Irs transmit power optimization method based on quasi-affine transformation evolutionary algorithm

Abstract

The application provides an IRS transmission power optimization method based on a quasi-affine transformation evolution algorithm, and comprises the following steps: step 1, system model construction and parameter initialization; step 2, channel modeling; step 3, constructing a target for minimizing transmission power while meeting the constraint condition of the signal-to-noise ratio of all users; step 4, searching by using a quasi-affine evolution-based meta-heuristic algorithm; and step 5, outputting an IRS phase shift vector and an AP beamforming vector matrix. The application has the beneficial effect of improving the quasi-affine transformation evolution algorithm framework, aiming to overcome the problems of the traditional optimization method, such as the dramatic increase in the calculation complexity under the condition of a large number of IRS unit numbers N and user numbers K, and the defects of the existing heuristic algorithm (such as the particle swarm optimization) such as being prone to local optimization and low search efficiency.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, specifically to an IRS transmit power optimization method based on a quasi-affine transformation evolution algorithm. Background Technology

[0002] With the deepening of 5G commercialization and the advancement of 6G research, wireless communication faces severe challenges such as scarce spectrum resources, uncontrollable channel environment, and escalating energy consumption of base stations (or access points, APs). Intelligent Reflecting Surfaces (IRS), as a cost-effective solution, utilize large-scale, low-cost passive reflective elements to reconstruct the wireless propagation environment by actively modulating the reflected phase shift of the incident signal, providing a new approach to achieving high spectrum and energy efficiency in future wireless networks.

[0003] In a Smart Reflector (IRS) assisted downlink serving multi-user (MISO-DL-MU) base station (AP) system, minimizing the transmit power at the AP is one of the core objectives. This requires jointly optimizing the continuous beamforming vector matrix (transmit precoding matrix) at the AP and the discrete reflection phase shift vector on the IRS, while simultaneously meeting the minimum signal-to-interference-to-noise ratio (SINR) requirement specified by each user. However, this joint optimization problem exhibits high non-convexity due to the non-convex fractional nature of the SINR constraint and the discrete magnitude constraint (usually discrete phase) of the IRS phase shift unit.

[0004] Traditional optimization methods, such as alternating optimization and semidefinite relaxation, can find feasible solutions in some scenarios, but their computational complexity increases sharply when the number of IRS units (N) and the number of users (K) increases, making it difficult to meet the needs of practical applications.

[0005] Existing heuristic algorithms, such as particle swarm optimization, often struggle to achieve a good balance between convergence speed and solution accuracy because they are inefficient in searching high-dimensional variable spaces and are prone to getting trapped in local optima. Summary of the Invention

[0006] The purpose of this invention is to provide an IRS transmit power optimization method based on the Quasi-Affine Transformation Evolutionary (QUATRE) algorithm. This method is based on an improved Quasi-Affine Transformation Evolutionary (QUATRE) framework and aims to overcome the shortcomings of traditional optimization methods, such as the increased computational complexity in high-dimensional environments (large IRS unit number N and user number K) and the tendency of existing heuristic algorithms (such as particle swarm optimization) to get trapped in local optima and have low search efficiency.

[0007] This invention is achieved through the following technical solution: 1. An IRS transmit power optimization method based on a quasi-affine transformation evolution algorithm, comprising the following steps:

[0008] Step 1, System Model Construction and Parameter Initialization: Construct a multi-user communication system consisting of a multi-antenna base station, a smart reflector, and multiple single-antenna users; simultaneously initialize basic physical parameters and system channel parameters, including carrier frequency. speed of light ,wavelength Path loss factor Rician factor Reference path loss and noise power ;

[0009] Step 2, Channel Modeling: Construct the following three types of channel matrices, namely the base station to smart reflector channel: Intelligent reflector to user channel: Base station direct user channel: Where K represents the number of users, N represents the intelligent reflector with adjustable phase reflective elements, and M represents the number of antennas in the base station.

