Millimeter wave movable array beam training method based on quantum correlated simulated annealing

Abstract

The application discloses a millimeter wave movable array beam training method based on quantum correlation simulated annealing, and relates to the technical field of wireless communication.The application proposes a quantum correlation simulated annealing (QCSA) algorithm aiming at the high-dimensional, non-convex and strongly coupled beam-array position joint optimization problem caused by the movable array, and adopts an alternating optimization framework to decompose the joint optimization problem into iterative solving of the transmitting and receiving subspaces; in each subspace optimization, the physical correlation between parameters is learned through Gaussian sampling based on an adaptive covariance matrix, the global search capability is enhanced by using an acceptance criterion containing a thermodynamic term and a quantum tunneling term to escape from a local optimum, and a periodic oscillation thermal scheduling strategy is adopted to dynamically balance exploration and utilization, so that the application has the characteristics of low overhead, fast convergence and high robustness, and is suitable for 6G millimeter wave and terahertz movable array MIMO systems.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a method for training millimeter-wave movable array beams based on quantum correlation simulated annealing. Background Technology

[0002] With the acceleration of social informatization, we are moving towards an era of the Internet of Everything. The sixth generation (6G) mobile communication system is highly anticipated, with its core vision being to achieve peak data rates at the terabit-per-second (Tbps) level, ultra-low latency at the microsecond (μs) level, and massive device connectivity to support the implementation of cutting-edge applications such as holographic communication, autonomous driving, industrial IoT, and metaverse.

[0003] To realize this ambitious vision, the communication spectrum must expand to higher frequency bands. Millimeter wave (30-300 GHz) and terahertz (0.3-10 THz) bands, with their abundant spectral resources, have become key to overcoming the bandwidth bottleneck of traditional microwave bands. However, high-frequency electromagnetic waves face severe challenges during propagation, including significant path loss and poor diffraction capabilities, making them susceptible to obstruction. To overcome these inherent physical limitations, massive MIMO (Multiple-Input Multiple-Output) technology focuses signal energy into a narrow beam through beam training, generating extremely high directional gain to establish stable and reliable high-frequency communication links.

[0004] In this context, beam training—finding the optimal transmit and receive beam directions to maximize the received signal-to-noise ratio—is a core element in ensuring successful communication. Traditional beam training methods are mainly divided into two categories. The first is sequence search, which typically uses a quasi-omnidirectional beam to broadcast on one side while the other side scans all possible narrow beams. However, its pilot number becomes unbearable in systems with large-scale antenna arrays. The second is hierarchical search, which uses a codebook to start probing from a wide beam and then gradually narrows the beam width for a refined search. Although this reduces the search space, the pilot number remains significant, and the optimal direction may be missed due to initial errors.

[0005] In recent years, to further improve channel quality, a revolutionary technology called "mobile array" has been proposed. Unlike traditional arrays with fixed positions, this technology allows antenna arrays to dynamically adjust their physical location within a predefined area, thereby actively "reshaping" the wireless channel environment and fundamentally improving channel conditions. However, this advantage also brings unprecedented challenges, constituting a high-dimensional "beam-array position joint optimization" problem. This problem has several significant characteristics. First, it is high-dimensional and non-convex, with optimization variables including the array position coordinates and beam direction at both the transmitting and receiving ends, forming a complex 8-dimensional parameter space, whose objective function is filled with numerous local optima. Second, it is strongly coupled, with the physical location of the antenna array and the optimal beam direction being closely related, requiring joint optimization. Finally, it is a black-box problem, as a precise analytical model of channel state information cannot be obtained in actual communication; evaluation can only be performed through pilot measurements.

