Distributed RIS fast beam forming method based on quantum annealing

Abstract

The invention discloses a distributed RIS fast beam forming method based on quantum annealing. Comprising three parts: phase quantization of discrete units, quantization mapping of variables and quantum annealing solution. The distributed RIS-assisted communication system comprises at least two RISs which are deployed at proper positions to assist guiding of communication signals. The phase quantization of the RIS reflection unit is used for constructing discrete variables, so that the corresponding variables can conform to the topological structure of the quantum computer and are mapped to quantum bits. The quantization mapping of the variables is based on a series of operations of fractional programming and matrix transformation, and an original optimization problem is mapped to an unconstrained Hamiltonian, so that the quantization mapping can be deployed on a quantum computer for annealing solution. And evolving a target function formed by the superposition state of the quantum states of the combination of all possible solutions according to a Schrodinger equation to find a global optimal solution.

Description

Technical Field

[0001] The invention relates to the field of beamforming, and comprises a distributed RIS fast beamforming method based on quantum annealing. Background Art

[0002] 6G communication networks are expected to provide a 10-fold increase in throughput, and are therefore receiving increasing attention. The core technology of RIS-assisted millimeter wave communication has a wide range of application scenarios, and has therefore received significant attention from the global industry.

[0003] As a promising enabling technology, smart metasurfaces have gained wide interest in the academic community due to their ability to intelligently program the electromagnetic environment to improve the data transmission rate of wireless networks. Currently, most existing studies are devoted to the ideal scenario, where the wireless communication system is assisted by only one RIS. In fact, distributed RIS-assisted communication systems are more practical and common. However, most previous algorithms designed for single-user systems are usually not applicable to distributed communication networks. The main reason is that these methods are usually based on approximate optimization techniques. These algorithms are feasible for the case of a single RIS, but not for the case of multiple RIS because they usually have very high computational complexity. Therefore, we need to develop a low-complexity optimization algorithm to solve this multivariable non-convex problem.

[0004] Existing methods at this stage include approximate methods based on optimization algorithms and machine methods based on data, but both have some unsatisfactory limitations. Let's take a look at the optimization method first. Specifically, the maximum minimization (MM) method simplifies the calculation by optimizing the upper bound of the objective function. However, there is a major challenge in constructing a feasible upper bound function for multiple variables. Under the constant modulus constraint of RIS, the manifold optimization (MO) method can be used to perform gradient descent on the Riemann manifold, which leads to high computational complexity. The block coordinate descent (BCD)-based method decomposes the original problem into many sub-problems, called blocks, and searches for the minimum along the coordinates respectively. In addition, traditional optimization methods such as the alternating direction multiplier method (ADMM) or the penalized convex-concave process (CCP) are further adopted to optimize the problem in an iterative manner by introducing auxiliary variables. Nevertheless, these methods usually involve matrix inversion or calculation of non-polynomial forms of variables, making them unsuitable for high-dimensional communication systems.

[0005] In contrast, data-driven machine learning methods have also been used to solve this problem. For example, previous methods have used deep reinforcement learning techniques to fully utilize trial-and-error interactions with the environment and gradually improve their behavior. In addition, passive beamforming methods based on unsupervised learning can reduce computational complexity and achieve real-time prediction during online deployment. However, learning-based methods usually take a lot of time in the training process, and due to lack of robustness, they are sensitive to environmental changes and may experience significant performance degradation in specific experiments due to reasons such as overfitting. Therefore, there is an urgent need to develop a low-complexity algorithm with high performance to solve the problem accurately and quickly.

[0006] On the other hand, the classical Ising model is usually solved using various computer simulation techniques, such as Monte Carlo simulation, simulated annealing, parallel annealing, and population annealing. These algorithms are effective in finding local optimal solutions or even global optimal solutions, which correspond to the second-lowest or lowest energy state of the system, but they may not always be the most efficient, especially when there are high potential barriers. Therefore, researchers began to seek the help of quantum computing and disclosed this new method based on quantum annealing to solve the Ising model. This method uses the principles of quantum mechanics and the adiabatic theorem to find the ground state of the Ising model more efficiently than classical algorithms. The quantum annealing solver runs on a cloud platform and has been shown to achieve a higher global optimal hit rate compared to classical simulation. By leveraging the power of quantum annealing, researchers and engineers can speed up the process of finding the optimal phase configuration of RIS and other complex systems modeled by the Ising Hamiltonian. This quantum method provides a promising path for the development of computational materials science and interdisciplinary optimization problems. In summary, while classical simulation techniques have been the mainstay of solving the Ising model, the emergence of quantum annealing provides a powerful and potentially transformative approach to solving complex optimization problems. As quantum computing technology continues to develop, it is expected to play an increasingly important role in scientific research and industrial applications of wireless communications. Summary of the invention

[0007] The present invention aims to address the deficiencies of the prior art and propose a distributed RIS fast beamforming method based on quantum annealing.

[0008] The object of the present invention is achieved through the following technical solution: a distributed RIS fast beamforming method based on quantum annealing, the method comprising the following steps:

[0009] S1, initialize the number of iterations, channel and beamforming parameters;

[0010] S2. Update the beamforming matrix at the base station;

[0011] S3. Perform iterative quantum annealing on each RIS to solve passive beamforming, including:

[0012] S3.1, performing phase quantization on the phase shift matrix;

[0013] S3.2. According to the closed-form solution of fractional programming, the constant modulus constraint of the RIS unit in the beamforming optimization problem is converted into an unconstrained beamforming problem, and the parameters are updated;

[0014] S3.3, calculating the optimization function in the form of the Ising model according to the updated parameters, specifically calculating the weighted sum rate after fractional programming;

[0015] S3.4, converting the optimization function in the form of the Ising model into a quantum binary quadratic model, solving it using a solver to obtain all discrete phase variables, and restoring the discrete phase variables to a phase shift matrix;

[0016] S4, repeat steps S2 and S3 to iterate until the growth rate of the weighted sum rate is lower than the set threshold or reaches the maximum number of iterations, and obtain the final optimized beamforming matrix, the optimized phase shift matrix and the optimal sum rate after optimization.

