Distributed beam forming method and device

Abstract

The embodiment of the invention relates to the technical field of distributed beam forming, and provides a distributed beam forming method and device, and the method comprises the steps: constructing an antenna array model meeting a specific condition according to the position and excitation phase of each antenna unit in an antenna array; constructing a target function according to the optimization target; discretizing the target function to obtain a target function satisfying a quadratic unconstrained binary optimization problem form; respectively using a coherent Isin machine and a simulated annealing algorithm to solve the objective function satisfying the secondary unconstrained binary optimization problem form to obtain a corresponding coherent Isin machine solving result and a corresponding simulated annealing solving result; comparing the solution result of the coherent Isin machine with the solution result of the simulated annealing, and selecting the most suitable solution result; and converting the selected most appropriate solution result into a phase parameter of the antenna array, and optimizing the antenna array according to the phase parameter. According to the embodiment of the invention, the optimization effect can be greatly improved, and the optimization efficiency is improved.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of distributed beamforming, in particular to a distributed beamforming method and device. BACKGROUND

[0002] Distributed beamforming is a technology that concentrates signal energy in a specific direction through the cooperative work of multiple nodes, and is widely used in wireless communication, radar and other fields. Due to the special design of the antenna, its radiation field can be concentrated in a certain spatial direction. The directivity of the antenna is the relative value of the antenna radiation field and the spatial direction under the condition of the same distance in the far field. The directivity of the antenna can be represented by the antenna pattern. The antenna pattern usually includes at least two lobes, of which the lobe with the maximum radiation intensity is called the main lobe, and the remaining lobes are called side lobes or side lobes. The more concentrated the radiation is in the main lobe, the better the directivity and the stronger the anti-interference ability. Side lobes will cause energy diffusion and increased attenuation, so they need to be reduced.

[0003] In the prior art, there are various distributed beamforming methods, each with advantages and disadvantages. For example, feedback-based methods such as 1-bit feedback mechanism 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 require high hardware precision and synchronization. Position information-based methods are suitable for static scenarios but require strict position accuracy. Array antenna beamforming methods can flexibly adjust beam direction and width, but have high system complexity. In actual applications, the most suitable beamforming method needs to be selected according to the specific scene and system requirements to achieve the best signal transmission effect. SUMMARY

[0004] The present disclosure aims to at least solve one of the problems existing in the prior art and provide a distributed beamforming method and device.

[0005] In one aspect of the present disclosure, a distributed beamforming method is provided, which comprises:

[0006] constructing an antenna array model that satisfies a certain condition according to the positions and excitation phases of the antenna elements in the antenna array;

[0007] constructing an objective function according to an optimization target;

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

[0009] solving the objective function that satisfies 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;

[0010] Comparing the coherent Ising machine solution result and the simulated annealing solution result, the most suitable solution result is selected out;

[0011] The selected most suitable solution result is converted into a phase parameter of the antenna array, and the antenna array is optimized according to the phase parameter.

[0012] Optionally, the antenna array model satisfying a certain condition is constructed according to the position and excitation phase of each antenna element in the antenna array, comprising:

[0013] Let the antenna array be symmetrically distributed about the origin, and the position vector of the antenna element i in the antenna array is denoted as where λ is the wavelength of the electromagnetic wave, d is the spacing 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 the antenna element i and the antenna element i' symmetrically distributed about the origin be α i , and satisfy where is the position vector of the antenna element i', is the vector from the origin to the field point n and r is the distance from the origin to the field point, θ n is the zenith angle between the line connecting the origin to the field point n and the positive z-axis, is the azimuth angle between the projection line of the line connecting the origin to the field point on the xy plane and the positive x-axis, is the wave vector in the direction of electromagnetic wave propagation and its magnitude is the wave number and let the excitation amplitude of each antenna element be the same;

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

[0016] Optionally, the objective function is constructed according to the optimization objective, comprising:

[0017] The optimization objective is to minimize the sidelobe level and control the main beam pointing direction to enable energy concentration in a certain direction, and the objective function H is constructed according to the following formula: where δ n is a weighting factor and takes a negative value at the main lobe position and a positive value at the sidelobe position.

[0018] Optionally, the objective function is constructed according to the optimization objective, further comprising:

[0019] Weighting factor And The objective function H is expressed as H = ∑ i,j A ij cosα i cosα j , wherein the coefficient A ij is is the position vector of the antenna unit j in the antenna array.

