Wireless control system performance optimization method based on mode selection and power distribution

Abstract

The invention discloses a wireless control system performance optimization method based on mode selection and power distribution, belongs to the field of wireless communication, and aims to improve system communication performance and control performance on the basis of maximization of system spectrum efficiency based on an uplink and downlink communication system model and a control model of a wireless control system. Constructing an optimization problem of spectrum efficiency maximization by taking transmission mode selection, channel selection, user transmitting power and control convergence rate as optimization variables; the method comprises the following steps: firstly, providing a selection and distribution algorithm for interference equalization, and updating a weight matrix and interference values in two modes in real time on the basis of a Hungary algorithm; secondly, a game model is constructed based on the relationship between the users and the relationship between the users and the base station in the two modes, and a distributed pricing strategy is constructed based on a mechanism of maximizing D2D and cellular communication total utility. By adopting the method, the problems of interference and power distribution among users are effectively solved through a game playing method.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and in particular to a method for optimizing the performance of a wireless control system based on mode selection and power allocation. Background Art

[0002] At present, the main communication methods of real-time wireless control systems are D2D and traditional cellular communication networks. D2D communication can reduce resource consumption, reduce communication latency and improve reliability. However, in the face of complex and changeable communication situations, the D2D communication method may face the situation of low communication reliability, while the traditional cellular communication network faces the situation of low frequency efficiency. With the support of D2D technology, compared with the traditional cellular network, the spectrum efficiency can be increased by up to 50%, and the overall system performance can be significantly enhanced. Therefore, the cooperation of D2D and cellular networks is a very promising communication technology. D2D communication allows the reuse of the existing spectrum of cellular users. Although this method improves communication efficiency, it also causes interference between cellular users and D2D users. In industrial scenarios, the scenario of D2D users and cellular users working together has been widely studied, but the control performance in the real-time wireless control scenario has not been considered. Therefore, a scenario of a wireless control system in which cellular communication and D2D communication work together is proposed. Under the collaborative design and joint optimization of communication and control, the performance of control and communication is considered. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for optimizing the performance of a wireless control system based on mode selection and power allocation to solve the problems existing in the background art.

[0004] To achieve the above purpose, the present invention provides a method for optimizing the performance of a wireless control system based on mode selection and power allocation, including the following steps:

[0005] S1. With the goal of maximizing the spectrum efficiency of the wireless control system and improving the system communication performance and control performance, an optimization problem P0 for maximizing the spectrum efficiency is constructed with transmission mode selection, channel selection, user transmit power, and control convergence rate as optimization variables, and the optimization problem P0 is transformed by a method of communication and control collaboration;

[0006] S2. Using the idea of the bipartite graph matching algorithm in graph theory, an optimal channel and transmission mode allocation scheme under a fixed power is obtained;

[0007] S3. Based on the allocation scheme in S2, the optimal transmit power allocation is solved.

[0008] Preferably, the content of S1 is as follows:

[0009] The spectral efficiency of the wireless control system in D2D mode transmission, cellular mode uplink transmission, and cellular mode downlink transmission is expressed as the overall spectral efficiency:

[0010]

[0011] where x m,l,1 and x m,l,2 are parameters for mode selection and are binary variables; x m,l,1 indicates whether user m uses mode 1 (i.e., D2D dedicated mode) on channel l; similarly, x m,l,2 indicates whether user m uses mode 2 (i.e., cellular dedicated mode) on channel l; where x m,l,1 = 1 means user m uses mode 1 on channel l, and x m,l,1 = 0 means the opposite, and similarly for x m,l,2 ; λ d , and represent the payload of user m in the dedicated mode, the uplink payload of user m in the cellular mode, and the downlink payload of user m in the cellular mode, respectively; M represents that there are M sensors and controllers in the wireless communication control system; N represents the sampling time index in the control process; ε m represents the transmission error probability; assuming that the sizes of the payloads in the same mode are the same, for a given payload λ, it is expressed as λ = R m T u B m ; B m represents the occupied bandwidth; R m represents the maximum transmission rate of the m-th user in the case of finite block length; T u is the allocated time resource and is regarded as the transmission delay;

[0012] To simplify the discussion, assume that the allocated time resource (i.e., transmission delay) T u and the bandwidth B m are fixed;

[0013] Based on the above, the optimization problem P0 is established:

[0014]

[0015] p m ≤ p max ; (a)

[0016] ε m,1 ≤ ε th ; (b)

[0017] ε m,2 ≤ ε th ; (c)

[0018] ε m,3 ≤ ε th ; (d)

[0019] x m,l,k ∈ {0, 1}; (e)

[0020]

[0021] where N max is the total number of channels in the uplink; p m represents the user transmission power; p max represents the maximum value of the user transmission power; ε th represents the maximum threshold of the packet loss rate; Equation (a) is the objective function (maximizing spectral efficiency) subject to communication and control constraints; Equation (b) is the power constraint for each user; Equations (c)-(d) are the reliability constraints of URLLC; Equation (e) is the channel parameter constraint; Equations (f)(g) are the constraints for users on channel usage;

[0022] The expression is affected by the packet transmission probability, and the class Lyapunov function is expressed as:

[0023]

[0024] where is the idle period; Pr{α n = 1} is the packet transmission success probability; Pr{α n = 0} is the packet transmission failure probability;

[0025] Therefore, it is transformed into:

[0026]

[0027] where ξ n ≠ 0, let [[ID=5�]]represent the supremum of the right-hand term in the above formula; Through the above formula, the control constraint that determines the control convergence speed ρ of the communication service quality is obtained, and is affected by the control constraint, c * (ρ); Then problem P0 is rewritten as P1:

[0028]

[0029] p m ≤ p max ; (h)

[0030] ε m,1 ≤ 1 - c * ; (i)

[0031] ε m,2 ≤ 1 - c * ; (j)

[0032] ε m,3 ≤ 1 - c * ; (k)

[0033] x m,l,k ∈ {0, 1}; (l)

[0034]

[0035] where c * represents the maximum value of the packet loss rate under control constraints; Equation (h) is the objective function (maximizing spectral efficiency) subject to communication and control constraints; Equation (i) is the power constraint for each user; Equations (j)-(k) are the reliability constraints for URLLC; Equation (l) is the channel parameter constraint; Equations (m)(n) are the constraints for users on channel usage.

