Self-adaptive sampling method for risk-sensitive state updating service

Abstract

The invention belongs to the technical field of wireless state updating, and relates to a risk-sensitive state updating service-oriented adaptive sampling method, which comprises the following steps of: 1, introducing a concept of statistical information age, 2, recording a statistical AoI minimization problem of key state updating in a wireless fading channel as P0; step 3, finding out a sampling and power distribution solution of the P0 problem, namely realizing minimum statistics AoI under a given peak age violation probability; according to the method, the minimum statistical information age can be realized all the time, and the statistical information age is kept unchanged and then is reduced along with the increase of the violation probability; therefore, according to the method, the minimum statistical information age can be realized, and the requirement of risk sensitive state updating can be better met.

Description

Technical Field

[0001] The invention belongs to the technical field of wireless status update, and relates to an adaptive sampling method for risk-sensitive status update services. Background Art

[0002] Wireless state update systems are a typical class of time-sensitive applications. In particular, some state update systems are risk-sensitive, and the key state information on the target side should always be as fresh as possible. Otherwise, even a small amount of outdated information may lead to undesirable system behavior or even damage.

[0003] In wireless status update systems, how to evaluate the freshness of status information is crucial. Age of Information (AoI) is a recently emerging and interesting concept in this field, which is defined as the time elapsed since the source generated the last received status information. Based on this idea, AoI presents a sawtooth function characteristic over time. Unlike traditional delay indicators, AoI is affected not only by the end-to-end delay of the network, but also by the sampling rate of the source. By fine-tuning the sampling rate of the source, the freshness of the information can be significantly improved.

[0004] Average AoI is widely used to evaluate the long-term performance of information freshness in various state update systems. However, the derivation of average AoI is often very complicated due to the coupling between the arrival interval of state packets and the system time. In contrast, since AoI is a sawtooth function of time, peak AoI is able to capture the core characteristics of the aging process. Therefore, average peak AoI can be used as an alternative long-term performance metric to circumvent the complex derivation caused by the correlation between arrival interval and system time, but it cannot meet the requirements of critical state update systems. Using minimized maximum peak AoI can mitigate the worst impact of outdated information, but minimizing maximum peak AoI often produces biases that degrade the overall performance. The minimum peak Age of Information (AoI) achievable at a given violation probability can meet the requirements of various critical state update systems, and the level of violation probability can be associated with the risk sensitivity of the state update system.

[0005] The disadvantages of the existing technology are that the average AoI or the average peak AoI is not sensitive to risk and is not suitable for use in wireless status update systems. The maximum peak AoI is too sensitive to certain key status update systems, and there is a possibility of allocating too many resources to the worst case, which significantly reduces the overall performance of the system. The probability distribution function of the minimum peak age information that can be achieved under a given violation probability usually lacks a closed-form expression, so it is difficult to derive the minimum peak AoI that can be achieved under a given violation probability, and it is even more difficult to optimize it.

[0006] Therefore, an adaptive sampling method is needed to solve the above technical problems, which can achieve the minimum statistical information age and better meet the needs of risk-sensitive state updates. Summary of the invention

[0007] The technical solution adopted by the present invention to solve the technical problem is: an adaptive sampling method for risk-sensitive status update services, the method comprising the following steps:

[0008] Step 1: Introduce the concept of statistical information age, which is a tight upper bound of the average peak age of the tail under a given violation probability; because the statistical age information considers the average value of the peak age of the tail, it can better reflect the risk level; the statistical information age is defined as Δ(ρ), expressed as:

[0009]

[0010] In formula (5), A represents the peak information age, θ represents the age information index, and M A (θ) represents the moment generating function MGF of the peak age, which is e θA The mathematical expectation of ; 1 / λ(γ,ρ) represents the sampling interval, γ represents the channel power gain;

[0011] Step 2: Minimize the statistical AoI of the key state update in the wireless fading channel, denoted as P0:

[0012]

[0013] stτBlog2(1+P(γ,ρ)γ)≥D, (5b)

[0014]

[0015] τλ(γ,ρ)≤1, (5d)

[0016] Tλ(γ,ρ)≥1 (5e)

[0017] Among them, the constraint condition formula (5b) is obtained based on Shannon capacity, where the noise power is assumed to be 1, B represents the bandwidth, P(γ,ρ) represents the transmission power that varies with γ and ρ, and D represents the number of bits of a state data packet;

[0018] The constraint condition (5c) is the constraint condition for the average transmission power. Indicates the average transmission power of the source;

[0019] Constraint (5d) ensures that the sampling interval is greater than the transmission time, thus ensuring that each state data packet can be transmitted in time after being generated;

[0020] The constraint condition (5e) indicates that a channel must be sampled at least once within the coherence time;

[0021] Step 3: Find the sampling and power allocation solution for the P0 problem to achieve the minimum statistical AoI under a given peak age violation probability.

