CN105356953B - Frequency spectrum detection systematic function parameter preparation method after any moving period is undergone in cognitive radio networks - Google Patents

Abstract

The invention discloses a method for obtaining performance parameters of a frequency spectrum detection system after an arbitrary moving period in a cognitive radio network, and relates to the field of information and communication technologies. The present invention aims to solve the problem that the existing method cannot sense the cooperation of single node and multi-node in the mobile scene in the cognitive radio network. The present invention first obtains the functional relationship between the moving speed and direction of the cognitive user, the distance between the starting point of the cognitive user and the main user in the current period, and the distance between the end point and the main user. Then obtain the PDF of the distance between the main user and the end point of the cognitive user's movement. Then obtain the functional relationship between the signal power of the primary user detected by the mobile user at the mobile end point in the current mobile cycle and the distance between the mobile end point of the cognitive user and the primary user in the current mobile cycle, and obtain the PDF of this power. Finally, the results of detection probability, missed detection probability and false alarm probability in single-node sensing, hard-decision multi-node cooperative sensing and soft-decision cooperative sensing systems in mobile scenarios are obtained.

Description

Performance parameters of spectrum detection system after experiencing any mobile period in cognitive radio network Quantity acquisition method

technical field

The invention relates to the field of information and communication technologies, in particular to a method for obtaining detection performance indicators of a spectrum sensing system in a mobile scene where cognitive users are constantly moving randomly.

Background technique

In recent years, the rapid development of wireless communication technology has led to a sharp increase in the demand for wireless spectrum resources. However, the current fixed spectrum allocation method makes most frequency bands not fully utilized. In order to improve spectrum utilization, researchers proposed cognitive radio (CR) technology. As a key technology to solve the problem of scarcity of wireless spectrum resources, CR has attracted great interest and research enthusiasm from the International Organization for Standardization, national spectrum resource allocation management agencies, academia and industry in recent years. CR is to allow the wireless communication equipment with radio environment awareness function to dynamically access the authorized frequency band of the main user without affecting the authorized frequency band of the main user signal, that is, the frequency band fixedly allocated to the user, and to communicate normally, so as to complete the allocation of spectrum resources. shared. Cognitive radio technology is a complex technology, and its research content includes wireless spectrum sensing, dynamic spectrum sharing and management and many other technologies. Spectrum sensing is one of the core technologies of cognitive radio, a basic function of cognitive systems, and a prerequisite for spectrum management and spectrum sharing.

Spectrum sensing technology has two tasks. First, it needs to detect the spectrum gap when the cognitive user needs to transmit data, and it needs to continuously detect whether the authorized user is present during the data transmission process of the cognitive user. Research on various spectrum sensing algorithms has become a research hotspot in wireless communication technology. Spectrum sensing can be divided into single-user spectrum detection method and multi-user cooperative detection method. The energy detection algorithm is a single-node spectrum detection algorithm. Its principle is simple and easy to implement, and it does not need to know the prior information of the primary user, and does not make any assumptions about the signal. The energy detection method is applicable to any signal, so it has been widely used. In the actual cognitive system, the single-node spectrum sensing algorithm has relatively large limitations, such as hidden terminal problems and shadow effects, which will greatly reduce the detection performance of single-node detection. Therefore, single-node detection is often not feasible in practical systems. In this context, multi-user collaborative detection method has attracted the attention of many researchers.

The vast majority of current research on spectrum sensing in cognitive radios is conducted on the assumption that cognitive users remain stationary, however, the mobility of cognitive users is an inherent property of wireless networks. Existing methods cannot perceive single-node and multi-node cooperation in mobile scenarios in cognitive radio networks.

Contents of the invention

The present invention aims to solve the problem that existing methods cannot perceive single-node and multi-node cooperation in a mobile scene in a cognitive radio network, thereby providing a method for obtaining performance parameters of a spectrum detection system in a cognitive radio network after experiencing any mobile cycle.

A method for obtaining performance parameters of a spectrum detection system after experiencing any mobile period in a cognitive radio network,

The method can be applied to a single-node spectrum detection system;

Assume that in the mobile scenario, cognitive users obey the random walk model, and there is a primary user and a cognitive user in the cognitive network;

Step 1. Use the formula:

y _n =K/(d _n ) ² (2)

Obtain the real-time power y _n of the primary user signal detected by the cognitive user;

Where: K is a constant, and:

K＝G _r P _t G _t (λ _w /4π) ²

In the formula: G _r represents the antenna gain of the cognitive user, P _t represents the transmit signal power of the primary user, G _t is the antenna gain of the authorized user; λ _w is the wavelength of the primary user signal;

Step 2. In each energy detection, the cognitive user collects M points, where M is a positive integer; and in the Gaussian channel, the mean value of the noise is 0, the variance is σ ² , and the preset energy detection threshold is λ;

Then after the nth sensing period, the detection probability of single-node spectrum sensing for:

Probability of missed detection for:

false alarm probability for:

In the formula:

Step 3, according to the formula:

Obtain the distance d _i,n between the cognitive user and the end point of the nth mobile cycle; 1≤i≤N; v _i,n represents the moving speed of the cognitive user in the nth mobile cycle; θ _{i , n} represents the moving direction of the cognitive user in the nth moving cycle; Δt is the time interval between two detections, that is, the duration of each moving cycle;

Step 4, according to the formula:

Obtain the conditional probability density function of the distance d _{i, n} ; v _max represents the maximum moving speed of the cognitive user; v _min represents the minimum moving speed of the cognitive user;

Step 5, deduce according to formula (4):

In the formula:

In the formula: PQ is the moving distance of the cognitive user in the nth mobile period;

Step 6. Use expressions Replacement formula (5) in Then the conditional probability density function of d _i,n is:

Step 7, according to formula (2), obtain the relationship between y _i,n and d _i,n :

y _i,n =K/(d _i,n ) ² (7)

Then, the conditional probability density function of y _i,n is:

In the formula: by putting d _i, n in is replaced by y _i,n ;

Step eight, pass the formula:

Calculate the conditional mathematical expectation of y _i,n ;

Step nine, through the formula:

Probability density function of y _i,n ;

in: is calculated by formula (6), formula (8) and the following formula (11):

The mathematical expectation of y _i,n is:

in, is calculated by formula (6), formula (9) and the following formula (13):

Step 10. The detection probability of single-node spectrum sensing in mobile scenarios for:

Probability of missed detection for:

false alarm probability for:

in: is calculated by (6) and the following formulas (15), (16):

will detect probability Probability of missed detection and false alarm probability As a detection performance parameter of a single-node spectrum sensing system, a method for obtaining the performance parameter of a spectrum detection system after an arbitrary movement period in a cognitive radio network is completed.