[0036] Preferably, the content of S2 is as follows:

[0037] Using the idea of the bipartite graph matching algorithm in graph theory, a channel mode allocation scheme is formulated; to simplify the complexity of the allocation problem, channel mode allocation is performed under a given transmit power; by given the transmit power, problem P1 is rewritten as the following sub-problem P2:

[0038]

[0039] x m,l,k ∈ {0, 1};

[0040]

[0041] Taking the channel rate C m,l,k as the reward for allocating channel L to the m-th user in mode k, problem P2 can be regarded as a matching problem between modes and users. To solve this problem, by setting U m,l,k = -C m,l,k the reward is converted into cost and the constraint C m,l,k ≥ C th sets all costs less than the threshold to +∞. Thus, problem P2 is converted into an allocation problem. Based on the Hungarian algorithm, it is improved by establishing a dynamic weight matrix to update the mode, and a more effective transmission mode allocation scheme is obtained.

[0042] Preferably, the specific process of the improved Hungarian algorithm is as follows:

[0043] First, set the total interference I1 and I2 of the two modes to the same initial value. Use the Hungarian algorithm to match channels and modes for one of the users, and set the interference generated by the mode currently used by the user as the total interference in the corresponding mode. Subsequently, repeatedly use the Hungarian algorithm to match channels and modes for the remaining users and update the total interference of the corresponding mode until all users are matched.

[0044] Preferably, the content of S3 is as follows:

[0045] S31. Establish a game model that comprehensively considers D2D mode users and cellular mode users to solve the optimal power allocation problem;

[0046] S32. On the basis of the game model, adopt a distributed iterative method to solve the Nash equilibrium point;

[0047] S33. Propose a pricing strategy to determine the price on the basis of maximizing social utility, thereby coordinating and controlling the transmission power of users.

[0048] Preferably, the content of S31 is as follows:

[0049] Regard both D2D mode users and cellular mode users as players in the game (only the transmission power of the uplink is considered in the cellular mode), and select their own transmission power p under limited information m , and the goal of each player is to maximize its own utility.

[0050] In game theory, the utility function is used to quantify the benefit of each player. In the game model, considering pricing, the utility function of each user can be expressed as:

[0051] where represents the channel rate used by the user;

[0052]

[0053] is the SINR. Since the interference is different in different modes, it can be expressed as:

[0054]

[0055] is the SINR in the D2D mode, is the SINR in the cellular mode; is the penalty term and is the price function:

[0056]

[0057] is the interference generated in the D2D mode, For the interference and transmission power in the cellular mode (in this embodiment, it is assumed that the transmission power of the user is equal to the reception power of the base station. Since the base station power is limited, the power of the uplink will affect the transmission power of the downlink, so a price needs to be paid).

[0058] Obtained through the above formula and are both the transmission powers of the users, only the transmission objects are different; for better readability, the utility function is abbreviated as:

[0059]

[0060] To verify the rationality of the equation, the utility function of each user is defined as the data rate minus the price that each user needs to pay. λ m is a non - negative parameter, which can be expressed as the "willingness" of the user to increase the data rate; from an economic perspective, λ m reflects the "willingness" of player m to pay for a higher data rate. v is the price per unit of interference power (in the cellular network, it is the price per unit of interference power and transmission power).

[0061] Preferably, the content of S32 is as follows:

[0062] To find the Nash equilibrium point, the solutions of the following system of equations must be found:

[0063]

[0064] Based on the established game model, a distributed iterative method is adopted to propose a distributed power allocation mechanism. Numerically, the non - linear equations in the above formula are solved by the fixed - point iteration method. First, this system of equations is converted into the fixed - point form. Consider the following form of the fixed - point equation:

[0065]

[0066] For any m ∈ {1, 2,....M}.

[0067] For this fixed - point form, calculate p m The only common information required is the price v. It is reasonable to assume that the user knows its own transmission power and the total reception power of the receiver. Using this fixed - point form, user m does not need to know the λ m of other users during the iterative process of calculating p m 、p m . Therefore, the iterative process can be implemented in a distributed manner with limited information;

[0068] During the iterative process, p m [t], Wm [t] respectively represent the transmission power of user m and the total received power of the receiving object. The iterative formula is as follows, for all m:

[0069]

[0070] Where

[0071]

[0072] The steps to calculate the expected transmission power of each user m in a distributed manner are as follows:

[0073] a. Each user m takes an initial value p m [0], where p m [0] ∈ [p min , p max ;

[0074] b. Each user updates its transmission power according to the equation and then calculates U by the equation m [t], during which all users update their calculations simultaneously;

[0075] c. If in the t-th round of calculation, for a predetermined threshold, if |U m [t] - U m [t - 1|] ≤ ∈, then terminate the calculation of user m, and p m * = p m [t]. Otherwise, continue with the next round of calculation.