[0006] Existing optimization strategies either employ decoupled suboptimal methods or traditional global optimization algorithms such as simulated annealing. However, these methods suffer from numerous shortcomings when dealing with such high-dimensional, strongly coupled black-box problems, including inefficiency, susceptibility to local optima, slow convergence, or premature convergence. Therefore, a novel technical solution is urgently needed to efficiently and rapidly address this joint training problem. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a millimeter-wave movable array beam training method based on quantum correlation simulated annealing. This invention introduces a hierarchical optimization algorithm architecture to decouple the high-dimensional joint search space into two low-dimensional subspaces: the transmitter and the receiver, thereby reducing optimization complexity. It employs quantum correlation simulated annealing as the core search engine, which incorporates Gaussian sampling based on adaptive covariance matrices to maintain the correlation between parameters. Simultaneously, a quantum tunneling term is introduced into the probabilistic acceptance criterion to maintain the ability to escape local optima when the temperature drops to a low-temperature state. (The "low-temperature state" described in this invention has a clear quantitative definition at the algorithm execution level, specifically referring to the optimization stage where the temperature value drops below 5. The reason for setting this threshold is that when the temperature is below 5, the thermodynamic term relied upon by the traditional simulated annealing algorithm decays sharply, making the algorithm almost unable to accept any candidate solutions that lead to performance degradation, thus losing its ability to escape local optima. The core advantage of the quantum tunneling term introduced in this invention lies in its ability to provide a continuous and significant non-zero acceptance probability under this low-temperature state, thereby effectively maintaining the algorithm's global search performance.) Furthermore, this invention combines an alternating optimization strategy of oscillating temperature scheduling to balance global exploration and local exploitation, preventing premature convergence. This method can quickly obtain near-optimal beam direction and array center position configuration with extremely low pilot numbers under black-box channel conditions, thereby achieving near-optimal spectral efficiency and excellent engineering practicality.

[0008] A method for training millimeter-wave movable array beams based on quantum correlation simulated annealing includes the following steps: S1: The joint optimization problem of antenna position and beam direction of the transmitter and receiver is decomposed into transmitter terminal space and receiver terminal space. Iterative solution is performed through an alternating optimization strategy. Each complete iteration includes optimizing transmitter parameters with fixed receiver parameters and optimizing receiver parameters with fixed updated transmitter parameters. S2: When optimizing each subspace, the parameters are updated using a quantum correlation simulated annealing algorithm, which includes: S2.1: Generate candidate solutions by Gaussian sampling based on the current optimized solution and the adaptive covariance matrix. The adaptive covariance matrix is ​​used to learn the physical correlation between optimization variables and is iteratively updated according to the acceptance of candidate solutions. S2.2: The quantum tunneling acceptance criterion is used to determine whether to accept the candidate solution. The acceptance criterion includes a thermodynamic term and a quantum tunneling term. When the received signal-to-noise ratio of the candidate solution is lower than that of the current optimized solution, the acceptance probability is determined by the thermodynamic term and the quantum tunneling term together based on the current temperature and energy difference. The quantum tunneling term provides a non-zero acceptance probability at low temperature to allow the algorithm to escape local optima. S2.3: A periodic oscillation thermal scheduling strategy is adopted to control the evolution of temperature. The strategy superimposes periodic oscillations on a monotonically decaying trend to balance the global exploration and local development capabilities of the dynamic balancing algorithm.

[0009] Furthermore, the alternating optimization strategy specifically includes: In the k-th iteration, the array center position and receiving beam direction of the receiver are fixed, and the parameters of the transmitter terminal space are optimized by the quantum correlation simulated annealing algorithm with the receiving signal-to-noise ratio as the objective function. With the optimized parameters of the transmitter fixed, and the received signal-to-noise ratio as the objective function, the parameters of the receiver terminal space are optimized using the quantum correlation simulated annealing algorithm. Determine the convergence condition; if convergence is not achieved, proceed to the (k+1)th iteration.

[0010] Furthermore, the Gaussian sampling based on the adaptive covariance matrix includes: Based on the current optimal solution and the current adaptive covariance matrix, a perturbation vector is generated by sampling through a multivariate Gaussian distribution, and the perturbation vector is applied to the current optimal solution to generate candidate solutions; When the candidate solution is accepted, the adaptive covariance matrix is ​​updated according to the perturbation vector, so that subsequent sampling processes learn and utilize the correlation of the historical update direction of the optimized solution.

[0011] Furthermore, the acceptance probability of the quantum tunneling acceptance criterion is the smaller of the sum of the thermodynamic term and the quantum tunneling term and 1. When the reception signal-to-noise ratio of the candidate solution is lower than that of the current optimized solution, the thermodynamic term and the quantum tunneling term decrease as the temperature decreases, wherein the thermodynamic term is exponentially related to the temperature, and the quantum tunneling term is exponentially related to the square root of the temperature.

[0012] Furthermore, the periodic oscillation thermal scheduling strategy sets the temperature as the product of a reference temperature that decays exponentially with the number of iterations and a periodic oscillation factor, wherein the periodic oscillation factor oscillates within a preset amplitude range with a fixed period.

[0013] Furthermore, the physical location of the antenna array is dynamically adjustable within a preset area.

[0014] Furthermore, the beam direction and the array center position together determine the transmit and receive beamforming vectors. The array center position and beam direction are variables to be optimized, and the optimization problem aims to maximize the receive signal-to-noise ratio.

