimization goals required by the user.

[0085] The more concentrated the antenna radiation is in the main lobe, the better the directivity; therefore, it is necessary to reduce the side lobes. To achieve this, a weighting factor δ can be set. n Let it take negative values ​​at the main lobe position and positive values ​​at the side lobe positions. The objective function can be expressed as: Summation is performed over the measurement area.

[0086] The electric field energy density w satisfies: Furthermore, to facilitate the subsequent transformation of the objective function into a QUBO problem form, the objective function can be set as follows:

[0087] Therefore, step S120 may include: with the optimization objective of minimizing sidelobe levels and controlling the main beam pointing to concentrate energy in a specific direction, constructing an objective function H according to the following formula: Where, δ n It is a weighting factor that takes a negative value at the main lobe position and a positive value at the side lobe position.

[0088] In particular, to make the beam stronger in the center, the main lobe portion can be made to satisfy... The portion is the lobes, and the remaining portion is the sidelobe portion. In this case, the weighting factor δ... n satisfy:

[0089]

[0090] Therefore, the objective function H can be in the form of H = ∑ i,j A ij cosα i cosα j Among them, coefficient A ij for

[0091] Therefore, step S120 may also include:

[0092] Let the weighting factor and The objective function H is expressed as H = ∑ i,j A ij cosα i cosα j , where coefficient A ij for Let be the position vector of antenna element j in the antenna array.

[0093] Specifically, when the objective function is H = ∑ i,jA ij cosα i cosα j In such cases, traditional algorithms such as genetic algorithms can be used to optimize antenna directivity.

[0094] For example, when optimizing antenna directivity using a genetic algorithm, the process of biological evolution can be simulated. In the initialization phase, the excitation phase distribution of antenna elements is randomly generated, and the fitness function is defined as the objective function H determined earlier. The optimization objective is to increase the main lobe gain and suppress sidelobe energy. During the iterative optimization process, a roulette wheel selection strategy is adopted, prioritizing the retention of individuals with higher fitness, and a single-point crossover operator α is used. i =(1-b)α i +bα i Information exchange is conducted to explore better solutions, where b is a weighting parameter, which can be a randomly generated number in the interval [0,1] to control the proportion of information exchange between the two parent individuals when generating offspring. Simultaneously, a low-probability mutation operation α... i =α i The addition of Δ introduces a random perturbation to prevent the algorithm from getting trapped in local optima, and an elitist retention strategy ensures that the optimal solution is not lost. Here, Δ is a random perturbation term, typically a small random number, used to introduce minute changes during mutation operations. Finally, through multiple generations of evolution, the algorithm converges to the optimal excitation phase configuration, thereby effectively reducing sidelobe levels and improving beam control capabilities.

[0095] Step S130: Discretize the objective function to obtain an objective function that satisfies the form of a quadratic unconstrained binary optimization problem.

[0096] Specifically, step S130 mainly involves discretizing the objective function to satisfy the form of the QUBO problem, and calculating the QUBO matrix based on the parameters in the model.

[0097] For example, a more natural approach is to treat the decision variable cosα... i Perform a binary expansion. Considering cosα i ∈[-1,1], here are two ways to expand:

[0098] First unfolding method:

[0099] The second way to unfold:

[0100] Where kmax is the total number of terms in the expansion, x ik x ik1 x ik2The two variables introduced during the corresponding binary expansion process all take values ​​within the range of ±1. Each expansion method has its advantages and disadvantages. The objective function obtained by the first expansion method contains both quadratic and linear terms, but has fewer variables. The objective function obtained by the second expansion method does not contain linear terms, but requires twice the number of variables to solve the same problem.

[0101] Since the second deployment method is inherently linear and more suitable for linear antenna arrays, it can be chosen when the antenna array is a uniform linear array. In this case, step S130 may include:

[0102] The decision variable cosα i Performing a binary expansion, we get Where k is cosα i The corresponding binary expansion term number, where k = 1, 2, ..., kmax; kmax is cosα i The total number of terms in the corresponding binary expansion; x ik1 x ik2 cosα i The two binary variables corresponding to the binary expansion both take values ​​in the range of ±1.