[0010] Step 3, construct a constraint that minimizes the transmit power while satisfying the signal-to-noise ratio for all users: define the function to minimize the transmit power as follows: Define the AP transmission precoding matrix Define the IRS reflection phase vector. , where the symbol This represents the transpose of a vector, used to convert the row vector of IRS reflection phases into a column vector; the corresponding reflection matrix is ​​in diagonal form. , where the symbol Represents the imaginary unit With phase angle The product of these terms is used to generate the complex exponential phase factor of the reflection unit to achieve phase modulation of the incident signal. The equivalent complex channel for the k-th user is: ,in Let K be the equivalent downlink channel vector of user k, which is formed by the reflection link after phase modulation by the smart reflector. Direct links to users via access points The combined effective channel from the access point to user k is obtained by superposition; the signal-to-noise ratio for each user in the system is: ,in This represents the standard deviation of additive white Gaussian noise in the receiving link corresponding to the k-th user. The power of white Gaussian noise is equal to its variance, i.e., the square of the standard deviation. This is the power of the noise; the signal-to-noise ratio (SNR) constraints are as follows: (a) User SNR constraints , where γ k (a) The signal-to-noise ratio threshold for user k; (b) The IRS phase shift constraint is defined as... ;

[0011] Step 4: Use a metaheuristic algorithm based on quasi-affine evolution to search: continuously obtain individual optimal solutions through a metaheuristic algorithm based on quasi-affine evolution. And the individual optimal solution The update is used as the global optimal solution; if the minimum transmit power change does not decrease significantly after exceeding a set threshold number of generations, early termination is triggered, and the current global optimal solution is saved as the final output.

[0012] Step 5, Output IRS phase shift vector and AP beamforming vector matrix: This will determine the final globally optimal individual... Decoded into IRS phase shift vector θ * and AP beamforming vector matrix W * .

[0013] Compared with previous technologies, the beneficial effects of the present invention are as follows:

[0014] 1. The output IRS phase shift vector and AP beamforming vector matrix can be used to configure the IRS phase array and base station transmit beam direction in actual communication systems, which is suitable for high energy efficiency, low power consumption, and multi-user MISO communication deployment scenarios. Attached Figure Description

[0015] Figure 1 This is a flowchart of the IRS transmit power optimization method based on the quasi-affine transformation evolution algorithm of the present invention.

[0016] Figure 2 It is the system model diagram described in step 1.

[0017] Figure 3 This is a flowchart of the algorithm for step 4 of the present invention, which uses a meta-heuristic algorithm based on quasi-affine evolution to perform the search.

[0018] Figure 4 This is a diagram illustrating the AP transmit power optimization process based on the quasi-affine transformation evolution algorithm in an embodiment of the present invention.

[0019] Figure 5 This is a comparison diagram of the AP transmit power optimization process between the present invention and different algorithms. Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings:

[0021] like Figure 1The following is an example of an IRS transmit power optimization method based on a quasi-affine transformation evolution algorithm, comprising the following steps:

[0022] Step 1, System Model Construction and Parameter Initialization: Construct a multi-user communication system consisting of a multi-antenna base station, a smart reflector, and multiple single-antenna users; simultaneously initialize basic physical parameters and system channel parameters, including carrier frequency. speed of light ,wavelength Path loss factor Rician factor Reference path loss and noise power ;

[0023] Specifically, in step 1, the construction of the multi-user communication system enables the antenna base station to have... One antenna, intelligent reflector includes One adjustable phase reflector unit, serving a number of users. The antenna array of the base station is a one-dimensional uniform linear array, and the intelligent reflector is a two-dimensional uniform rectangular array. The array is located in the XZ plane, and the center point of the intelligent reflector is set at the coordinate system. The spacing between the reflective elements is half the wavelength.

[0024] Step 2, Channel Modeling: Construct the following three types of channel matrices, namely the base station to smart reflector channel: Intelligent reflector to user channel: Base station direct user channel: Where K represents the number of users, N represents the intelligent reflector with adjustable phase, and M represents the number of antennas at the base station; channel modeling is a conventional technique, so it will not be elaborated upon in this application. It should be noted that the path loss of each channel is calculated using the following model: ,in Where α is the link distance and α is the path loss factor.