[0015] Furthermore, the adaptive covariance matrix is ​​updated using an exponential moving average method, and the adaptive learning rate of the exponential moving average is used to balance the influence weights of the historical adaptive covariance matrix and the current perturbation vector.

[0016] Furthermore, in the quantum tunneling acceptance criterion, when the received signal-to-noise ratio of a candidate solution is higher than that of the current optimized solution, the candidate solution is determined to be accepted; when the received signal-to-noise ratio of a candidate solution is lower than that of the current optimized solution, the decision on whether to accept the candidate solution is made randomly based on the probability calculated from the thermodynamic term and the quantum tunneling term.

[0017] Furthermore, the movable array beam training method is applied to millimeter-wave or terahertz communication systems employing movable arrays.

[0018] The beneficial effects of this invention are as follows: The technical solution proposed in this invention has achieved significant and practical benefits in terms of performance. The most prominent effect is the substantial reduction in the number of pilots required for training and the achievement of ultra-fast convergence speed. Simulation results show that the QCSA algorithm of this invention only requires approximately 160 pilots to converge, which is only 7.29% of the high-complexity baseline method (ACD-ES) and 64.51% of the traditional simulated annealing (SA). This is of great significance for reducing communication latency and improving system response speed.

[0019] Secondly, despite the extremely low number of pilots, this invention does not compromise on performance, but rather achieves near-optimal spectral efficiency. At convergence, QCSA achieves 93.52% of the spectral efficiency achievable by the benchmark method, while its performance far exceeds that of the traditional SA method by 73.27%, achieving an unprecedentedly excellent trade-off between pilot number and system performance.

[0020] Furthermore, this invention demonstrates excellent robustness and environmental adaptability. Under varying system conditions, such as different array mobility ranges and channel multipath richness, QCSA can consistently converge to a high-quality optimized solution and effectively utilize the spatial freedom provided by the movable array. Compared to a fixed array, it achieves a performance gain of over 19%, proving its practical application value and reliability in complex and ever-changing wireless communication environments. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the movable array millimeter-wave MIMO system structure involved in this invention. Figure 2 This is a comparison chart of the relationship between the spectral efficiency and the number of pilots for different algorithms. Figure 3 This is a comparison chart showing the relationship between the spectral efficiency of different algorithms and the size of the array's movable range. Figure 4 This is a comparison chart of the relationship between the spectral efficiency of different algorithms and the number of channel multipaths. Detailed Implementation

[0022] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings: This invention proposes a millimeter-wave movable array beam training method based on quantum correlation simulated annealing, the core innovation of which is reflected in three mutually synergistic levels.

[0023] First, regarding the acceptance criteria of the algorithm, this invention breaks through the limitation of traditional simulated annealing relying solely on thermodynamic terms and creatively introduces the quantum tunneling acceptance criterion.

[0024] The quantum tunneling acceptance criterion allows the algorithm to accept a poor optimization solution with a non-zero probability even at low temperatures, thus "tunneling" through the energy barrier. This greatly enhances the algorithm's global search capability and effectively overcomes the local optimum trap commonly found in high-dimensional non-convex optimization problems. Secondly, regarding the candidate solution generation mechanism, this invention abandons the traditional random perturbation method and designs a Gaussian sampling method based on an adaptive covariance matrix. This method learns and utilizes the inherent physical correlation between parameters such as position coordinates and beam angles through a dynamically updated adaptive covariance matrix, making the search process more guided and intelligent, thereby significantly improving the exploration efficiency in high-dimensional spaces. Finally, regarding the algorithm's annealing strategy, this invention designs a periodic oscillating thermal scheduling mechanism.

[0025] The periodic oscillating thermal scheduling mechanism introduces a periodic "reheating" process within the overall exponential cooling trend, dynamically balancing the exploration and utilization of the algorithm and effectively preventing the loss of the globally optimal solution due to premature convergence. The organic combination of these three innovations constitutes a complete and efficient technical solution specifically designed to solve high-dimensional, strongly coupled, black-box joint optimization problems.