[0103] The decision variable cosα after binary expansion i Substituting into the expression of the objective function H, H = ∑ i,j A ij cosα i cosα j We obtain the objective function that initially satisfies the form of a quadratic unconstrained binary optimization problem. Where l is cosα j The corresponding binary expansion term number; x jl1 x jl2 cosα j The corresponding binary variables in their binary expansion all take values ​​in the range of ±1;

[0104] Let the Ising model have a total of N·kmax spins, and let x ik1 and x ik2 These are respectively used as the (2kmax(i-1)+2(k-1)+1)th and (2kmax(i-1)+2(k-1)+2)th spins in the Ising model, and the objective function is... Let H = xQx be the objective function that satisfies the standard form of a quadratic unconstrained binary optimization problem. T Where x is based on x ik1 x ik2 x jl1 x jl2 The size of the creation is Let Q be a matrix, where each element takes values ​​in the range ±1. Let Q be a quadratic unconstrained binary optimization matrix, and let the (ik,jl)th element be denoted as... T stands for transpose.

[0105] Step S140: The objective function satisfying the form of a quadratic unconstrained binary optimization problem is solved using the coherent Ising machine and the simulated annealing algorithm, respectively, to obtain the corresponding coherent Ising machine solution and simulated annealing solution.

[0106] Specifically, step S140 is mainly used to solve the QUBO problem, including solving it using a coherent Ising machine and solving it using a simulated annealing algorithm, thereby obtaining the solution to the QUBO problem using the two algorithms.

[0107] The Ising Hamiltonian can be written as: Q ik,jl As the coupling coefficient of the Ising model, the problem of solving the objective function that satisfies the standard form of the quadratic unconstrained binary optimization problem can be transformed into finding the ground state of the corresponding Ising problem.

[0108] For example, step S140, using a coherent Ising machine to solve the objective function that satisfies the form of a quadratic unconstrained binary optimization problem, may include:

[0109] The expression for the Ising model is determined as follows: Among them, H is For the Ising-Hamiltonian, J mm′ σ is the coupling coefficient between the m-th spin and the m′-th spin; m σ represents whether the m-th spin is up or down. m′ σ represents whether the m′-th spin is spinning up or down. m or σ m′ The value σ is 1 when it rotates upwards. m or σ m′ The value is -1 when rotating downwards;

[0110] Let Isin Hamidon quantity H is Equal to the objective function H, Q ik,jl The value of is used as the Ising Hamiltonian H is The coupling coefficient J in mm′ The value of will be used to solve the objective function H = xQx, which satisfies the standard form of a quadratic unconstrained binary optimization problem. T The problem is transformed into the problem of finding the ground state of the corresponding Ising problem;

[0111] Based on formula The dynamic evolution of the coherent Ising machine was numerically simulated using the Euler method in MATLAB software, and the Ising Hamiltonian H was calculated. isThe spin state corresponding to the minimum value of μ is taken as the solution result of the coherent Ising machine; where μ m μ represents the amplitude of the m-th degenerate optical parametric oscillator, used to simulate the spin state of the m-th spin in the Ising model; m′ denoted by , m′, represents the amplitude of the m′-th degenerate optical parametric oscillator, used to simulate the spin state of the m′-th spin in the Ising model; t represents time, p represents the pump coefficient, and c represents the coupling strength between the degenerate optical parametric oscillator pulses.

[0112] Specifically, after the evolution begins, the system composed of degenerate optical parametric oscillators begins to exhibit collective symmetry breaking. Each spin spontaneously selects a low-energy spin state, and some spins, influenced by other spins, will jump from their initial selection state to another state, causing the system energy to decrease rapidly. Eventually, the system composed of degenerate optical parametric oscillators stabilizes near the lowest energy level. The corresponding spin state at this point is the optimal solution to the QUBO problem, i.e., the objective function H = xQx. T The optimal solution.

[0113] For example, step S140, which uses the simulated annealing algorithm to solve the objective function that satisfies the form of a quadratic unconstrained binary optimization problem, may include:

[0114] Let the temperature start from the set initial temperature T max The evolution begins. At each temperature, the spin in the Ising model corresponding to the objective function is flipped N·kmax times, and the current temperature is multiplied by the annealing factor to obtain the next temperature, until the temperature evolution reaches the set minimum temperature T. min The lowest temperature T min The spin state of the Ising model corresponding to the lower objective function is used as the result of simulated annealing;

[0115] In each flip, a spin from the Ising model corresponding to the objective function is randomly selected for flipping. If the value of the objective function after the flip is less than the value of the objective function before the flip, the flip is accepted; otherwise, it is performed with probability. Accept this flip, where ΔH represents the difference between the objective function value after the spin flip and the objective function value before the spin flip, e represents the base of the natural logarithm, and T′ represents the current temperature.

