A Beam Optimization Method for Amorphous Symbiotic Communication Systems Assisted by Intelligent Reflecting Surfaces

Abstract

The present invention discloses a beam optimization method for an amorphous coexisting communication system assisted by intelligent reflecting surfaces: (1) The base station obtains the average achievable rate of the primary user and the theoretical bit error rate of the secondary user according to the wireless channels of the primary user and the secondary user; (2) The base station establishes an optimization problem based on the average achievable rate and the theoretical bit error rate and conducts beam design to obtain the jointly optimized active beam and passive beam; (3) The base station transmits the optimized optimal reflecting surface phase design / optimized passive beam to the intelligent reflecting surface through a separate link line, and the optimized active beam is used for the base station beam design. The beam optimization method provided by the present invention can effectively improve the communication performance of the amorphous coexisting communication system.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication, and particularly to a beam optimization method for an amorphous coexisting communication system assisted by an intelligent reflecting surface. Background Art

[0002] With the extensive development of the Internet of Things (IoT) network, the number of future access devices will increase to dozens or even hundreds per square meter, which poses a huge challenge to the limited spectrum resources. The coexisting communication system is a technology that holds promise for solving the above problems. In a coexisting system, the primary signal source and the secondary signal source cooperate within a specific transmission protocol to transmit information to the corresponding primary users and secondary users, thereby improving energy utilization efficiency and spectrum efficiency. However, due to the double path loss of the system, the communication distance is severely limited.

[0003] In recent years, researchers have proposed a scheme to use an intelligent reflecting surface as a secondary signal source to assist the coexisting communication system. The intelligent reflecting surface consists of a large number of low-cost passive reflecting elements. Each passive reflecting element can adaptively adjust the wireless propagation environment by independently changing the phase or amplitude of the incident signal, thereby achieving passive beamforming at the IRS without the need for a radio frequency chain and improving energy utilization efficiency. For example, Chinese Patent No. CN114928838A discloses an intelligent reflecting surface-assisted coexisting communication information transmission system and method, which relates to the field of wireless communication and solves the information security problem of the coexisting wireless communication system. Its technical solution includes a base station, an intelligent reflecting surface, an IoT device, a user terminal, and an eavesdropping terminal: the base station sends active information to the user terminal to construct a primary transmission link to achieve active information transmission; the IoT device sends IoT information to the intelligent reflecting surface; the intelligent reflecting surface modulates the IoT information onto the active information of the primary transmission link to generate passive information, and sends the passive information to the user terminal to construct a secondary transmission link to achieve passive information transmission; the eavesdropping terminal eavesdrops on the active information transmitted on the primary transmission link and the passive information transmitted on the secondary transmission link, and the user terminal demodulates the active information sent by the base station and the passive information sent by the intelligent reflecting surface. For example, Chinese Patent No. CN109451591A discloses a coexisting system transmission method integrating a cellular network and the IoT, and gives two schemes for IoT devices to access the network: in Scheme 1, the reflecting device (i.e., the IoT device) uses the uplink signal in the cellular network to access the network, and the base station demodulates the signals of the users in the cellular network and the reflecting device in the IoT at the same time; in Scheme 2, the reflecting device uses the downlink signal in the cellular network to access the network, and the user terminal in the cellular network demodulates the signals of the base station in the cellular network and the reflecting device in the IoT at the same time.

[0004] However, due to the existence of a large number of passive reflection elements, the joint design of the primary and secondary beam designs is complex. Therefore, researchers have conducted a large number of studies on the joint beam design in cellular networks. However, in the transmission protocol of the symbiotic system, secondary users will be interfered by primary users, resulting in a low transmission rate. Considering that users in cellular communication systems are simultaneously interfered by adjacent cells, in order to better serve all users, it is necessary to consider the joint beam design in amorphous systems to better improve energy utilization and spectral efficiency.

