Information age low-complexity estimation method under imperfect feedback

Abstract

The invention provides an information age low-complexity estimation method under imperfect feedback. The method is applicable to a downlink scene under imperfect feedback and long-term transmission frequency constraint, and consists of N source nodes with different priorities, a public access point and N users. The information age estimation method specifically comprises the following steps: at the beginning of each time slot, the public access point estimates the real-time information age of each user by using obtained feedback information with delay and errors and local known information (such as packet generation information and historical decision information) based on the Bayesian theory. According to the method, the real-time information age under different feedback mechanisms can be accurately estimated, and the estimation method is of great significance to scheduling strategy design and system average information age optimization.

Description

Technical Field

[0001] This invention relates to the field of wireless network communication technology, specifically to a method for estimating information age with low complexity under imperfect feedback. Background Technology

[0002] In IoT downlink scenarios, the access point (AP) needs to schedule different source nodes to send data updates to corresponding users in real time so that each user can receive the latest data promptly. Age of Information (AoI), as an important performance indicator characterizing the freshness of information received by the receiver, is optimized in various communication scenarios. Accurate real-time AoI information is crucial for designing scheduling strategies. However, in real-world scenarios, due to unreliable channels, it is often impossible to obtain perfect feedback information without delay or errors. Therefore, estimating real-time AoI based on imperfect feedback information is of great significance for designing scheduling strategies and optimizing the system's average AoI. Summary of the Invention

[0003] This invention aims to provide a low-complexity method for estimating information age under imperfect feedback, which can provide a relatively accurate real-time AoI estimation method in downlink scenarios with imperfect feedback and transmission frequency constraints. The technical solution to achieve this objective is as follows: At the beginning of each time slot, the AP estimates the real-time expected AoI of each user terminal based on the obtained historical feedback information with delays and errors, historical scheduling decision information, and historical packet generation information of each source node. Then, a scheduling decision is made based on the estimated real-time expected AoI. At the end of each time slot, each user sends imperfect feedback information with delays and errors to estimate the real-time expected AoI at the beginning of the next time slot.

[0004] Compared with the prior art, the significant advantages of this invention are: this invention considers the downlink scenario with imperfect feedback and long-term transmission frequency constraints with delay and error, effectively utilizes all historical information to estimate the age of real-time information, and the proposed estimation method is applicable to different feedback mechanisms, which is of great significance for designing scheduling strategies and optimizing the average AoI of the system. Attached Figure Description

[0005] Figure 1 This is a schematic diagram illustrating an application scenario of the present invention;

[0006] Figure 2 This is a flowchart illustrating the scheduling strategy based on the information age estimation method implemented in this invention.

[0007] Figure 3-4 This is a comparison chart of the actual and estimated values ​​of the real-time AoI under the ACKs feedback mechanism and different system parameter settings, using the low-complexity information age estimation method of this invention.

[0008] Figure 5-6 This is a comparison chart of the actual and estimated values ​​of the real-time AoI under the ACKs / NACKs feedback mechanism and different system parameter settings, using the low-complexity information age estimation method of this invention.

[0009] Figure 7 The figure shows the expected weighted average AoI curve of the system under different transmission frequency constraints for the scheduling strategy with a threshold structure designed based on the estimated real-time information age in this invention. Detailed Implementation