This method can be applied to a multi-node hard-decision cooperative spectrum detection system,

Assume that in a mobile scenario, cognitive users obey the random walk model, and there are N mobile cognitive users and a fusion center FC in the cognitive network; N is a positive integer;

Step 1. Use the formula:

y _n =K/(d _n ) ² (2)

Obtain the real-time power y _n of the primary user signal detected by the cognitive user;

Where: K is a constant, and:

K＝G _r P _t G _t (λ _w /4π) ²

In the formula: G _r represents the antenna gain of the cognitive user, P _t represents the transmit signal power of the primary user, G _t is the antenna gain of the authorized user; λ _w is the wavelength of the primary user signal;

Step 2. In each energy detection, each cognitive user collects M points, where M is a positive integer; and in a Gaussian channel, the mean value of the noise is 0, the variance is σ ² , and the preset energy detection threshold is λ;

Then after the nth sensing period, the detection probability of multi-node hard-decision cooperative spectrum sensing for:

Probability of missed detection for:

false alarm probability for:

In the formula:

Step 3, according to the formula:

Obtain the distance d _i,n between any cognitive user SU _i and the end point of the nth mobile cycle; 1≤i≤N; v _i,n means that in the nth mobile cycle, the cognitive user SU _i The moving speed of ; θ _{i, n} represents the moving direction of the cognitive user SU _i in the nth moving cycle; Δt is the time interval between two detections, that is, the duration of each moving cycle;

Step 4, according to the formula:

Obtain the conditional probability density function of distance d _{i, n} ; v _max represents the maximum moving speed of the cognitive user SU _i ; v _min represents the minimum moving speed of the cognitive user SU _i ;

Step 5, deduce according to formula (4):

In the formula:

In the formula: PQ is the moving distance of the cognitive user in the nth mobile cycle;

Step 6. Use expressions Replacement formula (5) in Then the conditional probability density function of d _i,n is:

Step 7, according to formula (2), obtain the relationship between y _i,n and d _i,n :

y _i,n =K/(d _i,n ) ² (7)

Then, the conditional probability density function of y _i,n is:

In the formula: by putting d _i, n in is replaced by y _i,n ;

Step eight, pass the formula:

Calculate the conditional mathematical expectation of y _i,n ;

Step nine, through the formula:

Probability density function of y _i,n ;

in: is calculated by formula (6), formula (8) and the following formula (11):

The mathematical expectation of y _i,n is:

in, is calculated by formula (6), formula (9) and the following formula (13):

Step 10: The detection probability of spectrum sensing in the multi-node hard-decision cooperative spectrum detection system in the mobile scene for:

Probability of missed detection for:

false alarm probability for:

in: is calculated by formula (6), formula (18) and formula (19):

in:

And f(y _1,n ,…,y _N,n| d _i,n-1 ,θ _i,n ) represents the joint conditional probability density function of y _1,n ,y _2,n ,…,y _N,n :

q represents the total number of scenarios in which no less than k users among all N cognitive users believe that the main user signal exists;

will detect probability Probability of missed detection and false alarm probability As a detection performance parameter of a multi-node hard-decision cooperative spectrum detection system, a method for obtaining the performance parameter of the spectrum detection system after an arbitrary movement period in a cognitive radio network is completed.

The method can also be applied to a multi-node soft-decision cooperative spectrum detection system,

Assume that in a mobile scenario, cognitive users obey the random walk model, and there are N mobile cognitive users and a fusion center FC in the cognitive network; N is a positive integer;

Step 1. Use the formula:

y _n =K/(d _n ) ² (2)

Obtain the real-time power y _n of the primary user signal detected by the cognitive user;

Where: K is a constant, and:

K＝G _r P _t G _t (λ _w /4π) ²

In the formula: G _r represents the antenna gain of the cognitive user, P _t represents the transmit signal power of the primary user, G _t is the antenna gain of the authorized user; λ _w is the wavelength of the primary user signal;

Step 2. In each energy detection, each cognitive user collects M points, where M is a positive integer; and in a Gaussian channel, the mean value of the noise is 0, the variance is σ ² , and the preset energy detection threshold is λ;

Then after the nth sensing period, the detection probability of the multi-node soft-decision cooperative spectrum for:

Probability of missed detection for:

false alarm probability for:

In the formula:

Step 3, according to the formula:

Obtain the distance d _i,n between any cognitive user SU _i and the end point of the nth mobile cycle; 1≤i≤N; v _i,n means that in the nth mobile cycle, the cognitive user SU _i The moving speed of ; θ _{i, n} represents the moving direction of the cognitive user SU _i in the nth moving cycle; Δt is the time interval between two detections, that is, the duration of each moving cycle;

Step 4, according to the formula:

Obtain the conditional probability density function of distance d _{i, n} ; v _max represents the maximum moving speed of the cognitive user SU _i ; v _min represents the minimum moving speed of the cognitive user SU _i ;

Step 5, deduce according to formula (4):

In the formula:

In the formula: PQ is the moving distance of the cognitive user in the nth mobile cycle;

Step 6. Use expressions Replacement formula (5) in Then the conditional probability density function of d _i,n is:

Step 7, according to formula (2), obtain the relationship between y _i,n and d _i,n :

y _i,n =K/(d _i,n ) ² (7)

Then, the conditional probability density function of y _i,n is:

In the formula: by putting d _i, n in is replaced by y _i,n ;

Step eight, pass the formula:

Calculate the conditional mathematical expectation of y _i,n ;

Step nine, through the formula:

Probability density function of y _i,n ;

in: is calculated by formula (6), formula (8) and the following formula (11):

The mathematical expectation of y _i,n is:

in, is calculated by formula (6), formula (9) and the following formula (13):

Step 10. The detection probability of spectrum sensing in the multi-node soft-decision cooperative spectrum detection system in the mobile scene for:

Probability of missed detection for:

false alarm probability for:

in: is calculated by formula (6), formula (22) and formula (23):

in:

λ _s represents the preset threshold at the fusion center, w _i,n represents the weighting factor of cognitive user SU _i in the nth perception cycle;

will detect probability Probability of missed detection and false alarm probability As a detection performance parameter of a multi-node soft-decision cooperative spectrum detection system, a method for obtaining the performance parameter of the spectrum detection system after experiencing any mobile cycle in a cognitive radio network is completed.