[0076] Preferably, the content in S33 is as follows:

[0077] Social utility is a key indicator representing the common interests of all participants. Social utility U is defined as the sum of the utilities of each participant at the Nash equilibrium point, including the income of the base station:

[0078]

[0079] Where ∑vP m is the total income of the base station;

[0080] At the base station, it is necessary to maximize the social utility under the constraint condition γ m ≥ γ de , where γ m is the actual SINR of the user, and γ de is the desired SINR of the user. The key is to achieve smooth control of the object state through a lower control convergence rate, resulting in good control performance. Therefore, for users, it is necessary to maximize the social utility under the constraint condition p. Where εm is the packet loss rate of the user, c * (ρ th ) is the performance metric that converts the control constraint into a communication constraint. Thus, the total social utility optimization problem can be expressed as follows:

[0081]

[0082] To solve the above problem, the transmit power at Nash equilibrium is an implicit function of the unit price v, and this function has the following properties:

[0083] Theorem 1: At the Nash equilibrium point, for any v1 > v2 > 0, there is

[0084] Corollary 1: The social utility U decreases with respect to the unit price v, the SINR increases with respect to the unit price v, and the packet transmission success probability decreases with respect to the unit price v.

[0085] Therefore, through the above analysis, it is considered that the optimal unit price v should satisfy the following two equations simultaneously:

[0086] γ m (v*) ≥ γ de ;

[0087] ε m (v*) ≤ 1 - c * (ρ th )

[0088] To ensure the optimal property, it should be satisfied.

[0089] γ m (v*) = γ de ;

[0090] ε m (v*) = 1 - c * (ρ th ) = ε th ;

[0091] Since U decreases with respect to v and the packet transmission success probability decreases with respect to v, while γ m increases with respect to v. It is considered that the optimal pricing strategy v * is the lowest price that can simultaneously ensure γ m (v*) ≥ γ de and the highest price that can ensure ε m (v*) ≤ 1 - c * (ρ th ) (i.e., satisfy the equations simultaneously).

[0092] Therefore, finding the optimal solution to the following equation is equivalent to finding the roots that satisfy the above equation simultaneously.

[0093]

[0094] For the penalty term, there is

[0095]

[0096] For the packet successful transmission probability, through ε th Generate the expected power value p th :

[0097]

[0098] Assume that the equation P(v) is expressed as a functional equation for solving the price v, which is expressed as

[0099] P(v) = I(v);

[0100] The threshold of the equation P(v) can be expressed as:

[0101]

[0102] Since the closed interval of the optimal price v* cannot be determined, algorithms of the type such as the bisection method may not be applicable to finding the roots of this equation. The secant method is used to find the optimal price v*. This method starts from two initial values v[0] and v[1], and calculates the price v using the following formula until the price v converges. At this time, the price v is the optimal price v*.

[0103]

[0104] Due to different thresholds of the equation, two optimal pricing will be generated, corresponding to the pricing of the D2D dedicated mode and the cellular mode respectively.

[0105] Therefore, the wireless control system performance optimization method based on mode selection and power allocation adopted by the present invention has the following beneficial effects:

[0106] (1) Based on the communication model and the control model, considering the interference problem between D2D and cellular, aiming to improve the system communication performance and control performance on the basis of maximizing the system spectral efficiency, an optimization problem of maximizing spectral efficiency is constructed with transmission mode selection, channel selection, user transmit power, and control convergence rate as optimization variables;

[0107] (2) A selection and allocation algorithm for interference balancing is proposed. Based on the Hungarian algorithm, this algorithm updates the weight matrix and the interference values in the two modes in real time to achieve the purpose of interference balancing;

[0108] (3) Based on the relationships between users in two modes and the relationships between users and base stations, a game model is constructed using non - cooperative game theory, and a distributed pricing strategy is constructed based on the mechanism of maximizing the total utility of D2D and cellular communications. Finally, the problems of interference and power allocation among users are effectively solved through the game method;

[0109] (4) An uplink and downlink communication model and a control model of the wireless control system are constructed, and joint mode selection and power allocation are used to improve the communication performance and control performance of the wireless control system.

[0110] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Description of the Drawings

[0111] Figure 1 It is a communication model diagram of the wireless control system based on mode selection and power allocation according to an embodiment of the present invention;

[0112] Figure 2 It is an overall flow block diagram of the performance optimization method of the wireless control system based on mode selection and power allocation according to the present invention. Detailed Embodiment

[0113] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0114] As Figure 1 shown, this embodiment considers a centralized real - time wireless communication control system, which consists of multiple sensors, controllers, and actuators. There are a total of M sensors and controllers, all of which are independent users (in this embodiment, sensors and controllers are collectively referred to as mode - selecting users), and independently select the D2D communication mode or the cellular communication mode to provide services for the controller or actuator. The method proposed in this embodiment can be easily extended to scenarios with multiple factories. When the factory is working, the sensor first reads the working state of the factory and selects a better channel and transmission mode according to the communication situation to transmit the state to the controller. After reading the factory state, the controller generates control information and selects a better channel and transmission mode according to the communication situation to transmit it to the actuator, and the actuator executes the command to update the current state of the factory.

[0115] System Control Model:

[0116] A real-time control model with communication delay and communication reliability is provided. When activated, the sensor samples the current factory state and transmits it to the controller inside the factory. The controller calculates its state using the Kalman filter based on the strongest signal transmitted by the sensor and calculates the control command, and then transmits the control command to the actuator inside the factory. The Kalman filter inside the controller performs state estimation by combining prior information and posterior information, and finally the actuator receives the control command to execute the action and updates the factory state.

[0117] Based on the above control process, the linear differential equation of the factory can be expressed as:

[0118] dx(t) = Ax(t)dt + Bu(t)dt + dn(t);

[0119] where x(t) is the factory state, u(t) is the control input, and n(t) is the perturbation caused by additive white Gaussian noise (AWGN) with zero mean and variance R. In addition, A and B are physical system parameter matrices

[0120] Assume s n represents the sampling period at time index n, which is composed of the wireless transmission delay T u idle period and can be expressed as

[0121]

[0122] where n = 1, 2,..., N represents the sampling time index in the control process.

