CN108063642B - Channel capacity optimization method of multi-user molecular communication model based on diffusion - Google Patents

Abstract

A channel capacity optimization method based on a diffusion-based multi-user molecular communication model, comprising the following steps: in the first step, a normal distribution is used to approximate a binomial distribution to obtain the number of molecules received by RN in the current time slot; The hypothesis of the diffusion molecular communication model detects the channel model; in the third step, the mathematical expression of the optimal decision threshold is obtained by using the minimum error probability decision criterion, so as to obtain the optimal decision threshold η; in the fourth step, in the optimal decision threshold η Based on this, the optimal channel capacity value is obtained. The invention provides a channel capacity optimization method based on a diffusion-based multi-user molecular communication model that effectively improves the channel capacity.

Description

A Channel Capacity Optimization Method Based on Diffusion-Based Multi-User Molecular Communication Model

technical field

The invention relates to biotechnology, nanotechnology and communication technology, and is a channel capacity optimization method based on a diffusion-based multi-user molecular communication model.

Background technique

In recent years, the rapid development of nanotechnology has paved the way for the fabrication of nanomachines as the basic unit of nanoscale communication. Since the functional and communication capabilities ^of individual nanomachines are rather limited, nanoscale communication networks that can interconnect and cooperate with these nanomachines to accomplish more complex tasks are constantly being proposed. At the micro- and nano-scale, due to the limitation of electromagnetic signal wavelength and antenna size ratio, electromagnetic-based nano-communication is not suitable, and the molecular communication model with molecules as information transfer carriers is generally considered to be the most promising. one of the solutions.

In molecular communication, molecules can follow a specific path or be guided by a fluid medium to their destination, and their propagation is often limited to diffusion, such as between insects via air-diffusing pheromones or calcium signaling between living cells conduct. In a diffusion-based multi-user molecular communication system, multiple transmitter nanomachines (TN) release the modulated and encoded information molecules into a shared fluid medium, and the motion of the molecules follows the Brownian motion rule through free diffusion. The reception range that enters the receiver nanomachine (RN) is absorbed and no longer exists in the medium, and is decoded in a specific way.

In the diffusion-based multi-user molecular communication model, since the molecules follow the Brownian motion rule, the intersymbol interference of all previous time slots to the receiver nanomachine in the current time slot is inevitable; and because multiple sender nanomachines simultaneously Due to work, shared channels, and the indistinguishability of identical information molecules, the receiving nanomachine is also subject to interference between users. Therefore, the research of diffusion-based multi-user molecular communication model also faces many challenges, one of which is how to improve the channel capacity of diffusion-based multi-user molecular communication model considering multi-slot intersymbol interference and multi-user interference.

SUMMARY OF THE INVENTION

In order to overcome the shortage of the low channel capacity of the existing diffusion multi-user molecular communication model, the present invention provides a channel capacity optimization method based on the diffusion molecular communication model that effectively improves the channel capacity.

In order to solve the above-mentioned technical problems, the present invention adopts the following technical solutions:

A channel capacity optimization method based on a diffusion-based multi-user molecular communication model, the optimization method comprises the following steps:

The first step is to use the normal distribution to approximate the binomial distribution to obtain the number of molecules received by the nanomachine at the receiver of the current time slot;

The second step is to establish the hypothesis detection channel model of the diffusion-based multi-user molecular communication model;

In the third step, the mathematical expression of the optimal decision threshold is obtained by using the normal distribution, so as to obtain the optimal decision threshold η;

The fourth step is to obtain the optimal channel capacity value based on the optimal decision threshold η.