[0010] This invention focuses on downlink scenarios under imperfect feedback and long-term transmission frequency constraints, such as... Figure 1 As shown, there are N source nodes with different priorities, one common access point (AP), and N different users. Assume the timeline is divided into equal-length time slots, and that each source node, user, and AP can accurately locate the boundaries of its time slot. Assume any source node... In each time slot At the initial time, with probability λ n Generate data packets in the region ∈(0,1], and the newly generated data packets will replace the old data packets; let d n,t ∈{0,1} indicates whether the source node n generates a new data packet at the beginning of time slot t, where d n,t =1 indicates that the source node n generates a new data packet at the beginning of time slot t; otherwise, d n,t =0. Assume that at the beginning of each time slot, the AP schedules no more than one source node to transmit the latest generated data packet to the corresponding user through an unreliable channel, and the channel transmission error probability for each source node n is ε. n ∈[0,1). At the end of each time slot, the user sends feedback information with delay and error to the AP. Assume each user The feedback delay is The probability of feedback error is σ n ∈[0,1]. The age (referred to as local age) of the latest data packet generated by the initial source node n in any time slot t and the Age of Information (AoI) of the latest data packet successfully received by the user terminal are respectively w n,t and h n,t and set initial values. If a new data packet is generated by the initial source node n in time slot t, then w n,t =0, otherwise w n,t =w n,t-1 +1; If source node n successfully transmits its latest generated data packet in time slot t, then h n,t+1 =w n,t +1, otherwise h n,t+1 =h n,t+1. Let a n,t ∈{0,1} represents the transmission behavior of source node n in time slot t, where a n,t =1 indicates that the source node n is scheduled for transmission by the AP in time slot t; otherwise, a n,t =0. Let u n,t ∈{0,1} represents the transmission result of source node n in time slot t, where u n,t =1 indicates that the data packet transmitted by the source node n in time slot t was successfully received by the corresponding user; otherwise, u n,t =0. Assume that either an ACKs / NACKs feedback mechanism or an ACKs feedback mechanism can be chosen. Under the ACKs / NACKs feedback mechanism, when the user successfully receives a data packet from the source node, it sends an ACK to the AP to confirm successful reception; when the user fails to receive the data packet, it sends a NACK to the AP. Let v n,t ∈{0,1,-1} represents the feedback information received by AP from user n at the end of time slot t-1, where v n,t =0 indicates that the AP did not receive any feedback information from user n at the end of time slot t-1, v n,t =1 indicates that the AP received a delayed ACK from user n at the end of time slot t-1 (indicating) ), v n,t =-1 indicates that the AP received a delayed NACK from user n at the end of time slot t-1 (indicating) Under the ACK feedback mechanism, an ACK is sent to the AP to confirm successful reception only when the user successfully receives a data packet from the source node; otherwise, the user does not send any feedback. Let v n,t ∈{0,1} indicates whether the AP received feedback information from user n at the end of time slot t-1, where v n,t =0 indicates that the AP did not receive any feedback information from user n at the end of time slot t-1, v n,t =1 indicates that the AP received a delayed ACK from user n at the end of time slot t-1 (indicating) ).make This represents the set of all historical information about the source node n that the AP can obtain before making a scheduling decision at the beginning of time slot t. Indicates the expected AoI of user n at the beginning of time slot t; sets the initial value. Assuming that at the beginning of time slot t+1, the AP estimates the real-time expected AoI of each user terminal based on the obtained historical feedback information with delays and errors, historical scheduling decisions, and historical packet generation information of each source node. The specific steps of the method for estimating the expected AoI are as follows:

[0011] Step 1: At the beginning of time slot t+1, AP updates time slot tD based on Bayesian update theory according to the following formula.n The expected value of AoI with +1 is updated as follows if an ACKs / NACKs feedback mechanism is adopted:

[0012]

[0013] If the ACKs feedback mechanism is adopted, the update is as follows:

[0014]

[0015] Step 2: Under the ACKs / NACKs feedback mechanism and the ACKs feedback mechanism, at the beginning of time slot t+1, AP updates time slot tD sequentially according to the following formula. n Expected AoI value from +2 to time slot t+1:

[0016]

[0017] Where t′∈{tD n +1,...,t}.

[0018] Preferably, based on the estimated real-time AoI, a scheduling strategy needs to be designed to optimize the system's average AoI. It is assumed that all considered scheduling strategies are unpredictable, meaning they do not use future information when making scheduling decisions. Let Π denote the set of unpredictable strategies. The expected weighted average information age (EWSAoI) of the system in the infinite time domain under any unpredictable scheduling strategy π∈Π is defined as:

[0019]

[0020] Where T represents the total number of time slots, and the expected symbol is... It is the expectation of all system randomness and transmission behavior under policy π, α n Let n represent the weight of each source node n. Assume the sum of the weights of all source nodes is 1, i.e., Define the expected transmission frequency in the infinite time domain under strategy π as:

[0021] The optimization problem under study is defined as follows:

[0022] min π∈Π J π , st q π ≤ρ, (6)

[0023] Where ρ represents the highest allowed transmission frequency of the system.