[0123] Then, based on the above discrete-time control model with time delay T u can be expressed as

[0124]

[0125] where

[0126] Assume is the generalized state; the above discrete-time control model can be rewritten as:

[0127]

[0128] where Assume Ω n = Ω,

[0129] Considering packet loss, there is a packet transmission success probability Pr{α n = 1} = 1 - ε and a packet transmission failure probability Pr{α n= 0} = ε, where ε represents the probability of user transmission failure. Additionally, it is assumed that the state estimator is perfect. Then the above equation can be expressed as a closed-loop control system:

[0130]

[0131] which can be rewritten in a general form as:

[0132]

[0133] where K is the control command feedback parameter.

[0134] System communication model:

[0135] A communication model with transmission delay, packet error probability, and mutual interference between transmission modes is provided. M users with D2D and cellular communication capabilities are collectively referred to as users, and all users coexist within the same uplink spectrum resource (complete frequency reuse within the cell). According to the QOS, rate, and control performance requirements of the above users and other users, the mode selection for users to transmit data will be optimized. For each user, a D2D dedicated mode and a cellular dedicated mode will be provided. In the D2D dedicated mode, the user will select a channel with good transmission conditions according to the channel state and reuse the uplink resources, that is, share the uplink resources with users in the cellular mode. In the cellular dedicated mode, the user selects a suitable channel according to the channel state to transmit information to the base station, and the base station then transmits it to the receiving user through the downlink.

[0136] The maximum transmission rate of the m-th user in the case of finite block length is

[0137]

[0138] In the above formula, the first term on the right side is the Shannon capacity that can be achieved without transmission errors, the second term is the negative error bits introduced by channel dispersion, and the third term is the order. Additionally, B m is the occupied bandwidth, ε m is the transmission error probability, is the inverse function of the Q function. T u is the allocated time resource and is regarded as the transmission delay.

[0139] According to the rate formula, the packet error probability can be expressed as

[0140]

[0141] Let N c be the set of channels used by the cellular mode (this set only considers the uplink and does not consider the downlink), N dThe set of channels used in the dedicated mode. Since the resources of the uplink are limited, the two sets satisfy the following constraints:

[0142] 2N c +N d ≤N max ;

[0143] where N max is the total number of channels in the uplink.

[0144] In addition, assuming that all links experience independent block fading, the channel gain of user i on channel k in the dedicated mode can be expressed as H i,k,1 , and similarly, the channel gain of user i on channel k in the cellular mode is expressed as H i,k,2 . When using the D2D dedicated mode, since the resources of the uplink are reused, the cellular mode users will interfere with the dedicated mode users. In this embodiment, it is assumed that there is also interference under different modes of the same channel. Then the interference generated in the dedicated mode can be expressed as:

[0145]

[0146] When using the cellular mode, since the dedicated mode reuses the uplink resources that the cellular mode needs to use, the dedicated mode users will also interfere with the cellular mode users. In this embodiment, it is assumed that there is also interference under different modes of the same channel. Then the interference generated in the cellular mode can be expressed as:

[0147]

[0148] Assuming that the unilateral noise spectral density is expressed as N0, the Shannon capacity channel rate and channel dispersion are as follows:

[0149] C m =T u B m log(1 + γ m );

[0150] Channel dispersion:

[0151]

[0152] where γ m is the signal-to-interference-plus-noise ratio (SINR). Through the above analysis of interference, the SINR under different modes can be expressed as follows

[0153] SINR in the D2D mode:

[0154]

[0155] SINR of the uplink in the cellular mode:

[0156]

[0157] Since there is no resource reuse in the downlink, there is no interference and the SINR can be expressed as

[0158]

[0159] where h m is the small-scale fading coefficient of user m, g m is the path loss coefficient of user m

[0160] See also Figure 2 , a wireless control system performance optimization method based on mode selection and power allocation, comprising the following steps:

[0161] S1. With the goal of improving the system communication performance and control performance based on maximizing the spectrum efficiency of the wireless control system, an optimization problem P0 for maximizing spectrum efficiency is constructed with transmission mode selection, channel selection, user transmit power, and control convergence rate as optimization variables. The optimization problem P0 is transformed through the communication and control collaborative method.

[0162] The goal of this embodiment is to maximize the communication spectrum efficiency (SE) and maintain good performance of the overall system. The spectrum efficiency of the wireless control system in D2D mode transmission, cellular mode uplink transmission and cellular mode downlink transmission is expressed as the overall spectrum efficiency:

[0163]

[0164] where x m,l,1 and x m,l,2 Parameter for mode selection, which is a binary variable; x m,l,1 Indicates whether user m uses mode 1 (i.e., D2D dedicated mode) on channel l; similarly, x m,l,2 Indicates whether user m uses mode 2 (i.e., cellular-only mode) on channel l; where x m,l,1 =1 means user m uses mode 1 on channel l, x m,l,1 =0, on the contrary, x m,l,2 Similarly; d 、 and are the payload of user m in dedicated mode, the payload of user m in uplink in cellular mode, and the payload of user m in downlink in cellular mode, respectively; assuming that the payloads in the same mode have the same size, for a given payload λ, it is expressed as λ = R m T u B m ;

[0165] For simplicity of discussion, assume that the allocated time resource (i.e., transmission delay) T u and the bandwidth B m are fixed;

[0166] Based on the above, the optimization problem P0 is established as follows:

[0167]

[0168] p m ≤p max ; (a)

[0169] ε m,1 ≤ε th ; (b)

[0170] ε m,2 ≤ε th ; (c)

[0171] ε m,3 ≤ε th ; (d)