[0026] To achieve the above objectives, this invention proposes a Quantum-Correlated Simulated Annealing (QCSA) algorithm, based on... Figure 1 As shown, its core technical solution includes the following aspects: System Model and Problem Formalization The system considered in this invention has a millimeter-wave channel that follows the geometric Saleh-Valenzuela (SV) model. The channel matrix H is not only a function of the beam angle, but also represents the center position of the transmitter (TX) and receiver (RX) antenna arrays. and The function (where the superscript) This represents the transpose operation of a vector or matrix (the same applies below). and These represent the center positions of the uniform planar array (UPA) at the transmitter, respectively. Figure 1 In the two-dimensional movable region coordinate system shown shaft and The coordinate values ​​of the axis. This represents the set of all permissible center locations of the uniform planar array at the transmitting end. Similarly, and These represent the center positions of the uniform planar array at the receiving end, respectively, as shown in the figure. Figure 1 In the two-dimensional movable region coordinate system shown shaft and The coordinate values ​​of the axis. This represents the set of all allowed center positions of the uniform planar array at the receiving end.

[0027] The absolute positions of each antenna element in the transmit and receive arrays are as follows: From the center position of their respective arrays and fixed relative offset The position of the (i, j)th element of the transmission array is determined jointly. in It is a two-dimensional column vector representing the position of the (i, j)th antenna element of the transmit array relative to its array center. The fixed relative offsets, i and j, represent the row index and column index of the antenna element in the transmitter array, respectively. The center position of the transmitting array The coordinate values ​​on the x-axis and z-axis, and These respectively indicate that the array element is in shaft and Offset component along the axis. Similarly, for a receiving array, the absolute position of its (m, n)th element is given by the following formula: in Similarly, it is a two-dimensional column vector representing the position of the (m, n)th antenna element of the receiving array relative to its array center. The fixed relative offset, where m and n represent the row index and column index of the antenna element in the receiver array, respectively. The center position of the receiving array is respectively The coordinate values ​​on the x-axis and z-axis, These respectively indicate that the array element is in shaft and Offset component in the axial direction.

[0028] Relative position offset matrix of the transmitting array It is given by the following formula: in, These represent the number of antennas at the transmitting end in the horizontal and vertical directions, respectively. For each element in the relative position offset matrix of the transmitter array, represents the fixed relative offset of the (i, j)th antenna element at the transmitter. Similarly, the relative position offset matrix of the receiver array... It is given by the following formula: in These represent the number of antennas at the receiver in the horizontal and vertical directions, respectively; furthermore, the elements in the relative position offset matrix of the receiver array are... , which represents the fixed relative offset of the (m, n)th antenna element at the receiver.

[0029] The overall displacement of the transmitting and receiving uniform planar arrays is determined by adjusting the center positions of the arrays separately. and To achieve this.

[0030] The channel matrix can be represented as the superposition of L multipath components, as shown in the following equation: in, and These represent the number of antennas for the transmitting array and the receiving array, respectively. as well as These represent the number of antennas in the horizontal and vertical directions of the transmitting and receiving arrays, respectively. L is the number of multipath antennas. Let be the complex gain of the l-th path, which follows a function with mean 0 and variance . The complex Gaussian distribution. The direction of the transmitted beam is represented by the departure angle vector of the l-th path at the transmitter, which includes the azimuth angle. With pitch angle Similarly, The direction of the received beam is represented by the angle of arrival vector of the l-th path at the receiver, which includes the azimuth angle. With pitch angle . These belong to predefined beam sets at the transmitting and receiving ends, respectively. in These are the beam sets for the transmitting and receiving ends, respectively. and These are the transceiver steering vectors that depend on the center position of the uniform planar array at the transceiver end and the beam direction, respectively.

[0031] Transmitter steering vector Its expression is: in It is a direction vector. This refers to the number of transmitting array antennas. These represent the number of antennas in the horizontal and vertical directions of the transmitting array, respectively. For wavelength, For the direction of the transmitted beam, These represent the azimuth and elevation angles along the l-th path from the transmitter, respectively. The center position of the transmitter array. Let be the absolute position of the (i,j)th transmitting antenna element in the xz plane. The imaginary unit (i.e.) (The same applies below). Receiver steering vector The definition is similar, and its expression is: in It is a direction vector. The number of receiving array antennas, These represent the number of antennas in the horizontal and vertical directions of the receiver array, respectively. For wavelength, To receive the beam direction, These represent the azimuth and elevation angles on the l-th path at the receiving end, respectively. The center position of the receiver array. Let be the absolute position of the (m,n)th receiving antenna element in the xz plane.

[0032] The ultimate goal of optimization is to jointly find the optimal TX / RX array center location under black-box channel conditions. } and optimal TX / RX beam direction { The goal is to maximize the received signal-to-noise ratio (SNR). This optimization problem can be formalized as solving the following objective function: in, It is the set of all optimization variables. and These are the transmit beamforming vector and the receive beamforming vector, respectively (where the superscript is...) This represents the conjugate transpose operation of a vector or matrix (hereinafter the same), where Corresponding to the transmit steering vector that maximizes the receive signal-to-noise ratio , Corresponding to the corresponding receiving guide vector This is a high-dimensional non-convex optimization problem with multiple constraints.