[0005] In summary, it is very important to comprehensively consider and study the intelligent reflecting surface-assisted amorphous symbiotic communication system, which is of great significance for the deployment of actual Internet of Things scenarios. Summary of the Invention

[0006] The purpose of the present invention is to provide a beam optimization method for an intelligent reflecting surface-assisted amorphous symbiotic communication system. The beam optimization method provided by the present invention can effectively improve the communication performance of the system.

[0007] The present invention adopts the following technical solutions:

[0008] A beam optimization method for an intelligent reflecting surface-assisted amorphous symbiotic communication system, the amorphous symbiotic communication system includes an environmental radio frequency signal source base station, an intelligent reflecting surface, a primary user, and a secondary user, and the beam optimization method includes the following steps:

[0009] (1) The base station obtains the average achievable rate of the primary user and the theoretical bit error rate of the secondary user according to the wireless channels of the primary user and the secondary user;

[0010] (2) The base station establishes an optimization problem based on the average achievable rate and the theoretical bit error rate and conducts beam design to obtain the jointly optimized active beam and passive beam;

[0011] (3) The base station transmits the optimized optimal reflecting surface phase design / optimized passive beam to the intelligent reflecting surface through a separate link line, and the optimized active beam is used for the base station beam design.

[0012] In the present invention, the transmission protocol of the amorphous symbiotic communication system is: at the beginning of each coherence interval, pilots are used for channel estimation, and the remaining time is used for information transmission; let s i [l] represent the l-th symbol received by the i-th primary user from the base station, which follows a zero-mean complex Gaussian signal with a variance of 1, that is x ∈ {0, 1} represents the symbol using phase shift keying modulation sent by the intelligent reflecting surface with equal probability; s i [l] has a symbol period that is 1 / L times that of x, that is, within the transmission time of each secondary symbol, L primary transmission symbols are sent;

[0013] Let and represent the channels from the \(b\)-th base station to the \(k\)-th primary user, from the \(b\)-th base station to the intelligent reflecting surface, from the intelligent reflecting surface to the \(k\)-th primary user, from the \(b\)-th base station to the secondary user, and from the intelligent reflecting surface to the secondary user, respectively. In addition, define as the reflection coefficient vector of the IRS, where \(\beta\ m = 1 and represent the amplitude reflection coefficient and the phase shift coefficient of the \(m\)-th element of the intelligent reflecting surface, respectively.

[0014] In step (1), the base station obtaining the average achievable rate of the primary user and the bit error rate of the secondary user according to the wireless channels of the primary user and the secondary user includes:

[0015] (1-1) Obtain the received signal at the \(k\)-th primary user in the \(l\)-th primary symbol period according to the transmission protocol, and obtain the signal-to-interference-plus-noise ratio for decoding \(s\ i [l] at the \(k\)-th primary user based on this received signal, and then obtain the average achievable rate of the \(k\)-th primary user according to the signal-to-interference-plus-noise ratio;

[0016] (1-2) Obtain the received signal at the secondary user in the \(l\)-th primary transmission symbol period according to the transmission protocol; based on this received signal, the secondary user perfectly decodes \(s\ i [l] and uses the successive interference cancellation method to remove the signal from the direct link to obtain the remaining signal at the secondary user;

[0017] (1-3) Based on the remaining signal at the secondary user, use an energy detector to derive the theoretical bit error rate of the on-off keying modulation signal (phase shift keying modulation data) from the intelligent reflecting surface.