[0017] Furthermore, the parameters of the initialization iteration number, channel and beamforming specifically include: initialization convergence accuracy ∈, auxiliary variable MMSE filter U k , MSE weight matrix W k , dimension reduction precoding matrix X k , the beamforming matrix V of the base station k , the phase shift matrix Φ of each RIS r and the number of iterations iter, input base station BS to RIS r and RIS r To user user k The channel matrix G r 、h rk , and calculate the cascade channel matrix Set the maximum number of iterations iter max .

[0018] Further, the updating of the beamforming matrix at the base station specifically includes:

[0019] For each user k, update the auxiliary variable MMSE filter U k , MSE weight matrix W k and the dimension-reduced precoding matrix X k , the equation is:

[0020]

[0021]

[0022]

[0023] Calculate the scaling factor in is satisfied X k The stable point, and follow To update V k ;

[0024] Among them, K is the total number of service users, I is the unit matrix, and are the Gaussian white noise to which the signal of user k is subjected during transmission in the channel, and P max is the maximum total transmit power.

[0025] Furthermore, the phase quantization of the phase shift matrix is ​​specifically as follows: the complex reflection coefficient of each RIS reflection unit is as follows:

[0026]

[0027] If the phase is quantized by 2 bits, then θ m ∈{0,π / 2,π,3π / 2}, if 1-bit quantization is used, the phase is θ m ∈{0,π}; change the Φ in the phase shift matrix r,m Using Γ m To replace the expression, and are introduced intermediate variables, satisfying and and denote the real and imaginary parts of the variable respectively, and m∈{1,2,...,M} denotes the mth reflection unit of RIS.

[0028] Furthermore, in the phase quantization of the phase shift matrix, if the phase of each reflection unit needs to be quantized using more than 2 bits, a one-hot encoding strategy is used to map them to 2 on the quantum computer. n On quantum bits, we get

[0029]

[0030] The Φ in the phase shift matrix r,m Using Γ m The expression is replaced by m,i Represents the i-th quantization bit level of the m-th reflection unit of RIS.

[0031] Furthermore, the parameter update in S3.2 is specifically as follows: solving the following optimization problem according to the closed-form solution of fractional programming:

[0032]

[0033] Among them, w k is the user weight vector, and is the optimal value of the auxiliary parameter introduced in the fractional programming expression, the receiving end signal A k =H k V k The sum of the received signal, interference and noise energy is the intermediate variable defined, where the cascade channel Contains the phase shift matrix, V k is the BS beamforming matrix;

[0034] according to renew

[0035] according to renew

[0036] According to A k =H k V k Update A k ,

[0037] according to

[0038]

[0039]

[0040] Update B k ,in is the intermediate auxiliary variable introduced, H Σ(m,n) is a matrix The (m,n)th element of k represents the signal-to-interference-noise ratio of user k, where is the channel matrix deformation representation, and denote the real and imaginary parts of the variable, respectively. and It represents the m%M-th quantization level of the real and imaginary parts of the m / M-th reflection unit of RIS, and / and % represent integer division and remainder operations.

[0041] Furthermore, the optimization function of the Ising model is specifically: w k is the user weight vector, represents taking the real part of the variable, and It is the optimal value of the auxiliary parameter introduced in the fractional programming expression.

[0042] Furthermore, the conversion of the optimization function in the form of the Ising model into the quantum binary quadratic model is specifically as follows:

[0043] To B k After transformation, a simpler solution is obtained:

[0044]

[0045] in

[0046] R θ r Perform vectorization combination and obtain θ=[θ1,θ2,...,θ R ]; R h rj Perform vectorization combination to obtain The expression is adjusted to:

[0047]

[0048] in

[0049]

[0050] The obtained A k and B k The expression of is introduced into the original optimization problem to obtain the converted quantum binary quadratic model, where H Σ(m,n) is a matrix The (m,n)th element of and It means taking its real and imaginary parts; and It represents the m%Mth quantization level of the real and imaginary parts of the m / Mth reflection unit of RIS, and so on for other variables, where / and % represent integer division and remainder operations.

[0051] On the other hand, the specification provides a distributed RIS fast beamforming device based on quantum annealing, including a memory, a storage, a communication transceiver and one or more processors, wherein the memory stores executable code, and when the processor executes the executable code, the distributed RIS fast beamforming method based on quantum annealing is implemented.

[0052] On the other hand, the specification provides a computer-readable storage medium having a program stored thereon, and when the program is executed by a processor, the distributed RIS fast beamforming method based on quantum annealing is implemented.

[0053] Beneficial effects:

[0054] 1. The proposed method for solving non-convex optimization problems based on quantum computing can effectively reduce the computational complexity and total computing time, ensuring that the algorithm can meet application requirements when actually deployed;

[0055] 2. In this method, the optimization variables are quantized, and different quantization levels can be selected according to the actual equipment parameters to meet the phase discreteness of the actual RIS, while ensuring that the solution obtained from the optimization problem is the setting for phase configuration;

[0056] 3. The algorithm can converge quickly and can be used to achieve fast configuration for different situations;

[0057] 4. This algorithm greatly improves the throughput of multi-user communication systems with obstructed communication links. It performs better than some classic methods and greatly reduces the time compared to some previous baseline algorithms, achieving a good balance between performance and computing time.

