A unified duplex resource allocation method for a cell-free industrial internet of things under a limited block length

Abstract

The application discloses a kind of unified duplex resource allocation methods of cell-free industrial internet of things under limited block length, belong to ultra-reliable low-latency communication technical field.The method includes: two kinds of modes of unified network auxiliary full duplex and half duplex are established, and closed loop transmission mathematical model is established;With the optimization problem of minimizing overall decoding error probability as the goal, it is decomposed into three sub-problems of power and beamforming design, half duplex block length allocation and full duplex access point selection;Power and beamforming sub-problem is converted into convex problem;Based on the unimodality of block length allocation, golden section search is used to optimize block length;Transmitting and receiving selection of access point is optimized using center exchange matching algorithm.The application can effectively improve the reliability under limited block length transmission, and adaptively selects duplex strategy according to environment.

Description

Technical Field

[0001] This invention relates to the technical field of duplex resource allocation in cellular massive MIMO systems, and in particular to a unified duplex resource allocation method for cellular industrial IoT systems with finite block length. Background Technology

[0002] As the core of Industry 4.0, the Industrial Internet of Things (IIoT) places extreme demands on communication reliability and latency, requiring end-to-end latency of less than 1 millisecond and reliability exceeding 99.9999%. Traditional communication models and Shannon's theory based on infinite block lengths are insufficient to meet these requirements. Ultra-reliable low-latency communication under finite block length mechanisms has become a key direction for 6G, but it faces a "triangular dilemma" where high reliability, low latency, and high speed are mutually constrained. To overcome this limitation, a cellular-free massive MIMO architecture has been introduced into the IIoT, demonstrating significant advantages in providing spatial freedom, enhancing reliability and coverage, and reducing transmission latency through distributed access point collaborative services.

[0003] Current research on uplink and downlink resource allocation in the Industrial Internet of Things (IIoT) largely focuses on improving spectrum efficiency or optimizing reliability only in single-antenna, single-user scenarios, failing to effectively address the challenges of multi-device access and strong interference. Existing solutions based on orthogonal duplexing or relays struggle to fully utilize spatial degrees of freedom in multi-antenna, multi-user scenarios, while cross-link interference severely impacts reliability in co-frequency full-duplex systems. Furthermore, existing methods often rely on heuristic or suboptimal approximation algorithms, failing to guarantee globally optimal performance in resource allocation. Therefore, a unified duplex resource allocation method is urgently needed to achieve joint optimization of multi-user, high reliability, and low latency in non-cellular IIoT networks. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a unified duplex resource allocation method for cellular industrial IoT under finite block length. This method studies the problem of minimizing the maximum overall decoding error probability of cellular industrial IoT systems under finite block length transmission through joint optimization of power control, beamforming design, block length allocation and AP selection.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A unified duplex resource allocation method for cellular-free industrial IoT with finite block length, the method comprising:

[0007] Step S1: For a non-cellular industrial IoT system, a mathematical model of a finite block length non-cellular industrial IoT system is established, unifying the network-assisted full-duplex and half-duplex operating modes. The mathematical model includes: the closed-loop transmission model of the non-cellular industrial IoT system and the expression for the maximum overall decoding error probability.

[0008] Step S2: For the non-cellular industrial IoT mathematical model constructed in Step S1, with the objective function of minimizing the overall decoding error probability, and with constraints such as Shannon capacity limit, maximum power consumption limit, block length constraint, access point selection constraint and integer constraint, construct the system reliability problem under finite block length transmission, decompose the problem into three sub-problems to optimize power and beamforming design, block length allocation and AP selection respectively;

[0009] Step S3: Transform the decomposed subproblems of joint optimization of power and beamforming design into convex problems. This includes: First, introducing auxiliary variables to replace the signal-to-interference-plus-noise ratio (SINR) and linearly decomposing the overall decoding error probability of the cascaded downlink into an additive form. Then, performing an exact Prony approximation on the Gaussian Q-function contained in the objective function. Next, approximating the channel dispersion term of the objective function as a constant under high SNR. Finally, transforming the original power allocation and beamforming subproblems into convex problems through a first-order Taylor approximation.

[0010] Step S4: Based on the power and beamforming obtained in step S3, prove the monotonicity and unimodality of the block length allocation problem, and use a nested double-iteration optimization algorithm to solve the half-duplex block length allocation problem in step S4.

[0011] Step S5: Based on the power and beamforming obtained in step S3, the center-switching matching algorithm is used to optimize the access point transmit / receive selection, and a nested double-iteration optimization algorithm is used to solve the network-assisted full-duplex AP selection subproblem.

[0012] Furthermore, step S1 specifically includes the following sub-steps:

[0013] Step S101: Construct a cellular-free industrial IoT system with finite block length transmission. In this system, EDU Management One AP, connected to the CPU via fiber optic cable. Each equipment The root antenna AP coordinates service A single antenna sensor and A single-antenna actuator. We consider two duplex modes: i.e., time-division half-duplex (HD) and network-assisted full-duplex (NAFD). In HD, uplink and downlink occupy different block lengths. and Satisfying constraints All access points (APs) can participate in uplink and downlink transmissions. In NAFD, uplink and downlink transmissions occupy the same block length. APs can be flexibly configured as transmitting APs (T-APs) and receiving APs (R-APs) to reduce inter-AP interference (IAI).

