WO2025102480A1 - Age-of-sensing analysis and optimization method for wireless power supply sensor network - Google Patents

Abstract

Disclosed in the present invention are an age-of-sensing analysis and optimization method for a wireless power supply sensor network. The method comprises the following steps: S1, determining a network model; S2, determining a MAC layer model; S3, determining a channel model; S4, on the basis of a multi-segment formula, fitting a nonlinear energy-receiving model, and calculating the decoding success probability of a single sensor; S5, calculating the possibility of information being successfully received in a fusion center under a sensing information requirement threshold; S6, using a hypothesis testing theory to model a fusion-sensing reliability model, so as to obtain the probability of credible fusion; S7, by means of a joint sensing-transmission success possibility, acquiring a closed-form expression of age of sensing, and formulating an information timeliness optimization problem; and S8, respectively optimizing a sensor power supply duration, a fusion information demand threshold, and sensor deployment, so as to give a minimum age of sensing. By means of the present invention, age of sensing is optimized on the basis of the analysis thereof, thereby improving the timeliness of sensing information.

Description

Perception age analysis and optimization method for wireless powered sensor networks Technical Field

The present invention belongs to the technical field of wireless power transmission and information age, and specifically relates to a perception age analysis and optimization method for a wireless power supply sensor network.

Background Art

As one of the most critical technologies for the future, the Internet of Everything (IoE) supports groundbreaking applications such as agriculture, industry, transportation, and home, where thousands of low-power sensing micro devices are deployed on a large scale to support its wide range of functions. These sensing devices usually generate sensing information by monitoring some physical processes or by sensing the surrounding environment in order to return feedback to the access point (AP) for intelligent management of the network. Since a single sensor can only collect part of the required information, multiple sensors are deployed in a single network to expand the sensing coverage. The sensing information from different sensors is delivered to the fusion center (FC) for arbitration, and then the concept of fusion sensing in wireless sensor networks is generated. For example, temperature and humidity sensors sense and perform wireless sensing information transmission (WSIT) to FC.

In addition, real-time perception information is needed to reflect the true state of dynamic objects or environments. Since outdated perception information is meaningless or even misleading, the age of information (AoI) is proposed to measure the freshness of uploaded information, which is defined as the time between the current moment and the moment when the newly uploaded information is generated. However, traditional AoI only focuses on a single information stream, which makes it unable to effectively measure the freshness of fused information in wireless sensor networks with multiple sensors. Therefore, it is urgent to propose a metric for this purpose.

In addition, due to the existence of a large number of devices, the lack of energy in the Internet of Things has become a recognized problem. Once the sensor fails, it will significantly reduce the timeliness of the network and even cause the network to paralyze. Therefore, long-distance wireless power supply has attracted the attention of industry and academia.

Summary of the invention

The purpose of the present invention is to overcome the shortcomings of the prior art and provide a method for analyzing and optimizing the perception age of wireless power supply sensor networks, which uses classical hypothesis testing theory to model the reliability of fused information and construct a closed-form expression of the perception age; optimizes the three parts of sensor power supply duration, fused information demand threshold and sensor deployment, and optimizes them based on the analysis of the perception age, thereby improving the timeliness of the perception information.

The object of the present invention is achieved through the following technical solution: a perception age analysis and optimization method for a wireless power supply sensor network, comprising the following steps:

S1. Determine the network model: The network includes a fusion center, multiple sensors and a monitoring target. The fusion center transmits a dedicated RF energy signal to charge the sensor. It is also responsible for receiving the information transmitted uplink by the sensor and fusing the received uplink information to determine whether the fused information is reliable. Each sensor is equipped with two antennas: one receiving antenna and one A rectenna dedicated to energy and an information transmission antenna for transmitting perceived wireless information. The sensor harvests the dedicated RF energy signal sent downlink from the fusion center through the rectenna; the sensor communicates with the fusion center through the information transmission antenna;

S2. Determine the MAC layer model: A complete frame structure includes the following four stages:

S21, energy transfer phase: All sensors will harvest energy in this phase. The duration of this phase is recorded as T _wpt , which includes K time slots.