[0058] 5. The D-wave quantum computer server used in this algorithm is located in the cloud and can be accessed from anywhere. It is low-cost and easy to deploy and use.

[0059] 6. The proposed beamforming algorithm at the RIS can be performed independently of the beamforming at the BS. It has a black box characteristic for phase configuration and does not need to consider how the internal annealing process is performed, which is convenient for technicians to use. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a theoretical illustration of the quantum annealing algorithm of the present invention;

[0061] Figure 2 It is a schematic diagram of the communication scenario and parameter settings of the present invention;

[0062] Figure 3 It is a schematic diagram of the influence of the signal-to-noise ratio on the weighted sum rate of the distributed RIS fast beamforming algorithm based on quantum annealing of the present invention;

[0063] Figure 4 It is a schematic diagram of the influence of the RIS area on the weighted sum rate of the distributed RIS fast beamforming algorithm based on quantum annealing of the present invention;

[0064] Figure 5It is a schematic diagram of the influence of the RIS area on the average iteration time of the distributed RIS fast beamforming algorithm based on quantum annealing of the present invention;

[0065] Figure 6 It is a schematic diagram of the influence of the number of transmitting antennas on the weighted sum rate of the distributed RIS fast beamforming algorithm based on quantum annealing of the present invention;

[0066] Figure 7 It is a schematic diagram of the effect of the number of transmitting antennas on the average iteration time of the distributed RIS fast beamforming algorithm based on quantum annealing of the present invention;

[0067] Figure 8 It is a schematic diagram for comparing the algorithm convergence curves of the distributed RIS fast beamforming algorithm based on quantum annealing of the present invention;

[0068] Fig. 9 It is a structural diagram of the device used in the distributed RIS fast beamforming algorithm based on quantum annealing of the present invention;

[0069] Fig.10 It is a flow chart of the distributed RIS fast beamforming algorithm based on quantum annealing of the present invention. DETAILED DESCRIPTION

[0070] The specific implementation modes of the present invention are further described in detail below with reference to the accompanying drawings.

[0071] In order to adopt a collaborative optimization strategy under the premise of the maximum transmit power limit of the base station BS, the transmitting end beamforming V and the phase offset θ of each smart metasurface are r Optimization is performed to improve the quality of received signals and data transmission rate, thereby improving the throughput in a distributed RIS-assisted millimeter wave communication system. The present invention hopes to solve the following problems by designing a distributed RIS fast beamforming method based on quantum annealing:

[0072]

[0073] in, Represents the signal interference noise ratio of user k. In the present invention, the optimization problem of the passive phase shift matrix at each RIS is mainly considered, that is, the optimization of the second constraint term. Similarly, in order to maintain a low computational complexity in the operation process of high-dimensional variables, the present invention considers using a new quantum annealing computing paradigm, which is suitable for solving the optimal solution of discrete valued variable optimization problems and is very suitable for the phase configuration of RIS.

[0074] Next, we first introduce the quantum Ising model, such as Figure 1As shown. Similar to classical annealing, quantum annealing works on the basis of adiabatic evolution. The difference is that QA does not use temperature annealing, but is completed through quantum tunneling effect under ideal conditions. Specifically, it can be written as:

[0075]

[0076] The first term explains the external magnetic field h at the jth spin position. j The second term is the interaction J between the i-th and j-th positions ij is modeled. Any two positions can interact only if they are adjacent, so the second term is only on the edges of the graph represented by E(G), while the first term is on the vertex set V(G). If h j >0, then s j Prefer to be arranged in the positive direction; if h j <0, the opposite is true. ij > 0, the interaction between the two spin positions is ferromagnetic, otherwise it is antiferromagnetic. The above Ising model has statistical properties, so any possible spin configuration has a certain probability of occurrence. As the temperature decreases, the algorithm becomes very sensitive to the detailed changes in energy and can eventually find the global minimum.

[0077] Specifically, Fig.10 As shown, the present invention provides a distributed RIS fast beamforming method based on quantum annealing.

[0078] S1, initialize convergence accuracy ∈, auxiliary variable U k , W k , X k , the beamforming matrix V of the base station k , the phase shift matrix Φ of each RIS r and the number of iterations iter. Input base station BS to RIS r and RIS r To user user k The channel matrix G r 、h rk , and calculate the cascade channel matrix Set the number of iterations iter max .

[0079] S2, beamforming matrix V at the base station k The update method is based on the R-DPC algorithm modified from R-WMMSE. Here we directly give the update equation.

[0080] For each user k, the update equation is:

[0081]

[0082]

[0083]

[0084] Afterwards, the scaling factor is calculated in is satisfied X k The stable point, and follow To update V k . Where I is the identity matrix, and are the Gaussian white noise to which the signal of user k is subjected during transmission in the channel, and P max is the maximum total transmit power,

[0085] This method can ensure that beamforming at the BS achieves better performance results.

[0086] S3. Perform iterative quantum annealing on each RIS to solve passive beamforming, including:

[0087] S3.1. First, perform phase quantization. The complex reflection coefficient of each RIS reflection unit is as follows:

[0088]

[0089] Later, we phase shift the matrix Φ r,m Using Γ m The expression can be replaced by , where m∈{1,2,...,M} represents the mth reflection unit of RIS, θ is a passive phase variable that can be manually controlled and set, and are introduced intermediate variables, satisfying and and Represent the real and imaginary parts of the variable respectively.