[0014] Step S102, use To represent duplex mode, where and These correspond to half-duplex and full-duplex respectively. Represents AP selection. A unified AP selection matrix is ​​defined as follows:

[0015]

[0016] in, , In EDU In the middle, if AP Working in the receiving (sending) role, Similarly, we define a uniform block length allocation variable as...

[0017]

[0018] in, and It is established in HD and NAFD respectively.

[0019] During the uplink detection phase, the received signal-to-interference-plus-noise ratio (SIR) of sensor s at the CPU is... Represented as

[0020]

[0021] in, and These represent the interference power and noise between APs, respectively. This indicates the transmit power of sensor s. Indicates EDU m The uplink Rayleigh fading channel between the receiving AP and the sensor. This is the received combining vector used to detect the sensor's signal s. To effectively suppress co-channel interference between sensors and improve the uplink received signal-to-interference-plus-noise ratio, this invention designs a locally linear receiver based on the minimum mean square error (MMSE) criterion. To characterize the length of the uplink block. SINR and information bits Regarding the relationship, we use the finite block length capacity to express the spectral efficiency of sensor s as:

[0022]

[0023] in, Indicates channel dispersion, It is the Gaussian Q function.

[0024] During the downlink transmission phase, the signal-to-interference-plus-noise ratio (SIR) at actuator k is specifically expressed as:

[0025]

[0026] in, This indicates inter-user interference (IUI) between uplink and downlink. This represents the downlink Rayleigh fading channel between AP m and actuator k. This represents the downlink beamforming vector. It is the variance of additive white Gaussian noise.

[0027] Step S103: For the non-cellular industrial IoT system constructed in step S101, establish a closed-loop error propagation model for the system, which specifically includes: uplink decoding error probability, downlink decoding error probability, and an expression for the overall system decoding error probability. Sensors The decoding error probability (DEP) can be derived as follows:

[0028]

[0029] in, Since successful control requires correctly decoding information from all sensors, the overall uplink error probability is expressed as...

[0030]

[0031] Similarly, the downlink decoding error probability corresponding to actuator k is given by the following formula.

[0032]

[0033] In this system architecture, downlink control information is generated in the CPU based on uplink sensing information. This process introduces error propagation from uplink to downlink. The overall downlink decoding error probability is expressed as:

[0034]

[0035] Furthermore, step S2 specifically includes the following sub-steps:

[0036] The objective function is to minimize the overall decoding error probability, specifically as follows:

[0037]

[0038] , , , , This invention, through analysis, discovered that the objective function... Relative to packet size and It possesses a hidden monotonically increasing property. Based on this monotonicity, the optimal solution to the optimization problem is obtained when the data packet size takes its threshold value, i.e. and Similarly, we can also prove... It's about block length. , and Decreasing, which means and This holds true in the optimal solution. Therefore, only HD requires block length allocation, while NAFD has a fixed block length. .

[0039] The specific constraints are as follows:

[0040] The capacity of a finite block should be less than the capacity of Shannon:

[0041]

[0042] System power consumption constraints:

[0043]

[0044] in, This is the maximum power consumption of sensor s. It is AP Maximum power consumption, This represents the total power consumption of the system.

[0045] AP selection constraints:

[0046]

[0047] Block length constraint:

[0048]

[0049] in, Let represent the set of positive integers. The optimization problem can be expressed as:

[0050]

[0051] The problem is broken down into three sub-problems: optimizing power and beamforming design, block length allocation, and AP selection.

[0052] Furthermore, step S3 specifically includes the following sub-steps:

[0053] Step S301: Introduce an auxiliary variable to replace the signal-to-interference-plus-noise ratio (SINR) and rephrase the problem as follows:

[0054]

[0055] in, objective function Update , .

[0056] Step S302: Linearly decompose the overall decoding error probability of the cascaded downlink into an additive form, as follows:

[0057]

[0058] Step S303: Perform an exact Prony approximation on the Gaussian Q-function contained in the objective function, specifically as follows:

[0059] The Gaussian Q function is approximated as:

[0060]

[0061] Here, Established, because and The decreasing Q function ensures In URLLC systems, it is non-negative. The objective function can be approximated as... ,in , .

[0062] Step S304: Under high signal-to-interference-plus-noise ratio (SNR), the channel dispersion term of the objective function is approximated as a constant, specifically as follows:

[0063]

[0064] get:

[0065]

[0066] Step S305: Using the continuous convex approximation theory, construct a convex surrogate upper bound for the objective function. The specific process is as follows:

[0067] Based on the aforementioned high signal-to-interference-plus-noise ratio (SINR) approximation processing, the function and The signal-to-interference-plus-noise ratio has been discussed separately. and It exhibits concaveness. Therefore, using a first-order Taylor expansion, a convex upper bound approximation is constructed for the decoding error probability represented by the Gaussian Q-function:

[0068] For uplink and downlink, at point The upper bound function for the proxy at the specified location is constructed as follows:

[0069]

[0070] in Given by a first-order Taylor series expansion:

[0071]

[0072] The approximate objective function and constraints are as follows:

[0073]

[0074] Wherein, the objective function is .