The invention studies the mobile cognitive user spectrum detection system after any mobile cycle in the cognitive radio network, and provides a calculation method for detection performance indexes (detection probability, missed detection probability, false alarm probability). In the present invention, at first according to the network model of the system and the mobile model of the cognitive user, the functional relationship between the moving speed, the direction of motion, and the distance between the cognitive user and the main user at each moment is obtained; then according to the speed in this mobile cycle, The probability density function of the distance between the direction and the starting point and the primary user is obtained to obtain the probability density function of the distance between the end point and the primary user; then according to the channel model and the detection model, the function between the signal power of the primary user detected by the mobile user in real time and the distance function is obtained relationship and use this relationship and the probability density function of the distance function to calculate the probability density function of this power. Finally, use the probability density function of this power and the knowledge of probability theory and signal detection theory to obtain three indicators describing the detection performance in single-node sensing, hard-decision multi-node cooperative sensing and soft-decision cooperative sensing systems at any time in mobile scenarios. That is, the calculation method of detection probability, missed detection probability and false alarm probability. The simulation results show that the simulated value is consistent with the theoretical value calculated by this calculation method, which shows the correctness of this calculation method.

Description of drawings

FIG. 1 is a schematic diagram of a cognitive network model of a single-node spectrum sensing system;

2 is a schematic diagram of a cognitive network model of a multi-node cooperative spectrum sensing system;

3 is a schematic diagram of a cognitive user mobility model in a single-node spectrum sensing system in a mobile scenario in a cognitive radio network;

4 is a schematic diagram of a cognitive user mobility model in a multi-node cooperative spectrum sensing system in a mobile scenario in a cognitive radio network;

Fig. 5 is after a mobile period, when any mobile cognitive user (the rth) real-time received simulation value of the main user signal power and the theoretical value simulation schematic diagram obtained by utilizing the calculation of the present invention when different moving speed lower limits; Wherein v _max = 60km/h, a = 40km, △t = 1s; where:

Curve 41 is a simulation curve under K=50(w×km ² );

Curve 42 is a theoretical curve under K=50(w×km ² );

Curve 43 is a simulation curve under K=100(w×km ² );

Curve 44 is a theoretical curve under K=100(w×km ² );

Curve 45 is a simulation curve under K=200(w×km ² );

Curve 46 is a theoretical curve under K=200(w×km ² );

Curve 47 is a simulation curve under K=400(w×km ² );

Curve 48 is a theoretical curve under K=400(w×km ² );

Fig. 6 is after two mobile cycles, when any mobile cognitive user (the rth) real-time received simulation value of the main user signal power and the theoretical value simulation schematic diagram obtained by utilizing the calculation of the present invention when different moving speed lower limits; Wherein v _max ＝60km/h, a＝40km, △t＝1s; where:

Curve 51 is a simulation curve under K=50(w×km ² );

Curve 52 is a theoretical curve under K=50(w×km ² );

Curve 53 is a simulation curve under K=100(w×km ² );

Curve 54 is a theoretical curve under K=100(w×km ² );

Curve 55 is a simulation curve under K=200(w×km ² );

Curve 56 is a theoretical curve under K=200(w×km ² );

Curve 57 is a simulation curve under K=400(w×km ² );

Curve 58 is a theoretical curve under K=400(w×km ² );

Fig. 7 is after three mobile periods, when any mobile cognitive user (the rth) real-time received simulation value of the main user signal power and the simulation schematic diagram of the theoretical value calculated by the present invention when different mobile speed lower limits; v _max ＝60km/h, a＝40km, △t＝1s; where:

Curve 61 is a simulation curve under K=50(w×km ² );

Curve 62 is a theoretical curve under K=50(w×km ² );

Curve 63 is a simulation curve under K=100(w×km ² );

Curve 64 is a theoretical curve under K=100(w×km ² );

Curve 65 is a simulation curve under K=200(w×km ² );

Curve 66 is a theoretical curve under K=200(w×km ² );

Curve 67 is a simulation curve under K=400(w×km ² );

Curve 68 is a theoretical curve under K=400(w×km ² );

detailed description

Specific Embodiments 1. A method for obtaining performance parameters of a spectrum detection system after experiencing any movement period in a cognitive radio network is implemented by the following steps:

First of all, it needs to be pointed out that in order to be able to give the expressions corresponding to each step in detail without loss of generality, we take the following specific models as examples, but in fact the method of the present invention is also applicable to other cognitive network models and cognitive User (Secondary User, SU) mobility model. Assume that there is a primary user (Primary User, PU) in the cognitive network (located in the center of a circular network area with a radius of a). The invention can calculate the detection performance of a single-node spectrum sensing algorithm and a multi-node cooperative spectrum sensing algorithm in a mobile scene.

For a single-node system, there is only one mobile cognitive user in the network, as shown in Figure 1.

For a multi-node cooperative system, there are N mobile cognitive users and a fusion center (FusionCenter, FC) in the network, as shown in FIG. 2 .

For the mobility model, it is assumed that cognitive users obey a random walk model. Figure 3 shows the movement model of the mobile cognitive user in the single-node spectrum sensing system, and its movement route can be expressed as AB-…-PQ-…. Each line segment in Fig. 3 represents a movement period, eg line segment PQ. The endpoint of each line segment represents a perception cycle, such as point P. The time Δt represents the time interval between two detections, that is, the duration of each movement cycle. In the nth mobile cycle, the cognitive user moves from point P to point Q, and once moving to point Q, an energy detection (EnergyDetection, ED) is performed, which is recorded as the energy detection in the nth detection cycle . Cognitive users move independently at speed v _n in direction θ _n during the nth movement period independently. v _n obeys the uniform distribution, and the uniform distribution is in the range from v _min to v _max . θ _n is evenly distributed in the range of 0 to 2π. In the next movement cycle, the cognitive user randomly picks a new speed and direction and continues to move randomly. The starting point A is randomly selected in the whole network, and _d0 is the interval between the main user and A. P represents the moving start point of the nth movement cycle, Q represents the end point, and is also the starting point of the n+1th movement cycle. d _n-1 and d _n represent the distances between the primary user and points P and Q, respectively. Then the probability density functions of v _n , θ _n and d ₀ are respectively

For cognitive users in a collaborative spectrum sensing system, each user obeys the same mobility model as described above. Figure 4 shows the mobility model of any mobile cognitive user SU _i , 1≤i≤N. The superscript "i" is used below to distinguish each cognitive user in the cooperative spectrum sensing system. Then the moving speed and moving direction of SU _i in the nth moving cycle are v _i,n and θ _i,n respectively. The distance between SU _i and the end of the nth travel cycle is d _i,n .

In the single-node spectrum detection system, because the energy detection method is easy to implement and can be used to detect the characteristics of arbitrary waveform signals, it is assumed that the cognitive user uses the energy detection method to determine whether the primary user exists. Let y _n denote the real-time primary user signal power detected by the cognitive user in the nth sensing period. y _n can be a function of distance, perceived user location, or even time. For simplicity and without loss of generality, the following channel model is assumed, where y _n is only related to d _n (the distance between the primary user and the cognitive user at the nth sensing cycle). y _n =G _{r Pt} G _t (λ _w /4πd _n ) ² , where G _r represents the antenna gain of the cognitive user, P _t represents the transmitted signal power of the primary user, and G _r is the antenna gain of the authorized user. _λw is the wavelength of the primary user signal. Then the cognitive user detects the real-time power of the primary user signal as

y _n ＝K/(d _n ) ² , K＝G _r P _t G _t (λ _w /4π) ² (25)

Therefore, K is a constant.