[0033] Alternating optimization framework based on parameter space decomposition To reduce the complexity of the 8-dimensional joint optimization problem, this invention decomposes the parameter space into two related subspaces: the transmitter terminal space contains four transmitter terminal parameters, namely... , , , They are used to indicate the center position of the movable array of the transmitter. and the direction of the transmitted beam Similarly, the parameters contained in the receiver terminal space are receiver parameters, also four in total, namely... , , , They are used to indicate the array center position of the movable array at the receiving end. and the direction of the receiving beam Based on this parameter space decomposition, the original joint optimization problem is decoupled into two subproblems that can be solved alternately in the transmit terminal space and the receive terminal space. The subproblem in the transmit terminal space can be formally represented as: in, This represents the optimized solution at the transmitter end, which uniformly encapsulates the four parameters to be optimized in the transmitter terminal space. These are the x-axis and z-axis coordinates of the center position of the transmitter UPA, and their values ​​are included in the set of center positions of the transmitter array. In addition, such as Figure 1 As shown, the transmitter establishes a right-handed Cartesian coordinate system with the center of its movable area as the origin. Therefore, the azimuth angle of the transmitter beam direction is... The range of values ​​is Pitch angle The range of values ​​is Similarly, The corresponding optimized solution for the receiving end. These are the x-axis and z-axis coordinates of the center position of the receiver UPA, and their values ​​are contained within the set of receiver array center positions. In addition, such as Figure 1 As shown, the receiver also establishes a right-handed Cartesian coordinate system with the center of its movable area as the origin. Therefore, the azimuth angle of the receiver beam direction is... The range of values ​​is Pitch angle The range of values ​​is . Based on optimization solutions Constructed transmit and receive beamforming vectors. For array center location The channel matrix. The mathematical expression for the system's received signal-to-noise ratio, calculated under given optimal solutions at the transmitter and receiver, is as follows: ,in For transmission power, This represents noise power. Because when formalizing the subproblem, and Since it is a constant and does not affect the optimization process, it is used in the objective function. The term is omitted. Subsequently, an iterative strategy of alternating optimization is employed. In the k-th iteration, the optimization process follows the alternating steps of the following formula: in This represents the optimized solution after the (k-1)th iteration at the receiving end. Let represent the optimized solutions for the transmitter and receiver obtained in the k-th iteration, respectively. In the k-th iteration, the optimized solution for the transmitter is first optimized, while the receiver parameters are fixed to the results from the previous iteration. And in the candidate solutions at the transmitting end In the value space of , search for what makes the objective function The optimal solution that reaches the maximum value is established as the optimal solution for the transmitter in this round. Subsequently, in the immediate receiver optimization, the algorithm fixed the transmitter parameters to the newly updated values. And candidate solutions at the receiving end A similar maximization search is performed in the value space of to determine the optimal solution for the receiver in this round. This strategy iteratively decomposes a high-dimensional problem into two more manageable 4-dimensional subproblems and ensures convergence toward a joint optimal solution.

[0034] Core design of the quantum correlated simulated annealing (QCSA) algorithm For each of the above four-dimensional subproblems, this invention proposes the QCSA algorithm for solving them, which includes three core innovations: 1. To efficiently explore the parameter space, this invention employs multivariate Gaussian distribution sampling to generate perturbation vectors. This method utilizes adaptive covariance matrix-based Gaussian sampling. This leads to the generation of candidate solutions. Furthermore, this invention utilizes a dynamically updated adaptive covariance matrix to guide the sampling process, enabling it to learn and leverage the physical correlations between the parameter components of the optimized solution, thereby achieving guided random search. This method specifically includes the following two key steps: Step 1, candidate solution generation: based on the current optimal solution and the current adaptive covariance matrix Perturbation vectors are generated by sampling using a multivariate Gaussian distribution. This perturbation vector is then applied to the current optimization solution. This generates candidate solutions. The process is shown in the following formula: in, In order to find the current optimal solution Based on the candidate solutions generated, This indicates that the disturbance vector follows a vector with zero mean and a covariance matrix of... The multivariate Gaussian distribution. Let represent the adaptive covariance matrix at the k-th round of optimization.