[0018] In step (1-1), the received signal at the \(k\)-th primary user in the \(l\)-th primary symbol period is given by:

[0019]

[0020] where is additive white Gaussian noise with variance \(\sigma\ 2 and mean zero, \(w\ b,i represents the beamforming vector from the \(b\)-th base station to the \(i\)-th primary user, with power constraint where \(P\ b is the maximum transmit power of the \(b\)-th base station;

[0021] The signal-to-interference-plus-noise ratio for decoding \(s\ i [l] at the \(k\)-th primary user is given by:

[0022]

[0023] Then the instantaneous achievable rate of the \(k\)-th primary user is given by:

[0024]

[0025] Therefore, by averaging the symbols transmitted by the IRS, the average achievable rate of the \(k\)-th primary user is given by:

[0026]

[0027] In step (1-2), the received signal at the secondary user during the \(l\)-th primary transmission symbol period is given by:

[0028]

[0029] Define \(H\) 1 and \(H\) 0 as the events \(x = 1\) and \(x = 0\), respectively. Therefore, the remaining signal at the secondary user after using the successive interference cancellation method is given by:

[0030]

[0031] And in terms of distribution:

[0032]

[0033] where

[0034] In step (1-3), define to represent the total received energy in each secondary communication symbol interval. According to the central limit theorem, can be approximated as a Gaussian distribution, so there is:

[0035]

[0036] where represents the probability density function of under hypothesis \(i\). Therefore, using the energy detector, there is:

[0037]

[0038] where is the optimal threshold for separating the two hypotheses, given by:

[0039]

[0040] Therefore, the bit error rate can be approximately calculated as follows:

[0041]

[0042] In step (2), the base station establishes an optimization problem based on the average achievable rate and the theoretical bit error rate and performs beam design. The method for obtaining the jointly optimized active beam and passive beam includes:

[0043] (2-1) Establish an optimization problem based on the average achievable rate and the theoretical bit error rate, and introduce a penalty function to further transform the optimization problem;

[0044] (2-2) Solve the transformed optimization problem after introducing the penalty function by using the method of double-layer alternating iterative optimization, including inner-layer optimization and outer-layer optimization: the inner-layer optimization is to optimize the auxiliary variable, the active beam of the base station, and the passive beam at the intelligent reflecting surface respectively, and the outer-layer optimization is to update the penalty coefficient.

[0045] In the present invention, the beam design is a joint beam optimization design. According to the derived bit error rate structure, a penalty algorithm is designed, and the alternating optimization method is used to transform the quartic programming problem into a quadratic programming problem, reducing the problem complexity, so as to transform the joint beam optimization design into the active beam and passive beam optimization design. Among them, for the active beam optimization design, given the passive beam, based on the alternating direction method of multipliers, with the goal of minimizing the theoretical bit error rate of the secondary user, the problem can be decomposed into two quadratic programming problems and a single-constraint quadratic-constrained quadratic programming problem, and the optimal solution can be obtained by finding the zero point of its derivative function. For the passive beam optimization design, by introducing an auxiliary variable, the original quartic programming problem is transformed into an unconstrained quadratic programming problem and a single-mode constrained quadratic programming problem, and the optimal setting can be obtained by finding the zero point of its derivative function and the MM algorithm.

[0046] Specifically:

[0047] In step (2-1), the following optimization problem is established according to the average achievable rate and the theoretical bit error rate:

[0048]

[0049] By introducing a penalty function, the optimization problem is further transformed into:

[0050]

[0051] Among them,

[0052]

[0053] And μ 1,k , μ 2,kis the introduced auxiliary variable, and ρ is the penalty coefficient.

[0054] In step (2-2), the inner-layer optimization includes:

[0055] (2-2-1) Auxiliary variable optimization: Based on the active beam and the passive beam θ, obtain the update of the auxiliary variable μ 1,k , μ 2,k ;

[0056] (2-2-2) Active beam optimization: Based on the auxiliary variable μ 1,k , μ 2,k and the passive beam θ, obtain the update of the active beam Specifically: Transform the original quartic programming problem into two unconstrained quadratic programming problems and a single-constrained quadratic programming problem; for the unconstrained quadratic programming problem, the optimal variable setting can be obtained by finding the zero point of its derivative function, and for the single-constrained quadratic programming problem, the optimal setting can be obtained by introducing an auxiliary variable and performing a binary search for the zero point of its derivative function;

[0057] (2-2-3) Passive beam optimization: Based on the auxiliary variable μ 1,k , μ 2,k and the active beam obtain the update of the passive beam θ, and continuously repeat the above three steps until convergence. Specifically: Transform the original quartic programming problem into an unconstrained quadratic programming problem and a constant modulus constraint quadratic programming problem. For the unconstrained quadratic programming problem, the optimal variable setting can be obtained by finding the zero point of its derivative function, and for the constant modulus constraint quadratic programming problem, the optimal setting can be obtained by the MM algorithm.