In each energy detection, each cognitive user takes M points, and in the Gaussian channel, the mean value of the noise is 0, the variance is σ ² , and the preset energy detection threshold is λ. Then after the nth sensing cycle, the calculation results of the detection performance parameters (detection probability, missed detection probability, false alarm probability) of single-node spectrum sensing are

in In a multi-node cooperative spectrum sensing system, all N cognitive users perform energy detection and upload the final detection results to the fusion center, and the fusion center makes the final decision on whether the primary user signal exists and broadcasts the result to each cognitive user. The detection performance parameters of the cooperative spectrum sensing system can be calculated by (26). It should be noted that the correct premise of the calculation result of (26) is that each cognitive user is stationary. On the basis of Equation (26), considering the mobility of cognitive users, the parameters of detection performance can be calculated by the following method.

First, according to the geometric relationship shown in Figure 3, the expression of d _{i, n} can be obtained.

Then according to (27) and the probability density function of v _{i, n} , the conditional probability density function of d _{i, n} is

Among them, the value range of d _{i, n} It can be obtained from the geometric relationship in Figure 3. According to (27), the derivative can be found in

So with Both are functions of (d _i,n-1 ,d _i,n ,θ _i,n ). use replace Then the conditional probability density function of d _i,n is

According to (25), the functional relationship between y _i,n and d _i,n can be obtained:

Therefore, the conditional probability density function of y _i,n is

in is a function of (d _i,n-1 ,y _i,n ,θ _i,n ), and This can be done by passing d _i,n in is obtained by replacing y _i,n . At the same time, the value range of y _{i, n} able to pass get. Therefore, the conditional mathematical expectation of y _i,n is

Then according to (32), the probability density function of y _{i, n} is

in is calculated by (30), (32) and the following formula (35):

The mathematical expectation of y _i,n is

in, is calculated by (30), (33) and the following formula (37):

Then the detection probability, missed detection probability, and false alarm probability of single-node spectrum sensing in mobile scenarios are:

in is calculated by (30) and the following formulas (39), (40):

In fact, the single-node spectrum sensing algorithm has many disadvantages, such as hidden terminal problems, channel fading and multi-channel effects, which lead to a great decline in system detection performance. To address these issues, researchers propose collaborative spectrum sensing techniques. Cooperative spectrum sensing technologies include hard-decision cooperative spectrum sensing and soft-decision cooperative spectrum sensing.

Firstly, the expression of detection performance parameters of hard-decision cooperative spectrum sensing technology in mobile scenarios is derived. Since "AND", "OR", "MAJORITY" and other hard-decision collaborative perceptions are all "K rank" (only when there are no less than k cognitive users in the system who think that the main user signal exists, the fusion center can judge the main user's signal. user exists), here are the calculation results of the detection performance (detection probability, missed detection probability, false alarm probability) of a more general "K rank" hard decision cooperative spectrum sensing system.

in is calculated by (30), (42) and (43).

in,

And f(y _1,n ,…,y _N,n |d _i,n-1 ,θ _i,n ) represents the joint conditional probability density function of y _1,n ,y _2,n ,…,y _N,n :

q represents the total number of scenarios where no less than k users among all N cognitive users believe that the main user signal exists, and the corresponding probability is

The detection performance parameters (detection probability, missed detection probability, and false alarm probability) of soft-decision cooperative spectrum sensing in mobile scenarios are:

in is calculated by (30), (46) and (47).

in,

Moreover, λ _s represents the preset threshold at the fusion center, and w _i,n represents the weighting factor of SU _i in the nth perception cycle.

The invention studies the mobile cognitive user spectrum detection system after any mobile cycle in the cognitive radio network, and provides a calculation method for detection performance indexes (detection probability, missed detection probability, false alarm probability). In the present invention, firstly, according to the network model of the system and the movement model of the cognitive user, the functional relationship between the moving speed, the direction of movement, and the distance between the cognitive user and the main user at each moment is obtained. Then obtain the probability density function of the distance between the end point and the main user according to the speed, direction and the probability density function of the distance between the starting point and the main user in this mobile cycle. According to the channel model and the detection model, the functional relationship between the real-time detected primary user signal power and the distance function is obtained, and the probability density function of this power is calculated by using this relationship and the probability density function of the distance function. Finally, use the probability density function of this power and the knowledge of probability theory and signal detection theory to obtain three indicators describing the detection performance in single-node sensing, hard-decision multi-node cooperative sensing and soft-decision cooperative sensing systems at any time in mobile scenarios. That is, the method of obtaining detection probability, missed detection probability and false alarm probability. The simulation result shows that the simulated value coincides with the theoretical value obtained by using the method of the present invention, which illustrates the correctness of the present invention.

The correctness of the method of the present invention is proved by the fact that the theoretical value coincides with the experimental value.

The present invention has following characteristics and remarkable progress:

1. The method of the present invention is proposed for mobile cognitive users. Compared with most of the current methods that assume that cognitive users are stationary, it is more in line with the actual cognitive network situation.

2. The method of the present invention can be widely used in single-node spectrum sensing, hard-decision cooperative spectrum sensing and soft-decision cooperative spectrum sensing systems.

3. The method of the present invention can be used in cognitive networks of any shape, and can be used in a cognitive user detection system for any movement, and has a wide range of applications.

4. The method of the present invention can calculate the spectrum sensing detection performance parameters after any movement period and give a generalized result.

Claims (3)