[0035] The second step is the adaptive covariance matrix update: the key here is that the adaptive covariance matrix is ​​dynamic and explicitly maintains the correlation between parameters. "Dynamic" specifically means that the matrix update does not necessarily occur in every iteration, but is conditional: the matrix is ​​only updated based on an exponential moving average when a generated candidate solution is accepted by the quantum tunneling acceptance criterion; if a candidate solution is rejected, the matrix remains unchanged. Optimization solution at the transmitter For example, the corresponding adaptive covariance matrix structure of the transmitter is shown in the following equation: in, For the first The adaptive covariance matrix of the transmitter in the next iteration, its diagonal elements These represent the variances of the transmitter's horizontal position, vertical position, azimuth angle, and elevation angle parameters, respectively; off-diagonal elements. This characterizes the covariance between these parameters pairwise, which is used to maintain the physical correlation between position and beam pointing during iterative sampling.

[0036] Similarly, with the optimized solution at the receiving end The corresponding adaptive covariance matrix structure of the receiver is shown in the following equation: in, Let be the adaptive covariance matrix of the receiver in the k-th iteration, and its diagonal elements These represent the variances of the receiver's horizontal position, vertical position, azimuth angle, and elevation angle parameters, respectively; off-diagonal elements. This represents the covariance between these parameters pairwise, used to maintain the physical correlation between position and beam pointing during iterative sampling. In the algorithm, the transmitter and receiver each maintain their own covariance matrix. Therefore, in the k-th iteration optimization, the adaptive covariance matrix... In optimizing the transmitter terminal space, it refers to the transmitter's adaptive covariance matrix. In optimizing the receiver terminal space, it refers to the receiver's adaptive covariance matrix. Both have identical structures, except that the matrix elements are determined by the parameters of their respective subspaces (transmitter parameters: Receiver parameters: The variance and covariance constitute the variance and covariance of the equation.

[0037] Whenever a better candidate solution is accepted, the adaptive covariance matrix is ​​updated using an exponential moving average, as shown in the following equation: in, Indicates the first The adaptive covariance matrix used in each iteration is derived from the adaptive covariance matrix of the previous iteration. With the perturbation vector generated in the current iteration outer product The weighted fusion is obtained. Represents a vector The transpose operation. Coefficients This is called the adaptive learning rate, which ranges from 0 to 1 in an open interval. It controls the weight balance between the information of the historical adaptive covariance matrix and the current perturbation vector during the update process, thereby achieving dynamic learning and adjustment of the adaptive covariance matrix. This mechanism of continuously adjusting the matrix's parameters (variance and covariance) based on historical information from accepted solutions (carried by the perturbation vector generated by sampling the current adaptive covariance matrix through a multivariate Gaussian distribution) is the core manifestation of its "adaptive" characteristic. This mechanism allows the sampling process to "learn" the inherent structure of the optimization problem, thus achieving a more targeted and efficient search.

[0038] 2. Quantum Tunneling Acceptance Criterion: To enhance the global search capability of the algorithm and effectively escape local optima, this invention introduces an acceptance criterion inspired by the quantum tunneling effect. In the mathematical model of this criterion, the system's performance index (received signal-to-noise ratio) is considered. This is analogous to "energy" in quantum mechanics. When a candidate solution leads to a performance degradation (i.e., an energy difference)... When ), its acceptance probability Determined by the following formula: The formula consists of two parts: the first term The first term is the thermodynamic term of traditional simulated annealing, which allows the algorithm to escape local optima at high temperatures; the second term... This is the quantum tunneling term, where η controls the tunneling depth. This term enables the algorithm to operate even at low temperatures (i.e., temperatures as low as 100°C). Even when the energy barrier is "tunneled" through, there is still a non-zero probability of accepting a poor optimization solution, thus significantly enhancing the global exploration capability.

[0039] 3. Periodic Oscillatory Thermal Scheduling: To achieve a dynamic balance between exploration and exploitation, this invention designs a composite, periodic oscillatory temperature scheduling strategy. In the k-th iteration, the temperature... It is given by the following formula: The temperature curve consists of two parts: one is composed of... The controlled exponential decay term, where The initial temperature. One term is the temperature decay coefficient, ensuring the overall decreasing trend of temperature and guiding the algorithm from global exploration to local refinement; the other is a periodic oscillation term consisting of 1 + ζ·cos(...), which has a thermal oscillation period. The oscillation amplitude ζ introduces a periodic "reheating" process on the decay curve. This mechanism can "reactivate" the algorithm's exploration capability, effectively preventing it from falling into local optima due to excessive cooling, thereby avoiding premature convergence.