[0172] x m,l,k ∈{0,1}; (e)

[0173]

[0174] Equation (a) is the objective function (maximizing spectral efficiency) subject to communication and control constraints; equation (b) is the power constraint for each user; equations (c)-(d) are the reliability constraints of URLLC; equation (e) is the channel parameter constraint; equations (f)(g) are the constraints for users on channel usage;

[0175] According to dx(t) = Ax(t)dt + Bu(t)dt + dn(t), it can be seen that the expression is affected by the packet transmission probability, and the class Lyapunov function is expressed as:

[0176]

[0177] Therefore, it is transformed into:

[0178]

[0179] where ξ n ≠0, let represent the supremum of the right-hand term in the above formula; the control constraint that determines the control convergence speed ρ of the communication service quality is obtained through the above formula, and is affected by the control constraint, c * (ρ); then the problem P0 is rewritten as P1:

[0180]

[0181] p m ≤p max ; (h)

[0182] ε m,1 ≤1 - c * ; (i)

[0183] ε m,2 ≤1 - c * ; (j)

[0184] ε m,3 ≤1 - c * ; (k)

[0185] x m,l,k ∈ {0, 1}; (l)

[0186]

[0187] Equation (h) is the objective function (maximizing spectral efficiency) subject to communication and control constraints; Equation (i) is the power constraint for each user; Equations (j)-(k) are the reliability constraints for URLLC; Equation (l) is the channel parameter constraint; Equations (m)(n) are the constraints for users on channel usage.

[0188] S2. Using the idea of the bipartite graph matching algorithm in graph theory, obtain the optimal channel and transmission mode allocation scheme under the fixed power condition.

[0189] Using the idea of the bipartite graph matching algorithm in graph theory, formulate the channel mode allocation scheme; To simplify the complexity of the allocation problem, perform channel mode allocation under the given transmit power; By given the transmit power, problem P1 is rewritten as the following sub-problem P2:

[0190]

[0191] x m,l,k ∈ {0, 1};

[0192]

[0193] Since users in different modes will interfere with each other, users using the same transmission mode on the same channel will not interfere with each other while users using different transmission modes will interfere with each other. Therefore, the key of the channel mode allocation scheme lies in mode allocation rather than channel allocation. Solving this problem requires considering the interference impact on users using the same channel after allocating the channel mode, and minimizing the channel interference as much as possible (that is, the number of users allocated to the mode is relatively uniform).

[0194] Since users in different modes will interfere with each other, in this embodiment, users using the same transmission mode under the same channel will not interfere with each other, while users using different transmission modes will interfere with each other. Therefore, the key of the channel mode allocation scheme lies in mode allocation rather than channel allocation. To solve this problem, it is necessary to consider the interference impact on users using the same channel after allocating the channel mode, and try to minimize the channel interference (that is, the number of users allocated to the mode is relatively uniform).

[0195] Taking the channel rate C m,l,k as the reward for allocating channel L to the m-th user in mode k, problem P2 can be regarded as a matching problem of modes and users. To solve this problem, by setting U m,l,k =-C m,l,k the reward is converted into cost and the constraint C m,l,k ≥C th is set, and all costs less than the threshold are set to +∞. Therefore, problem P2 is converted into an allocation problem. However, since a new interference value will be generated for each matched user, the traditional Hungarian algorithm is not applicable. Based on the Hungarian algorithm, it is improved by establishing a dynamic weight matrix to update the mode, and a more effective transmission mode allocation scheme is obtained.

[0196] The specific process of the improved Hungarian algorithm is shown in Algorithm 1, and the algorithm example is as follows. First, set the total interferences I1 and I2 of the two modes to the same initial value, use the Hungarian algorithm to match a channel and a mode for one user, and set the interference generated by the mode currently used by the user to the total interference of the corresponding mode (in this way, it can effectively solve the problem that when the interference generated by one mode increases, the same mode is always matched, making the other mode unable to be matched by the user, resulting in no change in the interference of the corresponding mode. At the same time, it can also ensure that the interference difference generated by each match will not be too large). Subsequently, repeatedly use the Hungarian algorithm to match channels and modes for the remaining users and update the total interference of the corresponding mode until all users are matched.

[0197]

[0198] S3. On the basis of the allocation scheme in S2, solve the optimal transmit power allocation.

[0199] S31. Establish a game model that comprehensively considers D2D mode users and cellular mode users to solve the optimal power allocation problem.

[0200] In S2, the optimal channel and transmission mode allocation scheme under a fixed power is obtained. In this subsection, based on the allocation scheme in S2, the optimal power allocation will be solved. Since the users in the dedicated mode and the cellular mode interfere with each other, the optimal power allocation problem is solved in a distributed manner by means of the non - cooperative game theory method. The non - cooperative game is an effective tool to describe the selfish behavior of self - interested players and has been proven to be restrictive when designing distributed systems. The game model of this embodiment will comprehensively consider the D2D - mode users and the cellular - mode users, and both are regarded as players of the game (only the transmit power of the uplink is gamed in the cellular mode). The players can choose their transmit power p m , and the goal of each player is to maximize its own utility.

[0201] In game theory, the utility function is used to quantify the benefit of each player. In the game model, considering pricing, the utility function of each user can be expressed as:

[0202] where represents the channel rate used by the user;

[0203]

[0204] is the SINR. Since the interference is different in different modes, it can be expressed as:

[0205]

[0206] is the SINR in the D2D mode, and is the SINR in the cellular mode;

[0207]

[0208] is the interference generated in the D2D mode, is the interference and transmit power in the cellular mode (in this embodiment, it is assumed that the transmit power of the user is equal to the receive power of the base station. Since the base - station power is limited, the power of the uplink will affect the transmit power of the downlink, so a cost needs to be paid);

[0209] Through the above formula, it can be obtained that and are both the transmit power of the user, only the transmission objects are different; for better readability, the utility function is abbreviated as:

[0210]

[0211] To verify the rationality of the equation, the utility function of each user is defined as the data rate minus the price that each user needs to pay. λ m is a non - negative parameter, which can be expressed as the "willingness" of the user to increase the data rate; from an economic perspective, λ m reflects the "willingness" of player m to pay for a higher data rate. v is the price per unit of interference power (in a cellular network, it is the price per unit of interference power and transmit power).