[0090] S3.2, then update the parameters, this part uses the closed-form solution of fractional programming to solve the following optimization problem:

[0091]

[0092] Among them, w k is the user weight vector, and is the optimal value of the auxiliary parameter introduced in the fractional programming expression, A k =H k V k Indicates the receiving end signal and Represents the sum of the received signal and the interference and noise energy, which is the intermediate variable defined, among which the cascade channel Contains the phase shift matrix, V k is the BS beamforming matrix required in the previous article. The subsequent update process is as follows:

[0093] according to renew

[0094] according to renew

[0095] According to A k =H k V k Update A k ,

[0096] according to

[0097]

[0098] Update B k ,in is the introduced intermediate auxiliary variable, where In order to conveniently abbreviate the deformation representation of the channel matrix, we will H Σ The value of the (m,n)th element of the matrix is ​​recorded as H Σ(m,n) .

[0099] In the actual simulation experiment verification process, it was found that the most time-consuming part was to convert B k The steps to convert it into a binary quadratic model that can be solved by the solver are as follows: k After some transformation, we get a simpler solution:

[0100]

[0101]

[0102] Furthermore, R θ r Perform vectorization combination and obtain θ=[θ1,θ2,...,θ R ]; R h rj Perform vectorization combination to obtain The above expression becomes:

[0103]

[0104] Among them, H Σ(m,n) is a matrix The (m,n)th element of and It means taking its real part and imaginary part. and It represents the m%Mth quantization level of the real and imaginary parts of the m / Mth reflection unit of RIS, and so on for other variables, where / and % represent integer division and remainder operations.

[0105] S3.3. Bring in A k and B k , calculate the optimization function in the form of the Ising model, that is, the weighted sum rate after fractional programming. The optimization function in the form of the Ising model is specifically:

[0106] S3.4. Convert -R into a quantum BQM model and use D-Wave's open source cloud QA, SA or hybrid solver to solve it. This part is implemented by executing the API dimod.binary.as_bqm() in the D-wave open source code library dimod.

[0107] After solving, the API will automatically output all discrete phase variables Γ m , then we restore the above solution to the phase shift matrix Φ r Then recalculate the optimized new sum rate R.

[0108] S4. Put the above steps S2 and S3 into a loop and execute them alternately. Each time the number of iterations is updated iter=iter+1. The condition for terminating the loop is set until the growth rate of the target value (weighted sum rate) is lower than the threshold ∈>0 or iter reaches the maximum number of iterations iter. max , jump out of the loop and get the final optimization result.

[0109] S5, output the final optimized beamforming matrix V k , the optimized phase shift matrix Φ r The optimal sum rate R obtained after optimization max .

[0110] Specifically, let's consider the principle and derivation of the entire algorithm. Since the existing problem is not in the form of a polynomial, but a transcendental function containing logarithmic terms, it is impossible to directly deploy and solve it using the above model. Therefore, we consider converting the original logarithm and expression into a polynomial form through a closed-form solution of fractional programming, and converting the constant modulus constraint of the RIS unit into an unconstrained beamforming problem through variable substitution to facilitate the solution.

[0111] The transmitting end beamforming vector is fixed and the constraints are considered as follows:

[0112]

[0113] First, several auxiliary variables are introduced. Since fractional programming can handle the logarithm and problem of ratios well, the closed-form solution of fractional programming (FP) is used to transform the above problem into a low-complexity problem according to the following two transformations.

[0114] Further, regarding the question:

[0115]

[0116] Transformation 1 Lagrange dual transformation introduces auxiliary variables α to facilitate derivation and simplify calculation k , the logarithmic function can be written as follows:

[0117]

[0118]

[0119] Transformation 2 Secondary transformation Given that the auxiliary variable β is introduced to facilitate derivation and simplify calculation k , then:

[0120]

[0121] in First use transformation 1 to get:

[0122]

[0123] in

[0124] Furthermore, let the partial derivative Then we can obtain Fixed alpha k , omitting log(1+α k )-α k Term, and then use the second transformation to introduce auxiliary variables, the previous problem becomes the following form:

[0125]

[0126] in

[0127] Furthermore, let the partial derivative Then we can find

[0128] So far, we have obtained the optimization problem that only contains the phase shift constraints of each RIS. Then the problem to be optimized can be written as follows:

[0129]

[0130] Next, the present invention considers that the RIS in the actual situation is often a 1-bit or 2-bit quantized phase, and its optimization problem is generally a discrete problem. In order to accurately represent and facilitate the solution of the Ising model, a 2-bit quantized phase is used as an example for explanation (if it is a 1-bit quantization case, that is, the phase is degraded to 2-bit quantization and only takes θ m ∈{0,π}, for higher quantization resolutions, one-hot encoding will be used and further explained later). Specifically, for a 2-bit quantized phase, satisfying θ m ∈{0,π / 2,π,3π / 2}. The expression of complex reflection coefficient is as follows:

[0131]

[0132] Each reflection unit is represented by two Ising spin variables, namely and They represent the four phase configurations of each reflection unit in the case of 2-bit quantization. Considering that the spin variable in the actual calculation is represented by a binary variable, and Do an equivalent linear substitution as follows:

[0133]

[0134]

[0135] Furthermore, the specific phase configuration is shown in the following table. and No matter how to take the value, the amplitude is always 1, that is to say, this transformation can omit the constant modulus constraint term, making the original problem become an unconstrained optimization problem, that is:

[0136]

[0137] Among them, A k =H k V k ,

[0138] Quantized Phase Configuration

[0139]

[0140] Furthermore, we only need to organize the above problem into a form that can be solved by the Ising model. By observing the form of the expression, it is easy to see that: Only binary variables are generated and The first-order term of kThis includes both linear and quadratic terms.