S22, perception phase: All sensors perceive the target and collect perception information in this phase. This phase lasts for a very short time, so the analysis of its duration is ignored;

S23, wireless sensing information transfer phase: in this phase, the sensors will upload sensing information in sequence. The duration of this phase is recorded as T _wsit , which includes M time slots.

S24, information fusion stage: the fusion center integrates all successfully received information and makes decisions;

S3. Determine the channel model: The wireless channel between the fusion center and the sensor undergoes uncorrelated block Rayleigh fading; assume that the wireless channel remains flat within a single transmission frame and varies in different frames; the normalized multipath fading coefficient of the downlink channel from the fusion center to the mth sensor S _m is denoted by h _wpt,m , and the normalized multipath fading coefficient of the uplink channel from the mth sensor to the fusion center is denoted by h _wsit,m , where |h _wpt,m | ² and |h _wsit,m | ² both obey an exponential distribution with parameter λ. The path loss coefficients for downlink and uplink are denoted by Ω _wpt,m and Ω _wsit,m , respectively;

S4, fitting a nonlinear energy receiving model according to a multi-segment formula to calculate the decoding success probability of a single sensor;

S5. Calculate the probability of successful information reception in the fusion center under the threshold of perception information requirement: Assume that the threshold of fusion information requirement is M _th , and the probability of successful information reception is expressed as π _m is the probability that the fusion center successfully decodes the signal;

S6. By using hypothesis testing theory to model the fusion perception reliability model, the probability of fusion credibility Pr _IF is obtained;

S7. By combining the perception-transmission success probability, a closed-form expression of the perceived age is obtained, and an information timeliness optimization problem is established; the quantitative perceived age is defined as the difference between the current moment and the moment when the latest reliable fusion information is generated; the formula for the perceived age is:

Where T ₀ represents the time slot length, Pr _SC is the joint sensing-transmission success probability, Pr _SC = Pr _WSIT Pr _IF ;

The information timeliness optimization problem is modeled as

Step S8: Optimize the sensor power supply duration, fusion information demand threshold and sensor deployment respectively to give the minimum sensor The algorithm solves the three variables iteratively: for variables M and K, the integer optimization method based on Fibonacci idea is used to obtain the optimal solution; for the distance d _t between the sensor and the fusion center, a one-dimensional search algorithm is used to solve it; finally, the current variable is optimized while the other two variables are fixed each time, and the final optimal solution and perceived age are obtained by iterating repeatedly until convergence.

The specific method of step S4 is: model the downlink signal power received by the mth sensor S _m as Among them, P _FC is the downlink signal power sent by the fusion center; the energy receiving curve of each sensor is a nonlinear saturation curve. The piecewise linear function is used to fit this nonlinear saturation curve, and the power harvested by the sensor S _m is expressed as:

Where i = 1, 2, ..., I, I is the number of matching segments in the growth interval of the energy harvesting curve; P ₁ = P _th , P _I+1 = P _st ; P _th represents the minimum signal power at which the energy harvesting circuit can be activated, P _st represents the signal power when the energy harvesting circuit reaches saturation, and P _sat is the output power when the energy harvesting circuit is saturated; η _i and μ _i are the slope and intercept of the fitting curve;

The signal-to-noise ratio of the signal uploaded by sensor S _m is Where P _wsit,m is the transmit power of sensor S _m , is the Gaussian white noise variance;

Assuming that S _m clears the energy storage each time it uploads information, P _wsit,m ＝KP _dc,m ; when the signal-to-noise ratio is greater than the predetermined threshold γ _th , the uplink signal is considered to be decoded successfully. Therefore, the probability of successful decoding is expressed as Pr{γ _wsit,m ≥γ _th }, which is calculated as:

λ is the parameter of the exponential distribution to which |h _wpt,m | ² and |h _wsit,m | ² obey.