[0025] Step 3, construct a constraint that minimizes the transmit power while satisfying the signal-to-noise ratio for all users: define the function to minimize the transmit power as follows: Define the AP transmission precoding matrix Define the IRS reflection phase vector. , where the symbol This represents the transpose of a vector, used to convert the row vector of IRS reflection phases into a column vector; the corresponding reflection matrix is ​​in diagonal form. , where the symbol Represents the imaginary unit With phase angle The product of these terms is used to generate the complex exponential phase factor of the reflection unit to achieve phase modulation of the incident signal. The equivalent complex channel for the k-th user is: ,in Let K be the equivalent downlink channel vector of user k, which is formed by the reflection link after phase modulation by the smart reflector. Direct links to users via access points The combined effective channel from the access point to user k is obtained by superposition; the signal-to-noise ratio for each user in the system is: ,in This represents the standard deviation of additive white Gaussian noise in the receiving link corresponding to the k-th user. The power of white Gaussian noise is equal to its variance, i.e., the square of the standard deviation. This is the power of the noise; the signal-to-noise ratio (SNR) constraints are as follows: (a) User SNR constraints , where γ k (a) The signal-to-noise ratio threshold for user k; (b) The IRS phase shift constraint is defined as... ;

[0026] Step 4: Use a metaheuristic algorithm based on quasi-affine evolution to search: Obtain the continuously updated individual optimal solution through a metaheuristic algorithm based on quasi-affine evolution. and the individual optimal solution Further updates that are better than the current global optimum are taken as the global optimum. If the change in minimum transmit power does not decrease significantly after exceeding a set threshold number of generations, early termination is triggered, and the current global optimum is saved as the final output. Here, a label matrix is ​​introduced to control the update dimension, thereby achieving dimension-selective perturbation. Combined with an adaptive scaling mechanism and an early stopping strategy, optimization efficiency and robustness are improved.

[0027] Step 4 includes the following process:

[0028] Step 1: Initialize algorithm parameters: Construct a label matrix for each individual. D is the solution space dimension and the solution space dimension D = N + 2MK, P is the population size; where N is the number of IRS reflective units. This refers to the number of base station antennas. For the number of users; algorithm parameters include population size NP, problem dimension D, maximum fitness evaluation count MaxNFE, and scaling factor F;

[0029] Step 2: Evaluate the initial population: Calculate the initial fitness value and record the optimal position P of each individual. best and the global optimal position G best ;

[0030] Step 3: Generate the tag matrix: Construct the tag matrix ; Divide the population into Grouping; after randomly shuffling the rows and columns of each group, stacking them to achieve cross-overlap;

[0031] Step 4: Perform quasi-affine difference evolution transformation: Let the current global optimal individual be... The optimal historical individual is Candidate solutions are generated by using difference terms and disturbance terms: ,in , For two randomly selected individuals from the population, This is the scaling factor;

[0032] Step 5: Update position: based on the tag matrix Perform variable crossover and recombination operation: ;in This represents the new position component of the i-th individual in the d-th dimension of the solution space. It is the element in the i-th row and d-th column of the label matrix M, and its value is either 0 or 1; d represents the dimension index of the solution space, and D represents the total number of dimensions of the solution space;

[0033] Step 6: Boundary Handling: For variable components in newly generated individuals that exceed the allowed domain, a boundary symmetry correction strategy is adopted, namely: ,in , These are the lower / upper values ​​of the j-th dimension, respectively. This represents the value of the component at the individual's historical best position. For the input variable to be corrected, determine whether it exceeds the boundary;

[0034] Step 6 is to ensure that all variables are always within the domain. Therefore, boundary processing is introduced based on the quasi-affine transformation evolution algorithm. If a variable in a certain dimension exceeds the boundary, median shrinkage is performed according to the above formula. This processing method has better convergence stability than traditional mirror reflection and effectively avoids numerical mutations caused by variable out-of-bounds.

[0035] Step 7: Evaluate the new population and update the individual best and global best: If the current individual fitness value is better than the individual's historical best, then replace the individual best. Record; if it is the current global optimum, then it is the global optimum. Updated;

[0036] Step 8: Output: The algorithm terminates when the number of evolutions reaches the maximum number of generations (MaxGen) or the number of evaluations reaches the maximum number of function evaluations (MaxNFE), and outputs the optimal individual. .

[0037] In process 8, to prevent getting stuck in the stagnation interval, an adaptive scaling mechanism and an early stopping judgment mechanism are introduced: if continuous No power drop greater than 100% within the generation Improvements will trigger a scaling factor update. ,in =0.4, =0.95. If there is still no significant decrease after exceeding the set threshold number of algebras (MaxGen), early termination is triggered, and the current global optimal solution is saved as the final output.

[0038] Step 5, Output IRS phase shift vector and AP beamforming vector matrix: This will determine the final globally optimal individual... Decoded into IRS phase shift vector θ * and AP beamforming vector matrix W * .