[0022] Preferably, in step 3, P0 is equivalently converted to P1:

[0023]

[0024] τλ(γ,ρ)≤1,(8c)

[0025] Tλ(γ,ρ)≥1(8d)

[0026] Let f(θ,λ(γ,ρ)) represent the objective function of P1, which consists of two parts, expressed as:

[0027]

[0028] Preferably, in step 3, a two-step method is used to solve problem P1; in the first step, the AoI index is regarded as a constant and an optimal sampling scheme is found. In the second step, based on the optimal sampling scheme obtained in the first step, an optimal AoI index is searched.

[0029] Preferably, in step 3, the sub-problem of the first step is expressed as problem P2:

[0030]

[0031] τλ(γ,ρ)≤1, (10c)

[0032] Tλ(γ,ρ)≥1 (10d)

[0033] In problem P2, the objective function is the first part of f(θ,λ(γ,ρ)) P2 is a standard convex-concave fractional programming problem, where the objective function follows a convex-concave form and the constraints are convex.

[0034] Preferably, in step 3, P2 is converted to P3 by Dinkelbach transformation:

[0035]

[0036] τλ(γ,ρ)≤1, (11c)

[0037] Tλ(γ,ρ)≥1 (11d)

[0038] In formula (11a), β represents a newly introduced auxiliary variable; the auxiliary variable is iteratively updated by formula (12):

[0039]

[0040] In formula (12), i represents the i-th iteration, and i = 1, 2, 3, etc. The initial value of the auxiliary variable β is set to e by selecting λ(γ, ρ)[0] = 1 / T. θT , by iteratively updating β and solving P3 until its value converges, at which point the optimal solution of P3 is also the optimal solution of P2.

[0041] More preferably, in step 3, the optimal solution of P3 is:

[0042]

[0043] in, and The two thresholds representing the channel power gain are equal to η / (1-βe θT (1-θT)) and η / (1-βe θτ (1-θτ)), is the Lambert W function, and η is given by Sure.

[0044] Preferably, in step 3, the second step is specifically: find the optimal AoI index under a given peak age violation probability, and use a binary search method to find the optimal AoI index; assuming that in the binary search, the interval of the parameter θ is [θ left ,θ right ], in (θ left +θ right ) / 2, and if the first derivative of the function f(θ,λ(γ,ρ)) is less than zero, then θ left Update to (θ left +θ right ) / 2, otherwise θ right Update to (θ left +θ right ) / 2; According to the optimal AoI index derived above, substituting it into formula (16) can obtain the optimal sampling scheme.

[0045] The beneficial effects of the present invention are:

[0046] The present invention can always achieve a minimum statistical information age, which remains unchanged at the beginning and then decreases as the probability of violation increases, and can better meet the needs of risk-sensitive status updates. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is an AoI process diagram and a peak age influence diagram of an adaptive sampling method for risk-sensitive status update services of the present invention, wherein Figure 1 (a) is the AoI process at the source and destination ends. Figure 1 (b) is the effect of sampling rate on peak age;

[0048] Figure 2 The present invention And the trend diagram of f(θ,λ(γ,ρ)) changing with AOI index;

[0049] Figure 3 It is a probability distribution comparison diagram of the peak age of the sampling schemes of the Avg-PAoI-O sampling scheme, the Max-PAoI-O sampling scheme and the scheme proposed in the present invention under different risk sensitivity requirements;

[0050] Figure 4 It is a performance comparison chart of the present invention, the Avg-PAoI-O sampling scheme, and the Max-PAoI-O sampling scheme. DETAILED DESCRIPTION

[0051] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the relevant technologies in the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0052] refer to Figures 1 to 4 This embodiment is an adaptive sampling method for risk-sensitive status update services. Considering the insensitivity of average AoI and average peak AoI to risk, the concept of statistical information age is introduced. The statistical information age is a tight upper bound of the average peak age of the tail under a given violation probability. Because the statistical age information considers the average value of the peak age of the tail, it can better reflect the risk level.

