A low-complexity transmission scheduling method based on error information age

Abstract

A low-complexity transmission scheduling method based on error information age is proposed. This invention presents an online AoII optimization method for frequency-constrained state update systems under a perfect feedback mechanism. The method is applicable to infinite time-domain scenarios and aims to reduce the long-term average AoII of the system. The method transforms the average transmission frequency constraint into a virtual queue stability problem and performs the following steps in each time slot: At the beginning of each time slot, the transmitter calculates the impact of the current transmission on AoII reduction based on the current source state, the receiver's estimated state, and the virtual queue length; subsequently, a transmission decision criterion is constructed based on the drift-penalty function, resulting in a dynamic threshold-type transmission rule; if the current AoII state satisfies the transmission conditions, the transmitter sends a state update packet to the receiver through an unreliable channel; otherwise, it remains silent; at the end of each time slot, the receiver updates its state estimate based on the transmission result and returns the reception status to the transmitter through perfect feedback; the transmitter updates the system state and the virtual queue based on the feedback information.

Description

Technical Field

[0001] This invention relates to the field of wireless network communication technology, specifically to a low-complexity transmission scheduling method based on error information age. Background Technology

[0002] In IoT scenarios, the transmitter typically needs to send the changing state of information sources to the receiver in a timely manner so that the receiver can make state estimates and decisions. Traditional research often uses the Age of Information (AoI) to characterize the freshness of information, but AoI only reflects the interval between the information generation time and the current time, and cannot directly indicate whether the receiver's estimate has deviated from the true state. The Age of Incorrect Information (AoII) can simultaneously characterize the receiver's estimation error and the duration of the error, making it more suitable for IoT systems that are sensitive to state estimation errors. However, transmitters in resource-constrained IoT are usually limited by energy, spectrum, or access opportunities, and cannot send state update packets in every time slot. Therefore, the AoII-based state update problem usually manifests as an infinite time-domain stochastic optimization problem with a long-term average transmission frequency constraint. Existing AoII studies typically employ Lagrange relaxation or dynamic programming methods to solve such problems and have proven that the optimal policy has a threshold structure. However, these methods require solving average-cost Markov Decision Processes (MDPs) or Constrained Markov Decision Processes (CMDPs), which becomes cumbersome when the state space is large or the cost function is complex. Therefore, it is necessary to propose a low-complexity transport scheduling method based on error information ageing. Summary of the Invention

[0003] This invention aims to provide a low-complexity transmission scheduling method based on error information age, which can reduce the average error information age of the system while meeting long-term average transmission frequency constraints in resource-constrained Internet of Things (IoT) systems. The technical solution to achieve this objective is as follows: In a point-to-point state update system consisting of a transmitter and a receiver, the transmitter performs the following steps in each time slot: Step 1: At the beginning of each time slot, the transmitting end observes the current state of the information source and determines the estimated state of the information source by the receiving end. Based on the deviation between the current state of the information source and the current estimated state of the receiving end, it is determined whether the estimation by the receiving end is in an unacceptable mismatch state, and the current AoII is calculated. Step 2: The sending end updates the virtual queue used to characterize the cumulative violation degree of the transmission frequency constraint based on the current AoII and transmission frequency constraints; Step 3: The sending end calculates the transmission decision index of the current time slot based on the hybrid Lyapunov function and the drift-plus-penalty (DPP) function, and obtains the dynamic threshold-type transmission rule to determine whether the current time slot should send a status update packet; Step 4: If the sender chooses to transmit, the update packet is sent to the receiver through an unreliable channel. If the transmission is successful, the receiver updates its state estimate, and the system AoII is reduced or set to zero accordingly. If the transmission fails or the sender remains idle in the current time slot, the receiver maintains the original estimate, and the AoII continues to evolve according to the system state.

[0004] Step 5: At the end of each time slot, the receiving end feeds back the transmission result to the sending end. The sending end updates the system status and virtual queue based on the feedback information and proceeds to the transmission decision for the next time slot.