[0039] Step 5 is performed as follows: The optimal individual is structurally decoded to recover the IRS phase reflection vector. Complex precoding matrix of base station: ,in and Each by The real and imaginary parts are decoded to obtain the result.

[0040] The present invention will now be described in conjunction with specific embodiments:

[0041] like Figure 2 As shown, the system model includes a multi-antenna base station, a two-dimensional array IRS, and several single-antenna users. The base station is configured with M=8 transmit antennas, and the IRS is configured with N=48 programmable reflector elements, with its center point located at the reference point (0,d0,0), where d0=50 meters. All users are configured as single-antenna terminals, with a total of K=8 users. The first four users are arranged at equal angles in the near-field region (within 2 meters) of the IRS, while the last four users are arranged on a far-field arc with a radius of 50 meters, thus simulating a typical mixed coverage area.

[0042] The system's physical parameters include: carrier frequency fc = 100 GHz, speed of light Wavelength λ = c / fc; Path loss model parameters include reference loss. The path loss factors α are 2.2 for the AP-IRS link, 2.8 for the IRS-User link, and 3.5 for the AP-User link. The noise power is set to -90dBm.

[0043] Figure 4This diagram illustrates the AP transmit power optimization process based on the quasi-affine transformation evolution algorithm, visually demonstrating the dynamic convergence characteristics of the algorithm in optimizing base station transmit power within an IRS-assisted system model. The vertical axis represents the total base station transmit power (dBm), and the horizontal axis represents the number of algorithm iterations (0-1000). The curve reflects the trend of the optimal transmit power during the iteration process. In the initial stage (0-200 iterations), the transmit power rapidly decreases from approximately 70.5dBm to 66dBm. This is due to the QUATRE algorithm's efficient search of high-potential solution space through dimension-selective perturbation controlled by the label matrix. In the middle stage (200-600 iterations), the power decrease rate slows and stabilizes in the 65-66dBm range, demonstrating the algorithm's fine-grained search capability in local optima. In the later stage (600-1000 iterations), the power tends to stabilize, eventually converging to an optimal solution of approximately 64.06dBm (labeled "optimal solution"), indicating that the minimum transmit power satisfying all user SINR constraints has been found. The key system parameters "AP antenna: 8, IRS unit: 48" are simultaneously labeled in the figure, corresponding to the typical scenario of M=8 and N=48 in the invention content. This verifies the effectiveness of the QUATRE algorithm under multi-antenna base station and large-scale IRS configuration. Even in a high-dimensional space composed of 48 discrete phase shift variables and 128 precoded variables (8 antennas × 8 users × 2 real and imaginary parts), it can still efficiently converge to the optimal solution.

[0044] like Figure 5 As shown, the QUATRE algorithm of this invention is compared with the Differential Evolution (DE) algorithm and the Particle Swarm Optimization (PSO) algorithm. It can be seen that the quasi-affine transformation evolution algorithm has a better effect on emission power optimization than the Differential Evolution (DE) algorithm and the Particle Swarm Optimization (PSO) algorithm.