The specific method of step S6 is: using Neyman-Pearson in hypothesis testing theory to model the reliability of fusion information; specifically, assuming that the fusion perception information z obeys two Gaussian distributions with different parameters under the unreliable hypothesis H ₀ and the reliable hypothesis H ₁ , respectively, and their means and variances are u _{0 and} u 1 respectively. and u ₁ , Divide z into two non-intersecting regions D ₀ and D ₁ in its domain. When z is in region D ₀ , i.e. z∈D ₀ , the fusion center makes a decision The fusion information z is Untrustworthy; when z is in region D ₁ , i.e. z∈D ₁ , the fusion center makes a decision It means that the fusion information z is credible; therefore, the probability of fusion credibility is expressed as:

Pr(H ₀ ) and Pr(H ₁ ) represent the probability of the occurrence of hypothesis H ₀ and H ₁ respectively. Indicates making a decision under the assumption H ₀ The probability of Indicates making a decision under the assumption H ₁ The probability of, Pr _f and Pr _d are the abbreviations of two conditional probabilities; Pr(H ₁ )＝exp(-κd _s ), Pr(H ₀ )＝1-exp(-κd _s ), κ represents the sensor perception distortion coefficient;

Finally, the Neyman-Pearson criterion is used to maximize Pr _d under the condition that Pr _f is equal to the acceptable threshold Pr'_f; the following formula is obtained Where v represents a threshold mapping about Pr'_f; when The relationship between the two is as follows:

in,

Q(·) represents the Q function; the formula is monotonic, so v is obtained by bisection; finally, we get Pr _d is obtained under the condition of Pr _f =Pr' _f , so we finally get Pr _IF =Pr' _f Pr(H ₀ )+Pr _d Pr(H ₁ ).

The beneficial effects of the present invention are as follows: the present invention uses the classical hypothesis testing theory to model the reliability of fusion information and construct a closed-form expression of perception age; optimizes the three parts of sensor power supply duration, fusion information demand threshold and sensor deployment, and optimizes them based on the analysis of perception age, thereby improving the timeliness of perception information.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a method for analyzing and optimizing the perceived age of a wireless power supply sensor network according to the present invention;

FIG2 is a schematic diagram of a network model of the present invention;

FIG. 3 shows the perceived age trend of the present invention.

DETAILED DESCRIPTION

In order to overcome the shortcomings of the information age measurement for a single data stream, a perceptual age is proposed for multi-data stream information fusion networks, which is defined as the difference between the generation time of fresh reliable fusion information and the current moment. The fusion center, multiple sensor nodes and a monitoring target are combined, and the reliability of fusion information is modeled using the classic hypothesis testing theory to quantify the perception age of the network, construct a closed-form expression and analyze it. The sensor power supply time, fusion information demand threshold and sensor deployment are further optimized to greatly improve the freshness of network information. The technical solution of the present invention is further explained in conjunction with the accompanying drawings.

As shown in FIG1 , a method for analyzing and optimizing the perceived age of a wireless power supply sensor network according to the present invention comprises the following steps:

S1. Determine the network model: The network includes a fusion center (FC), multiple sensors Sensor1~SensorM and a monitoring target, as shown in Figure 2; the fusion center transmits RF energy signals downlink to charge the sensors, and is also responsible for receiving the information transmitted uplink by the sensors and fusing the received uplink information to determine whether the fused information is reliable; each sensor is equipped with two antennas: a rectifying antenna dedicated to receiving energy and an information transmission antenna for transmitting perceived wireless information. The sensor harvests the dedicated RF energy signal sent downlink from the fusion center through the rectifying antenna, stores and consumes the dedicated RF energy signal to charge the sensor, which is the RF Chain-Energy Harvester branch in Figure 2; the sensor communicates with the fusion center through the information transmission antenna to exchange information, which is the RF Chain-Info.Encoder branch in the figure. After completing charging, it immediately senses the monitoring target and sends the sensed signal to the fusion center through the information transmission antenna.

S2. Determine the MAC layer model: Considering the time division multiple access method to allow sensors to access the network one by one, the network completes four operation stages in a single transmission frame. As shown in Figure 2, a complete frame (A Single Transmission Frame) structure includes the following four stages:

S21, Energy Transfer Phase (WPT): All sensors will harvest energy in this phase. The duration of this phase is recorded as T _wpt , which includes K time slots.