1. A method for obtaining performance parameters of a spectrum detection system after experiencing any mobile period in a cognitive radio network, characterized in that: The method is applied to a single-node spectrum detection system; Assume that in the mobile scenario, cognitive users obey the random walk model, and there is a primary user and a cognitive user in the cognitive network; Step 1. Use the formula: y _n =K/(d _n ) ² (2) In the formula: d _n represents the distance between the primary user and the cognitive user during the nth sensing cycle; Obtain the real-time power y _n of the primary user signal detected by the cognitive user; Where: K is a constant, and: K＝G _r P _t G _t (λ _w /4π) ² In the formula: G _r represents the antenna gain of the cognitive user, P _t represents the transmit signal power of the primary user, G _t is the antenna gain of the authorized user; λ _w is the wavelength of the primary user signal; Step 2. In each energy detection, the cognitive user collects M points, where M is a positive integer; and in the Gaussian channel, the mean value of the noise is 0, the variance is σ ² , and the preset energy detection threshold is λ; Then after the nth sensing period, the detection probability of single-node spectrum sensing for: <mrow> <msub> <mi>P</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> </msub> <mo>=</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&amp;lambda;</mi> <mo>-</mo> <mrow> <mo>(</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>y</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow> <msqrt> <mrow> <mn>2</mn> <msup> <mrow> <mo>(</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>y</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>/</mo> <mi>M</mi> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> Probability of missed detection for: <mrow> <msub> <mi>P</mi> <msub> <mi>m</mi> <mi>n</mi> </msub> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> false alarm probability for: <mrow> <msub> <mi>P</mi> <msub> <mi>f</mi> <mi>n</mi> </msub> </msub> <mo>=</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&amp;lambda;</mi> <mo>-</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> <msqrt> <mrow> <mn>2</mn> <msup> <mi>&amp;sigma;</mi> <mn>4</mn> </msup> <mo>/</mo> <mi>M</mi> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>-</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> In the formula: <mrow> <mi>Q</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mi>x</mi> <mrow> <mo>+</mo> <mi>&amp;infin;</mi> </mrow> </msubsup> <mfrac> <mn>1</mn> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mi>t</mi> <mn>2</mn> </msup> <mn>2</mn> </mfrac> </mrow> </msup> <mi>d</mi> <mi>t</mi> </mrow> Step 3, according to the formula: <mrow> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mi>&amp;Delta;</mi> <mi>t</mi> <mi> </mi> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mi>&amp;Delta;</mi> <mi>t</mi> <mi> </mi> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> Obtain the distance d _{i,n between} the i-th cognitive user and the end point of the n-th mobile cycle; 1≤i≤N, N is the total number of cognitive users in the network; cycle, the moving speed of the cognitive user; θi _,n represents the moving direction of the cognitive user in the nth mobile cycle; Δt is the time interval between two detections, that is, the continuous time; Step 4, according to the formula: <mrow> <msub> <mi>f</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>v</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>v</mi> <mi>min</mi> </msub> </mrow> </mfrac> <mo>|</mo> <mo>&amp;part;</mo> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> </mrow> Obtain the conditional probability density function of the distance d _{i, n} ; v _max represents the maximum moving speed of the cognitive user; v _min represents the minimum moving speed of the cognitive user; Step 5, deduce according to formula (4): <mrow> <mo>|</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </mfrac> <mo>|</mo> <mo>=</mo> <mo>|</mo> <mfrac> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mrow> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mi>&amp;Delta;</mi> <mi>t</mi> <mi> </mi> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mover> <mrow> <mi>P</mi> <mi>Q</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>&amp;CenterDot;</mo> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>|</mo> </mrow> In the formula: <mrow> <mover> <mrow> <mi>P</mi> <mi>Q</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mo>-</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>+</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>-</mo> <mrow> <mo>(</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> In the formula: PQ is the moving distance of the cognitive user in the nth mobile period; Step 6. Use expressions Replacement formula (5) in Then the conditional probability density function of d _i,n is: <mrow> <msub> <mi>f</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>v</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>v</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> </mfrac> <msub> <mi>V</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> Step 7, according to formula (2), obtain the relationship between y _i,n and d _i,n : y _i,n =K/(d _i,n ) ² (7) Then, the conditional probability density function of y _i,n is: <mrow> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>v</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>v</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> </mfrac> <msub> <mi>V</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mfrac> <msqrt> <mi>K</mi> </msqrt> <mrow> <mn>2</mn> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <msqrt> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </msqrt> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow> In the formula: by putting d _i, n in is replaced by y _i,n ; Step eight, pass the formula: <mrow> <msub> <mi>E</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> </msub> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <msub> <mi>dy</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow> In the formula: Indicates the value range of y _{i, n} ; Calculate the conditional mathematical expectation of y _i,n ; Step nine, through the formula: <mrow> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msubsup> <mo>&amp;lsqb;</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>a</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mfrac> <mrow> <mn>2</mn> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> </mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> </mfrac> <mo>)</mo> </mrow> <msub> <mi>dd</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> Probability density function of y _i,n ; in: is calculated by formula (6), formula (8) and the following formula (11): <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </munderover> <munder> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> </munder> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>f</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>dd</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow> 2 In the formula: Indicates the value range of d _i,n-1 ; The mathematical expectation of y _i,n is: <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msubsup> <mo>&amp;lsqb;</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>a</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mo>(</mo> <mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> </mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> </mfrac> <mo>)</mo> </mrow> <msub> <mi>dd</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow> in, is calculated by formula (6), formula (9) and the following formula (13): <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </munderover> <munder> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> </munder> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>f</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>dd</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow> Step 10. The detection probability of single-node spectrum sensing in mobile scenarios for: <mrow> <msubsup> <mi>P</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> <mi>v</mi> </msubsup> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msubsup> <mo>&amp;lsqb;</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>a</mi> </msubsup> <mi>Pr</mi> <mrow> <mo>(</mo> <msubsup> <mi>Pd</mi> <mi>n</mi> <mi>v</mi> </msubsup> <mo>|</mo> <msub> <mi>d</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mfrac> <mrow> <mn>2</mn> <msub> <mi>d</mi> <mn>0</mn> </msub> </mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> </mfrac> <msub> <mi>dd</mi> <mn>0</mn> </msub> <mo>&amp;rsqb;</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mn>1</mn> </msub> </mrow> Probability of missed detection for: <mrow> <msubsup> <mi>P</mi> <msub> <mi>m</mi> <mi>n</mi> </msub> <mi>v</mi> </msubsup> <mo>=</mo> <mn>1</mn> <mo>-</mo> <msubsup> <mi>P</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> <mi>v</mi> </msubsup> </mrow> false