[0045] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An IRS transmit power optimization method based on a quasi-affine transformation evolutionary algorithm, characterized in that: Comprising the following steps: Step 1, system model construction and parameter initialization: a multi-user communication system composed of a multi-antenna base station, a smart reflecting surface and multiple single-antenna users is constructed; at the same time, basic physical parameters and system channel parameters are initialized; the basic physical parameters and system channel parameters include carrier frequency , speed of light , wavelength , path loss factor , Rician factor , reference path loss , and noise power ; Step 2, Channel Modeling: Construct the following three channel matrices, i.e., base station to intelligent reflecting surface channel: , intelligent reflecting surface to user channel: , base station direct-to-user channel: ; where K represents the number of users, represents the adjustable phase reflecting unit of the intelligent reflecting surface, represents the number of antennas of the base station; Step 3, constructing the target is to minimize the transmit power, while meeting all user signal-to-noise ratio constraints; Step 4, search using the meta-heuristic based on quasi-affine evolution: obtain the constantly updated individual optimal solution by the meta-heuristic based on quasi-affine evolution and further update the individual optimal solution better than the current global optimal solution as the global optimal solution; if the minimum transmit power change still has no significant decline after exceeding the set threshold number of generations, trigger early termination, save the current global optimal solution as the final output; Said step 4 includes the following flow: Flow 1: Initialization of algorithm parameters: construct label matrix for each individual ; D is the dimension of solution space and the dimension of solution space D = N + 2MK, P is the population size; wherein, N is the number of IRS reflecting elements, is the number of base station antennas, is the number of users; the algorithm parameters include the population size NP, the dimension of solution space D, the maximum number of fitness evaluations MaxNFE, and the scaling factor F; Flow 2: Evaluate initial population: Calculate initial fitness values, record individual best position P best and global best position G best ; Flow 3: Generating label matrix: Constructing label matrix ; dividing the population into groups; stacking the groups after row and column random shuffling to achieve cross-overlapping; Flow 4: Perform the quasi-affine difference evolution transformation: Let the current global optimal individual be , the historical individual optimal be , and the candidate solution be generated by the difference item and the perturbation item: , where , are two randomly selected population individuals, is a scaling factor; Flow 5: Update position; according to label matrix , perform variable crossover-recombination operation: ; wherein represents the new position component of the ith individual on the dth dimension of the solution space, is the element of the ith row and dth column of the label matrix M, which takes only 0 or 1; , d for d represents the dimension index of the solution space, and D represents the total dimension number of the solution space; Flow 6: boundary processing; Flow 7: evaluate the new population and update the individual optimal and global optimal; Flow 8: output results; Step 5, output IRS phase shift vector and AP beamforming vector matrix: the final global optimal individual decoded into IRS phase shift vector θ * and AP beamforming vector matrix W * .

2. The IRS transmit power optimization method based on the quasi-affine transformation evolutionary algorithm according to claim 1, characterized in that: In step 1, the construction of a multi-user communication system, the antenna base station has antennas, the intelligent reflecting surface contains adjustable phase reflecting units, and the number of service users is ; the antenna array of the antenna base station is a one-dimensional uniform linear array, the intelligent reflecting surface is a two-dimensional uniform rectangular array, the array is located in the X-Z plane, the center point of the intelligent reflecting surface is set at coordinates , and the interval between the reflecting units is half a wavelength.

3. The IRS transmit power optimization method based on the quasi-affine transformation evolutionary algorithm according to claim 1, characterized in that: Step 3 is specifically defined as: defining a minimum transmit power function as , defining an AP transmit precoding matrix ; defining an IRS reflection phase vector , wherein the symbol represents the transpose of the vector, and is used to convert the IRS reflection phase row vector into a column vector; the corresponding reflection matrix is diagonal: , wherein the symbol represents the imaginary unit and the phase angle , which is used to generate the complex exponential phase factor of the reflection unit to achieve phase regulation of the incident signal, and the equivalent complex channel of the kth user is: , wherein is the equivalent downlink channel vector of the user k, which is obtained by superimposing the reflection link after the phase regulation by the intelligent reflecting surface and the direct link directly reaching the user from the access point, to characterize the comprehensive effective channel from the access point to the user k; the signal-to-noise ratio of each user in the system is: , wherein represents the standard deviation of the additive white Gaussian noise in the receiving link corresponding to the kth user, and the power of the Gaussian white noise is equal to its variance, i.e. the square of the standard deviation, is the power of the noise; The signal-to-noise ratio constraints are as follows, (a) user signal-to-noise ratio constraint where γk k is a signal-to-noise ratio threshold value for user k; (b) IRS phase shift constraint defined as .

4. The IRS transmit power optimization method based on the pseudo-affine transformation evolutionary algorithm according to claim 1, characterized in that: Flow 6: Boundary handling: for variable components in the newly generated individual that exceed the allowed definition domain, a boundary symmetric correction strategy is adopted, i.e.: wherein , are the lower / upper limit values for the j-th dimension, is the value of the component at the individual's historical best position, is the input variable to be corrected, and a decision is made as to whether the boundary is exceeded; Process 7: Evaluate new population and update individual best and global best: if the current individual fitness value is better than the individual historical best, replace the individual best record; if it is the current global best, the global best is updated is updated; Flow 8: output result: when the evolution times reach the maximum generation MaxGen or the evaluation times reach the maximum function evaluation MaxNFE, the algorithm terminates and outputs the optimal individual .

5. The IRS transmit power optimization method based on the quasi-affine transformation evolutionary algorithm according to claim 1, characterized in that: Step 5 is performed in the following specific way: structural decoding of the best individual to recover the IRS phase reflection vector: and the base station complex precoding matrix: where and are decoded from the real and imaginary parts of respectively.

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