S22, perception phase: All sensors perceive the target and collect perception information in this phase. This phase lasts for a very short time, so the analysis of its duration is ignored;

S23, Wireless Sensing Information Transfer Phase (WSIT): In this phase, the sensors will upload sensing information in sequence. The duration of this phase is recorded as T _wsit , which includes M time slots.

S24, information fusion stage: the fusion center integrates the information just successfully received and makes a decision;

S3. Determine the channel model: The wireless channel between the fusion center and the sensor undergoes uncorrelated block Rayleigh fading; assume that the wireless channel remains flat within a single transmission frame and varies in different frames; the normalized multipath fading coefficient of the downlink channel from the fusion center to the mth sensor S _m is denoted by h _wpt,m , and the normalized multipath fading coefficient of the uplink channel from the mth sensor to the fusion center is denoted by h _wsit,m , where |h _wpt,m | ² and |h _wsit,m | ² both obey an exponential distribution with parameter λ. The path loss coefficients for downlink and uplink are denoted by Ω _wpt,m and Ω _wsit,m , respectively; since the distance between the transmitting and receiving antennas of the sensors is close, When d _t,m ≥ d ₀ , the path loss coefficient is modeled as Ω _wpt,m ＝Ω _wsit,m ＝Ω ₀ (d _t,m /d ₀ ) ^α ; when d _t,m ＜d ₀ , the path loss coefficient is modeled as Ω _wpt,m ＝Ω _wsit,m ＝Ω ₀ . Where d _t,m represents the distance between the sensor m and FC, and Ω ₀ represents the path loss at the reference distance d _0. Since d ₀ is very small in actual situations, and the path loss of the sensor at any position within the distance FC d ₀ is the same, in the research process, only the case of d _t,m ≥ d ₀ is usually considered, so as to study the impact of the distance between the sensor and FC on the system performance. In addition, for the convenience of modeling, we consider the case where the distance between sensors is relatively close, so the distance between all sensors and FC can be approximately expressed as d _t , and the distance from the sensor to the monitoring target is expressed as d _s .

S4. Fitting a nonlinear energy receiving model according to a multi-segment linear formula to calculate the decoding success probability of a single sensor; the specific method is as follows:

The downlink signal power received by the mth sensor S _m is modeled as Where P _FC is the downlink signal power sent by the fusion center. The energy receiving curve of each sensor is a nonlinear saturation curve. It is very difficult to analyze the network performance based on the curve theory. Therefore, the present invention uses a piecewise linear function to fit this nonlinear saturation curve, and the power harvested by the sensor S _m is expressed as:

Where i = 1, 2, ..., I, I is the number of matching segments in the growth interval of the energy harvesting curve; P ₁ = P _th , P _I+1 = P _st ; the parameter size in the formula should be determined by the actual energy harvester circuit. Specifically, we use the above multi-segment linear formula to fit the input-output test curve of the actual energy harvesting circuit, where the input is the received downlink RF energy signal power, and the output is the power harvested by the circuit. Considering that all sensors use the same energy harvesting circuit, represents the output power of the circuit when the received signal power is P _wpt . Based on this, we use P _th to represent the minimum signal power that can activate the energy receiving circuit, P _st to represent the signal power when the energy receiving circuit reaches saturation, and P _sat to represent the output power when the energy receiving circuit is saturated. In addition, in order to determine the slope η _i and the intercept μ _i , the following operations are performed: the growth interval of the test curve of the circuit is evenly divided into I segments, and the received signal power range in the i-th segment is [P _i ,P _i+1 ), so there is Because we consider replacing the original circuit curve in each section with a straight line, therefore,

The signal-to-noise ratio of the signal uploaded by sensor S _m is Where P _wsit,m is the transmit power of sensor S _m , is the Gaussian white noise variance;

Assuming that S _m clears the energy storage each time it uploads information, P _wsit,m ＝KP _dc,m ; when the signal-to-noise ratio is greater than the predetermined threshold γ _th , it is considered that the uplink signal (WSIT signal) is decoded successfully. Therefore, the probability of successful decoding can be expressed as Pr{γ _wsit,m ≥γ _th }. The probability of the fusion center successfully decoding the signal is calculated as:

λ is the parameter of the exponential distribution to which |h _wpt,m | ² and |h _wsit,m | ² obey. Denoted by f _m,i (x), since this integral is not elementary, it is approximated by the Gaussian method Approximately; x _max and x _min represent the upper and lower limits of the integral of π _m , respectively, and n', ω _j , and y _j are obtained from the data supporting the Gaussian approximation method. The Gaussian approximation rule provides a table of ω _j and y _j values corresponding to different n', and the corresponding values can be directly selected.