[0058] The outer-layer optimization is to update the penalty coefficient ρ = cρ, where c is a constant less than 1.

[0059] Compared with the prior art, in the coexisting communication scenario, the present invention considers the joint design of the base station active beam and the intelligent reflecting surface passive beam in an amorphous network assisted by an intelligent reflecting surface. First, the theoretical bit error rate of the secondary user in the system is derived, and then, from the perspective of minimizing the theoretical bit error rate of the secondary user, the base station active beam and the intelligent reflecting surface passive beam are optimized, effectively improving the communication performance of the coexisting communication system and making up for the deficiency that the methods of the previous cellular communication network are not applicable to the amorphous communication network. Description of the Drawings

[0060] Figure 1 is the communication structure diagram and transmission protocol diagram of the intelligent reflecting surface-assisted amorphous coexisting communication system in the embodiment of the present invention;

[0061] Figure 2 is the convergence curve diagram of the beam optimization method of the present invention in the embodiment;

[0062] Figure 3 This is a performance comparison diagram of the beam optimization method and the non-joint beam design method proposed in the embodiments of the present invention. Detailed implementation manners

[0063] The following combines the accompanying drawings and embodiments to describe in detail the specific implementation manners of the present invention.

[0064] Figure 1 The communication structure diagram and transmission protocol diagram of the intelligent reflecting surface-assisted amorphous coexisting communication system are given. The amorphous coexisting communication system consists of B base stations (BSs), an intelligent reflecting surface (IRS) composed of M elements, K primary users (PRs), and a secondary user (IR). Among them, the primary users receive the data transmitted from the base stations, and this communication process is called primary communication. The secondary user receives and decodes the phase shift keying modulated data from the intelligent reflecting surface, and this communication process is called secondary communication. In this embodiment, the transmission protocol adopted by the amorphous coexisting communication system is as follows:

[0065] At the beginning of each coherence interval, pilots are used for channel estimation, and the remaining time is used for information transmission. Let s i [l] represent the l-th symbol received by the i-th primary user from the base station, which follows a zero-mean complex Gaussian signal with a variance of 1, that is x ∈ {0, 1} represents the symbol transmitted by the intelligent reflecting surface using phase shift keying modulation. In addition, in the considered transmission protocol, the rate of s i [l] is L times that of x, that is, there are L primary transmission symbols transmitted within the transmission time of each secondary symbol.

[0066] Let and respectively represent the channels from the b-th base station to the k-th primary user, from the b-th base station to the intelligent reflecting surface, from the intelligent reflecting surface to the k-th primary user, from the b-th base station to the secondary user, and from the intelligent reflecting surface to the secondary user. In addition, is defined as the reflection coefficient vector of the IRS, where β m = 1 and respectively represent the amplitude reflection coefficient and phase shift coefficient of the m-th element of the intelligent reflecting surface.