[0020] Optionally, the objective function is discretized to obtain an objective function satisfying a quadratic unconstrained binary optimization problem form, comprising:

[0021] The decision variable cosα i is binary expanded to obtain wherein k is the number of the binary expansion item corresponding to cosα i , and k = 1, 2, …, kmax; kmax is the total number of binary expansions corresponding to cosα i ; x ik1 and x ik2 are two binary variables corresponding to the binary expansion of cosα i , both of which have a value range of ±1.

[0022] The decision variable cosα i after binary expansion is substituted into the expression of the objective function H = ∑ i,j A ij cosα i cosα j , to obtain an objective function preliminarily satisfying a quadratic unconstrained binary optimization problem form wherein l is the number of the binary expansion item corresponding to cosα j ; x jl1 and x jl2 are two binary variables corresponding to the binary expansion of cosα j , both of which have a value range of ±1.

[0023] x ik1 and x ik2 are respectively regarded as the (2kmax(i-1)+2(k-1)+1)th and the (2kmax(i-1)+2(k-1)+2)th spin in the Ising model, and the objective function is denoted as an objective function H = xQx satisfying a standard form of a quadratic unconstrained binary optimization problem T , wherein x is based on x ik1 , x ik2 , x jl1 , xjl2 a matrix of size , where each element ranges from ±1; Q is a quadratic unconstrained binary optimization matrix and the (ik, jl)th element of Q is denoted as T represents transposition.

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

[0025] The expression of the Ising model is determined as where H is is an Ising Hamiltonian, J mm′ is a coupling coefficient between the mth spin and the m'th spin; σ m represents the mth spin upward spin or downward spin, σ m′ represents the m'th spin upward spin or downward spin, σ m or σ m′ represents 1 when upward spin, σ m or σ m′ represents -1 when downward spin.

[0026] Let the Ising Hamiltonian H is be equal to the objective function H, and the value of Q ik,jl be taken as the value of the coupling coefficient J is in the Ising Hamiltonian H mm′ , the problem of solving the objective function H = xQx T satisfying the standard form of the quadratic unconstrained binary optimization problem is converted into the problem of finding the ground state of the corresponding Ising problem;

[0027] Based on the formula , the dynamics evolution process of the coherent Ising machine is simulated by using the Euler method, and the spin state corresponding to the minimum value of the Ising Hamiltonian H is is taken as the coherent Ising machine solution; where μ m represents the amplitude of the mth degenerate optical parametric oscillator, which is used to simulate the spin state of the mth spin in the Ising model; μ m′ represents the amplitude of the m'th degenerate optical parametric oscillator, which is used to simulate the spin state of the m'th spin in the Ising model; t represents time, p represents pump coefficient, and c represents coupling strength between degenerate optical parametric oscillator pulses.

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

[0029] temperature from the set initial temperature T max evolution, 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 minimum temperature T min The spin state of the Ising model corresponding to the objective function is taken as the simulated annealing solution result.

[0030] Wherein, each time the spin in the Ising model corresponding to the objective function is randomly selected for flipping, if the value of the objective function after flipping is less than the value of the objective function before flipping, the flipping is accepted, otherwise the flipping is accepted with a probability , wherein ΔH represents the difference between the value of the objective function after the spin is flipped and the value of the objective function before the spin is flipped, e represents the base of natural logarithm, and T' represents the current temperature.

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

[0032] Substituting the values of x ik1 and x ik2 into , the value of the decision variable cosα i is obtained.

[0033] Optionally, the optimizing the antenna array according to the phase parameter comprises:

[0034] Based on the value of the decision variable cosα i , the value of the excitation phase α i calculated by the inverse cosine function, and the value of the excitation phase α i optimizes the antenna array.

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

[0036] A model construction module is configured to construct an antenna array model satisfying a specific condition according to the positions and excitation phases of the antenna elements in the antenna array.

[0037] A target function construction module is configured to construct a target function according to an optimization target.

[0038] A discretization module is configured to perform discretization processing on the target function to obtain a target function satisfying a form of a quadratic unconstrained binary optimization problem.

[0039] a solving module configured to solve a target function in the form of a quadratic unconstrained binary optimization problem using a coherent Ising machine and a simulated annealing algorithm respectively, to obtain a coherent Ising machine solution and a simulated annealing solution;

[0040] a comparison module configured to compare the coherent Ising machine solution and the simulated annealing solution, and select the most suitable solution;

[0041] an optimization module configured to convert the selected most suitable solution into a phase parameter of the antenna array, and optimize the antenna array according to the phase parameter.