[0005] Compared with the prior art, the significant advantages of this invention are: this invention achieves low-complexity transmission scheduling through virtual queues and online dynamic threshold decision, and can obtain a lower AoII while satisfying the long-term average transmission frequency constraint. Attached Figure Description

[0006] Figure 1 This is a schematic diagram illustrating an application scenario of the present invention; Figure 2 The flowchart illustrates the low-complexity transmission scheduling method based on error information age as described in this invention. Figure 3-4 The invention implements a low-complexity transmission scheduling method based on error information age, and measures the mean AoII and actual transmission frequency under different system control parameters. Figure 5-6 The figure shows the system mean AoII curves for implementing the low-complexity transmission scheduling method based on error information age under different system state transition parameters. Detailed Implementation

[0007] This invention focuses on a point-to-point state update system consisting of one transmitter and one receiver. In this system, the time axis is divided into equal-length time slots, indexed using discrete time. This indicates the time slot number, and each user can accurately locate the time slot boundary; the transmitting end observes the information source status at the beginning of each time slot. And decide whether to send a status update packet, the sending end action is recorded as ,when When, it indicates that the sending end is in the time slot. Send status update packet, when When, it indicates that the sending end is in the time slot. Keep idle; the channel transmission result is denoted as ,when When, it indicates that the status update packet has been successfully decoded by the receiving end. When this occurs, it indicates that the state update packet transmission failed; the probability of successful channel transmission is... The probability of transmission failure is The receiver uses the most recent successfully received state update as the current estimate, if the time slot is... The timestamp of the last successful reception of a status update packet by the receiving end is Then the receiver estimates the state as follows: When no new state update packet arrives successfully, the receiver maintains the original estimated state.

[0008] Figure 2 This is a flowchart illustrating the low-complexity transmission scheduling method based on error information age, as described in this invention. Figure 2 As shown, a low-complexity transmission scheduling method based on error information age is proposed, wherein the method performs the following steps in each time slot: Step 1: The sending end in the time slot The current state of the information source is observed at the initial moment. The receiver's estimated state of the information source is determined. Based on the deviation between the current state of the information source and the current estimated state of the receiver, it is determined whether the receiver's estimation is in an unacceptable mismatch state, and the current AoII is calculated. Step 1-1: Set the estimation error tolerance threshold and define mismatch indicator variables. : (1) in, This is an indicator function; it takes the value 1 when the condition inside the parentheses is true, and takes the value 0 when the condition inside the parentheses is false. This indicates that the deviation between the receiver's estimate and the actual state of the information source is within an acceptable range. This indicates that the deviation between the receiver's estimate and the actual state of the information source exceeds the estimation error tolerance threshold.

[0009] Step 1-2: Record the most recent time when the receiver's estimate of being in an acceptable state is denoted as . The error message indicates the age status. Defined as: (2) Among them, when When, it indicates that the receiver estimates the current state is acceptable; when When this occurs, it indicates that the receiving end estimates that it is currently in an unacceptable mismatch state, and that the unacceptable mismatch state has persisted. Each time slot. The specific state transition relationship is as follows: (1) When At that time, regardless of whether the sender sends a state update packet, the state transition probability for the next time slot is: (3) (2) When And when the transmitter remains idle, the state transition probability for the next time slot is: (4) (3) When Furthermore, when the sender sends the state update packet, the state transition probability for the next time slot is: (5) in and satisfy This makes sending state update packets more beneficial for the system to recover from an unacceptable mismatch state to an acceptable state compared to keeping it idle.

[0010] Step 2: The sender updates the virtual queue used to characterize the cumulative violation degree of the transmission frequency constraint based on the current AoII and transmission frequency constraints. ,make (6) in , This indicates the maximum allowed average transmission frequency of the system; when the sender frequently sends status update packets, the virtual queue... Increase; when the sender reduces state update transmissions, the virtual queue... Decrease or maintain at zero; the virtual queue is used to transform the long-term average transmission frequency constraint into a queue stability constraint, and to ensure that the long-term average transmission frequency of the transmitter satisfies: (7) in, For mathematical expectation operators, Indicates time slot The expected value of the status update packet sent by the sender.