[0053] Mathematically, Δ(ρ) is defined as

[0054]

[0055] Where A represents the peak information age, θ is the age information index, M A (θ) is the moment generating function MGF of the peak age, which is e θA The mathematical expectation of .

[0056] Consider Figure 1The age variation process at the source and destination shown in (a) assumes that the channel coherence time is long enough, consistent with typical practical systems, so that multiple sampling steps can be performed within the channel coherence interval. As shown in the figure, t n represents the time of the nth sampling at the source. According to the definition of AOI, the age of the source is set to zero at each sampling moment and gradually increases between two adjacent sampling intervals. Since the transmission time is τ, once a new status data packet is received, the age of the destination is set to τ and gradually increases between the arrival of two adjacent status data packets. Then, the peak age A of the destination is expressed as:

[0057]

[0058] like Figure 1 As shown in (b), the higher the sampling rate, the more age peaks there are in a channel coherence interval. Since the duration of a channel coherence time is T and the sampling interval is 1 / λ(γ,ρ), the number of age peaks in the time interval [t, t+T) is approximately equal to Tλ(γ,ρ). In addition, the probability that the channel power gain is equal to γ ​​is f γ (γ)dγ, where f γ (γ) is the probability density function of the channel power gain γ. Therefore, the probability that the peak age is equal to A can be expressed as:

[0059]

[0060] According to equations (2) and (3), the moment generating function MGF of A can be deduced as:

[0061]

[0062] Then, according to the definition of statistical AoI in formula (1), the statistical information age of A can be expressed as

[0063]

[0064] The statistical AoI minimization problem of key state updates in wireless fading channels is denoted as P0:

[0065]

[0066] stτBlog2(1+P(γ,ρ)γ)≥D, (5b)

[0067]

[0068] τλ(γ,ρ)≤1, (5d)

[0069] Tλ(γ,ρ)≥1 (5e)

[0070] Constraint (5b) is obtained based on Shannon capacity, where the noise power is assumed to be 1, B represents the bandwidth, P(γ,ρ) represents the transmit power that varies with γ and ρ, and D represents the number of bits in a state data packet.

[0071] Constraint (5c) is a constraint on the average transmit power, Indicates the average transmission power of the source.

[0072] Constraint (5d) ensures that the sampling interval is greater than the transmission time, thereby ensuring that each state data packet can be transmitted in time after it is generated.

[0073] Constraint (5e) indicates that a channel is sampled at least once within the coherence time.

[0074] Under the above constraints, finding the sampling and power allocation solution for the P0 problem can achieve the minimum statistical AoI under a given peak age violation probability.

[0075] Since the statistical AoI of A specified in equation (4) decreases with the increase of sampling rate λ(γ,ρ), the feasible solution with a larger sampling rate is closer to the optimal solution under the condition that the constraints of equations (5b) to (5e) are satisfied. In order to obtain a larger sampling rate, the corresponding transmit power in equation (5c) should be smaller. To this end, the optimal solution should make the equal sign "=" in equation (5b) hold, and then equation (5b) can be simplified to

[0076]

[0077] in is equal to Dlog 2 / τB. Then, substituting equation (6) into equation (5c), the average transmit power constraint can be rewritten as follows:

[0078]

[0079] in Combining constraints (5b) and (5c) converts P0 to P1 equivalently as follows:

[0080]

[0081] τλ(γ,ρ)≤1, (8c)

[0082] Tλ(γ,ρ)≥1 (8d)

[0083] Let f(θ,λ(γ,ρ)) represent the objective function of P1, which consists of two parts and can be expressed as:

[0084]

[0085] Considering that λ(γ,ρ) and θ are highly coupled in the function f(θ,λ(γ,ρ)), and the derivatives of this function with respect to them are complex, it is very challenging to jointly optimize the sampling rate and the age of information AoI index. To this end, a two-step approach is proposed to solve problem P1. In the first step, the AoI index is considered as a constant and the optimal sampling scheme is sought. In the second step, based on the optimal sampling scheme obtained in the first step, the optimal AoI index is searched.