[0075] Step S306: Through monotonicity and first-order Taylor approximation, the optimization problem is finally transformed into a convex problem, specifically as follows:

[0076] Theoretical analysis proves that the objective function of the optimization problem is monotonically decreasing with respect to the signal-to-interference-plus-noise ratio (SINR) auxiliary variable, and all constraints are monotonic. Therefore, this problem is classified as a monotonic optimization problem. According to monotonic optimization theory, its optimal solution must lie on the boundary of the feasible region. Therefore, at the optimal solution, the auxiliary variable constraints introduced in the above steps will have an equality sign, i.e., ... and To handle non-convex signal-to-interference-plus-noise ratios (SIR), the SIR constraint is re-expressed as follows:

[0077]

[0078] in, , , , The non-convexity mainly stems from the right-hand side of the equation. To transform it into a convex constraint, a first-order Taylor series is used at the initial point. By approximating the non-convex term, we obtain its local convex upper bound, as follows:

[0079]

[0080]

[0081] in, Let represent the real part. The power control and beamforming design subproblems are approximated by a series of convex upper bounds and can be reformulated as follows:

[0082]

[0083] Furthermore, step S4 specifically includes the following sub-steps:

[0084] Step S401: Establish the block length allocation subproblem model:

[0085] Given the uplink power and downlink beamforming scheme, we establish a sub-problem of allocating uplink and downlink block lengths, with the objective of minimizing the system's maximum overall downlink decoding error probability:

[0086]

[0087] Step S402: Prove that the total block length constraint holds true at the optimal solution:

[0088] Through analysis, it is first proven that the objective function is relative to the length of the uplink block. With downlink block length All of them exhibit a monotonically decreasing property. Based on this monotonicity and the monotonic nature of all constraints, according to monotonic optimization theory, the subproblem is determined to be a monotonic optimization problem, and its optimal solution must lie on the boundary of the feasible region. Therefore, it is deduced that the total block length constraint holds equality at the optimal solution, i.e. .

[0089] Step S403: Establish the unimodality of the objective function with respect to the length of the uplink block:

[0090] The downlink block length is represented as The objective function is reconstructed to be only related to the length of the uplink block. function By analyzing the first and second derivative properties of the function, we prove that there exists a unique block length. Make the objective function Obtaining the minimum value proves that the objective function is unimodal within its defined interval.

[0091] Step S404: Initialize system parameters: Set the error tolerance for outer iteration (block length allocation). Golden Section Search Parameters And the maximum number of iterations for the inner layer iteration (power and beamforming optimization). With error tolerance .

[0092] Step S405: Initialize the block length search interval: Set the lower bound of the initial search interval for the uplink block length N1. With the upper realm .

[0093] Step S406: Execute the outer golden section search loop: when the block length search interval does not meet the convergence condition. Then, repeat the following steps S406.1 to S406.3:

[0094] Step S406.1: Calculate the golden ratio: Based on the golden ratio In the current search range Calculate two interior points and ,satisfy .

[0095] Step S406.2, Inner Iterative Solution for Power and Beamforming: For the current block length candidate points a and b, execute the inner iterative algorithm (a suboptimal power control and beamforming design algorithm based on the continuous convex approximation method) to obtain the corresponding power and beamforming schemes. The specific process is as follows:

[0096] 1) Initialize the inner iteration index and initial point .

[0097] 2) Iterate through the convex approximation problem reconstructed in step S306 to obtain the current optimal solution. .

[0098] 3) Update iteration points .

[0099] 4) Determine if the inner loop converges: If the improvement in the system's maximum downlink decoding error probability is... If the maximum number of iterations is reached, the loop will exit and a suboptimal solution will be returned. Otherwise, return to step 2) and continue iterating.

[0100] S406.3, Update block length search range: based on the obtained Calculate the objective function values ​​at candidate points a and b. and .like Then update the upper bound of the search interval. Otherwise, update the lower bound of the search interval. .

[0101] S407. Output the optimal resource allocation scheme: After the outer loop converges, calculate the optimal uplink block length. and rounded down to the nearest integer value. The optimal downlink block length is then Ultimately, the output system jointly optimizes the resource allocation scheme, including the optimal block length. Transmission power and beamforming vector .

[0102] Furthermore, step S5 specifically includes the following sub-steps:

[0103] Step S501: Establish the AP selection sub-problem model for NAFD:

[0104]

[0105] Step S502: Generate the initial AP selection matrix using a greedy algorithm. ;

[0106] Step S503: Select APs with different AP selection matrices within different EDUs, i.e. In and In (in We swap the sender and receiver roles of these two APs, defining the initial AP pair as follows: The new swap pair is The new exchange matrix is , .

[0107] Step S504: Calculate the overall decoding error probability through the following steps.

[0108] 1) Initialize the inner iteration index and initial point .

[0109] 2) Iterate through the convex approximation problem reconstructed in step S306 to obtain the current optimal solution. .

[0110] 3) Update iteration points .

[0111] 4) Determine if the inner loop converges: If the improvement in the system's maximum downlink decoding error probability is... If the maximum number of iterations is reached, the loop will exit and a suboptimal solution will be returned. Otherwise, return to step 2) and continue iterating.