[0042] Compared with the prior art, the present disclosure converts the optimization problem of the excitation phase of each antenna unit in the antenna array into a corresponding QUBO problem, solves the QUBO problem using a coherent Ising machine and a simulated annealing algorithm respectively, optimizes the antenna unit using the most suitable solution, greatly improves the optimization effect, and improves the optimization efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0043] One or more embodiments are illustrated by way of example in the figures that are part of this disclosure and which are included to further provide explanatory aspects of the present disclosure. Unless otherwise noted, elements of the figures having the same or similar reference numerals denote like or similar elements. The figures are not to scale, and the figures are not intended to limit the present disclosure to particular combinations or configurations of the various elements depicted.

[0044] Figure 1 a flow chart of a distributed beamforming method according to an embodiment of the present disclosure;

[0045] Figure 2 a flow chart of a distributed beamforming method according to another embodiment of the present disclosure. DETAILED DESCRIPTION

[0046] In the field of antenna array optimization, although traditional methods such as gradient descent and convex optimization are widely used, they often face challenges such as convergence to local optimal solution 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 are a global optimization method based on natural selection and genetic mechanisms, particularly suitable for complex search spaces. By simulating the biological evolution process, genetic algorithms are used in antenna design to optimize parameters such as element spacing, amplitude, and phase of the array to achieve specific radiation characteristics. For example, researchers have used genetic algorithms to optimize the element spacing and feed current amplitude of a linear antenna array, successfully reducing the sidelobe level and pointing the main beam in a specific direction. In addition, genetic algorithms have also been applied to the design optimization of microstrip patch antennas, demonstrating their wide applicability in the field of antenna design.

[0048] The objective 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 composed of binary variables (taking values 0, 1 or 1, -1), and Q is a symmetric weight matrix. The QUBO model aims to find the combination of binary variables that minimizes the objective function value. In the antenna array optimization problem, design objectives such as sidelobe level minimization, beam direction control, etc. can be represented by constructing an appropriate QUBO model. By defining a suitable weight matrix Q and binary variables x (for example, x can represent the on-off 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 quantum annealing and other optimization and coherent Ising machines to find the optimal antenna configuration scheme.

[0049] Simulated annealing is a stochastic search algorithm that simulates the physical annealing process and is suitable for global optimization problems. Simulated annealing allows accepting worse solutions in the initial stage to avoid getting stuck in local optima, 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 a circular antenna array to achieve the desired sidelobe level and minimum beam width. In addition, simulated annealing has also been applied to detect faulty antenna elements in linear arrays, demonstrating its effectiveness in complex optimization problems.

[0050] A coherent Ising machine is a computing device based on optical nonlinear effects, which uses an optical parametric oscillator (OPO), especially a degenerate optical parametric oscillator (DOPO), to simulate the evolution of the Ising model, thereby used to solve combinatorial optimization problems. The OPO is a nonlinear optical process that converts one high-energy photon into two low-energy photons through the interaction of a nonlinear crystal and a pump laser. The DOPO is a special case of the OPO, and the signal photon and the idler photon output by the DOPO have the same frequency. When a certain threshold is reached, a phase transition occurs, thereby exhibiting bistable characteristics in the output light pulse. When the pump intensity increases to exceed a certain threshold, the system undergoes a collective symmetry breaking. At this time, the output of the DOPO can be selected in two possible phase states. In the coherent Ising machine, the spin state can be represented by the phase of the output light of the DOPO. The same phase represents one spin state, and the different phase represents another spin state. Multiple DOPOs can be connected to form a network to simulate a multi-spin Ising model. By adjusting the coupling between the DOPOs, the spin-spin interaction in the Ising model can be simulated.

[0051] In recent years, the coherent Ising machine has attracted attention in antenna system optimization. Researchers have converted the reconfigurable antenna multiple input multiple output (MIMO) configuration selection problem into an Ising model and solved it using the CIM to maximize the signal-to-noise ratio of the received signal. The results show that the coherent Ising machine is superior to the traditional method in terms of computational complexity and performance, and approaches the optimal performance of the exhaustive search. In addition, the excellent performance of the coherent Ising machine in solving combinatorial optimization problems provides new application prospects for the fields of neural computing and optical computing.