[0011] Step 3-1: The transmitting end calculates the transmission decision index of the current time slot based on the hybrid Lyapunov function and the DPP function. The hybrid Lyapunov function is defined as follows: (8) in, For virtual queue weights, The age status weight for the error message has the following values: (9) Step 3-2: Define conditional drift as: (10) in Indicates time slot The previously available information set of the system includes the current virtual queue. and the current AoII state And historical feedback information.

[0012] Step 3-3: To reduce the age of error messages while controlling virtual queue drift, the drift-penalty function is defined as follows: (11) in Age penalty weights for erroneous information; given in each time slot Then, the sending end minimizes the action. The relevant drift-penalty term determines the sending action, i.e. .

[0013] Steps 3-4: When At that time, the conditional expectation of the age state of the error information in the next time slot is independent of the sending action, and Therefore, the sender remains idle; when If the sender remains idle, the corresponding DPP target item is: If the sender remains idle, the corresponding DPP target item is: The sender chooses to send a status update packet if and only if Therefore, the transmitter determines the transmission action in each time slot according to the following dynamic threshold rule: (12) Step 4: If the sender chooses to transmit, the update packet is sent to the receiver through an unreliable channel. If the transmission is successful, the receiver updates its state estimate. If the transmission fails or the sender remains idle in the current time slot, the receiver retains the original estimate, and AoII continues to evolve according to the system state. Step 5: At the end of each time slot, the receiving end feeds back the transmission result to the sending end. The sending end updates the system status and virtual queue based on the feedback information and proceeds to the transmission decision for the next time slot.

[0014] This invention uses MATLAB software to implement the method and sets the simulation time. Time slot.

[0015] Figures 3 to 4 The paper demonstrates the variation of the mean AoII and actual transmission frequency of the low-complexity transmission scheduling method described in this invention under different system control parameters. The results show that system control parameters can influence the trade-off between error information age performance and transmission frequency constraints.

[0016] Figures 5 to 6 The mean AoII curves of the method described in this invention are shown under different system state transition parameters. The results demonstrate that, under different state transition characteristics, the proposed low-complexity online strategy can achieve near-optimal AoII performance while avoiding complex dynamic programming solutions, thus verifying the effectiveness of this invention.

Claims

1. A low complexity transmission scheduling method based on error information age, the scenario contains 1 sender, 1 receiver and 1 unreliable channel, the sender can obtain perfect feedback, and the system is subject to long-term average transmission frequency constraint, characterized in that, Given the initial system state, the probability of successful channel transmission, and transmission frequency constraints, the following steps are performed in each time slot: ​ Step 1: At the beginning of each time slot, the transmitting end observes the current state of the information source and determines the estimated state of the information source by the receiving end. Based on the deviation between the current state of the information source and the current estimated state of the receiving end, it is determined whether the estimation by the receiving end is in an unacceptable mismatch state, and the current age of incorrect information (AoII) is calculated. Step 2: The sending end updates the virtual queue used to characterize the cumulative violation degree of the transmission frequency constraint based on the current AoII and transmission frequency constraints; Step 3: The sending end calculates the transmission decision index of the current time slot based on the hybrid Lyapunov function and the drift-plus-penalty (DPP) function, and obtains the dynamic threshold-type transmission rule to determine whether the current time slot should send a status update packet; Step 4: If the sender chooses to transmit, the update packet is sent to the receiver through an unreliable channel. If the transmission is successful, the receiver updates its state estimate. If transmission fails or the transmitter remains idle in the current time slot, the receiver maintains the original estimate, and AoII continues to evolve according to the system state. Step 5: At the end of each time slot, the receiving end feeds back the transmission result to the sending end. The sending end updates the system status and virtual queue based on the feedback information and proceeds to the transmission decision for the next time slot.