[0067] The specific beam optimization method adopted in this embodiment includes the following steps:

[0068] S1. The base station obtains the average achievable rate of the primary user and the theoretical bit error rate of the secondary user according to the wireless channels of the primary user and the secondary user

[0069] S1.1. Obtain the received signal at the \(k\)-th primary user in the \(l\)-th primary symbol period according to the transmission protocol, and obtain the signal-to-interference-plus-noise ratio (SINR) for decoding \(s[l]\) at the \(k\)-th primary user based on this received signal. Then, obtain the average achievable rate of the \(k\)-th primary user according to the SINR. i The received signal at the \(k\)-th primary user in the \(l\)-th primary symbol period is given by:

[0070] The received signal at the \(k\)-th primary user in the \(l\)-th primary symbol period is given by:

[0071]

[0072] where is additive white Gaussian noise with variance \(\sigma\) 2 and mean zero, and \(w\) b,i represents the beamforming vector from the \(b\)-th base station to the \(i\)-th primary user, with the power constraint where \(P\) b is the maximum transmit power of the \(b\)-th base station, \(diag\) is diagonalization, and \(H\) represents conjugate transpose. Therefore, the SINR for decoding \(s\) i [l] at the \(k\)-th primary user is given by:

[0073]

[0074] Then, the instantaneous achievable rate of the \(k\)-th primary user is given by:

[0075]

[0076] Therefore, by averaging the symbols transmitted by the intelligent reflecting surface, the average achievable rate of the \(k\)-th primary user is given by:

[0077]

[0078] S1.2. Obtain the received signal at the secondary user in the \(l\)-th primary transmission symbol period according to the transmission protocol; based on this received signal, the secondary user perfectly decodes \(s\) i [l] and uses successive interference cancellation (SIC) to remove the signal from the direct link, obtaining the residual signal at the secondary user.

[0079] Similarly, the received signal at the secondary user in the \(l\)-th primary transmission symbol period is given by:

[0080]

[0081] In the present invention, it is considered that the secondary user can perfectly decode \(s_i[l]\) and use SIC to remove the signal from the direct link. Define \(H\) 1 and \(H\) 0For events x = 1 and x = 0, thus, the residual signal at the secondary user is given by:

[0082]

[0083] And in terms of the distribution:

[0084]

[0085] Where denotes being subject to a complex Gaussian distribution, and overall it represents a complex Gaussian distribution with a mean of 0 and a variance of or σ 2 of the complex Gaussian distribution.

[0086] S1.3. Derive the theoretical bit error rate of the on-off keying modulation signal from the intelligent reflecting surface using the energy detector based on the residual signal at the secondary user

[0087] Define to represent the total received energy in each secondary communication symbol interval. According to the central limit theorem, when L is large, can be approximated as a Gaussian distribution. Thus, we have:

[0088]

[0089] Where represents the probability density function of under hypothesis i. Therefore, using the energy detector, we have:

[0090]

[0091] Where is the optimal threshold for separating the two hypotheses, given by:

[0092]

[0093] Therefore, when L is large enough, the bit error rate can be approximately calculated as:

[0094]

[0095] Where,

[0096]

[0097] Q represents the Q function, which is the right-tail function of the standard normal distribution and is also called the complementary cumulative distribution function (of the standard normal distribution).

[0098] S2. The base station establishes an optimization problem based on the average achievable rate and the theoretical bit error rate and conducts beam design to obtain the jointly optimized active beam and passive beam

[0099] S2.1. Establish an optimization problem based on the average achievable rate and the theoretical bit error rate, and further transform the optimization problem by introducing a penalty function.

[0100] The optimization problem is established as follows:

[0101]

[0102] where is the minimum rate required by the k-th primary user. By introducing a penalty function, the problem can be further transformed into:

[0103]

[0104] where,

[0105]

[0106] where,

[0107]

[0108] and μ 1,k ,μ 2,k are the introduced auxiliary variables, and ρ is the penalty coefficient.

[0109] S2.2. Consider using a two-layer alternating iterative optimization method to solve the above problem. The inner layer optimizes the auxiliary variables, the active beam design at the base station, and the passive beam design at the intelligent reflecting surface respectively, while the outer layer updates the penalty coefficient.

[0110] The whole process is as follows:

[0111] 1): Inner layer optimization

[0112] a) Based on the active beam and the passive beam θ, obtain the updated auxiliary variables μ 1,k ,μ 2,k .