[0141] Furthermore, it is important to note some simplification rules in the Ising model: since all variables are binary, quadratic terms only exist when they are multiplied by two different variables, not when they are multiplied by the same variable, e.g. And reasonable quadratic terms such as or In the actual simulation experiment verification process, it was found that the most time-consuming part was to convert B k The steps to convert the binary quadratic model (BQM) that can be solved by the solver are as follows: k After some transformation, we get a simpler solution:

[0142]

[0143] Furthermore, R θ r Perform vectorization combination and obtain θ=[θ1,θ2,...,θ R ]; R h rj Perform vectorization combination to obtain The above expression becomes:

[0144]

[0145] in

[0146]

[0147]

[0148] Furthermore, A k =H k V k , and B obtained above k By bringing the expression into the original optimization problem, the quantum annealing solver can be used to solve it, and the solution with the minimum energy is the optimal solution.

[0149] For RIS with higher phase resolution (i.e., the quantization order of the phase), it seems difficult to quantize the phase of the reflective element using a general method. Therefore, the present invention discloses a method that is more suitable for general scenarios to represent all different quantization levels. Consider a RIS with M reflective units, each of which needs to be quantized using n bits, and then they can be mapped to 2 on a quantum computer. n qubits, as shown in the following table

[0150] Quantized Phase Configuration

[0151]

[0152] As shown in the table, the present invention adopts a unique hot encoding strategy to sequentially convert 2 n The phase of the case is mapped to the quantum bit, so that a RIS will have a total of M×2 n The case of R distributed RIS is R×M×2 n When the total number of distributed RIS and the number of units in a single RIS grow to a relatively high value range, the total number of qubits required will increase dramatically, eventually exceeding the computational range that current quantum computers can handle. However, in reality, there is no need to worry about such a scenario, because the resolution of RIS in reality is usually 1 or 2 bits, so there is no need to deal with a super-large-scale quantization problem.

[0153] Furthermore, after quantization, a unique representation of the phase quantization of each reflection unit of each RIS can be obtained, as shown below:

[0154]

[0155] b m,i represents the quantized bit level of the i-th bit of the m-th reflection unit of RIS. However, this representation usually involves a very complicated calculation process for high-order terms, and such terms are not supported during the execution of the quantum annealing algorithm. Therefore, it is expected to decouple each high-order term into a combination of several first-order terms and second-order terms by introducing additional variables. This process can be called quadraticization. There are many ways to complete this process. Here is the most commonly used framework. The specific principle is as follows. First, assume that a cubic term is given.

[0156] b l b m b n

[0157] Furthermore, by m b n With a single variable z mn To express it, we can get a corresponding truth table, as shown in the following table.

[0158] Quantized Phase Truth Table

[0159]

[0160] Furthermore, in order to further complete the replacement, a penalty term needs to be introduced to enhance the truth table of the Ising model:

[0161] b m b n →zmn +λ(b m b n -2b m z mn -2b n z mn +3z mn )

[0162] A scaling factor λ is introduced here, which is generally set high enough to meet the needs of the penalty term. For the quartic term, this process is repeated twice, reducing the quartic term to a cubic term, and then reducing the cubic term to a combination of a linear and a quadratic term. For higher-order terms, the method is similar, and the above execution steps are repeated until only linear and quadratic terms are left. As a result, many undesirable auxiliary variables are introduced. The whole process looks simple, but in actual calculations, a higher complexity is introduced to locate the higher-order terms, and the selected replacement pair b is replaced in this expression. m b n Replaced by auxiliary variable z mn The steps will also be difficult to perform, involving complex matrix transformations and dimensional adjustments. Therefore, if this process needs to be implemented in an actual algorithm, a computer algorithm can be used to assist. In summary, this section promotes a general method to solve the problem for different quantization levels of the RIS reflection unit phase, but in actual practice, for simplicity, only the 2-bit case is generally considered.

[0163] In this section, the calculation process of the entire algorithm will be further given. Through the derivation in the previous article, the beamforming vectors at the BS and RIS are successfully decoupled, and two optimization problems are obtained. After that, we only need to solve the two problems alternately.

[0164] Stage 1: Iterative Dirty Paper Coding for Subspace Dimensionality Reduction

[0165] In order to solve the power allocation problem at the BS, the present invention discloses a low-complexity fast beamforming algorithm based on the R-WMMSE and DPC method, which is denoted as R-DPC.

[0166] Phase 2: Fast RIS phase configuration based on quantum annealing

[0167] This part of the algorithm is mainly aimed at the passive beamforming algorithm at RIS. Quantum annealing or simulated annealing can be used here to solve the combinatorial optimization problem disclosed in the previous article.

[0168] Then the specific algorithm can be obtained as follows:

[0169]

[0170]

[0171] The corresponding algorithm flow chart is as follows Fig.10 shown.