[0086] Based on this idea, the sub-problem of the first step can be expressed as problem P2:

[0087]

[0088] τλ(γ,ρ)≤1, (10c)

[0089] Tλ(γ,ρ)≥1 (10d)

[0090] In problem P2, the objective function is the first part of f(θ,λ(γ,ρ)) Because θ is considered a constant, it is omitted Operation. P2 is a standard convex-concave fractional programming problem, where the objective function follows a convex-concave form and the constraint is convex. Through Dinkelbach transformation, P2 is transformed into P3 as follows:

[0091]

[0092] τλ(γ,ρ)≤1, (11c)

[0093] Tλ(γ,ρ)≥1 (11d)

[0094] Among them, β is a newly introduced auxiliary variable. This variable is iteratively updated through formula (12).

[0095]

[0096] Here, i represents the i-th iteration, and i = 1, 2, 3, .... The initial value of the auxiliary variable β is set to e by selecting λ(γ,ρ)[0] = 1 / T. θT . By iteratively updating β and solving P3 until its value converges, the optimal solution of P3 is also the optimal solution of P2.

[0097] P3 is a convex problem and is solved using the Lagrange multiplier method. The Lagrangian function of P3 is constructed as follows:

[0098]

[0099] Among them, η,η τ ,η Tare the Lagrange multipliers associated with constraints (11b), (11c) and (11d) respectively. Taking the first-order derivative about λ(γ,ρ), we get

[0100]

[0101] The Karush-Kuhn-Tucker (KKT) conditions for P3 are as follows:

[0102]

[0103] By solving the above equation, the optimal solution of P3 can be obtained as follows:

[0104]

[0105] in, and are two thresholds of channel power gain, which are equal to η / (1-βe θT (1-θT)) and η / (1-βe θτ (1-θτ)), is the Lambert W function, and η is given by Sure.

[0106] The second step is to find the optimal AoI index under a given peak age violation probability. Figure 2 The f(θ,λ(γ,ρ)) in equation (9) and the two parts that make up the function are plotted. and It can be seen that as θ increases, Increasing, and Decreasing, together determine the trend that f(θ,λ(γ,ρ)) first decreases and then increases with θ. The binary search method can be used to find the optimal AoI index. Assume that in the binary search, the interval of parameter θ is [θ left ,θ right ], in (θ left +θ right ) / 2, and if the first derivative of the function f(θ,λ(γ,ρ)) is less than zero, then θ left Update to (θ left +θ right ) / 2, otherwise θ right Update to (θ left +θ right ) / 2. According to the optimal AoI index derived above, the optimal sampling scheme can be obtained by substituting it into formula (16). Since the binary search method is used to search for the optimal AoI index and the closed-form solution of the sampling rate has been derived, the corresponding computational complexity is relatively low.

[0107] The effectiveness of the proposed algorithm is verified by numerical simulation. The simulation parameters are set as follows: the average transmission power P is 0.1W, the bandwidth B is 1MHz, the state packet size D is 100bits, the channel power gain γ follows the Rayleigh distribution, and the average channel power gain is 1, the transmission time τ of a status packet is 1ms, and the channel coherence time T is 0.1s.

[0108] Figure 3 The probability distribution of peak age in the average peak information age oriented (Avg-PAoI-O) sampling scheme, the maximum peak information age oriented (Max-PAoI-O) sampling scheme, and the sampling schemes under different risk sensitivity requirements proposed in this paper are shown. The Avg-PAoI-O sampling scheme and the Max-PAoI-O sampling scheme represent the schemes derived with the average peak information age and the maximum peak information age as the targets, respectively. As can be seen from the figure, when the Avg-PAoI-O sampling scheme is used, there is an excessively large peak age because the average peak information age is not sensitive to risk. When the Max-PAoI-O sampling scheme is used, the peak age is stable at about 0.02 seconds. In the sampling scheme proposed in this paper, when ρ=0.7 is set, the peak age has a probability of 0.7 distributed around 0.002 seconds and a probability of 0.3 dispersed between 0.02 seconds and 0.05 seconds. At the same time, the maximum peak age is not very large. When ρ=0.5 is set, the probability distribution of the peak age is further concentrated.