[0116] For example, the process of solving an objective function that satisfies the form of a quadratic unconstrained binary optimization problem using the simulated annealing algorithm can also be implemented using MATLAB software.

[0117] Step S150: Compare the results of the coherent Ising machine solution and the results of the simulated annealing solution, and select the most suitable solution.

[0118] Specifically, step S150 mainly compares the results of the two algorithms, namely the coherent Ising machine solution and the simulated annealing solution, evaluates their performance differences, and analyzes and summarizes them in order to select the most suitable solution.

[0119] For example, by comparing the optimization effects and running time of the coherent Ising machine solution and the simulated annealing solution, the coherent Ising machine solution or the simulated annealing solution can be selected as the most suitable solution according to actual needs.

[0120] Step S160: The most suitable solution result is converted into the phase parameters of the antenna array, and the antenna array is optimized based on the phase parameters.

[0121] Specifically, step S160 mainly involves transforming the solution to the QUBO problem, i.e., the most suitable solution result, back into the optimization variables of the original problem, i.e., the antenna array optimization problem, so as to complete the optimization of the antenna array directivity based on the optimization variables.

[0122] For example, in step S160, converting the selected most suitable solution result into the phase parameters of the antenna array includes: converting the x corresponding to the selected most suitable solution result... ik1 and x ik2 Substitute the value In this process, we obtain the decision variable cosα. i The value of α can be determined using this decision variable. i The value of is used to optimize the excitation phase of the antenna array in order to improve beamforming performance and enhance the directivity of the antenna.

[0123] For example, in step S160, optimizing the antenna array based on the phase parameters includes: based on the decision variable cosα i The value of is determined by the inverse cosine function cos -1 The excitation phase α calculated by () i The value of α is determined by the excitation phase α. i The value of α is used to optimize the antenna array. Based on this, the excitation phase α can be directly used... i The value of is used to optimize the excitation phase of the antenna array in order to improve beamforming performance and enhance the directivity of the antenna.

[0124] Specifically, when the excitation phase α i When the value of α is the sum of the actual excitation phase and the k·r corresponding to the antenna array, the calculated excitation phase α can be obtained. i The actual excitation phase is obtained by subtracting the value of k·r corresponding to the antenna array. The actual excitation phase is then used to optimize the antenna array, thereby improving beamforming performance and enhancing the directivity of the antenna.

[0125] The distributed beamforming method provided in this disclosure, compared with the prior art, transforms the optimization problem of the excitation phase of each antenna element in the antenna array into a corresponding QUBO problem, solves the QUBO problem using a coherent Ising machine and a simulated annealing algorithm respectively, and optimizes the antenna element using the most suitable solution, which greatly improves the optimization effect and efficiency.

[0126] Another embodiment of this disclosure relates to a distributed beamforming device, including a model building module, an objective function building module, a discretization module, a solution module, a comparison module, and an optimization module.

[0127] The model building module is used to construct an antenna array model that meets specific conditions based on the position and excitation phase of each antenna element in the antenna array.

[0128] The objective function building module is used to construct the objective function based on the optimization objective.

[0129] The discretization module is used to discretize the objective function to obtain an objective function that satisfies the form of a quadratic unconstrained binary optimization problem.

[0130] The solution module is used to solve the objective function that satisfies the form of a quadratic unconstrained binary optimization problem using the coherent Ising machine and the simulated annealing algorithm, respectively, and obtain the corresponding coherent Ising machine solution and simulated annealing solution results.

[0131] The comparison module is used to compare the results of the coherent Ising machine solution and the results of the simulated annealing solution, and select the most suitable solution.

[0132] The optimization module is used to convert the most suitable solution into the phase parameters of the antenna array, and optimize the antenna array based on the phase parameters.

[0133] For a detailed implementation of the distributed beamforming device provided in this disclosure, please refer to the distributed beamforming method provided in this disclosure, which will not be repeated here.