[0040] Figure 2 This is a comparison chart of the relationship between the spectral efficiency and the number of pilots for different algorithms. Figure 3 This is a comparison chart showing the relationship between the spectral efficiency of different algorithms and the size of the array's movable range. Figure 4 This is a comparison chart of the relationship between the spectral efficiency of different algorithms and the number of channel multipaths.

[0041] The technical solution of the present invention will be described in detail below with reference to specific embodiments. This embodiment simulates a millimeter-wave communication system operating in the 35GHz frequency band, whose transmitter (TX) is configured with a The UPA receiver (RX) is configured with one The UPA has an antenna spacing of half a wavelength. The channel follows a geometric Saleh-Valenzuela (SV) model, with a total number of multipath components L = 5 and a reference transmit signal-to-noise ratio (SNR) of 0 dB. The transmit and receive beamcodebooks are generated based on a discretized angle space, with sizes of [missing information]. This corresponds to the discretized beam direction. The center position of the transmitting and receiving arrays can move freely within a preset two-dimensional square region, which is discretized in its respective dimension. The possible locations are discrete values ​​ranging from 0 to 50 half-wavelengths for the half-side length of the movable region. The goal of the algorithm is to find an optimal set of system parameters to maximize the received signal-to-noise ratio. The key parameter settings used in the proposed QCSA algorithm in this embodiment are as follows: initial temperature... Temperature decay coefficient oscillation amplitude thermal oscillation period Quantum tunneling coefficient Adaptive learning rate Maximum number of iterations Convergence threshold .

[0042] The execution of the algorithm begins with the initialization step. In this stage, the system randomly selects the initial array center position and beam direction of TX and RX, and sets the key parameters of the QCSA algorithm, such as initial temperature, attenuation coefficient, oscillation parameter, quantum tunneling coefficient and adaptive learning rate. At the same time, the adaptive covariance matrix is ​​initialized as a diagonal matrix, and the maximum number of iterations and convergence threshold are set.

[0043] In the subsequent iterative optimization process, taking the t-th iteration as an example, the algorithm first focuses on optimizing the TX subspace. Based on the current TX parameters and adaptive covariance matrix, a candidate solution is generated through Gaussian sampling, which is made more "intelligent" by the presence of the adaptive covariance matrix. The system uses this candidate solution to perform a channel measurement to evaluate its generated SNR. Next, based on the temperature and SNR changes calculated by the current periodic oscillation strategy, the quantum tunneling acceptance criterion is used to calculate the acceptance probability and make a decision. If the candidate solution is accepted, the TX parameters and adaptive covariance matrix are updated; otherwise, the parameters remain unchanged. After completing the optimization of the TX subspace, the algorithm fixes the just-updated TX parameters and performs the exact same QCSA procedure on the RX subspace to obtain the updated RX parameters. At the end of each iteration, the algorithm checks convergence by comparing the total SNR change between two iterations with a preset threshold. If convergence has not occurred and the maximum number of iterations has not been reached, the next iteration begins; otherwise, the algorithm terminates.

[0044] The results analysis intuitively demonstrates the beneficial effects of this invention. In terms of convergence, compared to traditional simulated annealing and high-complexity benchmark methods, QCSA can rapidly converge to a near-saturation high-performance level with a very small number of pilots, showcasing its significant advantage in training overhead. Regarding the impact on the movable range, QCSA's performance closely follows the near-optimal benchmark method and remains stable across different movable ranges, proving its effective utilization of the gain gained from antenna movement. In terms of adaptability to multipath environments, QCSA exhibits strong multipath diversity utilization capabilities, with particularly superior performance in complex scattering environments. Through the above specific implementation methods and results analysis, it is clear that the QCSA method proposed in this invention achieves unprecedented comprehensive performance in solving the beam-array position joint training problem of movable millimeter-wave MIMO systems, possessing the characteristics of low overhead, high performance, and strong robustness, and has extremely high theoretical research value and practical application prospects.

[0045] The embodiments and descriptions above are merely illustrative of the principles and preferred embodiments of the present invention. Various changes and modifications may be made to the present invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed.