[0172] Furthermore, numerical simulation results are given to comprehensively evaluate and verify the performance of the disclosed method, and a comparative analysis is performed with the established benchmarks. First, the simulation parameter settings are given, such as Figure 2 As shown. Assume that the base station BS is deployed at the origin (0,0), the user group is distributed at a distance of 101.12m from the origin, and there are K receivers randomly and evenly distributed in a circular area with a radius of 10m. The direct link between the user group and the BS is completely blocked by obstacles. When RIS is not deployed, the communication signal quality will become very poor. In order to effectively improve the communication quality, two RIS are deployed symmetrically above and below the direct link, and the position coordinates are set to (98.89m, 14.84m) and (98.89m, -14.84m) respectively. In order to facilitate simulation experiments and demonstrations, the number of RIS is set to R = 2 in the present invention, and each RIS is configured with M = M v ×M h The reflective element represents the surface area of ​​RIS. In this way, the channel matrices from BS to RIS, BS to user k, and RIS to user k can be written as G1 and G2, respectively. d 、h 1,k and h 2,k During the simulation, the parameters of each part are generated according to the structure of the geometric channel mentioned above. In order to ensure the reliability of the experiment, 500 sets of parameters are randomly generated each time for Monte Carlo simulation. Finally, the average result is taken as the final experimental result for comparison to avoid various unexpected noises affecting the fairness of the comparison with the baseline algorithm.

[0173] For comparison purposes, several classical baseline algorithms were selected and adapted to distributed RIS, namely, an alternating optimization method using WMMSE for BS beamforming and manifold optimization for phase configuration, an optimization minimization method, and a deep neural network-based method. For computational efficiency, all non-quantum computing aspects of the algorithms were performed on a computer equipped with an Intel Core i5-12400F CPU, while the quantum annealing process was performed using a D-Wave hybrid quantum processing unit (QPU).

[0174] Figure 3The relationship between the weighted sum rate and the signal-to-noise ratio (SNR) of the scheme disclosed in the present invention and the baseline algorithm under the condition of ideal channel estimation is evaluated. Here, the number of distributed RIS and the number of users are kept constant at R=2 and K=16, respectively, and the number of reflection units in each RIS is 50. As the transmit signal-to-noise ratio gradually increases, the adverse effect of thermal noise on the system decreases, thereby significantly improving the throughput of the entire system. It is particularly noteworthy that the DNN-based method fails to effectively learn the optimal precoding strategy, which leads to a significantly lower sum rate compared with other methods. Above it is the AO algorithm, which can achieve a weighted sum rate of nearly 10 dB in the area with high SNR. Compared with these two algorithms, the performance of the method disclosed in the present invention and the MM algorithm has consistent and significant performance improvements, and the weighted sum rate is increased by 20% to 30% when the SNR exceeds 0 dB. This comparison highlights the effectiveness of the disclosed method in balancing specific user needs and overall system performance. In summary, the disclosed method is proven to produce significant improvements in weighted sum rate, especially in high SNR scenarios. This highlights the effectiveness and superiority of the method of the present invention in improving the performance of communication systems using RIS technology.

[0175] exist Figure 4 In this paper, the impact of the number of RIS reflector elements M on the weighted sum rate of the entire system is mainly evaluated. For comparison, consider the number of transmitting antennas N t Set to 8, and let the BS serve 16 users at the same time. Then, the number of reflective elements is changed to 10, 20, 30, 40, 50, 100, and 200 in turn, so that it can reflect the wide range of changes in the weighted sum rate. It can be observed that as M increases, the four different algorithms all show an increasing trend in the weighted sum rate. As expected, the method disclosed in the present invention has the highest performance among the four algorithms, and when M is greater than 50, it is 1 to 2 bps / Hz / user higher than the second highest MM algorithm. Below this, the performance of the AO method is much worse than the previous two algorithms, especially when M is greater than 100, its growth rate with M decreases significantly. In addition, the DNN-based method still obtains the lowest weighted sum rate, although there is an increasing trend, it is less than 5bps / Hz / user, and changes very little with the increase of M. In short, all algorithms show a trend of increasing with the increase of RIS area. However, it can be inferred that when M approaches infinity, the growth trend will gradually slow down and approach a certain upper limit. In summary, the method disclosed in this paper is superior to the other three methods because it has a strong growth trend as M increases.

[0176] Next, in Figure 5 Observe the effect of the number of reflective elements M on the iteration time of all algorithms. Figure 4In the simulation parameter setting, the number of transmitting antennas N t Set to 8, and make the BS serve 16 users simultaneously. Here it is assumed that the transmit SNR is fixed at 10dB. Then, the number of reflection elements can be changed to 10, 20, 30, 40, 50, 100, 200 in turn, so that it can reflect the time change of each iteration of different M. It can be observed that as M increases, the four different algorithms show completely different increasing trends in computation time. As expected, the method disclosed in the present invention has the lowest performance among the four algorithms, with a single iteration time of less than 1 second and only linear computational complexity O(M). In addition, the computation time of the method disclosed in the present invention and the DNN method is shorter, significantly shorter than the other two baseline algorithms; the computational complexity of the other two baseline algorithms AO and MM increases successively, and also grows rapidly with the increase of M. In addition, it can be observed that although the DNN-based method has a large computation time at the beginning, it does not change much with the change of M. In summary, all algorithms show an increasing trend in time with the increase of RIS area. Although the growth trends between different algorithms often vary greatly, the method disclosed in the present invention always converges the fastest.

[0177] exist Figure 6 In the example, we will observe the number of transmitting antennas N t The impact on the weighted sum rate of the communication system. For convenience, consider setting the number of reflection elements at M to 50 and letting the BS serve 16 users at the same time. Then, the number of reflection elements is changed from 8 to 64 in steps of 8, so that it can reflect a wide range of changes in the weighted sum rate. It can be observed that as N t As the number of N increases, the weighted sum rates of the four different algorithms all show a slight increase trend, but the impact of M is not as obvious. As can be seen from the figure, in areas with a large number of antennas, the method disclosed in the article is about 0.5 to 2 bps / Hz / user higher than the second highest MM algorithm. The AO algorithm below it is 4 to 5 bps / Hz / user lower than the first two algorithms. The lowest is the DNN method, and its speed increases with N. t Compared with the effect of M on the weighted sum rate, N t The effect is much weaker when N t When increasing from 8 to 64, in all 4 methods, increase N t At most, it can only provide an improvement of 2 to 3 bps / Hz / user. Therefore, it can be concluded that as N t With the growth of , the weighted sum rates of the four algorithms all increase, but not significantly, and they differ slightly in speed.