[0112] Step S505: The CPU decides whether to accept the swap based on whether the system's maximum downlink decoding error probability has decreased. Repeat steps S502 to S504 until convergence; return to the AP selection matrix. The beneficial effects of this invention are:

[0113] This invention considers a unified duplex resource allocation method for non-cellular industrial IoT under finite block length. Using this invention can effectively improve the transmission reliability of non-cellular industrial IoT under finite block length transmission. It can select duplex resource allocation strategies according to different environmental conditions and has broad application prospects. Attached Figure Description

[0114] Figure 1 This is a flowchart illustrating a unified duplex resource allocation method for a cellular-free industrial IoT with finite block length, as provided in Example 1.

[0115] Figure 2 This is a flowchart illustrating the HD block length allocation double-iteration optimization algorithm provided in Example 1.

[0116] Figure 3 This is a flowchart illustrating the NAFD AP selection dual-iteration optimization algorithm provided in Example 1.

[0117] Figure 4 This is a performance comparison chart of HD and NAFD with respect to block length variations in Example 1. Detailed Implementation

[0118] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0119] Example 1

[0120] See Figures 1-4 This embodiment provides a unified duplex resource allocation method for cellular-free industrial IoT under finite block length. The process of this method is as follows: Figure 1 As shown, the method includes the following steps:

[0121] Step S1: For a non-cellular industrial IoT system, a mathematical model of a finite block length non-cellular industrial IoT system is established, unifying the network-assisted full-duplex and half-duplex operating modes. The mathematical model includes: the closed-loop transmission model of the non-cellular industrial IoT system and the expression for the maximum overall decoding error probability.

[0122] Specifically, in this embodiment, step S1 includes:

[0123] Step S101: Construct a cellular-free industrial IoT system with finite block length transmission. In this system, EDU Management One AP, connected to the CPU via fiber optic cable. Each equipment The root antenna AP coordinates service A single antenna sensor and A single-antenna actuator. We consider two duplex modes: i.e., time-division duplex (HD) and network-assisted full-duplex (NAFD).

[0124] In half-duplex, uplink and downlink each occupy different block lengths. and Satisfying constraints All access points (APs) can participate in uplink and downlink transmissions. In NAFD, uplink and downlink transmissions occupy the same block length. APs can be flexibly configured as transmitting APs (T-APs) and receiving APs (R-APs) to reduce inter-AP interference (IAI).

[0125] Step S102, use To represent duplex mode, where and These correspond to half-duplex and full-duplex respectively. Represents AP selection. A unified AP selection matrix is ​​defined as follows:

[0126]

[0127] in, , In EDU In the middle, if AP Working in the receiving (sending) role, Similarly, we define a uniform block length allocation variable as...

[0128]

[0129] in, and It is established in HD and NAFD respectively.

[0130] During the uplink detection phase, the received signal-to-interference-plus-noise ratio (SIR) of sensor s at the CPU is... Represented as

[0131]

[0132] in, and These represent the interference power and noise between APs, respectively. This indicates the transmit power of sensor s. Indicates EDU m The uplink Rayleigh fading channel between the receiving AP and the sensor. This is the received combining vector used to detect the sensor's signal s. To effectively suppress co-channel interference between sensors and improve the uplink received signal-to-interference-plus-noise ratio, this invention designs a locally linear receiver based on the minimum mean square error (MMSE) criterion. To characterize the length of the uplink block. SINR and information bits Regarding the relationship, we use the finite block length capacity to express the spectral efficiency of sensor s as:

[0133]

[0134] in, Indicates channel dispersion, It is the Gaussian Q function.

[0135] During the downlink transmission phase, the signal-to-interference-plus-noise ratio (SIR) at actuator k is specifically expressed as:

[0136]

[0137] in, This indicates inter-user interference (IUI) between uplink and downlink. This represents the downlink Rayleigh fading channel between AP m and actuator k. This represents the downlink beamforming vector. It is the variance of additive white Gaussian noise.

[0138] Step S103: For the non-cellular industrial IoT system constructed in step S101, establish a closed-loop error propagation model for the system, which specifically includes: uplink decoding error probability, downlink decoding error probability, and an expression for the overall system decoding error probability. Sensors The decoding error probability (DEP) can be derived as follows:

[0139]

[0140] in, Since successful control requires correctly decoding information from all sensors, the overall uplink error probability is expressed as...

[0141]

[0142] Similarly, the downlink decoding error probability corresponding to actuator k is given by the following formula.

[0143]

[0144] In this system architecture, downlink control information is generated in the CPU based on uplink sensing information. This process introduces error propagation from uplink to downlink. The overall downlink decoding error probability is expressed as:

[0145]

[0146] Step S2: For the non-cellular industrial IoT mathematical model constructed in Step S1, with the objective function of minimizing the overall decoding error probability, and with constraints such as Shannon capacity limit, maximum power consumption limit, block length constraint, access point selection constraint and integer constraint, construct the system reliability problem under finite block length transmission, decompose the problem into three sub-problems to optimize power and beamforming design, block length allocation and AP selection respectively;

[0147] Specifically, step S2 includes:

[0148] The objective function is to minimize the overall decoding error probability, specifically as follows:

[0149]

[0150] in, , , , , This invention, through analysis, discovered that the objective function... Relative to packet size and It possesses a hidden monotonically increasing property. Based on this monotonicity, the optimal solution to the optimization problem is obtained when the data packet size takes its threshold value, i.e. and Similarly, we can also prove... It's about block length. , and Decreasing, which means and This holds true in the optimal solution. Therefore, only HD requires block length allocation, while NAFD has a fixed block length. .