S5. Calculate the probability of successful information reception in the fusion center under the threshold of perception information requirement: First, calculate the probability of successful transmission of fusion information. Let the threshold of fusion information requirement be M _th . When we regard the information uploaded by a single sensor as a single amount of information, this threshold can be regarded as the number of sensors that successfully upload information required by the fusion center to perform fusion operations. Therefore, when the distance between sensors is negligible, the probability of successful reception of fusion information is expressed as π _m is the probability that the fusion center successfully decodes the signal.

S6. By using hypothesis testing theory to model the reliability model of fusion perception, the probability of fusion credibility Pr _IF is obtained. The specific method is: using Neyman-Pearson in hypothesis testing theory to model the reliability of fusion information; specifically, assuming that the fusion perception information z obeys two Gaussian distributions with different parameters under two different assumptions (unreliable assumption H ₀ and reliable assumption H ₁ ), and their means and variances are u ₀ , and u ₁ , Divide z into two non-intersecting regions D ₀ and D ₁ in its domain. When z is in region D ₀ , i.e. z∈D ₀ , FC makes a decision It means that the fusion information z is unreliable; accordingly, when z is in region D ₁ , that is, z∈D ₁ , the decision is made Indicates that the fused information z is credible; Therefore, the probability that the fusion is credible is expressed as:

Pr(H ₀ ) and Pr(H ₁ ) represent the probability of the occurrence of hypothesis H ₀ and H ₁ respectively. Indicates making a decision under the assumption H ₀ The probability of Indicates making a decision under the assumption H ₁ The probability of, Pr _f and Pr _d are the abbreviations of two conditional probabilities; Pr(H ₁ )＝exp(-κd _s ), Pr(H ₀ )＝1-exp(-κd _s ), κ represents the sensor perception distortion coefficient;

Finally, the Neyman-Pearson criterion is used to maximize Pr _d under the condition that Pr _f is equal to the acceptable threshold Pr'_f; the following formula is obtained Where v represents a threshold mapping about Pr'_f; when The relationship between the two is as follows:

in, Q(·) represents the Q function; the formula is monotonic, so v is obtained by bisection; finally, we get Note that Pr _d is obtained under the condition that Pr _f =Pr' _f , so we finally get Pr _IF =Pr' _f Pr(H ₀ )+Pr _d Pr(H ₁ ).

S7. Through the joint perception-transmission success probability, the closed-form expression of the perception age is obtained, and the information timeliness optimization problem is established; the quantitative perception age is defined as the difference between the current moment and the generation moment of the latest reliable fusion information; Figure 3 describes the schematic diagram of the perception age trend under this definition. _ti represents the moment when the sensor generates perception information i, and _t'i represents the moment when the fusion center decides that it is reliable information. In addition, _Xi represents the time between two consecutive reliable fusion information, and _Yi is the number of frames experienced in this short time. By calculating the perception age area corresponding to the _Xi period, the formula for perception age is obtained:

Where T ₀ represents the time slot length, Pr _SC is the joint sensing-transmission success probability, Pr _SC = Pr _WSIT Pr _IF ;

The information timeliness optimization problem is modeled as

Step S8: Optimize the sensor power supply duration, fusion information demand threshold and sensor deployment respectively to give the minimum sensor Know the age; use iterative method to solve the three variables: for the M and K variables, use the integer optimization method based on the Fibonacci idea to obtain the optimal solution; the specific algorithm is implemented as follows:

Input: M, K, d _t , P _FC , etc.