[0052] The present disclosure provides a distributed beamforming method and device suitable for coherent Ising machines and simulated annealing. In order to make the purposes, technical solutions and advantages of the embodiments of the present disclosure clearer, the embodiments of the present disclosure will be described in detail below with reference to the drawings. However, those skilled in the art can understand that in the embodiments of the present disclosure, many technical details are proposed in order to make the reader better understand the present disclosure. However, the technical solutions claimed by the present disclosure can be implemented even without these technical details and various changes and modifications based on the following embodiments. The division of the following embodiments is for the convenience of description, and should not constitute any limitation on the specific embodiments of the present disclosure. The 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 is the position vector of the antenna element i, and the far-field condition r » R is used i Approximately, the electric field produced by the antenna element i at the field point n is

[0062]

[0063] where α i is the excitation phase of the antenna element i, is the excitation amplitude E i of the antenna element i.

[0064] The electric field produced by the antenna element i at the field point n is The superposition of the electric fields produced by all the antenna elements at the field point n is

[0065]

[0066] Under the condition of r » R i , the beam directions of the antenna elements at the same field point are approximately the same. Therefore, let the electric field components of all the antenna elements be in the same direction and that is, the electric field directions of all the antenna elements are perpendicular to the plane where the field point is located, and take E i = 1, that is, let the excitation amplitudes of all the antenna elements be the same, and at the same time, in order to facilitate the generalization of the problem, (α i + kr) is recorded as a new α i , then we have:

[0067]

[0068] It should be noted that, can be applied to all antenna arrays that satisfy the central symmetric distribution. The following takes an antenna array that satisfies the origin symmetric distribution as an example for description.

[0069] Select a suitable origin O and antenna arrangement mode, so that the antenna array is symmetrically distributed about the origin O, and the antenna element i and its symmetric antenna element i' about the origin satisfy the condition:

[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 on the x-axis, and the interval between adjacent two antenna elements is half a wavelength, then we have:

[0072]

[0073] where d is the interval between adjacent two antenna elements.

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

[0075] Let the excitation phase of the antenna unit i and its origin-symmetric antenna unit i' be α i , then:

[0076]

[0077] In this way, the contribution of the excitation phase is successfully separated out, greatly facilitating the subsequent optimization, and the cosα i can be directly taken as a decision variable.

[0078] After the decision variable cosα i is set, a corresponding antenna array model can be constructed as an optimization model according to the decision variable, and a corresponding objective function can be determined.

[0079] In summary, step S110 can include:

[0080] Let the antenna array be symmetrically distributed about the origin, and let the position vector of the antenna unit i in the antenna array be denoted as where λ is the wavelength of the electromagnetic wave, d is the spacing between two adjacent antenna units, and N is the total number of antenna units included in the antenna array;

[0081] Let the excitation phase of the antenna unit i and its origin-symmetric antenna unit i' be α i , and satisfy where is the position vector of the antenna unit i', is the vector from the origin to the field point n and r is the distance from the origin to the field point, θ n is the zenith angle between the line connecting the origin to the field point n and the positive z-axis, is the azimuth angle between the projection line of the line connecting the origin to the field point on the xy plane and the positive x-axis, is the wave vector in the direction of electromagnetic wave propagation and its magnitude is the wave number and let the excitation amplitude of each antenna unit be the same;

[0082] According to the following formula, an antenna array model is constructed: where is the electric field at the field point n, is the direction of the electric field component of the antenna unit and

[0083] Step S120, according to the optimization objective, an objective function is constructed.

[0084] Specifically, step S120 is mainly to construct a suitable target function expression according to the optimization target of user demand.

[0085] The more the antenna radiation is concentrated in the main lobe, the better the directivity is, and thus it is necessary to reduce the sidelobe part. For this purpose, a weighting factor δ n may be set, which takes a negative value at the main lobe position and takes a positive value at the sidelobe position. The target function can be expressed as a sum over the measurement region.

[0086] The electric field energy density w satisfies: And, in order to facilitate the conversion of the target function into a form satisfying the QUBO problem in the later stage, the target function can be set as

[0087] Therefore, step S120 can include: taking minimizing the sidelobe level and controlling the main beam pointing to enable energy concentration in a specific direction as the optimization target, constructing a target function H according to the following formula: wherein δ n is a weighting factor and takes a negative value at the main lobe position and takes a positive value at the sidelobe position.

[0088] In particular, in order to make the beam stronger in the middle position, the main lobe part can be set as a part satisfying , and the remaining part is the sidelobe part, at this time, the weighting factor δ n satisfies:

[0089]

[0090] Therefore, the form of the target function H can be H = ∑ i,j A ij cosα i cosα j . Wherein the coefficient A ij is

[0091] Therefore, step S120 can further include:

[0092] Let the weighting factor be δ Express the target function H as H = ∑ i,j A ij cosα i cosα j , wherein the coefficient A ij is is the position vector of the antenna element j in the antenna array.