[0151] The specific constraints are as follows:

[0152] The capacity of a finite block should be less than the capacity of Shannon:

[0153]

[0154] System power consumption constraints:

[0155]

[0156] in, This is the maximum power consumption of sensor s. It is AP Maximum power consumption, This represents the total power consumption of the system.

[0157] AP selection constraints:

[0158]

[0159] Block length constraint:

[0160]

[0161] in, Let represent the set of positive integers. The optimization problem can be expressed as:

[0162]

[0163] The problem is broken down into three sub-problems, which are optimized separately for power and beamforming design, block length allocation, and AP selection.

[0164] Step S3: Transform the decomposed subproblems of joint optimization of power and beamforming design into convex problems. This includes: First, introducing auxiliary variables to replace the signal-to-interference-plus-noise ratio (SINR) and linearly decomposing the overall decoding error probability of the cascaded downlink into an additive form. Then, performing an exact Prony approximation on the Gaussian Q-function contained in the objective function. Next, approximating the channel dispersion term of the objective function as a constant under high SNR. Finally, transforming the original power allocation and beamforming subproblems into convex problems through a first-order Taylor approximation.

[0165] Specifically, in this embodiment, step S3 includes:

[0166] Step S301: Introduce an auxiliary variable to replace the signal-to-interference-plus-noise ratio (SINR) and rephrase the problem as follows:

[0167]

[0168] in, objective function Update , .

[0169] Step S302: Linearly decompose the overall decoding error probability of the cascaded downlink into an additive form, as follows:

[0170]

[0171] Step S303: Perform an exact Prony approximation on the Gaussian Q-function contained in the objective function, specifically as follows:

[0172] The Gaussian Q function is approximated as:

[0173]

[0174] Here, Established, because and The decreasing Q function ensures In URLLC systems, it is non-negative. The objective function can be approximated as... ,in , .

[0175] Step S304: Under high signal-to-interference-plus-noise ratio (SNR), the channel dispersion term of the objective function is approximated as a constant, specifically as follows:

[0176]

[0177] get:

[0178]

[0179] Step S305: Using the continuous convex approximation theory, construct a convex surrogate upper bound for the objective function. The specific process is as follows:

[0180] Based on the aforementioned high signal-to-interference-plus-noise ratio (SINR) approximation processing, the function and The signal-to-interference-plus-noise ratio has been discussed separately. and It exhibits concaveness. Therefore, using a first-order Taylor expansion, a convex upper bound approximation is constructed for the decoding error probability represented by the Gaussian Q-function:

[0181] For uplink and downlink, at point The upper bound function for the proxy at the specified location is constructed as follows:

[0182]

[0183] in Given by a first-order Taylor series expansion:

[0184]

[0185] The approximate objective function and constraints are as follows:

[0186]

[0187] Wherein, the objective function is .

[0188] Step S306: Through monotonicity and first-order Taylor approximation, the optimization problem is finally transformed into a convex problem, specifically as follows:

[0189] Theoretical analysis proves that the objective function of the optimization problem is monotonically decreasing with respect to the signal-to-interference-plus-noise ratio (SINR) auxiliary variable, and all constraints are monotonic. Therefore, this problem is classified as a monotonic optimization problem. According to monotonic optimization theory, its optimal solution must lie on the boundary of the feasible region. Therefore, at the optimal solution, the auxiliary variable constraints introduced in the above steps will have an equality sign, i.e., ... and To handle non-convex signal-to-interference-plus-noise ratios (SIR), the SIR constraint is re-expressed as follows:

[0190]

[0191] in, , , , The non-convexity mainly stems from the right-hand side of the equation. To transform it into a convex constraint, a first-order Taylor series is used at the initial point. By approximating the non-convex term, we obtain its local convex upper bound, as follows:

[0192]

[0193]

[0194] in, Let represent the real part. The power control and beamforming design subproblems are approximated by a series of convex upper bounds and can be reformulated as follows:

[0195]

[0196] Step S4: Based on the power and beamforming obtained in Step S3, prove the monotonicity and unimodality of the block length allocation problem, and use a nested double-iteration optimization algorithm to solve the HD block length allocation problem (e.g., Figure 2 (As shown).

[0197] Specifically, in this embodiment, step S4 includes:

[0198] Step S401: Establish the block length allocation subproblem model:

[0199] Given the uplink power and downlink beamforming scheme, we establish a sub-problem of allocating uplink and downlink block lengths, with the objective of minimizing the system's maximum overall downlink decoding error probability:

[0200]

[0201] Step S402: Prove that the total block length constraint holds true at the optimal solution:

[0202] Through analysis, it is first proven that the objective function is relative to the length of the uplink block. With downlink block length All of them exhibit a monotonically decreasing property. Based on this monotonicity and the monotonic nature of all constraints, according to monotonic optimization theory, the subproblem is determined to be a monotonic optimization problem, and its optimal solution must lie on the boundary of the feasible region. Therefore, it is deduced that the total block length constraint holds equality at the optimal solution, i.e. .

[0203] Step S403: Establish the unimodality of the objective function with respect to the length of the uplink block:

[0204] The downlink block length is represented as The objective function is reconstructed to be only related to the length of the uplink block. function By analyzing the first and second derivative properties of the function, we prove that there exists a unique block length. Make the objective function Obtaining the minimum value proves that the objective function is unimodal within its defined interval.