Claims

1. A millimeter-wave movable array beam training method based on quantum correlation simulated annealing, characterized in that, Includes the following steps: S1: The joint optimization problem of antenna position and beam direction of the transmitter and receiver is decomposed into transmitter terminal space and receiver terminal space. Iterative solution is performed through an alternating optimization strategy. Each complete iteration includes optimizing transmitter parameters with fixed receiver parameters and optimizing receiver parameters with fixed updated transmitter parameters. S2: When optimizing each subspace, the parameters are updated using a quantum correlation simulated annealing algorithm, which includes: S2.1: Generate candidate solutions by Gaussian sampling based on the current optimized solution and the adaptive covariance matrix. The adaptive covariance matrix is ​​used to learn the physical correlation between the array center position and the beam direction in the currently optimized subspace and is iteratively updated according to the acceptance of candidate solutions. S2.2: The quantum tunneling acceptance criterion is used to determine whether to accept the candidate solution. The acceptance criterion includes a thermodynamic term and a quantum tunneling term. When the received signal-to-noise ratio of the candidate solution is worse than that of the current optimized solution, the acceptance probability is determined by the thermodynamic term and the quantum tunneling term together based on the current temperature and the difference in received signal-to-noise ratio. The quantum tunneling term provides a non-zero acceptance probability when the temperature drops below 5 to allow the algorithm to escape local optima. S2.3: A periodic oscillation thermal scheduling strategy is adopted to control the evolution of temperature. The strategy superimposes periodic oscillations on a monotonically decaying trend to balance the global exploration and local development capabilities of the dynamic balancing algorithm.

2. The movable array beam training method according to claim 1, characterized in that, The alternating optimization strategy specifically includes: In the k-th iteration, the array center position and receiving beam direction of the receiver are fixed, and the parameters of the transmitter terminal space are optimized by the quantum correlation simulated annealing algorithm with the receiving signal-to-noise ratio as the objective function. With the optimized parameters of the transmitter fixed, and the received signal-to-noise ratio as the objective function, the parameters of the receiver terminal space are optimized using the quantum correlation simulated annealing algorithm. Determine the convergence condition; if convergence is not achieved, proceed to the (k+1)th iteration.

3. The movable array beam training method according to claim 1, characterized in that, The Gaussian sampling for generating candidate solutions based on the current optimized solution and the adaptive covariance matrix specifically includes: Candidate solution generation: Based on the current optimal solution and the current adaptive covariance matrix, a perturbation vector is generated by sampling through a multivariate Gaussian distribution, and the perturbation vector is applied to the current optimal solution to generate candidate solutions; Adaptive covariance matrix update: When the candidate solution is accepted, the adaptive covariance matrix is ​​updated according to the perturbation vector of the current sampling, so that the covariance matrix can learn and utilize the correlation of the historical update direction of the optimized solution, thereby guiding the subsequent sampling direction.

4. The movable array beam training method according to claim 1, characterized in that, The acceptance probability of the quantum tunneling acceptance criterion is the smaller of the sum of the thermodynamic term and the quantum tunneling term and 1. When the signal-to-noise ratio of the candidate solution is lower than that of the current optimized solution, the thermodynamic term and the quantum tunneling term decrease as the temperature decreases. The thermodynamic term is exponentially related to the temperature, and the quantum tunneling term is exponentially related to the square root of the temperature.

5. The movable array beam training method according to claim 1, characterized in that, The periodic oscillation thermal scheduling strategy sets the temperature as the product of a reference temperature that decays exponentially with the number of iterations and a periodic oscillation factor, which oscillates within a preset amplitude range with a fixed period.

6. The movable array beam training method according to claim 1, characterized in that, The positions of the antenna arrays at the transmitting and receiving ends are dynamically adjustable within a preset area.

7. The movable array beam training method according to claim 1, characterized in that, The beam direction and the array center position together determine the transmit and receive beamforming vectors. The array center position and beam direction are variables to be optimized. The optimization problem aims to maximize the receive signal-to-noise ratio.

8. The movable array beam training method according to claim 1, characterized in that, The adaptive covariance matrix is ​​updated using an exponential moving average method, and the adaptive learning rate of the exponential moving average is used to balance the influence weights of the historical adaptive covariance matrix and the current perturbation vector.

9. The movable array beam training method according to claim 1, characterized in that, In the quantum tunneling acceptance criterion, when the received signal-to-noise ratio of a candidate solution is better than that of the current optimized solution, the candidate solution is accepted; when the received signal-to-noise ratio of a candidate solution is lower than that of the current optimized solution, the decision on whether to accept the candidate solution is made randomly based on the probability calculated from the thermodynamic term and the quantum tunneling term.

10. The movable array beam training method according to any one of claims 1 to 9, characterized in that, The movable array beam training method is applied to millimeter-wave or terahertz communication systems employing movable arrays.

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