[0178] For the completeness of the study, Figure 7The number of transmitting antennas N t The impact on computational complexity. Similar to Figure 6 In the simulation parameter settings, the number of reflective elements M is set to 50, and the BS serves 16 users at the same time, with the transmit SNR fixed at 10dB. Then, consider increasing the number of transmit antennas from 8 to 64, increasing by 8 each time, to show that N t The impact on the weighted sum rate. It can be observed that as N t As N increases, the four different algorithms show completely different increasing trends in computing time. The method disclosed in the present invention has the lowest computing time per iteration, and as N increases, t The DNN-based method has similar simulation results to the method of the present invention, and as the number of transmitting antennas N t AO and MM are similar, and with the increase of N t The increase of is relatively stable, but the fluctuation and jump of the AO algorithm are more, which may be due to the error caused by insufficient Monte Carlo simulation times. Finally, the method disclosed in the present invention has the shortest calculation time among the four algorithms and is less affected by the number of transmitting antennas.

[0179] Figure 8 The relationship between the weighted sum rate and the number of iterations, i.e., the convergence curve, is shown, and the results show that the method of the present invention reaches convergence faster than the other three methods. In order to ensure a fair comparison, the present invention maintains a constant number of distributed RISs and users, i.e., R=2 RISs and K=16 users, respectively, and the number of reflection units of each RIS is 50. The present invention collects the weighted sum rate data of the first 30 iterations and analyzes the convergence behavior of the algorithm. It is observed that the method disclosed in the article converges faster than the other three methods and can reach convergence within 5 iterations, while the baseline algorithm converges on average until the 10th iteration. The method disclosed in the present invention shows a smoother iterative convergence curve than the other three. The MM method shows significant fluctuations after the fifth iteration before regaining the correct optimization direction. In summary, compared with the benchmark, the method disclosed in the present invention not only achieves superior performance in terms of weighted sum rate, but also converges faster.

[0180] Corresponding to the aforementioned embodiment of a distributed RIS fast beamforming method based on quantum annealing, the present invention also provides an embodiment of a distributed RIS fast beamforming device based on quantum annealing.

[0181] See also Fig. 9An embodiment of the present invention provides a distributed RIS fast beamforming device based on quantum annealing, comprising a memory, a storage device, a communication transceiver and one or more processors, wherein the memory stores executable codes, and when the processor executes the executable codes, it is used to implement a distributed RIS fast beamforming method based on quantum annealing in the above embodiment.

[0182] The embodiment of the distributed RIS fast beamforming device based on quantum annealing provided by the present invention can be applied to any device with data processing capability, and the device with data processing capability can be a device or apparatus such as a computer. The device embodiment can be implemented by software, or by hardware or a combination of software and hardware. Taking software implementation as an example, as a device in a logical sense, the processor of any device with data processing capability reads the corresponding computer program instructions in the non-volatile memory into the memory and runs them. From the hardware level, if Fig. 9 As shown, it is a hardware structure diagram of a distributed RIS fast beamforming device based on quantum annealing provided by the present invention, in which any device with data processing capability is located, except Fig. 9 In addition to the processor, memory, network interface, and non-volatile memory shown, any device with data processing capabilities in which the apparatus in the embodiments is located may also include other hardware, generally based on the actual functions of the device with data processing capabilities, which will not be described in detail.

[0183] The implementation process of the functions and effects of each unit in the above-mentioned device is specifically described in the implementation process of the corresponding steps in the above-mentioned method, and will not be repeated here.

[0184] For the device embodiment, since it basically corresponds to the method embodiment, the relevant parts can refer to the partial description of the method embodiment. The device embodiment described above is only schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of the present invention. Ordinary technicians in this field can understand and implement it without paying creative work.

[0185] An embodiment of the present invention further provides a computer-readable storage medium on which a program is stored. When the program is executed by a processor, a distributed RIS fast beamforming method based on quantum annealing in the above embodiment is implemented.

[0186] The computer-readable storage medium may be an internal storage unit of any device with data processing capability described in any of the aforementioned embodiments, such as a hard disk or a memory. The computer-readable storage medium may also be an external storage device of any device with data processing capability, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc. equipped on the device. Furthermore, the computer-readable storage medium may also include both an internal storage unit and an external storage device of any device with data processing capability. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capability, and may also be used to temporarily store data that has been output or is to be output.

[0187] The present invention also provides a computer program product, including a computer program, and when the computer program is executed by a processor, the distributed RIS fast beamforming method based on quantum annealing is implemented.

[0188] Those skilled in the art will readily appreciate other embodiments of the present application after considering the description and practicing the contents disclosed herein. The present application is intended to cover any modification, use or adaptation of the present application, which follows the general principles of the present application and includes common knowledge or customary techniques in the art that are not disclosed in the present application. The description and examples are intended to be exemplary only, and the true scope and spirit of the present application are indicated by the claims.

[0189] It should be understood that the above general description and the detailed description below are only exemplary and explanatory and cannot limit the present application. The present application is not limited to the precise structure described above and shown in the drawings, and various modifications and changes can be made without departing from the scope thereof. The scope of the present application is limited only by the attached claims.