[0205] Step S404: Initialize system parameters: Set the error tolerance for outer iteration (block length allocation). Golden Section Search Parameters And the maximum number of iterations for the inner layer iteration (power and beamforming optimization). With error tolerance .

[0206] Step S405: Initialize the block length search interval: Set the lower bound of the initial search interval for the uplink block length N1. With the upper realm .

[0207] Step S406: Execute the outer golden section search loop: when the block length search interval does not meet the convergence condition. Then, repeat the following steps S406.1 to S406.3:

[0208] Step S406.1: Calculate the golden ratio: Based on the golden ratio In the current search range Calculate two interior points and ,satisfy .

[0209] Step S406.2, Inner Iterative Solution for Power and Beamforming: For the current block length candidate points a and b, execute the inner iterative algorithm (a suboptimal power control and beamforming design algorithm based on the continuous convex approximation method) to obtain the corresponding power and beamforming schemes. The specific process is as follows:

[0210] 1) Initialize the inner iteration index and initial point .

[0211] 2) Iterate through the convex approximation problem reconstructed in step S306 to obtain the current optimal solution. .

[0212] 3) Update iteration points .

[0213] 4) Determine if the inner loop converges: If the improvement in the system's maximum downlink decoding error probability is... If the maximum number of iterations is reached, the loop will exit and a suboptimal solution will be returned. Otherwise, return to step 2) and continue iterating.

[0214] S406.3, Update block length search range: based on the obtained Calculate the objective function values ​​at candidate points a and b. and .like Then update the upper bound of the search interval. Otherwise, update the lower bound of the search interval. .

[0215] S407. Output the optimal resource allocation scheme: After the outer loop converges, calculate the optimal uplink block length. and rounded down to the nearest integer value. The optimal downlink block length is then Ultimately, the output system jointly optimizes the resource allocation scheme, including the optimal block length. Transmission power and beamforming vector .

[0216] Step 5: Based on the power and beamforming obtained in step S3, optimize the access point transmit / receive selection using the center-switching matching algorithm, and solve the AP selection subproblem in NAFD using a nested double-iteration optimization algorithm (e.g., Figure 3 (As shown).

[0217] Specifically, in this embodiment, step S5 includes:

[0218] Step S501: Establish the AP selection sub-problem model for NAFD:

[0219]

[0220] Step S502: Generate the initial AP selection matrix using a greedy algorithm. ;

[0221] Step S503: Select APs with different AP selection matrices within different EDUs, i.e. In and In (in We swap the sender and receiver roles of these two APs, defining the initial AP pair as follows: The new swap pair is The new exchange matrix is , .

[0222] Step S504: Calculate the overall decoding error probability through the following steps.

[0223] 1) Initialize the inner iteration index and initial point .

[0224] 2) Iterate through the convex approximation problem reconstructed in step S306 to obtain the current optimal solution. .

[0225] 3) Update iteration points .

[0226] 4) Determine if the inner loop converges: If the improvement in the system's maximum downlink decoding error probability is... If the maximum number of iterations is reached, the loop will exit and a suboptimal solution will be returned. Otherwise, return to step 2) and continue iterating.

[0227] Step S505: The CPU decides whether to accept the swap based on whether the system's maximum downlink decoding error probability has decreased. Repeat steps S502 to S504 until convergence; return to the AP selection matrix. The beneficial effects of this invention can be further verified through simulation results. For example... Figure 4 As shown, the performance of HD and NAFD under different block length allocations was compared, proving that the method proposed in this invention can effectively improve the transmission reliability of non-cellular industrial IoT under finite block length transmission. It has broad application prospects for selecting duplex resource allocation strategies according to different environmental conditions.

[0228] Any aspects of this invention not described in detail are well-known to those skilled in the art.

[0229] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A unified duplex resource allocation method for cellular-free industrial IoT with finite block length, characterized in that, The method includes: Step S1: For a non-cellular industrial IoT system, a mathematical model of a finite block length non-cellular industrial IoT system is established, unifying the network-assisted full-duplex and half-duplex operating modes. The mathematical model includes: a closed-loop transmission model of the non-cellular industrial IoT system, an uplink signal-to-interference-plus-noise ratio expression based on the finite block length capacity formula, a downlink signal-to-interference-plus-noise ratio expression, a decoding error probability expression, and a closed-loop error propagation expression. Step S2: For the non-cellular industrial IoT mathematical model constructed in Step S1, with the objective function of minimizing the overall decoding error probability, and with constraints such as Shannon capacity limit, maximum power consumption limit, block length constraint, access point selection constraint, and integer constraint, a system reliability problem under finite block length transmission is constructed. The problem is decomposed into three sub-problems: power and beamforming design sub-problem, half-duplex block length allocation sub-problem, and network-assisted full-duplex access point selection sub-problem. Step S3: Transform the decomposed power and beamforming design subproblems into convex problems. This includes: First, introducing auxiliary variables to replace the signal-to-interference-plus-noise ratio (SINR) and linearly decomposing the overall downlink decoding error probability into an additive form. Then, performing Prony approximation on the Gaussian Q-function contained in the objective function. Next, approximating the channel dispersion term of the objective function as a constant. Finally, transforming the original power allocation and beamforming subproblems into convex problems through first-order Taylor approximation. Step S4: Based on the power and beamforming obtained in step S3, prove the monotonicity and unimodality of the half-duplex block long allocation subproblem, and use a nested double-iteration optimization algorithm to solve the half-duplex block long allocation subproblem. Step S5: Based on the power and beamforming obtained in step S3, the central switching matching algorithm is used to optimize the access point transmit / receive selection in the network-assisted full-duplex access point selection subproblem. The inner power and beamforming optimization adopts a nested double-iteration optimization algorithm.