[0093] In particular, when the target function is H = ∑ i,jA ij cosα i cosα j In this case, traditional algorithms such as genetic algorithms can be applied to optimize the antenna directivity.

[0094] For example, when optimizing the antenna directivity using a genetic algorithm, the biological evolution process can be simulated, and the excitation phase distribution of the antenna unit is randomly generated in the initialization stage, and the fitness function is defined as the objective function H determined in the foregoing, and the optimization goal is to improve the main lobe gain and suppress the sidelobe energy. In the iterative optimization process, the roulette wheel selection strategy is adopted, and individuals with higher fitness are preferentially retained, and through the single-point crossover operator α i =(1-b)α i +bα i Exchange information to explore better solutions, where b is a weight parameter, which can be a randomly generated number in the interval [0, 1], used to control the information exchange ratio of the two parent individuals when generating offspring. At the same time, the small probability mutation operation α i =α i +Δ introduces random disturbance to avoid the algorithm falling into local optimum, and through the elite reservation strategy to ensure that the optimal solution will not be lost, where Δ is a random disturbance term, usually a small random number, used to introduce a small change in the mutation operation. Finally, through multiple generations of evolution, the algorithm converges to the optimal excitation phase configuration, thereby effectively reducing the sidelobe level and improving the beam control ability.

[0095] In step S130, the target function is discretized to obtain a target function that satisfies the form of a quadratic unconstrained binary optimization problem.

[0096] Specifically, step S130 mainly discretizes the target function to satisfy the form of the QUBO problem, and calculates the QUBO matrix according to the parameters in the model.

[0097] For example, a natural processing method is to expand the decision variable cosα i into binary. Considering that cosα i ∈[-1,1], two expansion methods are provided here:

[0098] The first expansion method is:

[0099] The second expansion method is:

[0100] Where kmax is the total number of expansion terms, x ik , x ik1 , x ik2The binary variables introduced in the corresponding binary expansion process have a value range of ±1. The two expansion methods have advantages and disadvantages. The first expansion method obtains a target function that contains both quadratic terms and linear terms, but has fewer variables. The second expansion method obtains a target function that does not contain linear terms, but the same problem requires a doubled number of variables.

[0101] Since the second expansion method is essentially linear, it is more suitable for linear antenna arrays. Therefore, when the antenna array is a uniform linear array, the second expansion method can be selected for expansion. At this time, step S130 can include:

[0102] The decision variable cosα i is binary expanded to obtain where k is the number of the corresponding binary expansion term of cosα i , k = 1, 2, …, kmax; kmax is the number of the corresponding binary expansion term of cosα i ; x ik1 and x ik2 are the binary variables corresponding to the binary expansion of cosα i , and have a value range of ±1;

[0103] The binary-expanded decision variable cosα i is substituted into the expression of the target function H = ∑ i,j A ij cosα i cosα j to obtain a target function that preliminarily satisfies the form of a quadratic unconstrained binary optimization problem where l is the number of the corresponding binary expansion term of cosα j ; x jl1 and x jl2 are the binary variables corresponding to the binary expansion of cosα j , and have a value range of ±1;

[0104] Let there be a total of N·kmax spins in the Ising model, and let x ik1 and x ik2 be the (2kmax(i-1)+2(k-1)+1)th and (2kmax(i-1)+2(k-1)+2)th spins in the Ising model, respectively. Let the target function be denoted as a target function H = xQx that satisfies the standard form of a quadratic unconstrained binary optimization problem T , where x is a vector of size ik1 , x ik2 , x jl1 , x jl2 , which is established based on x ik1 , x ik2 , x T , x ik1 , x ik2 , x jl1 , x jl2 . 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 the target function is taken as the solution result of the coherent Ising machine; wherein, μ m represents the amplitude of the mth degenerate optical parametric oscillator, and is used to simulate the spin state of the mth spin in the Ising model; μ m′ represents the amplitude of the m'th degenerate optical parametric oscillator, and is used to simulate the spin state of the m'th spin in the Ising model; t represents time, p represents the pumping coefficient, and c represents the coupling strength between the degenerate optical parametric oscillator pulses.