Create: a Fibonacci sequence F = [1, 1, 2, 3, 5, ...] containing N elements; let δ ₁ and δ ₂ represent the search values of the variables to be optimized;

Initialization parameters: the identifier of the number of elements in the search interval n←N, where n is a mapping of the number of elements remaining in the search interval, used to identify how many elements are left; the lower limit of the search interval δ _min ← ₁ , the upper limit of the search interval δ _max ←F(n)+δ _min , the variable search value δ ₁ ←F(n-2)+δ min, δ ₂ ←F(n-1)+δ _min , where F(n) represents the nth element in the Fibonacci sequence; the perceived age formula in step S7 is used to obtain and

(1) If Update n←n-1, δ _max ←δ ₂ , δ ₂ ←δ ₁ , δ ₁ ←F(n-2)+δ _min , and obtain the corresponding and

If δ ₁ = δ ₂ : end the loop;

(2) If Update n←n-1,δ _min ←δ ₁ ,δ ₁ ←δ ₂ ,δ ₂ ←F(n-1)+δ _min , and obtain the corresponding and

If δ ₁ = δ ₂ : end the loop;

(3) If Update n←n-3, δ _min ←δ ₁ , δ _max ←δ ₂ ;

If |δ ₁ -δ ₂ |＞1: Update δ ₁ ←F(n-2)+δ _min , δ ₂ ←F(n-1)+δ _min , and obtain the corresponding and Otherwise: end the loop;

Repeat the cycle;

Get δ'←[δ _min ,δ ₁ ,δ ₂ ,δ _max ] and in Representation vector The jth element in ;

Output: K ^* or in is the j*th element in the vector δ'.

For the distance d _t between the sensor and the fusion center, a one-dimensional search algorithm is used to solve it; finally, the current variable is optimized while the other two variables are fixed each time, and the final optimization solution and perceived age are obtained by iterating repeatedly until convergence.

Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the present invention. In principle, it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. A person skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical enlightenment disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims (3)