alarm probability for: <mrow> <msubsup> <mi>P</mi> <msub> <mi>f</mi> <mi>n</mi> </msub> <mi>v</mi> </msubsup> <mo>=</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&amp;lambda;</mi> <mo>-</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> <msqrt> <mrow> <mn>2</mn> <msup> <mi>&amp;sigma;</mi> <mn>4</mn> </msup> <mo>/</mo> <mi>M</mi> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> </mrow> in: is calculated by (6) and the following formulas (15), (16): <mrow> <mi>Pr</mi> <mrow> <mo>(</mo> <msubsup> <mi>Pd</mi> <mi>n</mi> <mi>v</mi> </msubsup> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </munderover> <munder> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> </munder> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <mi>Pr</mi> <mrow> <mo>(</mo> <msubsup> <mi>Pd</mi> <mi>n</mi> <mi>v</mi> </msubsup> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>f</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>dd</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mi>n</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>Pr</mi> <mrow> <mo>(</mo> <msubsup> <mi>Pd</mi> <mi>n</mi> <mi>v</mi> </msubsup> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> </munder> <msub> <mi>P</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>n</mi> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>dy</mi> <mi>n</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow> will detect probability Probability of missed detection and false alarm probability As a detection performance parameter of a single-node spectrum sensing system, a method for obtaining the performance parameter of a spectrum detection system after an arbitrary movement period in a cognitive radio network is completed. 2. A method for obtaining performance parameters of a spectrum detection system after experiencing any mobile cycle in a cognitive radio network, characterized in that: This method is applied to multi-node hard-decision cooperative spectrum detection system, Assume that in a mobile scenario, cognitive users obey the random walk model, and there are N mobile cognitive users and a fusion center FC in the cognitive network; N is a positive integer; Step 1. Use the formula: y _n =K/(d _n ) ² (2) In the formula: d _n represents the distance between the primary user and the cognitive user during the nth sensing cycle; Obtain the real-time power y _n of the primary user signal detected by the cognitive user; Where: K is a constant, and: K＝G _r P _t G _t (λ _w /4π) ² In the formula: G _r represents the antenna gain of the cognitive user, P _t represents the transmit signal power of the primary user, G _t is the antenna gain of the authorized user; λ _w is the wavelength of the primary user signal; Step 2. In each energy detection, each cognitive user collects M points, where M is a positive integer; and in a Gaussian channel, the mean value of the noise is 0, the variance is σ ² , and the preset energy detection threshold is λ; Then after the nth sensing period, the detection probability of multi-node hard-decision cooperative spectrum sensing for: <mrow> <msub> <mi>P</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> </msub> <mo>=</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&amp;lambda;</mi> <mo>-</mo> <mrow> <mo>(</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>y</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow> <msqrt> <mrow> <mn>2</mn> <msup> <mrow> <mo>(</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>y</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>/</mo> <mi>M</mi> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> Probability of missed detection for: <mrow> <msub> <mi>P</mi> <msub> <mi>m</mi> <mi>n</mi> </msub> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> false alarm probability for: <mrow> <msub> <mi>P</mi> <msub> <mi>f</mi> <mi>n</mi> </msub> </msub> <mo>=</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&amp;lambda;</mi> <mo>-</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> <msqrt> <mrow> <mn>2</mn> <msup> <mi>&amp;sigma;</mi> <mn>4</mn> </msup> <mo>/</mo> <mi>M</mi> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>-</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> In the formula: <mrow> <mi>Q</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mi>x</mi> <mrow> <mo>+</mo> <mi>&amp;infin;</mi> </mrow> </msubsup> <mfrac> <mn>1</mn> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mi>t</mi> <mn>2</mn> </msup> <mn>2</mn> </mfrac> </mrow> </msup> <mi>d</mi> <mi>t</mi> </mrow> Step 3, according to the formula: <mrow> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mi>&amp;Delta;</mi> <mi>t</mi> <mi> </mi> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mi>&amp;Delta;</mi> <mi>t</mi> <mi> </mi> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> Obtain the distance d _i,n between any cognitive user SU _i and the end point of the nth mobile cycle; 1≤i≤N; v _i,n means that in the nth mobile cycle, the cognitive user SU _i The moving speed of ; θ _{i, n} represents the moving direction of the cognitive user SU _i in the nth moving cycle; Δt is the time interval between two detections, that is, the duration of each moving cycle; Step 4, according to the formula: <mrow> <msub> <mi>f</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>v</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>v</mi> <mi>min</mi> </msub> </mrow> </mfrac> <mo>|</mo> <mo>&amp;part;</mo> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> </mrow> Obtain the conditional probability density function of distance d _{i, n} ; v _max represents the maximum moving speed of the cognitive user SU _i ; v _min represents the minimum moving speed of the cognitive user SU _i ; Step 5, deduce according to formula (4): <mrow> <mo>|</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </mfrac> <mo>|</mo> <mo>=</mo> <mo>|</mo> <mfrac> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mrow> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mi>&amp;Delta;</mi> <mi>t</mi> <mi> </mi> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mover> <mrow> <mi>P</mi> <mi>Q</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>&amp;CenterDot;</mo> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>|</mo> </mrow> 4 In the formula: <mrow> <mover> <mrow> <mi>P</mi> <mi>Q</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mo>-</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>+</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>-</mo> <mrow> <mo>(</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> In the formula: PQ is the moving distance of the cognitive user in the nth mobile period; Step 6. Use expressions Replacement formula (5) in Then the conditional probability density function of d _i,n is: <mrow> <msub> <mi>f</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>v</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>v</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> </mfrac> <msub> <mi>V</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> Step 7, according to formula (2), obtain the relationship between y _i,n and d _i,n : y _i,n =K/(d _i,n ) ² (7) Then, the conditional probability density function of y _{i, n} is: <mrow> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>v</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>v</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> </mfrac> <msub> <mi>V</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mfrac> <msqrt> <mi>K</mi> </msqrt> <mrow> <mn>2</mn> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <msqrt> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </msqrt> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow> In the formula: by putting d _i, n in is replaced by y _i,n ; Step eight, pass the formula: <mrow> <msub> <mi>E</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> </msub> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <msub> <mi>dy</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow> In the formula: Indicates the value range of y _{i, n} ; Calculate the conditional mathematical expectation of y _i,n ; Step nine, through the formula: <mrow> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msubsup> <mo>&amp;lsqb;</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>a</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mo>(</mo> <mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> </mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> </mfrac> <mo>)</mo> </mrow> <msub> <mi>dd</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> Probability density function of y _i,n ; in: is calculated by formula (6), formula (8) and the following formula (11): <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </munderover> <munder> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> </munder> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>f</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>dd</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow> In the formula: Indicates the value range of d _i,n-1 ; The mathematical expectation of y _i,n is: <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msubsup> <mo>&amp;lsqb;</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>a</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mo>(</mo> <mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> </mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> </mfrac> <mo>)</mo> </mrow> <msub> <mi>dd</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow> in, is calculated by formula (6), formula (9) and the following formula (13): <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </munderover> <munder> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> </munder> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>f</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>dd</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow> Step 10: The detection probability of spectrum sensing in the multi-node hard-decision cooperative spectrum detection system in the mobile scene for: <mrow> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msubsup> <mo>&amp;lsqb;</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>a</mi> </msubsup> <mi>Pr</mi> <mrow> <mo>(</mo> <msubsup> <mi>Pd</mi> <msub> <mi>H</mi> <mi>n</mi> </msub> <mi>v</mi> </msubsup> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mfrac> <mrow> <mn>2</mn> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> </mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> </mfrac> <msub> <mi>dd</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mrow> Probability of missed detection for: <mrow> <mn>1</mn> <mo>-</mo> <msubsup> <mi>Q</mi> <mrow> <mi>d</mi> <mo>-</mo> <msub> <mi>H</mi> <mi>n</mi> </msub> </mrow> <mi>v</mi> </msubsup> </mrow> false alarm probability for: <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mi>k</mi> </mrow> <mi>N</mi> </munderover> <msubsup> <mi>C</mi> <mi>N</mi> <mi>i</mi> </msubsup> <msup> <mrow> <mo>(</mo> <msubsup> <mi>P</mi> <mi>f</mi> <mi>v</mi> </msubsup> <mo>)</mo> </mrow> <mi>i</mi> </msup> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msubsup> <mi>P</mi> <mi>f</mi> <mi>v</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mi>i</mi> </mrow> </msup> </mrow> in: is calculated by formula (6), formula (18) and formula (19): <mrow> <mi>Pr</mi> <mrow> <mo>(</mo> <msubsup> <mi>Pd</mi> <msub> <mi>H</mi> <mi>n</mi> </msub> <mi>v</mi> </msubsup> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </munderover> <munder> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> </munder> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <mi>Pr</mi> <mrow> <mo>(</mo> <msubsup> <mi>Pd</mi> <msub> <mi>H</mi> <mi>n</mi> </msub> <mi>v</mi> </msubsup> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>f</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>dd</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>Pr</mi> <mrow> <mo>(</mo> <msubsup> <mi>Pd</mi> <msub> <mi>H</mi> <mi>n</mi> </msub> <mi>v</mi> </msubsup> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> </munder> <mo>...</mo> <munder> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> </munder> <msubsup> <mi>Q</mi> <mi>H</mi> <mi>v</mi> </msubsup> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>y</mi> <mrow> <mi>N</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>dy</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>...</mo> <msub> <mi>dy</mi> <mrow> <mi>N</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow> in: <mrow> <msubsup> <mi>Q</mi> <mi>H</mi> <mi>v</mi> </msubsup> <mo>=</mo> <munder> <mo>&amp;Sigma;</mo> <mi>q</mi> </munder> <mrow> <mo>(</mo> <msubsup> <mi>Q</mi> <mrow> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>d</mi> </mrow> <mi>v</mi> </msubsup> <mo>&amp;CenterDot;</mo> <munderover> <mo>&amp;Pi;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mrow> <mo>(</mo> <mi>j</mi> <mo>&amp;NotEqual;</mo> <mi>&amp;xi;</mi> <mo>,</mo> <mi>&amp;eta;</mi> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>&amp;omega;</mi> <mo>)</mo> </mrow> </mrow> <mi>N</mi> </munderover> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <msub> <mi>d</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow> And f(y _1,n ,…,y _N,n |d _i,n-1 ,θ _i,n ) represents the joint conditional probability density function of y _1,n ,y _2,n ,…,y _N,n : <mrow> <mtable> <mtr> <mtd> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>y</mi> <mrow> <mi>N</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mn>...</mn> <mo>&amp;CenterDot;</mo> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>N</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>N</mi> </msup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow> q represents the total number of scenarios in which no less than k users among all N cognitive users believe that the main user signal exists; will detect probability Probability of missed detection and false alarm probability As a detection performance parameter of a multi-node hard-decision cooperative spectrum detection system, a method for obtaining the performance parameter of the spectrum detection system after experiencing any mobile period in a cognitive radio network is completed. 3. A method for obtaining performance parameters of a spectrum detection system after experiencing any mobile period in a cognitive radio network, characterized in that: The method is applied to a multi-node soft-decision cooperative spectrum detection system, Assume that in a mobile scenario, cognitive users obey the random walk model, and there are N mobile cognitive users and a fusion center FC in the cognitive network; N is a positive integer; Step 1. Use the formula: y _n =K/(d _n ) ² (2) In the formula: d _n represents the distance between the primary user and the cognitive user during the nth sensing cycle; Obtain the real-time power y _n of the primary user signal detected by the cognitive user; Where: K is a constant, and: K＝G _r P _t G _t (λ _w /4π) ² In the formula: G _r represents the antenna gain of the cognitive user, P _t represents the transmitted signal power of the primary user, G _t is the antenna gain of the authorized user; λ _w is the wavelength of the primary user signal; Step 2. In each energy detection, each cognitive user collects M points, where M is a positive integer; and in a Gaussian channel, the mean value of the noise is 0, the variance is σ ² , and the preset energy detection threshold is λ; Then after the nth sensing period, the detection probability of the multi-node soft-decision cooperative spectrum for: <mrow> <msub> <mi>P</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> </msub> <mo>=</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&amp;lambda;</mi> <mo>-</mo> <mrow> <mo>(</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>y</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow> <msqrt> <mrow> <mn>2</mn> <msup> <mrow> <mo>(</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>y</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>/</mo> <mi>M</mi> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> Probability of missed detection for: <mrow> <msub> <mi>P</mi> <msub> <mi>m</mi> <mi>n</mi> </msub> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>-</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> false alarm probability for: <mrow> <msub> <mi>P</mi> <msub> <mi>f</mi> <mi>n</mi> </msub> </msub> <mo>=</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>&amp;lambda;</mi> <mo>-</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> <msqrt> <mrow> <mn>2</mn> <msup> <mi>&amp;sigma;</mi> <mn>4</mn> </msup> <mo>/</mo> <mi>M</mi> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>-</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> In the formula: <mrow> <mi>Q</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mi>x</mi> <mrow> <mo>+</mo> <mi>&amp;infin;</mi> </mrow> </msubsup> <mfrac> <mn>1</mn> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mi>t</mi> <mn>2</mn> </msup> <mn>2</mn> </mfrac> </mrow> </msup> <mi>d</mi> <mi>t</mi> </mrow> Step 3, according to the formula: <mrow> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mi>&amp;Delta;</mi> <mi>t</mi> <mi> </mi> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mi>&amp;Delta;</mi> <mi>t</mi> <mi> </mi> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> Obtain the distance d _i,n between any cognitive user SU _i and the end point of the nth mobile cycle; 1≤i≤N; v _i,n means that in the nth mobile cycle, the cognitive user SU _i The moving speed of ; θ _{i, n} represents the moving direction of the cognitive user SU _i in the nth moving cycle; Δt is the time interval between two detections, that is, the duration of each moving cycle; Step 4, according to the formula: <mrow> <msub> <mi>f</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>v</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>v</mi> <mi>min</mi> </msub> </mrow> </mfrac> <mo>|</mo> <mo>&amp;part;</mo> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>/</mo> <mo>&amp;part;</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> </mrow> Obtain the conditional probability density function of the distance