Claims

1. A distributed RIS fast beamforming method based on quantum annealing, characterized in that: The method comprises the following steps: S1, initialize the number of iterations, channel and beamforming parameters; S2. Update the beamforming matrix at the base station; S3. Perform iterative quantum annealing on each RIS to solve passive beamforming, including: S3.1, performing phase quantization on the phase shift matrix; S3.

2. According to the closed-form solution of fractional programming, the constant modulus constraint of the RIS unit in the beamforming optimization problem is converted into an unconstrained beamforming problem, and the parameters are updated; S3.3, calculating the optimization function in the form of the Ising model according to the updated parameters, specifically calculating the weighted sum rate after fractional programming; S3.4, converting the optimization function in the form of the Ising model into a quantum binary quadratic model, solving it using a solver to obtain all discrete phase variables, and restoring the discrete phase variables to a phase shift matrix; S4, repeat steps S2 and S3 to iterate until the growth rate of the weighted sum rate is lower than the set threshold or reaches the maximum number of iterations, and obtain the final optimized beamforming matrix, the optimized phase shift matrix and the optimal sum rate after optimization.

2. According to claim 1, a distributed RIS fast beamforming method based on quantum annealing is characterized in that: The parameters of the initialization iteration number, channel and beamforming specifically include: initialization convergence accuracy ∈, auxiliary variable MMSE filter U k , MSE weight matrix W k , dimension reduction precoding matrix X k , the beamforming matrix V of the base station k , the phase shift matrix Φ of each RIS r and the number of iterations iter, input base station BS to RIS r and RIS r To user user k The channel matrix G r 、h rk , and calculate the cascade channel matrix Set the maximum number of iterations iter max .

3. According to claim 2, a distributed RIS fast beamforming method based on quantum annealing is characterized in that: The updating of the beamforming matrix at the base station specifically includes: For each user k, update the auxiliary variable MMSE filter U k , MSE weight matrix W k and the dimension-reduced precoding matrix X k , the equation is: Calculate the scaling factor in is satisfied X k The stable point, and follow To update V k ; Among them, K is the total number of service users, I is the unit matrix, and are the Gaussian white noise to which the signal of user k is subjected during transmission in the channel, and P max is the maximum total transmit power.

4. According to claim 1, a distributed RIS fast beamforming method based on quantum annealing is characterized in that: The phase quantization of the phase shift matrix is ​​specifically as follows: the complex reflection coefficient of each RIS reflection unit is as follows: If the phase is quantized by 2 bits, then θ m ∈{0,π / 2,π,3π / 2}, if 1-bit quantization is used, the phase is θ m ∈{0,π}; Φ in the phase shift matrix r,m Using Γ m To replace the expression, and are introduced intermediate variables, satisfying and and denote the real and imaginary parts of the variable respectively, and m∈{1,2,...,M} denotes the mth reflection unit of RIS.

5. According to claim 1, a distributed RIS fast beamforming method based on quantum annealing is characterized in that: In the phase quantization of the phase shift matrix, if the phase of each reflection unit needs to be quantized using more than 2 bits, a one-hot encoding strategy is used to map them to 2 on the quantum computer. n On quantum bits, we get The Φ in the phase shift matrix r,m Using Γ m The expression can be replaced by m,i Represents the i-th quantization bit level of the m-th reflection unit of RIS.

6. The distributed RIS fast beamforming method based on quantum annealing according to claim 1 is characterized in that: The parameter update in S3.2 is specifically to solve the following optimization problem according to the closed-form solution of fractional programming: Among them, w k is the user weight vector, and is the optimal value of the auxiliary parameter introduced in the fractional programming expression, the receiving end signal A k =H k V k The sum of the received signal, interference and noise energy is the intermediate variable defined, where the cascade channel Contains the phase shift matrix, V k is the BS beamforming matrix; according to renew according to renew According to A k =H k V k Update A k , according to Update B k ,in is the intermediate auxiliary variable introduced, H Σ( m,n) is a matrix The (m,n)th element of k represents the signal-to-interference-noise ratio of user k, where is the channel matrix deformation representation, and denote the real and imaginary parts of the variable, respectively. and It represents the m%M-th quantization level of the real and imaginary parts of the m / M-th reflection unit of RIS, and / and % represent integer division and remainder operations.

7. The distributed RIS fast beamforming method based on quantum annealing according to claim 6 is characterized in that: The optimization function of the Ising model form is specifically: w k is the user weight vector, represents taking the real part of the variable, and It is the optimal value of the auxiliary parameter introduced in the fractional programming expression.

8. The distributed RIS fast beamforming method based on quantum annealing according to claim 1 is characterized in that: The conversion of the optimization function in the form of the Ising model into a quantum binary quadratic model is specifically: To B k After transformation, a simpler solution is obtained: in R θ r Perform vectorization combination and obtain θ=[θ1,θ2,…,θ R ]; R h rj Perform vectorization combination to obtain The expression is adjusted to: in The obtained A k and B k The expression of is introduced into the original optimization problem to obtain the converted quantum binary quadratic model, where H Σ(m,n) is a matrix The (m,n)th element of and It means taking its real and imaginary parts; and It represents the m%Mth quantization level of the real and imaginary parts of the m / Mth reflection unit of RIS, and so on for other variables, where / and % represent integer division and remainder operations.

9. A distributed RIS fast beamforming device based on quantum annealing, comprising a memory, a storage device, a communication transceiver and one or more processors, wherein the memory stores executable code, characterized in that: When the processor executes the executable code, a distributed RIS fast beamforming method based on quantum annealing as described in any one of claims 1 to 8 is implemented.

10. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, a distributed RIS fast beamforming method based on quantum annealing as described in any one of claims 1 to 8 is implemented.

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