[0109] Figure 4 The performance of the sampling scheme, Avg-PAoI-O sampling scheme, and Max-PAoI-O sampling scheme proposed in this embodiment are shown. It can be seen that as the probability of violation increases, the statistical information age of the Avg-PAoI-O sampling scheme gradually decreases. In contrast, no matter how the probability of violation changes, the statistical information age of the Max-PAoI-O sampling scheme remains unchanged. The reason for this phenomenon is that the sampling rate in the Max-PAoI-O sampling scheme is a constant. The scheme proposed in this embodiment can always achieve the minimum statistical information age, which remains unchanged at the beginning and then decreases as the probability of violation increases.

[0110] In summary, the present invention introduces the statistical information age, denotes the statistical AoI minimization problem of key state updates in wireless fading channels as P0, and finds the sampling and power allocation solutions of the P0 problem, so that the minimum statistical AoI can be achieved under a given peak age violation probability. Therefore, the present invention can always achieve the minimum statistical information age, which remains unchanged at the beginning and then decreases with the increase of the violation probability, which can better meet the needs of risk-sensitive state updates.

[0111] It should be emphasized that the above are only preferred embodiments of the present invention and do not limit the present invention in any form. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. An adaptive sampling method for risk-sensitive status update services, characterized in that: The method comprises the following steps: Step 1: Introduce the concept of statistical information age, which is a tight upper bound of the average peak age of the tail under a given violation probability; the statistical information age is defined as Δ(ρ), expressed as: In formula (5), A represents the peak information age, θ represents the age information index, and M A (θ) represents the moment generating function MGF of the peak age, which is e θA The mathematical expectation of ; 1 / λ(γ,ρ) represents the sampling interval, γ represents the channel power gain; Step 2: Minimize the statistical AoI of the key state update in the wireless fading channel, denoted as P0: Among them, in the constraint condition formula (5b), the noise power is assumed to be 1, B represents the bandwidth, P(γ,ρ) represents the transmission power that varies with γ and ρ, and D represents the number of bits of a state data packet; in the constraint condition formula (5c), Indicates the average transmission power of the source; Step 3: Find the sampling and power allocation solution for the P0 problem to achieve the minimum statistical AoI under a given peak age violation probability.

2. The adaptive sampling method for risk-sensitive status update services according to claim 1, characterized in that: In step 3, P0 is converted to P1 equivalently: The objective function of P1 consists of two parts, expressed as:

3. The adaptive sampling method for risk-sensitive status update services according to claim 2, characterized in that: In step 3, a two-step method is used to solve problem P1; in the first step, the AoI index is regarded as a constant and an optimal sampling scheme is found; in the second step, based on the optimal sampling scheme obtained in the first step, an optimal AoI index is searched.

4. The adaptive sampling method for risk-sensitive status update services according to claim 3, characterized in that: In step 3, the sub-problem of the first step is expressed as problem P2: In problem P2, the objective function is the first part of f(θ,λ(γ,ρ)) P2 is a standard convex-concave fractional programming problem, where the objective function follows a convex-concave form and the constraints are convex.

5. The adaptive sampling method for risk-sensitive status update services according to claim 4, characterized in that: In step 3, P2 is transformed into P3 by Dinkelbach transformation: In formula (11a), β represents a newly introduced auxiliary variable; the auxiliary variable is expressed by formula (12) Perform iterative updates: In formula (12), i represents the i-th iteration, and i = 1, 2, 3, etc. The initial value of the auxiliary variable β is set to e by selecting λ(γ, ρ)[0] = 1 / T. θT , by iteratively updating β and solving P3 until its value converges, at which point the optimal solution of P3 is also the optimal solution of P2.

6. The adaptive sampling method for risk-sensitive status update services according to claim 5, characterized in that: In step 3, the optimal solution of P3 is: in, and The two thresholds representing the channel power gain are equal to η / (1-βe θT (1-θT)) and η / (1-βe θτ (1-θτ)), is the Lambert W function, and η is given by Sure.

7. The adaptive sampling method for risk-sensitive status update services according to claim 3, characterized in that: In step 3, the second step is specifically: find the optimal AoI index under a given peak age violation probability, and use a binary search method to find the optimal AoI index; assuming that in the binary search, the interval of the parameter θ is [θ left ,θ right ], in (θ left +θ right ) / 2, and if the first derivative of the function f(θ,λ(γ,ρ)) is less than zero, then θ left Update to (θ left +θ right ) / 2, otherwise θ right Updated to (θ left +θ right ) / 2; According to the optimal AoI index derived above, substituting it into formula (16) can obtain the optimal sampling scheme.

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