[0112] Specifically, after the evolution starts, the system composed of various degenerate optical parametric oscillators starts to break the collective symmetry, and each spin starts to spontaneously select a low-energy spin state. Some spins will jump from the initial selected state to another state due to the influence of other spins, and the system energy will thus rapidly decrease. Finally, the system composed of various degenerate optical parametric oscillators stabilizes near the minimum energy, and the corresponding spin state is the optimal solution of the QUBO problem, i.e., the objective function H = xQx T .

[0113] For example, the step S140 uses the simulated annealing algorithm to solve the objective function satisfying the form of the quadratic unconstrained binary optimization problem, and can include the following steps.

[0114] Let the temperature start from a set initial temperature T max , and at each temperature, flip the spin in the Ising model corresponding to the objective function N*kmax times, and then multiply the current temperature by the annealing factor to obtain the next temperature, until the temperature evolution reaches the set minimum temperature T min , and take the spin state of the Ising model corresponding to the objective function at the minimum temperature T min as the simulated annealing solution result.

[0115] Wherein, each time the flip, a spin in the Ising model corresponding to the objective function is randomly selected for flipping. If the value of the objective function after the spin is flipped is less than the value of the objective function before the spin is flipped, then accept the flip. Otherwise, accept the flip with a probability of e , wherein ΔH represents the difference between the value of the objective function after the spin is flipped and the value of the objective function before the spin is flipped, e represents the base of the natural logarithm, and T' represents the current temperature.

[0116] For example, the process of using the simulated annealing algorithm to solve the objective function satisfying the form of the quadratic unconstrained binary optimization problem can also be implemented using MATLAB software.

[0117] Step S150, compare the solution result of the coherent Ising machine and the solution result of the simulated annealing, and select the most appropriate solution result.

[0118] Specifically, step S150 mainly compares the results solved by the two algorithms, i.e., the results solved by the coherent Ising machine and the results solved by the simulated annealing, evaluates the performance difference and analyzes and summarizes, so as to select the most suitable solving result.

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

[0120] In step S160, the selected most suitable solving result is converted into the phase parameter of the antenna array, and the antenna array is optimized according to the phase parameter.

[0121] Specifically, step S160 mainly reconverts the solution of the QUBO problem, i.e., the selected most suitable solving result, into the optimization variable of the original problem, i.e., the antenna array optimization problem, so as to complete the optimization of the directivity of the antenna array according to the optimization variable.

[0122] For example, in step S160, the selected most suitable solving result is converted into the phase parameter of the antenna array, including: substituting the values of x ik1 and x ik2 corresponding to the selected most suitable solving result into to obtain the value of the decision variable cosα i . Accordingly, the excitation phase of the antenna array can be optimized by using the value of the decision variable cosα i to improve the beamforming performance and enhance the directivity of the antenna.

[0123] For example, in step S160, the antenna array is optimized according to the phase parameter, including: based on the value of the decision variable cosα i , the value of the excitation phase α -1 calculated by the inverse cosine function cos i (), the antenna array is optimized according to the value of the excitation phase α i . Accordingly, the excitation phase of the antenna array can be directly optimized by using the value of the excitation phase α i to improve the beamforming performance and enhance the directivity of the antenna.

[0124] In particular, when the value of the excitation phase α i is the sum of the actual excitation phase and k·r corresponding to the antenna array, the value of the calculated excitation phase α i can be subtracted from k·r corresponding to the corresponding antenna array, so as to obtain the actual excitation phase, so as to optimize the antenna array by using the actual excitation phase, thereby improving the beamforming performance and enhancing the directivity of the antenna.

[0125] The distributed beamforming method provided by the embodiment of the present disclosure converts the optimization problem of the excitation phase of each antenna unit in the antenna array into a corresponding QUBO problem, solves the QUBO problem by using a coherent Ising machine and a simulated annealing algorithm respectively, optimizes the antenna unit by using the most suitable solution result, greatly improves the optimization effect, and improves the optimization efficiency.

[0126] Another embodiment of the present disclosure relates to a distributed beamforming device, comprising a model construction module, a target function construction module, a discretization module, a solving module, a comparison module, and an optimization module.

[0127] The model construction module is configured to construct an antenna array model satisfying a specific condition according to the position and excitation phase of each antenna unit in the antenna array.

[0128] The target function construction module is configured to construct a target function according to an optimization target.

[0129] The discretization module is configured to discretize the target function to obtain a target function satisfying a quadratic unconstrained binary optimization problem form.

[0130] The solving module is configured to solve the target function satisfying the quadratic unconstrained binary optimization problem form by using a coherent Ising machine and a simulated annealing algorithm respectively, to obtain a corresponding coherent Ising machine solution result and a simulated annealing solution result.