[0212] The price function defined here does not depend on the transmit power of each individual user, and all users need to pay the same price. This method is beneficial to the distributed power allocation mechanism because in most cases each user does not know the transmit power of other users. However, users can understand the total interference situation by measuring the interference temperature.

[0213] To sum up, in the proposed game model, the goal of each game user is to maximize its own utility by operating the transmit power when given the unit price v. The parameter λ m is regarded as the initial willingness of each player, which is private information and each player does not know the λ of other players m . Different unit prices will result in different interference levels for v. Therefore, an appropriate price v can be selected to improve the communication quality of users and reduce interference.

[0214] S32. Based on the game model, a distributed iterative method is used to solve the Nash equilibrium point.

[0215] To find the Nash equilibrium point, the solutions of the following system of equations must be found:

[0216]

[0217] To solve this system of equations more effectively, based on the established game model, a distributed iterative method is used to propose a distributed power allocation mechanism. Numerically, the non - linear equations in the above formula can be solved by the fixed - point iteration method. First, this system of equations is converted into the fixed - point form. Consider the fixed - point equation in the following form:

[0218]

[0219] For any m ∈ {1, 2,....M}

[0220] For this fixed - point form, calculate p m The only common information required is the price v. It is reasonable to assume that the user knows its own transmit power and the total received power of the receiving end. Using this fixed - point form, user m does not need to calculate p mknow the λ of other users during the iterative process m , p m . Therefore, the iterative process can be implemented in a distributed manner with limited information;

[0221] During the iterative process, p m [t], W m [t] represent the transmit power of user m and the total received power of the receiving object respectively. The iterative formula is as follows, for all m:

[0222]

[0223] where

[0224]

[0225] The steps to calculate the expected transmit power of each user m in a distributed manner are as follows:

[0226] a. Each user m takes an initial value p m [0], where p m [0] ∈ [p min , p max ;

[0227] b. Each user updates its transmit power according to the equation and then calculates U m [t] according to the equation. During this period, all users update their calculations simultaneously;

[0228] c. If during the t-th round of calculation, for a predetermined threshold, if |U m [t] - U m [t - 1]| ≤ ∈ is satisfied, then the calculation of user m is terminated, and p m * = p m [t]. Otherwise, the next round of calculation will continue.

[0229] The pseudocode of the distributed power allocation mechanism is listed in Algorithm 2. From the following simulation results, it can be seen that according to the fixed-point theory, the proposed algorithm is convergent.

[0230]

[0231] S33. Propose a pricing strategy to determine the pricing based on maximizing social utility, so as to coordinate and control the transmit power of users.

[0232] According to the definition of utility in Equation (28), it can be known that the pricing v plays a crucial role and has a strong impact on the behavior of users and the Nash equilibrium. The proposed pricing strategy for users is to determine v based on maximizing social utility, thereby coordinating and controlling the transmit power of users.

[0233] Social utility is a key indicator representing the common interests of all participants. Social utility U is defined as the sum of the utilities of each participant at the Nash equilibrium point, including the revenue of the base station:

[0234]

[0235] where ∑vP m is the total revenue of the base station;

[0236] At the base station, it is necessary to maximize social utility under the constraint γ m ≥γ de where γ m is the actual SINR of the user, and γ de is the desired SINR of the user. The key lies in achieving smooth control of the object state through a lower control convergence rate, thereby resulting in good control performance. And a higher transmission success rate leads to a lower control convergence rate, bringing better system stability. Therefore, it is necessary to ensure that while determining the pricing of v based on maximizing the utility function, the control convergence rate of the system can be guaranteed. Therefore, for users, it is necessary to maximize social utility under the constraint p. Where ε m is the packet loss rate of the user, and c * (ρ th ) is the performance index that converts the control constraint into a communication constraint. Therefore, the total social utility optimization problem can be expressed as follows:

[0237]

[0238] To solve the above problem, the transmit power at the Nash equilibrium is an implicit function of the unit price v, and this function has the following properties:

[0239] Theorem 1: At the Nash equilibrium point, for any v1>v2>0, there is

[0240] Corollary 1: Social utility U decreases with respect to the unit price v, SINR increases with respect to the unit price v, and the packet transmission success probability decreases with respect to the unit price v.

[0241] These monotonic properties indicate that if the base station is interested in improving, a higher unit price v should be set; if the base station is interested in a lower control convergence rate, a lower unit price v should be set; if the base station is interested in improving social utility, a lower unit price v should be adopted.

[0242] Therefore, through the above analysis, it is considered that the optimal unit price v should satisfy the following two equations simultaneously:

[0243] γ m (v*) ≥ γ de ;

[0244] ε m (v*) ≤ 1 - c * (ρ th )

[0245] To ensure the optimal property, it should be satisfied.

[0246] γ m (v*) = γ de ;

[0247] ε m (v*) = 1 - c * (ρ th ) = ε th ;

[0248] Since U decreases with respect to v, the packet transmission success probability decreases with respect to v, while γ m increases with respect to v. It is considered that the optimal pricing strategy v* is the lowest price that can ensure γ m (v*) ≥ γ de and the highest price that can ensure ε m (v*) ≤ 1 - c * (ρ th ) (i.e., satisfying the equations simultaneously).