Further, in the first step, in the binary diffusion-based multi-user molecular communication model, the input and output are both binary information bits 1 or 0, and OOK is used as the modulation technique, that is, the sender nanomachine TN releases a certain amount of Molecular means sending bit 1, not releasing any molecule means sending bit 0, once the molecule is released into the biological environment, it will diffuse freely. In the environment, after the transmitter nanomachine releases the molecule, the motion of the molecule in the medium will follow the law of Brownian motion, and the probability density of the time t required for a molecule to travel from the transmitter nanomachine T _i to the receiver nanomachine at a distance d _i The distribution function f(t) is, 1≤i≤M:

Among them, d is the distance from the sender's nanomachine to the center of the receiver's nanomachine, and D is the diffusion coefficient of the biological environment. The probability of arrival is expressed as F _i (t,d _i ) as follows:

Considering the time-slotted diffusion molecular communication model, it is assumed that all molecules received events occur at discrete time points, and the information transmission time is divided into time-slot intervals of equal size, denoted as T=nt _s , where T is the information transmission time time, _ts is the duration of each time slot, n is the number of divided time slots;

At the beginning of the nkth time slot, 1≤k≤n-1, TN _i releases Q _i numerators to send bit 1, no molecule to send bit 0, P _i (k) represents the release of the nkth time slot The probability that the numerator is received in the nth time slot is calculated as follows:

P _i (k)=Fi ₍ (k+1)t _s ) _{−Fi (kt s )}

Assuming that the number of molecules released by TN _i in the nk th time slot and received by the RN in the current n th time slot is represented by _Ni (k), _Ni (k) obeys the following binomial distribution:

N _i (k)～B(Q _i ,P _i (k))

Since the value of P _i (k) is around 0.1, the binomial distribution obeyed by the random variable N _i (k) is approximated by a normal distribution, and the approximate distribution formula is as follows:

Assuming that the optimal decision threshold of the current time slot is η, if Ni (k) _≥η , the RN outputs 1; if Ni ( _k )<η, the RN outputs 0.

Due to the randomness of Brownian motion, the remaining numerators not received by RN in the previous time slots will cause inter-symbol interference to subsequent bit receptions. Therefore, for the current time slot n, the (n-1) time slots generated by TN _i before The number of all interfering molecules is represented by ^{Ni ISI, and the normal distribution of Ni ISI} _{is expressed} ^as follows:

1≤j≤M，j≠i，服从的正态分布表示如下：For a diffusion-based multi-user molecular communication system, multiple sender nanomachines share the channel, and the RN will receive molecules from other TNs and cause inter-user interference. Therefore, for the current time slot n, TN _j , the current time slot and the previous ( The molecular sum of all interferences generated by n-1) time slot is denoted as

1≤j≤M, j≠i, the normal distribution obeyed is expressed as follows:

的正态分布，其中μ_C和

分别为该噪声的均值和方差；Considering that RN makes some unavoidable errors in statistical information molecules, an external noise is introduced, and it is assumed that the noise obeys

the normal distribution of , where μ _C and

are the mean and variance of the noise, respectively;

表示；3)IUI产生的分子，用

表示；4)外部噪声，用

表示。假设TN_i受到干扰的分子总数用

表示，则有

因此：The total number of numerators _yi [n] received by TN _i in the current time slot n consists of four parts: 1) numerators sent by TN _i in the nth time slot, denoted by _Ni [n]; 2) numerators generated by ISI, use

Representation; 3) The molecule produced by IUI, with

means; 4) External noise, with

express. Assuming that the total number of molecules disturbed by T _i is given by

means, there is

therefore:

和Y_n分别代表当前时隙的输入和输出，

表示误报率，即TN_i输入为0，RN输出为1的概率；

表示检测率，即TN_i输入为1，RN输出为1的概率，它们分别定义如下：Further, in the second step, let

and Y _n represent the input and output of the current slot, respectively,

Indicates the false alarm rate, that is, the probability that the input of TN _i is 0 and the output of RN is 1;

Represents the detection rate, that is, the probability that the TN _i input is 1 and the RN output is 1, and they are respectively defined as follows:

表示RN当前第n个时隙收到TN_i发送的分子数，H₀和H₁分别表示当前时隙发送0和1的情况。以连续型随机变量

为观测值的二元假设检验问题：use

Represents the number of numerators sent by TN _i in the current nth time slot of the RN, and H ₀ and H ₁ represent the situation of sending 0 and 1 in the current time slot, respectively. continuous random variable