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

[0132] The optimization module is configured to convert the selected most suitable solution result into a phase parameter of the antenna array, and optimize the antenna array according to the phase parameter.

[0133] The specific implementation method of the distributed beamforming device provided by the embodiment of the present disclosure can be referred to the distributed beamforming method provided by the embodiment of the present disclosure, which will not be described here.

[0134] The distributed beamforming device provided by the embodiment of the present disclosure converts the optimization problem of the excitation phase of each antenna unit in the antenna array into a corresponding QUBO problem, solves the QUBO problem by using a coherent Ising machine and a simulated annealing algorithm respectively, optimizes the antenna unit by using the most suitable solution result, greatly improves the optimization effect, and improves the optimization efficiency.

[0135] It is understood by those of ordinary skill in the art that the above embodiments are specific embodiments for implementing the present disclosure, and various changes can be made in form and details in practical applications without departing from the spirit and scope of the present disclosure.

Claims

1. A distributed beamforming method, characterized in that, The distributed beamforming method comprises: constructing an antenna array model meeting specific conditions according to the positions and excitation phases of each antenna unit in the antenna array; constructing an objective function according to an optimization target; discretizing the objective function to obtain an objective function meeting a form of a quadratic unconstrained binary optimization problem; solving the objective function meeting the form of the quadratic unconstrained binary optimization problem by using a coherent Ising machine and a simulated annealing algorithm respectively 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; transforming the selected most suitable solving result into phase parameters of the antenna array and optimizing the antenna array according to the phase parameters.

2. The distributed beamforming method of claim 1, wherein, The constructing an antenna array model meeting specific conditions according to the positions and excitation phases of each antenna unit in the antenna array comprises: Let the antenna array be distributed symmetrically to the origin, the position vector of the antenna element i in the antenna array is denoted as Let the antenna array be distributed symmetrically to the origin, the position vector of the antenna element i in the antenna array is denoted as wherein λ is the wavelength of the electromagnetic wave, d is the spacing of the two adjacent antenna elements, and N is the total number of antenna elements included in the antenna array. Let the excitation phase of the antenna element i and its origin-symmetric antenna element i' be α i , and satisfy where, is the position vector of the antenna element i', is the vector from the origin to the field point n and r is the distance from the origin to the field point, θ n is the zenith angle between the line from the origin to the field point n and the positive z-axis, is the azimuth angle between the projection of the line from the origin to the field point on the xy-plane and the positive x-axis, is the wave vector in the direction of electromagnetic wave propagation and its magnitude is the wave number and let the excitation amplitude of each antenna element be the same; The antenna array model is constructed according to the following formula: wherein, is the electric field at field point n, is the electric field component direction of the antenna element and 3. The distributed beamforming method of claim 2, wherein, The constructing an objective function according to an optimization target comprises: The optimization goal is to minimize the sidelobe level 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 is a weighting factor and takes a negative value at the main lobe position and a positive value at the sidelobe position.

4. The distributed beamforming method of claim 3, wherein, The constructing an objective function according to an optimization target further comprises: Let the weighting factor and n = 0, 1, 2,..., 180, the objective function H is expressed as H = ∑ i,j A ij cos a i cos a j where the coefficient A ij is is the position vector of the antenna element j in the antenna array.

5. The distributed beamforming method of claim 4, wherein, The discretizing the objective function to obtain an objective function meeting a form of a quadratic unconstrained binary optimization problem comprises: Let the decision variable cosα i be binary expanded to get where k is the binary expansion index of cosα i , and k = 1, 2, …, kmax; kmax is the total number of binary expansion terms of cosα i ; x ik1 , x ik2 are the two binary variables corresponding to the binary expansion of cosα i , both of which take values of ±1. cosα i Substitute the expression of the objective function H into the expression of the objective function H = ∑ i,j A ij cosα i cosα j , and obtain the objective function preliminarily satisfying the form of the quadratic unconstrained binary optimization problem where l is the number of the binary expansion item corresponding to cosα j ; x jl1 , x jl2 is the binary variable corresponding to cosα j , and the value range of each is ±1. Let x ik1 and x ik2 be the (2kmax(i-1)+2(k-1)+1)th and (2kmax(i-1)+2(k-1)+2)th spins in the Ising model, respectively, and let the objective function be denoted as the objective function H = xQx T satisfying the standard form of the quadratic unconstrained binary optimization problem, where x is based on x ik1 , x ik2 , x jl1 , x jl2 is a matrix of size established based on x ik1 , x ik2 , x jl1 , x jl2 , where each element in the matrix has a value range of ±1; Q is a quadratic unconstrained binary optimization matrix and the (ik,jl)th element in Q is expressed as T represents transposition.