[0249] Therefore, finding the optimal solution of the following equation is equivalent to finding the root that satisfies the above equations simultaneously.

[0250]

[0251] For the penalty term, there is

[0252]

[0253] For the packet success transmission probability, through ε th the expected power generation p th is generated:

[0254]

[0255] Assume that the equation P(v) is expressed as a functional equation for solving the price v, and it is expressed as

[0256] P(v) = I(v);

[0257] The threshold of the equation P(v) can be expressed as:

[0258]

[0259] Since it is impossible to determine the closed interval of the optimal price v*, algorithms such as the bisection method may not be applicable to solving the root of this equation. The secant method is used to find the optimal price v*. This method starts from two initial values v[0] and v[1], and calculates the price v by using the following formula until the price v converges, and at this time the price v is the optimal price v*.

[0260]

[0261] Due to the different thresholds of the equation, two optimal pricings will be generated, corresponding to the pricings of the D2D dedicated mode and the cellular mode respectively.

[0262] The pricing algorithm based on the secant method is as shown in Algorithm 3, where T m is the longest time required for the user to reach the Nash equilibrium. In other words, T m is the upper limit of the running time of Algorithm 2. During this period, each user updates the transmission power according to Algorithm 2. The advantages of this method are as follows:

[0263] The only information required for the user to execute this algorithm is interference. No additional information of other users is required, nor feedback information. In this way, the complexity of the pricing mechanism is effectively reduced.

[0264] The only computational overhead of the user in each iteration process is to calculate v[t] given v[t - 1], v[t - 2], P[t - 1] and P[t - 2].

[0265]

[0266] Therefore, the present invention adopts the above-mentioned method for optimizing the performance of a wireless control system based on mode selection and power allocation, effectively solving the problems of interference and power allocation among users.

[0267] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that: they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for optimizing the performance of a wireless control system based on mode selection and power allocation, characterized in that, It includes the following steps: S1. Aiming at maximizing the spectral efficiency of the wireless control system while improving the system communication performance and control performance, an optimization problem P0 for maximizing spectral efficiency is constructed with transmission mode selection, channel selection, user transmit power, and control convergence rate as optimization variables, and the optimization problem P0 is transformed by the method of communication and control coordination; S2. Using the idea of the bipartite graph matching algorithm in graph theory, an optimal channel and transmission mode allocation scheme under fixed power is obtained; S3. Based on the allocation scheme in S2, the optimal transmit power allocation is solved.

2. The method for optimizing the performance of a wireless control system based on mode selection and power allocation according to claim 1, characterized in that, The content of S1 is as follows: The spectral efficiency of the wireless control system in D2D mode transmission, cellular mode uplink transmission, and cellular mode downlink transmission is expressed as the overall spectral efficiency: where x m,l,1 and x m,l,2 are parameters for mode selection and are binary variables; x m,l,1 indicates whether user m uses mode 1, the D2D dedicated mode, on channel l; similarly, x m,l,2 indicates whether user m uses mode 2, the cellular dedicated mode, on channel l; where x m,l,1 = 1 means that user m uses mode 1 on channel l, and x m,l,1 = 0 means the opposite, and x m,l,2 similarly; λ d 、 and represent the payload of user m in the dedicated mode, the uplink payload of user m in the cellular mode, and the downlink payload of user m in the cellular mode, respectively; M represents that there are M sensors and controllers in the wireless communication control system; N represents the sampling time index in the control process; ε m represents the transmission error probability; it is assumed that the sizes of the payloads in the same mode are the same. For a given payload λ, it is expressed as λ = R m T u B m ; R m represents the maximum transmission rate of the m-th user in the case of finite blocklength. T u is the allocated time resource, regarded as the transmission delay; B m represents the occupied bandwidth; Let the allocated time resource be T u and the bandwidth be B m be fixed; establish the optimization problem P0: p m ≤p max (a) ε m,1 ≤ ε th (b) ε m,2 ≤ ε th (c) ε m,3 ≤ ε th (d) x m,l,k ∈ {0, 1} (e) where N max is the total number of channels in the uplink; p m represents the user transmit power; p max represents the maximum value of the user transmit power; ε th represents the maximum threshold of the packet loss rate; Equation (a) is the objective function subject to communication and control constraints; Equation (b) is the power constraint for each user; Equations (c)-(d) are the reliability constraints of URLLC; Equation (e) is the channel parameter constraint; Equations (f)(g) are the constraints for users on channel usage; Expression Affected by the packet transmission probability, the class Lyapunov function is expressed as: Among them, is the idle period; Pr{α n = 1} is the probability of successful data packet transmission; Pr{α n = 0} is the probability of packet transmission failure; It is transformed into: where ξ n ≠0, let represents the supremum of the right-hand term in the above formula; through the above formula, we can get the control constraint of the control convergence speed ρ determined by the communication service quality and affected by the control constraint, c * (ρ); then problem P0 can be rewritten as P1: p m ≤ p max (h) ε m,1 ≤ 1 - c * (i) ε m,2 ≤ 1 - c * (j) ε m,3 ≤ 1 - c * (k) x m,l,k ∈{0,1} (l) where c * represents the maximum value of the packet loss rate under control constraints; equation (h) is the objective function subject to communication and control constraints; equation (i) is the power constraint for each user; equations (j)-(k) are the reliability constraints of URLLC; equation (l) is the channel parameter constraint; equations (m)(n) are the constraints on user channel usage.