[0113] b) Based on the auxiliary variables μ 1,k ,μ 2,k and the passive beam θ, obtain the updated active beam

[0114] c) Based on the auxiliary variables μ 1,k ,μ 2,k and the active beam obtain the updated passive beam θ.

[0115] Repeat the above three steps continuously until convergence.

[0116] 2): Outer layer update the penalty coefficient ρ = cρ, where c is a constant less than 1.

[0117] Repeat the above four steps continuously until convergence.

[0118] a) Auxiliary variable optimization

[0119] Through the analysis of the original problem, given the active beam and the passive beam θ, the optimization problem can be formulated as:

[0120]

[0121] where and

[0122]

[0123] The above problem is a convex problem with respect to the optimization variables and can be solved by convex optimization tools.

[0124] b) Active beam optimization

[0125] Given the auxiliary variables μ 1,k , μ 2,k and the passive beam θ, the optimization problem can be formulated as:

[0126]

[0127] where

[0128]

[0129] where ρ 1 , ρ 2 is the penalty coefficient, is the dual variable, is the auxiliary variable and

[0130]

[0131] where Auxiliary variable where

[0132] This optimization problem can be solved by the method of alternating optimization:

[0133] When given , this problem can be transformed into the following unconstrained quadratic programming problem:

[0134]

[0135] where and

[0136]

[0137] It can be proved that this problem is a convex problem and can be solved by finding the zero point of the first derivative of the function.

[0138] When w and z are given w,B+1 this problem can be transformed into the following unconstrained quadratic programming problem:

[0139]

[0140] where and

[0141]

[0142] It can be proved that this problem is a convex problem and can be solved by finding the zero point of the first derivative of the function.

[0143] When w and are given, this problem can be transformed into the following single-constrained quadratic programming problem:

[0144]

[0145] It can be proved that this problem is a convex problem and can be solved by binary searching for the zero point of the first derivative of the function.

[0146] c) Passive beam optimization

[0147] Given the auxiliary variable μ 1,k , μ 2,k and the active beam w, the optimization problem can be formulated as:

[0148]

[0149] where

[0150]

[0151] where ρ 3 is the penalty coefficient, ξ 1 is the dual variable, is the auxiliary variable.

[0152] This optimization problem can be solved by the method of alternating optimization:

[0153] When is given, this problem can be transformed into the following unconstrained quadratic programming problem:

[0154]

[0155] where

[0156]

[0157]

[0158] It can be proved that this problem is a convex problem and can be solved by finding the zero point of the first derivative of the function.

[0159] When θ is given, this problem can be transformed into the following constant modulus constrained quadratic programming problem:

[0160]

[0161] where

[0162]

[0163]

[0164] It can be proved that this problem can be solved by the MM algorithm.

[0165] Next, the effectiveness of the beam optimization method for the intelligent reflecting surface-assisted amorphous coexisting communication system proposed in the present invention is proved by simulation results. The technical effects achieved in this embodiment are as follows:

[0166] Figure 2 and Figure 3 are the convergence curve graph and performance comparison graph of the method proposed in the invention in the embodiment. The simulation conditions are that three base stations are respectively deployed at positions (0m, 0m, 0m), (15m, 0m, 0m), and (30m, 0m, 0m), the intelligent reflecting surface is deployed at the position (0m, 150m, 5m), 4 primary users are evenly distributed on a circle centered at (10m, 150m, 0m), and the secondary user is deployed at the position (0m, 300m, 0m).

[0167] Figure 2 The convergence graph of the beam optimization method provided in this embodiment is given. As can be seen from Figure 2 the target value of the method provided in this embodiment increases rapidly in the first few iterations and gradually becomes slow until convergence.