6. The distributed beamforming method of claim 5, wherein, The solving the objective function meeting the form of the quadratic unconstrained binary optimization problem by using a coherent Ising machine and a simulated annealing algorithm respectively to obtain corresponding coherent Ising machine solving results and simulated annealing solving results comprises: The expression of the Ising model is determined as where H is is the Ising Hamiltonian, J mm′ is the coupling coefficient between the mth spin and the m' th spin; σ m represents the mth spin upward spin or downward spin, σ m′ represents the m' th spin upward spin or downward spin, σ m or σ m′ represents the value of 1 when upward spin, σ m or σ m′ represents the value of -1 when downward spin; Let the Ising Hamiltonian H is be equal to the objective function H, and let the values of Q ik,jl be the values of the coupling coefficients J is in the Ising Hamiltonian H mm′ . The problem of solving the standard form of a quadratic unconstrained binary optimization problem, which is to find the values of x that minimize the objective function H = xQx T , is transformed into the problem of finding the ground state of the corresponding Ising problem. Based on the formula The dynamics evolution process of the coherent Ising machine is simulated by using Euler method, and the spin state corresponding to the minimum value of the Ising Hamiltonian H is is taken as the solution result of the coherent Ising machine; wherein, μ m represents the amplitude of the mth degenerate optical parametric oscillator, which is used to simulate the spin state of the mth spin in the Ising model; μ m′ represents the amplitude of the m'th degenerate optical parametric oscillator, which is used to simulate the spin state of the m'th spin in the Ising model; t represents time, p represents pump coefficient, and c represents the coupling strength between the degenerate optical parametric oscillator pulses.

7. The distributed beamforming method of claim 6, wherein, The solving the objective function meeting the form of the quadratic unconstrained binary optimization problem by using a coherent Ising machine and a simulated annealing algorithm respectively to obtain corresponding coherent Ising machine solving results and simulated annealing solving results comprises: Let the temperature evolve from the set initial temperature T max Start evolution, at each temperature, spin flip N*kmax times in the Ising model corresponding to the objective function, and multiply the current temperature by the annealing factor to obtain the next temperature, until the temperature evolution reaches the set minimum temperature T min , the minimum temperature T min The spin state of the Ising model corresponding to the objective function is taken as the simulated annealing solution result; wherein, each time of flipping, a spin in the Ising model corresponding to the target function is randomly selected to flip, if the value of the target function after the spin flips is less than the value of the target function before the spin flips, the spin flip is accepted, otherwise, the spin flip is accepted with a probability of the spin flip is accepted, wherein, ΔH represents the difference between the value of the target function after the spin flips and the value of the target function before the spin flips, e represents the base number of the natural logarithm, and T' represents the current temperature.

8. The distributed beamforming method of claim 5, wherein, The transforming the selected most suitable solving result into phase parameters of the antenna array comprises: 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 .

9. The distributed beamforming method of claim 8, wherein, The optimizing the antenna array according to the phase parameters comprises: The value of the excitation phase a is calculated by an inverse cosine function on the basis of the value of the decision variable cos a i The value of the excitation phase a is calculated by an inverse cosine function on the basis of the value of the decision variable cos a i The value of the excitation phase a is calculated by an inverse cosine function on the basis of the value of the decision variable cos a i The value of the excitation phase a is calculated by an inverse cosine function on the basis of the value of the decision variable cos a 10. A distributed beamforming apparatus, comprising: The distributed beamforming device comprises: a model construction module configured to construct an antenna array model meeting specific conditions according to the positions and excitation phases of each antenna unit in the antenna array; an objective function construction module configured to construct an objective function according to an optimization target; a discretization module configured to discretize the objective function to obtain an objective function meeting a form of a quadratic unconstrained binary optimization problem; a solving module configured to solve the objective function meeting the form of the quadratic unconstrained binary optimization problem by using a coherent Ising machine and a simulated annealing algorithm respectively to obtain corresponding coherent Ising machine solving results and simulated annealing solving results; a comparison module configured to compare the coherent Ising machine solving results and the simulated annealing solving results to select the most suitable solving result; an optimization module configured to transform the selected most suitable solving result into phase parameters of the antenna array and optimize the antenna array according to the phase parameters.

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