[0134] The distributed beamforming device provided in this disclosure, compared with the prior art, transforms the optimization problem of the excitation phase of each antenna element in the antenna array into a corresponding QUBO problem, solves the QUBO problem using a coherent Ising machine and a simulated annealing algorithm respectively, and optimizes the antenna element using the most suitable solution, which greatly improves the optimization effect and increases the optimization efficiency.

[0135] Those skilled in the art will understand that the above embodiments are specific implementations of this disclosure, and in practical applications, various changes can be made to them in form and detail without departing from the spirit and scope of this disclosure.

Claims

1. A distributed beamforming method, characterized in that, The distributed beamforming method includes: Based on the position and excitation phase of each antenna element in the antenna array, construct an antenna array model that meets specific conditions; Based on the optimization objective, construct the objective function; Discretize the objective function to obtain an objective function that satisfies the form of a quadratic unconstrained binary optimization problem; The objective function satisfying the form of a quadratic unconstrained binary optimization problem was solved using the coherent Ising machine and the simulated annealing algorithm, respectively, and the corresponding coherent Ising machine solution and simulated annealing solution results were obtained. By comparing the coherent Ising machine solution results with the simulated annealing solution results, the most suitable solution result is selected. The most suitable solution result is converted into the phase parameters of the antenna array, and the antenna array is optimized based on the phase parameters. The step of constructing the objective function based on the optimization objective includes: The optimization objective is to minimize sidelobe levels and control the main beam pointing to concentrate energy in a specific direction. The objective function is constructed according to the following formula. : ;in, It is a weighting factor, and it takes a negative value at the main lobe position and a positive value at the side lobe position; As a venue The electric field at that location; The most suitable solution is selected by comparing the coherent Ising machine solution and the simulated annealing solution, including: by comparing the optimization effect and running time of the coherent Ising machine solution and the simulated annealing solution, the coherent Ising machine solution or the simulated annealing solution is selected as the most suitable solution according to actual needs.

2. The distributed beamforming method according to claim 1, characterized in that, The step of constructing an antenna array model that satisfies specific conditions based on the position and excitation phase of each antenna element in the antenna array includes: Let the antenna array be symmetrically distributed about the origin, and let the antenna elements in the antenna array be... position vector Recorded as ,in, The wavelength of electromagnetic waves. The spacing between two adjacent antenna elements. The total number of antenna elements included in the antenna array; Antenna element and its origin-symmetric antenna elements The excitation phase is And satisfy ,in, For antenna elements position vector, Origin and arrival points vector and , The distance from the origin to the field point. Origin and arrival points The connection and the correct The zenith angle between axes, The line connecting the origin to the field point The projection lines of the plane and the orthographic projection lines Azimuth angle between axes Let be the wave vector in the direction of electromagnetic wave propagation and its magnitude be the wave number. And ensure that the excitation amplitude of each antenna element is the same; The antenna array model is constructed according to the following formula: ,in, As a venue electric field at that location, The direction of the electric field component of the antenna element and .

3. The distributed beamforming method according to claim 2, characterized in that, The step of constructing the objective function based on the optimization objective also includes: Let the weighting factor ,and , , , the objective function Represented as , where the coefficient for , For the antenna elements in the antenna array The position vector.

4. The distributed beamforming method according to claim 3, characterized in that, The discretization of the objective function to obtain an objective function satisfying the form of a quadratic unconstrained binary optimization problem includes: decision variables Performing a binary expansion, we get ,in, for The corresponding binary expansion item number and ; for The total number of terms in the corresponding binary expansion; for The two binary variables corresponding to the binary expansion both have a value range of 1. ; decision variables after binary expansion Substitute into the objective function expression We obtain the objective function that initially satisfies the form of a quadratic unconstrained binary optimization problem. ,in, for The corresponding binary expansion item number; for The corresponding binary variable in its binary expansion has a value range of [missing information]. ; Will and As the first in the Ising model The and the first Each spin, the objective function Let be the objective function that satisfies the standard form of a quadratic unconstrained binary optimization problem. ,in, For based on The size of the creation is A matrix, where the values ​​of each element are in the range of 0. ; Let be a quadratic unconstrained binary optimization matrix and let the ()th be a quadratic unconstrained binary optimization matrix. Each element is represented as , This indicates transpose.