2. The unified duplex resource allocation method for cellular-free industrial IoT with finite block length as described in claim 1, characterized in that, Step S1 specifically includes: Step S101: Construct a cellular-free industrial IoT system with finite block length transmission. In this system, Each edge distributed unit (EDU) manages Each access point (AP) is connected to a central processing unit (CPU) via fiber optic cable. Each equipment The root antenna AP coordinates service A single antenna sensor and A single-antenna actuator is considered; two duplex modes are taken into account: half-duplex (HD) and network-assisted full-duplex (NAFD); in half-duplex, uplink and downlink occupy different block lengths. and Satisfying constraints ,in With the maximum total block length, all APs can participate in uplink and downlink transmissions; in NAFD, uplink and downlink transmissions occupy the same block length. APs can be flexibly configured as transmitting APs (T-APs) and receiving APs (R-APs) to reduce inter-AP interference (IAI). Step S102: For the non-cellular industrial IoT system constructed in step S101, establish the data transmission model of the uplink and downlink of the system, which includes: the expression of the signal-to-interference-plus-noise ratio and data rate of the sensor received at the CPU, and the expression of the signal-to-interference-plus-noise ratio at the actuator. Step S103: For the non-cellular industrial IoT system constructed in step S101, establish a closed-loop error propagation model for the system, which includes: uplink decoding error probability, downlink decoding error probability, and an expression for the overall system decoding error probability.

3. The unified duplex resource allocation method for cellular-free industrial IoT with finite block length according to claim 2, characterized in that, Step S102 specifically includes: Define duplex mode parameters ,in and These correspond to half-duplex and full-duplex respectively; define AP selection variables. ,in Indicates the first The first EDU within the Each AP is working in the receiving role. This indicates that the AP is operating in the transmitting role; the unified AP selection matrix is ​​defined as follows: ； in, , , for 3D identity matrix Represents the Kronecker product; the uniform block length assignment variable is... ； in, and This holds true in both HD and NAFD; During the uplink detection phase, the received signal-to-interference-plus-noise ratio (SIR) of sensor s at the CPU is... Represented as ； in, This indicates the transmit power of sensor s. This indicates that the EDU m receives the AP and sensor. The uplink Rayleigh fading channel vector between them Receiver merging vector designed based on the minimum mean square error (MMSE) criterion ,in For the first Number of APs received within each EDU The variance of the uplink noise; Inter-AP interference power, Noise power; The spectral efficiency of sensor s can be expressed using the finite block length capacity formula: ； in, For sensors The number of uplink information bits, This represents the uplink decoding error probability. Indicates channel dispersion, It is the Gaussian Q-function; During the downlink transmission phase, the signal-to-interference-plus-noise ratio (SIR) at actuator k is specifically expressed as: ； in, This indicates inter-user interference (IUI) between uplink and downlink. This represents the downlink Rayleigh fading channel between AP m and actuator k. This represents the downlink beamforming vector. It is the variance of additive white Gaussian noise. For sensors To the actuator Interference channels.

4. The method for unified duplex resource allocation in a finite block length industrial IoT system according to claim 2, characterized in that, Step S103 specifically includes: Uplink decoding error probability: sensor The decoding error probability (DEP) can be derived as follows: ； in, The overall error probability of the upward movement is expressed as: ； Downlink decoding error probability: The decoding error probability of executor k is: ； Closed-loop error propagation model: Downlink control information is generated in the CPU based on uplink sensing information; therefore, the overall downlink decoding error probability is: 。 5. The unified duplex resource allocation method for cellular-free industrial IoT with finite block length according to claim 1, characterized in that, In step S2, minimizing the overall decoding error probability is the objective function, which is specifically: ； in, This is the sensor transmit power vector. The block length vector, The vector formed by all downlink beamforming vectors. and Select vectors for the transmitting and receiving APs respectively. The specific constraints are as follows: The capacity of a finite block should be less than the capacity of Shannon: ； in These are the data packet size thresholds for sensors and actuators, respectively. System power consumption constraints: ； in, This is the maximum power consumption of sensor s. It is AP Maximum power consumption, This represents the total power consumption of the system. AP selection constraints: ； Block length constraint: Half-duplex mode: ; Full-duplex mode: ; in, Represents the set of positive integers; The optimization problem can be expressed as The optimization problem is decomposed into three sub-problems: the power and beamforming design sub-problem, the half-duplex block length allocation sub-problem, and the network-assisted full-duplex access point selection sub-problem.