[0024] Preferably, at the beginning of each time slot, for the optimization problem shown in equation (6), AP executes a low-complexity strategy π with the following threshold structure based on the real-time AoI estimated in claim 1. DPP :

[0025]

[0026] Where V is an adjustable positive real number used to balance queue convergence and policy performance. Q t This represents a virtual queue reflecting the satisfaction of transmission frequency constraints. Its initial value is Q0 = 0, and its evolution formula is:

[0027]

[0028] Preferably, at the end of each time slot, the user sends feedback information with delays and errors, which is used to estimate the expected value of the real-time information age at the beginning of the next time slot. Figure 2 A flowchart describing the specific execution process of the scheduling strategy designed based on the information age estimation method described in this invention is presented.

[0029] The present invention uses MATLAB software to implement the method, setting the number of source nodes in the network to N=4, the weight ratio between nodes to 1:4:7:10, the simulation time to T=100000 time slots, and V=1. Figure 3 and Figure 5 Set λ under ACKs and ACKs / NACKs mechanisms respectively n =0.5,σ n =0.1, ρ=0.5, ε n =0.2,D n =5 for any Observe and compare the actual and estimated values ​​of a user's real-time AoI; Figure 4 and Figure 6 Set λ under ACKs and ACKs / NACKs mechanisms respectively n =0.5,σ n =0.5, ρ=0.5, ε n =0.2,D n =3 for any Observe and compare the actual and estimated values ​​of a user's real-time AoI; Figure 7 Set the number of source nodes N=12, divide the 12 source nodes into four groups, each group contains 3 nodes with the same weight, and the weight ratio between the four groups is 1:4:7:10, and set λ. n = (N-n+1) / (2N),σ n = (n-1) / (2N),D n =10,ε n=ε for any The curve of EWSAoI as a function of the maximum allowed transmission frequency ρ was observed. The results show that the information age estimation value obtained by the proposed information age estimation method can match the actual value relatively accurately under different feedback mechanisms and system parameter settings. Furthermore, the scheduling strategy with a threshold structure designed based on the estimated real-time AoI has excellent system mean AoI performance, thus verifying the effectiveness of the present invention.