[0168] Figure 3 This is the comparison of the optimization performance of the amorphous coexisting communication system provided in this embodiment. The compared benchmark 1 adopts a random passive beam design and uses the active beam method provided in this embodiment for design. The compared benchmark 2 adopts a subspace method to design an active beam and uses the passive beam method provided in the present invention for design. From Figure 3It can be shown that the number of intelligent reflecting surface elements has a great influence on the bit error rate of secondary transmission symbols. Specifically, the bit error rate of secondary transmission symbols decreases as the number of intelligent reflecting surface elements increases because more intelligent reflecting surface elements can achieve higher passive beamforming performance gain, thereby reducing the bit error rate of secondary transmission. In addition, the performance of the beam optimization method provided by the present invention is superior to the two basic schemes, which highlights the advantages of jointly optimizing the active beamforming at the base station and the passive beamforming at the intelligent reflecting surface of the present invention.

[0169] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be covered by the protection scope of the present invention.

Claims

1. A beam optimization method for an amorphous coexisting communication system assisted by intelligent reflecting surface. The amorphous coexisting communication system includes an environmental radio frequency signal source base station, an intelligent reflecting surface, a primary user, and a secondary user. The beam optimization method is characterized in that it includes the following steps:

1. The base station obtains the average achievable rate of the primary user and the theoretical bit error rate of the secondary user according to the wireless channels of the primary user and the secondary user; 2. The base station establishes an optimization problem based on the average achievable rate and the theoretical bit error rate and conducts beam design to obtain the jointly optimized active beam and passive beam; 3. The base station transmits the optimized passive beam to the intelligent reflecting surface through a separate link line, and the optimized active beam is used for the base station beam design; The transmission protocol of the amorphous coexisting communication system is: at the beginning of each coherence interval, pilots are used for channel estimation, and the remaining time is used for information transmission; Let s i [l] represent the l-th symbol received by the i-th primary user from the base station, which follows a zero-mean complex Gaussian signal with a variance of 1, that is x ∈ {0, 1} represents the symbol transmitted by the intelligent reflecting surface with equal probability using phase shift keying modulation; s i [l] has a symbol period that is 1 / L times that of x, that is, there are L primary transmission symbols sent within each secondary symbol transmission time; Let and respectively represent the channels from the b-th base station to the k-th primary user, from the b-th base station to the intelligent reflecting surface, from the intelligent reflecting surface to the k-th primary user, from the b-th base station to the secondary user, and from the intelligent reflecting surface to the secondary user; In addition, is defined as the reflection coefficient vector of the IRS, where β m = 1 and θ m ∈ [0, 2π], respectively represent the amplitude reflection coefficient and phase shift coefficient of the m-th element of the intelligent reflecting surface, and j satisfies j 2 = -1; In step 1, the base station obtaining the average achievable rate of the primary user and the bit error rate of the secondary user according to the wireless channels of the primary user and the secondary user includes: 1.

1. Obtain the received signal at the k-th primary user in the l-th primary symbol period according to the transmission protocol, and obtain the signal-to-interference-plus-noise ratio (SINR) for decoding s i [l] at the k-th primary user based on this received signal. Then, obtain the average achievable rate of the k-th primary user according to the SINR. 1.

2. Obtain the received signal at the secondary user in the l-th primary transmission symbol period according to the transmission protocol; according to this received signal, the secondary user perfectly decodes s i [l] and uses the successive interference cancellation method to remove the signal from the direct link to obtain the remaining signal at the secondary user; 1.

3. Derive the theoretical bit error rate of the on-off keying modulation signal from the intelligent reflecting surface using an energy detector based on the remaining signal at the secondary user; In step 2, the method for the base station to establish an optimization problem based on the average achievable rate and the theoretical bit error rate and perform beam design to obtain the jointly optimized active beam and passive beam includes: 2.

1. Establish an optimization problem based on the average achievable rate and the theoretical bit error rate, and further transform the optimization problem by introducing a penalty function; 2.