6. The unified duplex resource allocation method for cellular-free industrial IoT with finite block length according to claim 5, characterized in that, In step S3, the power and beamforming design subproblem is transformed into a convex problem, which includes: Step S301: Introduce an auxiliary variable to replace the signal-to-interference-plus-noise ratio (SINR) and rephrase the problem as follows: in, objective function Update , ; Step S302: Linearly decompose the overall downlink decoding error probability into an additive form, as follows: ； Step S303: Perform Prony approximation on the Gaussian Q-function contained in the objective function, specifically as follows: The Gaussian Q function is approximated as: ； The objective function can be approximated as ,in , ; Step S304: Approximate the channel dispersion term of the objective function as a constant, specifically as follows: ； get: ； Step S305: Using the continuous convex approximation theory, a convex upper bound for the surrogate is constructed by using the first-order Taylor expansion as the decoding error probability represented by the Gaussian Q function. The specific process is as follows: Using a first-order Taylor expansion, a convex upper bound approximation is constructed for the decoding error probability represented by the Gaussian Q-function: For uplink and downlink, at point The upper bound function for the proxy at the specified location is constructed as follows: in Given by a first-order Taylor series expansion: ； The approximate objective function and constraints are as follows: Wherein, the objective function is ; Step S306: The objective function of the optimization problem is monotonically decreasing with respect to the signal-to-interference-plus-noise ratio (SINR) auxiliary variable, and all constraints are monotonic. Therefore, at the optimal solution, the auxiliary variable constraints will be equal to the objective function. and To handle non-convex signal-to-interference-plus-noise ratios (SIR), the SIR constraint is re-expressed as follows: in, , , , ; Using a first-order Taylor series at the initial point We approximate the non-convex term to obtain its local convex lower bound, as follows: ； in, The real part is represented; the power control and beamforming design subproblems are approximated by a series of convex upper bounds and reformulated as follows: 。 7. The unified duplex resource allocation method for cellular-free industrial IoT with finite block length according to claim 5, characterized in that, The nested double-iteration optimization algorithm for solving the half-duplex block long allocation subproblem in step S4 specifically includes: Step S401: Establish a model for the half-duplex block length allocation problem: Optimize uplink block length given uplink power and downlink beamforming. With downlink block length The objective is to minimize the system's maximum overall downlink decoding error probability: ； Step S402, the objective function with respect to and The trend is monotonically decreasing, therefore the optimal solution satisfies the total block length constraint and takes the equality sign. ; Step S403: Express the downlink block length as The objective function is reconstructed to be only related to the length of the uplink block. function The function is in its defined range The interior is unimodal, meaning it possesses a unique characteristic. Minimize the objective function; Step S404: Initialize outer iteration parameters: error tolerance Golden Section Search Parameters and the maximum number of inner iterations. With error tolerance ; Step S405: Initialize the block length search interval: Set the lower bound of the initial search interval for the uplink block length N1. With the upper realm ; Step S406: Execute the outer golden section search loop: when the block length search interval does not meet the convergence condition. Then, repeat the following steps S406.1 to S406.3: Step S406.1: Calculate the golden ratio: Based on the golden ratio In the current search range Calculate two interior points and ,satisfy ; Step S406.2, Inner Layer Iterative Solution for Power and Beamforming: For the current block length candidate points a and b, the convex optimization solver from step S306 is called respectively to obtain the corresponding power and beamforming schemes. And calculate the corresponding objective function value. and The specific process of the inner iteration is as follows: 71) Initialize the inner iteration index and initial point ; 72) Iterate through the convex approximation problem reconstructed in step S306 to obtain the current optimal solution. ; 73) Update Iteration Point ; 74) Determine if the inner loop converges: If the improvement in the system's maximum downlink decoding error probability is... If the maximum number of iterations is reached, the loop will exit and a suboptimal solution will be returned. Otherwise, return to step 72) and continue iterating; S406.3, Update block length search range: based on the obtained Calculate the objective function values ​​at candidate points a and b. and ;like Then update the upper bound of the search interval. Otherwise, update the lower bound of the search interval. ; S407. Output the optimal resource allocation scheme: After the outer loop converges, calculate the optimal uplink block length. and rounded down to the nearest integer value. The optimal downlink block length is then Finally, the output system jointly optimizes the resource allocation scheme, including the optimal block length. Transmission power and beamforming vector .

8. The method for unified duplex resource allocation in a finite block length industrial IoT system according to claim 5, characterized in that, The center exchange matching algorithm for solving the network-assisted full-duplex access point selection subproblem in step S5 specifically includes: Step S501: Establish a network-assisted full-duplex AP selection sub-problem model: ； Step S502: Generate the initial AP selection matrix using a greedy algorithm. ; Step S503: Select APs with different AP selection matrices within different EDUs, i.e. In and In (in ), swap the sender and receiver roles of these two APs, and define the initial AP pair as The new swap pair is The new exchange matrix is , ; Step S504: Calculate the overall decoding error probability using the following steps: 81) Initialize the inner iteration index and initial point ; 82) Iterate through the convex approximation problem reconstructed in step S306 to obtain the current optimal solution. ; 83) Update Iteration Point ; 84) Determine if the inner loop converges: If the improvement in the system's maximum downlink decoding error probability is... If the maximum number of iterations is reached, the loop will exit and a suboptimal solution will be returned. Otherwise, return to step 82) and continue iterating; Step S505: The CPU decides whether to accept the swap based on whether the system's maximum downlink decoding error probability has decreased; repeat steps S502 to S504 until convergence; return to the AP selection matrix. .

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