The method for analyzing and optimizing the perceived age of a wireless powered sensor network comprises the following steps: S1. Determine the network model: The network includes a fusion center, multiple sensors and a monitoring target. The fusion center transmits a dedicated RF energy signal downlink to charge the sensor. It is also responsible for receiving the information transmitted uplink by the sensor and fusing the received uplink information to determine whether the fused information is reliable. Each sensor is equipped with two antennas: a rectifying antenna dedicated to receiving energy and an information transmission antenna for transmitting the perceived wireless information. The sensor harvests the dedicated RF energy signal sent downlink from the fusion center through the rectifying antenna. The sensor communicates with the fusion center through the information transmission antenna. S2. Determine the MAC layer model: A complete frame structure includes the following four stages: S21, energy transfer phase: All sensors will harvest energy in this phase. The duration of this phase is recorded as T _wpt , which includes K time slots; S22, perception phase: All sensors perceive the target and collect perception information in this phase. This phase lasts for a very short time, so the analysis of its duration is ignored; S23, wireless sensing information transfer phase: in this phase, the sensors will upload sensing information in sequence. The duration of this phase is recorded as T _wsit , which includes M time slots. S24, information fusion stage: the fusion center integrates all successfully received information and makes decisions; S3. Determine the channel model: The wireless channel between the fusion center and the sensor undergoes uncorrelated block Rayleigh fading; assume that the wireless channel remains flat within a single transmission frame and varies in different frames; the normalized multipath fading coefficient of the downlink channel from the fusion center to the mth sensor S _m is denoted by h _wpt,m , and the normalized multipath fading coefficient of the uplink channel from the mth sensor to the fusion center is denoted by h _wsit,m , where |h _wpt,m | ² and |h _wsit,m | ² both obey an exponential distribution with parameter λ. The path loss coefficients for downlink and uplink are denoted by Ω _wpt,m and Ω _wsit,m , respectively; S4, fitting a nonlinear energy receiving model according to a multi-segment formula to calculate the decoding success probability of a single sensor; S5. Calculate the probability of successful information reception in the fusion center under the threshold of perception information requirement: Assume that the threshold of fusion information requirement is M _th , and the probability of successful information reception is expressed as π _m is the probability that the fusion center successfully decodes the signal; S6. By using hypothesis testing theory to model the fusion perception reliability model, the probability of fusion credibility Pr _IF is obtained; S7. By combining the perception-transmission success probability, a closed-form expression of the perceived age is obtained, and an information timeliness optimization problem is established; the quantitative perceived age is defined as the difference between the current moment and the moment when the latest reliable fusion information is generated; the formula for the perceived age is:
Where T ₀ represents the time slot length, Pr _SC is the joint sensing-transmission success probability, Pr _SC = Pr _WSIT Pr _IF ; The information timeliness optimization problem is modeled as Step S8, respectively optimize the sensor power supply duration, the fusion information demand threshold and the sensor deployment to give the minimum perception age; solve the three variables in an iterative manner: for the M and K variables, use the integer optimization method based on the Fibonacci idea to obtain the optimization solution; for the distance d _t between the sensor and the fusion center, use a one-dimensional search algorithm to solve; finally, optimize the current variable while fixing the other two variables each time, and iterate until convergence to obtain the final optimization solution and perception age. The method for perceptual age analysis and optimization for wireless power supply sensor networks according to claim 1 is characterized in that the specific method of step S4 is: the downlink signal power received by the mth sensor S _m is modeled as Among them, P _FC is the downlink signal power sent by the fusion center; the energy receiving curve of each sensor is a nonlinear saturation curve. The piecewise linear function is used to fit this nonlinear saturation curve, and the power harvested by the sensor S _m is expressed as:
Where i = 1, 2, ..., I, I is the number of matching segments in the growth interval of the energy harvesting curve; P ₁ = P _th , P _I+1 = P _st ; P _th represents the minimum signal power at which the energy harvesting circuit can be activated, P _st represents the signal power when the energy harvesting circuit reaches saturation, and P _sat is the output power when the energy harvesting circuit is saturated; η _i and μ _i are the slope and intercept of the fitting curve; The signal-to-noise ratio of the signal uploaded by sensor S _m is Where P _wsit,m is the transmit power of sensor S _m , is the Gaussian white noise variance; Assuming that S _m clears the energy storage each time it uploads information, P _wsit,m ＝KP _dc,m ; when the signal-to-noise ratio is greater than the predetermined threshold γ _th , the uplink signal is considered to be decoded successfully. Therefore, the probability of successful decoding is expressed as Pr{γ _wsit,m ≥γ _th }, which is calculated as:
λ is the parameter of the exponential distribution to which |h _wpt,m | ² and |h _wsit,m | ² obey. The perception age analysis and optimization method for wireless power supply sensor networks according to claim 1 is characterized in that the specific method of step S6 is: using Neyman-Pearson in hypothesis testing theory to model the reliability of fusion information; specifically, assuming that the fusion perception information z obeys two Gaussian distributions with different parameters under the unreliable hypothesis H ₀ and the reliable hypothesis H ₁ , respectively, and their means and variances are u ₀ , and u ₁ , Divide z into two non-intersecting regions D ₀ and D ₁ in its domain. When z is in region D ₀ , i.e. z∈D ₀ , the fusion center makes a decision Indicates that the fused information z is unreliable; when z is in region D ₁ , i.e. z∈D ₁ , the fusion center makes a decision It means that the fusion information z is credible; therefore, the probability of fusion credibility is expressed as:
Pr(H ₀ ) and Pr(H ₁ ) represent the probability of the occurrence of hypothesis H ₀ and H ₁ respectively. Indicates making a decision under the assumption H ₀ The probability of Indicates making a decision under the assumption H ₁ The probability of, Pr _f and Pr _d are the abbreviations of two conditional probabilities; Pr(H ₁ )＝exp(-κd _s ), Pr(H ₀ )＝1-exp(-κd _s ), κ represents the sensor perception distortion coefficient; Finally, the Neyman-Pearson criterion is used to maximize Pr _d under the condition that Pr _f is equal to the acceptable threshold Pr'_f; the following formula is obtained Where v represents a threshold mapping about Pr'_f; when The relationship between the two is as follows:
in, Q(·) represents the Q function; the formula is monotonic, so v is obtained by bisection; finally, we get Pr _d is obtained under the condition of Pr _f =Pr' _f , so we finally get Pr _IF =Pr' _f Pr(H ₀ )+Pr _d Pr(H ₁ ).