5. The distributed beamforming method according to claim 4, characterized in that, The objective function satisfying the form of a quadratic unconstrained binary optimization problem is solved using the coherent Ising machine and simulated annealing algorithms, respectively, to obtain the corresponding coherent Ising machine solution and simulated annealing solution results, including: The expression for the Ising model is determined as follows: ,in, For Isin Hamidon, For the first The first spin and the second The coupling coefficient between the spins; Indicates the first Each spin can either spin upwards or downwards. Indicates the first Each spin can either spin upwards or downwards. or The value is taken when rotating upwards. , or The value is taken when rotating downwards. ; Let Isin Hamidon measure equal to the objective function ,Will The value of is taken as the Ising Hamiltonian. Coupling coefficients in The value of will be used to solve the objective function that satisfies the standard form of a quadratic unconstrained binary optimization problem. The problem is transformed into the problem of finding the ground state of the corresponding Ising problem; Based on formula The dynamic evolution of the coherent Ising machine was numerically simulated using the Euler method, and the Ising Hamiltonian was calculated. The spin state corresponding to the minimum value of is taken as the solution result of the coherent Ising machine; where Indicates the first The amplitude of a degenerate optical parametric oscillator is used to simulate the first... A spin state of one spin; Indicates the first The amplitude of a degenerate optical parametric oscillator is used to simulate the first... A spin state of one spin; Indicates time, Indicates the pumping coefficient. This indicates the coupling strength between pulses in a degenerate optical parametric oscillator.

6. The distributed beamforming method according to claim 5, characterized in that, The objective function satisfying the form of a quadratic unconstrained binary optimization problem is solved using the coherent Ising machine and simulated annealing algorithms, respectively, to obtain the corresponding coherent Ising machine solution and simulated annealing solution results, including: Set the temperature from the initial set temperature. The evolution begins, and at each temperature, the spin in the Ising model corresponding to the objective function is flipped. Then, the current temperature is multiplied by the annealing factor to obtain the next temperature, and this process continues until the temperature evolution reaches the set minimum temperature. , to the lowest temperature The spin state of the Ising model corresponding to the lower objective function is used as the solution result of the simulated annealing; In each flip, a spin from the Ising model corresponding to the objective function is randomly selected for flipping. If the value of the objective function after the flip is less than the value of the objective function before the flip, the flip is accepted; otherwise, it is performed with probability. Accept this flip, where, This represents the difference between the value of the objective function after spin flip and the value of the objective function before spin flip. The base of the natural logarithm. This indicates the current temperature.

7. The distributed beamforming method according to claim 4, characterized in that, The process of converting the selected most suitable solution result into the phase parameters of the antenna array includes: The most suitable solution result is selected. and Substitute the value In this process, decision variables are obtained. The value of .

8. The distributed beamforming method according to claim 7, characterized in that, The optimization of the antenna array based on the phase parameters includes: Based on decision variables The value of is obtained by calculating the excitation phase using the inverse cosine function. The value of is determined by the excitation phase. The value of is used to optimize the antenna array.

9. A distributed beamforming device, characterized in that, The distributed beamforming device includes: The model building module is used to build an antenna array model that meets specific conditions based on the position and excitation phase of each antenna element in the antenna array. The objective function construction module is used to construct the objective function based on the optimization objective. The discretization module is used to discretize the objective function to obtain an objective function that satisfies the form of a quadratic unconstrained binary optimization problem. The solution module is used to solve the objective function that satisfies the form of a quadratic unconstrained binary optimization problem using the coherent Ising machine and the simulated annealing algorithm, respectively, and obtain the corresponding coherent Ising machine solution and simulated annealing solution. The comparison module is used to compare the solution results of the coherent Ising machine with the solution results of the simulated annealing and select the most suitable solution result; The optimization module is used to convert the most suitable solution result into the phase parameters of the antenna array, and optimize the antenna array based on the phase parameters; The step of constructing the objective function based on the optimization objective includes: The optimization objective is to minimize sidelobe levels and control the main beam pointing to concentrate energy in a specific direction. The objective function is constructed according to the following formula. : ;in, It is a weighting factor, and it takes a negative value at the main lobe position and a positive value at the side lobe position; As a venue The electric field at that location; The most suitable solution is selected by comparing the coherent Ising machine solution and the simulated annealing solution, including: by comparing the optimization effect and running time of the coherent Ising machine solution and the simulated annealing solution, the coherent Ising machine solution or the simulated annealing solution is selected as the most suitable solution according to actual needs.

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