Claims

1. A low-complexity estimation method of information age under imperfect feedback, the application scenario of the method is a downlink scenario under imperfect feedback and long-term transmission frequency constraint, containing N source nodes with different priorities, 1 common access point (AP) and N corresponding users, characterized in that, The application divides the time axis into equal length time slots, and each source node, each user and the AP can accurately locate the boundary of the time slot; assuming any source node In each time slot At the initial moment, a data packet is generated with a probability λ n ∈(0,1], and the newly generated data packet will replace the old data packet; let d n,t ∈{0,1} represent whether the source node n generates a new data packet at the beginning of the time slot t, wherein d n,t =1 represents that the source node n generates a new data packet at the beginning of the time slot t, otherwise d n,t =0; it is assumed that the AP schedules no more than one source node to transmit the latest generated data packet to the corresponding user through an unreliable channel at the beginning of each time slot, and the channel transmission error probability of each source node n is ε n ∈[0,1); at the end of each time slot, the user sends feedback information with delay and error to the AP, and it is assumed that the feedback delay of each user is and the feedback error probability is σ n ∈[0,1]; the age of the latest data packet generated by any source node n at the beginning of any time slot (referred to as local age) and the information age (Age of Information, AoI) of the latest data packet successfully received by the user end are respectively w n,t and h n,t , and the initial value is set as If the source node n generates a new data packet at the beginning of the time slot t, then w n,t =0, otherwise w n,t =w n,t-1 +1; if the source node n successfully transmits its latest generated data packet at the time slot t, then h n,t+1 =w n,t +1, otherwise h n,t+1 =h n,t +1; let a n,t ∈{0,1} represent the transmission behavior of the source node n at the time slot t, wherein a n,t =1 represents that the source node n is scheduled by the AP for transmission at the time slot t, otherwise a n,t =0; let u n,t ∈{0,1} represent the transmission result of the source node n at the time slot t, wherein u n,t =1 represents that the data packet transmitted by the source node n at the time slot t is successfully received by the corresponding user, otherwise u n,t =0; it is assumed that ACKs / NACKs feedback mechanism or ACKs feedback mechanism can be selected, wherein in the ACKs / NACKs feedback mechanism, when the user successfully receives the data packet from the source node, ACK is sent to the AP to confirm successful reception, and when the user fails to receive the data packet, NACK is sent to the AP; let v n,t v e {0, 1, -1} denotes the feedback information received by the AP from user n at the end of time slot t - 1, where v n,t = 0 denotes that the AP did not receive any feedback information from user n at the end of time slot t - 1, v n,t = 1 denotes that the AP received a delayed ACK from user n at the end of time slot t - 1 (indicating ), v n,t = -1 denotes that the AP received a delayed NACK from user n at the end of time slot t - 1 (indicating ); and under the ACKs feedback mechanism, the AP sends an ACK to indicate successful reception only when the user successfully receives a data packet from the source node, and the user does not send any feedback in other cases; let v n,t v e {0, 1} denotes whether the AP received feedback information from user n at the end of time slot t - 1, where v n,t = 0 denotes that the AP did not receive any feedback information from user n at the end of time slot t - 1, v n,t = 1 denotes that the AP received a delayed ACK from user n at the end of time slot t - 1 (indicating ); let denote the set of all historical information about the source node n available to the AP before making a scheduling decision at the beginning of time slot t, and define denote the expected AoI of user n at the beginning of time slot t; set its initial value Assume that at the beginning of time slot t + 1, the AP estimates the real-time expected AoI of each user end according to the obtained historical feedback information with delay and error, historical scheduling decisions, and historical packet generation information of each source node, The specific steps of the estimation method of the expected AoI are: Step 1: At the beginning of time slot t+1, AP updates the AoI expectation value at time slot t-D based on Bayesian update theory as follows: n If ACKs / NACKs feedback mechanism is adopted, the AoI expectation value at time slot t+1 is calculated as follows: If ACKs feedback mechanism is adopted, the calculation is as follows: Step 2: At the beginning of slot t+1, APs update the AoI expected value from slot t-D to slot t+1 according to the following formula under ACKs / NACKs feedback mechanism and ACKs feedback mechanism respectively: n AoI expected value from slot t+1 to slot t+2: where t' e {t-D n +1,...,t}.

2. The low-complexity estimation method of information age under imperfect feedback according to claim 1, characterized in that, Based on the estimated expected AoI, a scheduling strategy needs to be designed to optimize the system average AoI; it is assumed that the scheduling strategies considered are all non-anticipatory, that is, the considered strategies do not use future information when making scheduling decisions; let Π represent the set of non-anticipatory strategies; the system expected weighted sum AoI (EWSAoI) in the infinite time domain under any non-anticipatory scheduling strategy π∈Π is defined as: where T denotes the total number of time slots, E is the expectation over all system randomness and transmission behavior under policy π, α n denotes the weight of each source node n, assuming that the sum of weights of all source nodes is 1, i.e., The expected transmission frequency in the infinite time domain under policy π is defined as: The optimization problem is defined as: min π∈Π J π ,s.t.q π ≤ρ, (6) Where ρ represents the highest transmission frequency allowed by the system.

3. The low-complexity estimation method of information age under imperfect feedback according to claim 1, characterized in that, At the beginning of each time slot, for the optimization problem shown in equation (6), the AP performs the following low-complexity policy π with threshold structure based on the estimated expected AoI of claim 1 DPP : where V is a positive real number that can be adjusted to trade off queue convergence and policy performance, Q t denotes a virtual queue reflecting the satisfaction of the transmission frequency constraint, whose initial value is set to Q0= 0, and whose evolution formula is 4. The method for low-complexity estimation of information age in the presence of imperfect feedback according to claim 1, characterized in that, At the end of each time slot, the user sends feedback information with delay and error, which is used to estimate the real-time information age expectation value at the beginning of the next time slot.

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