d _{i, n} ; v _max represents the maximum moving speed of the cognitive user SU _i ; v _min represents the minimum moving speed of the cognitive user SU _i ; Step 5, deduce according to formula (4): <mrow> <mo>|</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>v</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </mfrac> <mo>|</mo> <mo>=</mo> <mo>|</mo> <mfrac> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mrow> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mi>&amp;Delta;</mi> <mi>t</mi> <mi> </mi> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mover> <mrow> <mi>P</mi> <mi>Q</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>&amp;CenterDot;</mo> <mrow> <mo>(</mo> <mi>&amp;Delta;</mi> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>|</mo> </mrow> In the formula: <mrow> <mover> <mrow> <mi>P</mi> <mi>Q</mi> </mrow> <mo>&amp;OverBar;</mo> </mover> <mo>=</mo> <mo>-</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>+</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msup> <mi>cos</mi> <mn>2</mn> </msup> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>-</mo> <mrow> <mo>(</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> In the formula: PQ is the moving distance of the cognitive user in the nth mobile period; Step 6. Use expressions Replacement formula (5) in Then the conditional probability density function of d _i,n is: <mrow> <msub> <mi>f</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>v</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>v</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> </mfrac> <msub> <mi>V</mi> <msub> <mi>d</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> Step 7, according to formula (2), obtain the relationship between y _i,n and d _i,n : y _i,n =K/(d _i,n ) ² (7) Then, the conditional probability density function of y _i,n is: <mrow> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>v</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>v</mi> <mi>min</mi> </msub> </mrow> </mfrac> <msub> <mi>V</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mfrac> <msqrt> <mi>K</mi> </msqrt> <mrow> <mn>2</mn> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <msqrt> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </msqrt> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow> In the formula: by putting d _i, n in is replaced by y _i,n ; Step eight, pass the formula: <mrow> <msub> <mi>E</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> </msub> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <msub> <mi>dy</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow> In the formula: Indicates the value range of y _{i, n} ; Calculate the conditional mathematical expectation of y _i,n ; Step nine, through the formula: <mrow> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msubsup> <mo>&amp;lsqb;</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>a</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mo>(</mo> <mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> </mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> </mfrac> <mo>)</mo> </mrow> <msub> <mi>dd</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> Probability density function of y _i,n ; in: is calculated by formula (6), formula (8) and the following formula (11): <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </munderover> <munder> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> </munder> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>f</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>f</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>dd</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow> In the formula: Indicates the value range of d _i,n-1 ; The mathematical expectation of y _i,n is: <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msubsup> <mo>&amp;lsqb;</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>a</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mo>(</mo> <mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> </mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> </mfrac> <mo>)</mo> </mrow> <msub> <mi>dd</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow> in, is calculated by formula (6), formula (9) and the following formula (13): <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </munderover> <munder> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> </munder> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>E</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>E</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>dd</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow> Step 10. The detection probability of spectrum sensing in the multi-node soft-decision cooperative spectrum detection system in the mobile scene for: <mrow> <msubsup> <mi>Q</mi> <mrow> <mi>d</mi> <mo>-</mo> <msub> <mi>S</mi> <mi>n</mi> </msub> </mrow> <mi>v</mi> </msubsup> <mo>=</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msubsup> <mo>&amp;lsqb;</mo> <msubsup> <mo>&amp;Integral;</mo> <mn>0</mn> <mi>a</mi> </msubsup> <mi>Pr</mi> <mrow> <mo>(</mo> <msubsup> <mi>Pd</mi> <msub> <mi>S</mi> <mi>n</mi> </msub> <mi>v</mi> </msubsup> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> </mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> </mfrac> <msub> <mi>dd</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mrow> Probability of missed detection for: <mrow> <msubsup> <mi>Q</mi> <mrow> <mi>m</mi> <mo>-</mo> <msub> <mi>S</mi> <mi>n</mi> </msub> </mrow> <mi>v</mi> </msubsup> <mo>=</mo> <mn>1</mn> <mo>-</mo> <msubsup> <mi>Q</mi> <mrow> <mi>d</mi> <mo>-</mo> <msub> <mi>S</mi> <mi>n</mi> </msub> </mrow> <mi>v</mi> </msubsup> </mrow> false alarm probability for: <mrow> <msubsup> <mi>Q</mi> <mrow> <mi>f</mi> <mo>-</mo> <msub> <mi>S</mi> <mi>n</mi> </msub> </mrow> <mi>v</mi> </msubsup> <mo>=</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>&amp;lambda;</mi> <mi>s</mi> </msub> <mo>-</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>&amp;CenterDot;</mo> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </msubsup> <msub> <mi>w</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> <msqrt> <mrow> <mn>2</mn> <msup> <mi>&amp;sigma;</mi> <mn>4</mn> </msup> <mo>/</mo> <mi>M</mi> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> </mrow> in: is calculated by formula (6), formula (22) and formula (23): <mrow> <mi>Pr</mi> <mrow> <mo>(</mo> <msubsup> <mi>Pd</mi> <msub> <mi>S</mi> <mi>n</mi> </msub> <mi>v</mi> </msubsup> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Integral;</mo> <mn>0</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </munderover> <munder> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> </munder> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <mi>Pr</mi> <mrow> <mo>(</mo> <msubsup> <mi>Pd</mi> <msub> <mi>S</mi> <mi>n</mi> </msub> <mi>v</mi> </msubsup> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>f</mi> <msub> <mi>d</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>dd</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>d&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>22</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>Pr</mi> <mrow> <mo>(</mo> <msubsup> <mi>Pd</mi> <msub> <mi>S</mi> <mi>n</mi> </msub> <mi>v</mi> </msubsup> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> </munder> <mn>...</mn> <munder> <mo>&amp;Integral;</mo> <msub> <mi>&amp;Phi;</mi> <msub> <mi>y</mi> <mi>n</mi> </msub> </msub> </munder> <msubsup> <mi>Q</mi> <mi>S</mi> <mi>v</mi> </msubsup> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>y</mi> <mrow> <mi>N</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>d</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>dy</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mn>...</mn> <msub> <mi>dy</mi> <mrow> <mi>N</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>23</mn> <mo>)</mo> </mrow> </mrow> in: <mrow> <msubsup> <mi>Q</mi> <mi>S</mi> <mi>v</mi> </msubsup> <mo>=</mo> <mi>Q</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>&amp;lambda;</mi> <mi>s</mi> </msub> <mo>-</mo> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </msubsup> <mrow> <mo>(</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <msub> <mi>w</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mrow> <msqrt> <mrow> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </msubsup> <mn>2</mn> <msubsup> <mi>w</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> <mn>2</mn> </msubsup> <msup> <mrow> <mo>(</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>/</mo> <mi>M</mi> </mrow> </msqrt> </mfrac> <mo>)</mo> </mrow> </mrow> λ _s represents the preset threshold at the fusion center, w _i,n represents the weighting factor of cognitive user SU _i in the nth perception cycle; will detect probability Probability of missed detection and false alarm probability As a detection performance parameter of a multi-node soft-decision cooperative spectrum detection system, a method for obtaining the performance parameter of the spectrum detection system after experiencing any mobile period in a cognitive radio network is completed.