2. The low-complexity transmission scheduling method based on error information age according to claim 1, characterized in that, The present application divides the time axis into equal length time slots, using discrete time index to represent time slot number, and each user can accurately locate the boundary of time slot; the sender observes the state of information source at the beginning of each time slot , and decides whether to send state update package, the action of sender is recorded as , when , it means that the sender sends state update package in time slot , when , it means that the sender keeps idle in time slot ; The channel transmission result is denoted as ,when When, it indicates that the status update packet has been successfully decoded by the receiving end. When this happens, it indicates that the status update packet transmission failed; The probability of successful channel transmission is The probability of transmission failure is The receiver uses the most recent successfully received state update as the current estimate, if the time slot is... The timestamp of the last successful reception of a status update packet by the receiving end is Then the receiver estimates the state as follows: When no new state update packet arrives successfully, the receiver maintains the original estimated state.

3. The low-complexity transmission scheduling method based on error information age according to claim 1, characterized in that, The calculation method for AoII in step 1 is as follows: Step 1-1: Set the estimation error tolerance threshold and define mismatch indicator variables. : (1) in, This is an indicator function; it takes the value 1 when the condition inside the parentheses is true, and takes the value 0 when the condition inside the parentheses is false. This indicates that the deviation between the receiver's estimate and the actual state of the information source is within an acceptable range. This indicates that the deviation between the receiver's estimate and the actual state of the information source exceeds the estimation error tolerance threshold; Step 1-2: Record the most recent time when the receiver's estimate of being in an acceptable state is denoted as . The error message indicates the age status. Defined as: (2) Among them, when When, it indicates that the receiver estimates the current state is acceptable; when When this occurs, it indicates that the receiving end estimates that it is currently in an unacceptable mismatch state, and that the unacceptable mismatch state has persisted. Each time slot.

4. The low-complexity transmission scheduling method based on error information age according to claim 1, characterized in that, The error message "Age Status" mentioned in Step 1 The state evolution process satisfies the following relationship: (1) When At that time, regardless of whether the sender sends a state update packet, the state transition probability for the next time slot is: (3) (2) When And when the transmitter remains idle, the state transition probability for the next time slot is: (4) (3) When Furthermore, when the sender sends the state update packet, the state transition probability for the next time slot is: (5) in and satisfy This makes sending state update packets more beneficial for the system to recover from an unacceptable mismatch state to an acceptable state compared to keeping it idle.

5. The low-complexity transmission scheduling method based on error information age according to claim 1, characterized in that, The update of the virtual queue in step 2 The specific process is as follows: (6) in , This indicates the maximum allowed average transmission frequency of the system; when the sender frequently sends status update packets, the virtual queue... Increase; when the sender reduces state update transmissions, the virtual queue... Decrease or maintain at zero; the virtual queue is used to transform the long-term average transmission frequency constraint into a queue stability constraint, and to ensure that the long-term average transmission frequency of the transmitter satisfies: (7) in, For mathematical expectation operators, Indicates time slot The expected value of the status update packet sent by the sender.

6. The low-complexity transmission scheduling method based on error information age according to claim 1, characterized in that, In step 3, the specific process by which the transmitting end determines the transmitting action based on the hybrid Lyapunov function and the drift-penalty criterion is as follows: Step 3-1: Define the mixed Lyapunov function as: (8) in, For virtual queue weights, The age status weight for the error message has the following values: (9) Step 3-2: Define conditional drift as: (10) in Indicates time slot The previously available information set of the system includes the current virtual queue. and the current AoII state And historical feedback information; Step 3-3: To reduce the age of error messages while controlling virtual queue drift, the drift-penalty function is defined as follows: (11) in Age penalty weights for erroneous information; given in each time slot Then, the sending end minimizes the action. The relevant drift-penalty term determines the sending action, i.e. ; Steps 3-4: When At that time, the conditional expectation of the age state of the error information in the next time slot is independent of the sending action, and Therefore, the sender remains idle; when If the sender remains idle, the corresponding DPP target item is: If the sender remains idle, the corresponding DPP target item is: The sender chooses to send a status update packet if and only if Therefore, the transmitter determines the transmission action in each time slot according to the following dynamic threshold rule: (12)。

Images