3. The method for optimizing the performance of a wireless control system based on mode selection and power allocation according to claim 2, wherein The content of S2 is as follows: Using the idea of the bipartite graph matching algorithm in graph theory, channel mode allocation is performed under a given transmit power; by giving the transmit power, problem P1 is rewritten as the following sub-problem P2: x m,l,k ∈{0,1}； Taking the channel rate C m,L,k as the reward for allocating channel L to the m-th user in mode k, problem P2 is regarded as a matching problem of modes and users. By setting U m,l,k =-C m,l,k the reward is transformed into a cost and the constraint C m,l,k ≥C th is set. All costs less than the threshold are set to +∞; Problem P2 is transformed into an allocation problem; then the improved Hungarian algorithm is used to update the mode by establishing a dynamic weight matrix to allocate the transmission mode scheme.

4. The method for optimizing wireless control system performance based on mode selection and power allocation according to claim 3, characterized in that: The specific process of the improved Hungarian algorithm is as follows: First, set the total interference I1 and I2 of the two modes to the same initial value, use the Hungarian algorithm to match channels and modes for one user, and set the interference generated by the mode currently used by the user to the total interference in the corresponding mode; then repeatedly use the Hungarian algorithm to match channels and modes for the remaining users and update the total interference in the corresponding mode until all users are matched.

5. The method for optimizing the performance of a wireless control system based on mode selection and power distribution according to claim 1, wherein The content of S3 is as follows: S31. Establish a game model that comprehensively considers D2D mode users and cellular mode users to solve the optimal power allocation problem; S32. Based on the game model, a distributed iterative method is used to solve the Nash equilibrium point; S33. A pricing strategy is proposed to determine the pricing based on maximizing social utility, thereby coordinating and controlling the transmit power of users.

6. The method for optimizing the performance of a wireless control system based on mode selection and power allocation according to claim 5, wherein The content of S31 is as follows: Both D2D mode users and cellular mode users are regarded as players in the game, and they choose their respective transmission powers p under limited information m , in game theory, the utility function is used to quantify the benefits of each player. In the game model, considering pricing, the utility function of each user is expressed as: wherein represents the channel rate used by the user; is SINR. Since the interference in different modes is different, it is expressed as: is the SINR in D2D mode, is the SINR in cellular mode; is the penalty term and is the price function: is the interference generated in the D2D mode, is the interference and transmission power in the cellular mode; Through the above formula we can get and are all user transmission powers, but the transmission objects are different; the abbreviated utility function is: The utility function of each user is defined as the data rate minus the price paid by each user; λ m reflects the willingness of player m to pay for a high data rate; v is the price per unit of interference power.

7. The method for optimizing the performance of a wireless control system based on mode selection and power distribution according to claim 6, wherein The content of S32 is as follows: The Nash equilibrium point is found through the solution of the following system of equations: Based on the established game model, a distributed iterative method is used to propose a distributed power allocation mechanism; numerically, the non-linear equation in the above formula is solved by the fixed-point iteration method; first, the system of equations is transformed into a fixed-point form; Consider the following form of the fixed-point equation: For any m ∈ {1, 2,....M}; Calculate p m The public information is the price v; assume that the user knows his own transmission power and the total receiving power for receiving; using the fixed point form, user m calculates p m There is no need to know other users’ λ in the iterative process m 、p m ; During the iteration process, p m [t], W m [t] represent the transmit power of user m and the total received power of the receiving object respectively; the iteration formula is as follows, for all m: where The steps to calculate the expected transmit power of each user m in a distributed manner are as follows: a. For each user m, an initial value p m [0] is taken, where p m [0] ∈ [p min , p max ; b. Each user updates its transmission power according to the equation and then calculates U m [t], during which all users update their calculations simultaneously; c. If, during the t-th round of calculation, for a predetermined threshold, if |U m [t] - U m [t - 1]| ≤ ∈, then terminate the calculation of user m, and p m * = p m [t]; otherwise, continue with the next round of calculation.

8. The method for optimizing the performance of a wireless control system based on mode selection and power allocation according to claim 7, wherein, The content in S33 is as follows: The social utility U is defined as the sum of the utilities of each participant at the Nash equilibrium point, including the income of the base station: where ∑vP m is the total revenue of the base station; On the base station, maximize the social utility under the constraint γ m ≥γ de where γ m is the actual SINR of the user, and γ de is the desired SINR of the user; For the user, to maximize the social utility under the constraint condition p; where ε m is the packet loss rate of the user, c * (ρ th ) is the performance index for converting the control constraint into a communication constraint; the total social utility optimization problem is expressed as follows: Transmission power at Nash equilibrium is an implicit function of the unit price v, and this function has the following properties: At the Nash equilibrium point, for any v1 > v2 > 0, we have The social utility U decreases with respect to the unit price v, the SINR increases with respect to the unit price v, and the packet transmission success probability decreases with respect to the unit price v; The optimal unit price v simultaneously satisfies the following two conditions: γ m (v*) ≥ γ de ; e m (v*)≤1-v * (r th ); The optimal property is satisfied: c m (v*)=γ de ; e m (v*)=1-c * (r th )=e th ; Since U decreases with respect to v, the packet transmission success probability decreases with respect to v, while γ m increases with respect to v; the optimal pricing strategy v* is considered to be the lowest price that can simultaneously ensure γ m (v*) ≥ γ de and the highest price that can ensure ε m (v*) ≤ 1 - c * (ρ th ); The optimal solution of the following equation is equal to the root of the total social utility optimization problem: For the penalty term: For the packet successful transmission probability, through ε th Generate the expected power value p th : Let the equation P(v) be expressed as a functional equation for solving the price v: P(v) = I(v); The threshold of the equation P(v) is expressed as: Use the secant method to find the optimal price v*, starting from two initial values v[0] and v[1], and calculate the price v using the following formula until the price v converges. At this time, the price v is the optimal price v*: Due to different thresholds of the equation, two optimal pricing will be generated, corresponding to the pricing of the D2D dedicated mode and the cellular mode respectively.

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