2. Solve the transformed optimization problem after introducing the penalty function by using a two-layer alternating iterative optimization method, including inner-layer optimization and outer-layer optimization: the inner-layer optimization is to optimize the auxiliary variable, the active beam of the base station, and the passive beam of the intelligent reflecting surface respectively, and the outer-layer optimization is to update the penalty coefficient; In step 2.2, the inner-layer optimization includes: 2.2.

1. Auxiliary variable optimization: Based on the active beam and the passive beam θ, the auxiliary variable update μ 1,k , μ 2,k ; 2.2.2, Active beam optimization: Based on the auxiliary variable μ 1,k , μ 2,k and the passive beam θ, the active beam update is obtained Specifically: Transform the original quartic programming problem into two unconstrained quadratic programming problems and one single-constrained quadratic programming problem; for the unconstrained quadratic programming problem, the optimal variable setting can be obtained by finding the zero point of its derivative function, and for the single-constrained quadratic programming problem, the optimal setting can be obtained by introducing an auxiliary variable and performing a binary search for the zero point of its derivative function; 2.2.3, Passive beam optimization: Based on the auxiliary variable μ 1,k , μ 2,k and the active beam to obtain the updated passive beam θ, specifically: transform the original quartic programming problem into an unconstrained quadratic programming problem and a constant modulus constrained quadratic programming problem. For the unconstrained quadratic programming problem, the optimal variable setting can be obtained by finding the zero point of its derivative function. For the constant modulus constrained quadratic programming problem, the optimal setting can be obtained by the MM algorithm; Repeat the above three steps continuously until convergence.

2. The beam optimization method for an amorphous symbiotic communication system assisted by an intelligent reflecting surface according to claim 1, wherein in step 1.1, the received signal at the k-th primary user in the l-th primary symbol period is given by the following formula: where is additive white Gaussian noise with variance σ 2 and zero mean, w b,i represents the beamforming vector from the b-th base station to the i-th primary user, with a power constraint where P b is the maximum transmit power of the b-th base station, is a complex Gaussian distribution; Decode s at the k-th primary user i The signal-to-interference-plus-noise ratio of [l] is given by: Then the instantaneous achievable rate of the k-th primary user is given by the following formula: Therefore, by averaging the symbols transmitted by the intelligent reflecting surface, the average achievable rate of the k-th primary user is given by the following formula:

3. The beam optimization method for an amorphous symbiotic communication system assisted by an intelligent reflecting surface according to claim 1, characterized in that, In step 1.2, the received signal at the secondary user in the l-th primary transmission symbol period is given by the following formula: Define H 1 and H 0 as the events x = 1 and x = 0, respectively. Thus, the residual signal at the secondary user after using the successive interference cancellation method is given by: And in terms of distribution: Among them 4. The beam optimization method for an amorphous symbiotic communication system assisted by an intelligent reflecting surface according to claim 3, characterized in that, In step 1.3, it is defined that represents the total received energy in each secondary communication symbol interval. According to the central limit theorem, is approximated as a Gaussian distribution. Therefore, we have: where i = {0, 1}, representing the probability density function under hypothesis i Therefore, using an energy detector, we have: where is the optimal threshold for separating the two hypotheses and is given by: Therefore, the bit error rate is approximately calculated as:

5. The beam optimization method for an amorphous symbiotic communication system assisted by an intelligent reflecting surface according to claim 1, characterized in that, In step 2.1, the following optimization problem is established according to the average achievable rate and the theoretical bit error rate: where is the minimum rate required by the k-th primary user. By introducing a penalty function, the optimization problem is further transformed into: where, and μ 1,k , μ 2,k is the introduced auxiliary variable, and ρ is the penalty coefficient.

6. The beam optimization method for an amorphous symbiotic communication system assisted by an intelligent reflecting surface according to claim 1, characterized in that, The outer-layer optimization is to update the penalty coefficient ρ = cρ, where c is a constant less than 1.

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