A binary hypothesis testing problem for observations:

Therefore, this binary hypothesis testing model can be transformed into:

Among them, the parameters of the above normal distribution are as follows:

μ ₀ =μ _i,I

μ ₁ =Q _i P _i (0)+μ ₀

Further, in the third step, the minimum error probability judgment criterion is:

Among them, P(H ₀ ) and P(H ₁ ) are the probabilities of sending 0 and 1 respectively in the current time slot, that is, P(H ₁ )= _pi , P(H ₀ )=1- _pi , p(z |H ₀ ) and p(z|H ₁ ) represent the probability that the RN receives z molecules when 0 and 1 are sent in the current time slot, respectively; the likelihood ratio is represented by Λ(z), which is determined by the minimum error probability above. The formula for calculating the likelihood ratio of the criterion is:

和

分别为H₀和H₁所服从的正态分布的概率密度函数，则得似然比满足：in,

and

are the probability density functions of the normal distributions obeyed by H ₀ and H ₁ respectively, then the likelihood ratio satisfies:

Taking the natural logarithm on both sides of the equation, we get:

According to the above equation obtained according to the minimum error probability judgment criterion, and further solve z, we get:

Among them, η is the best threshold, and the parameters A, B, and C are:

和检测率

计算公式如下：In the fourth step, use the cumulative distribution function of the normal distribution to calculate the false alarm rate

and detection rate

Calculated as follows:

in,

Through the above calculation formula, the channel capacity of the diffusion molecular communication model can be optimized. The calculation formula of the channel capacity is as follows:

C=max I(X;Y)

in

The technical idea of the present invention is as follows: the present invention fully combines the characteristics of the random behavior of molecules moving in the biological environment in the diffusion multi-user molecular communication model, and studies the channel capacity optimization scheme of the diffusion multi-user molecular communication model. In the diffusion multi-user molecular communication model, multiple sender nanomachines work simultaneously. By releasing a certain number of identical molecules into the biological environment, the molecules freely diffuse in the transmission channel following the law of Brownian motion, and finally arrive at the receiver randomly. Nanomachines. Therefore, the intersymbol interference of the molecules released by the sender nanomachines in all previous time slots to the current time slot and the mutual interference between different sender nanomachines are inevitable. Considering the intersymbol interference, it is particularly important to study how to improve the channel capacity of the diffusion molecular communication model. The present invention mainly develops a communication technology with optimal channel capacity based on molecular communication that can be used in nano-networks. The channel capacity is optimized by controlling the probability of the sender nanomachine sending 1 or 0 in each time slot, and at the same time using the minimum error probability decision criterion to obtain the mathematical expression of the optimal decision threshold.

The beneficial effects of the present invention are mainly manifested in: 1. Considering the inter-symbol interference of all previous time slots to the current time slot and the situation between users, at the same time, considering that different sender nanomachines send 1 or 0 in each time slot The probability of , uses the normal distribution to approximate the binomial distribution to obtain the number of molecules received by RN in the current time slot. On this basis, the mathematical expression of the optimal decision threshold is obtained by using the minimum error probability decision criterion. 2. Based on the optimal decision threshold, the optimal value of mutual information is obtained, and different parameters are shown including the distance from the nanomachine TN to the center of RN, and the number of molecules released by the sender nanomachine in each time slot. , the number of time slots, and the influence of external noise on mutual information. 3. Compared with the existing research on the diffusion-based multi-user molecular communication system, the present invention considers the influence of multi-slot user interference, multi-user and external noise on the system.

Description of drawings

Figure 1 is a topology diagram of a diffusion-based multi-user molecular communication model. The information source consists of multiple TNs with the same physical properties, they work simultaneously and release the same information molecules, and the receiver is an RN with a detection radius of R.

Figure 2 shows the relationship between the probability P _i (k) that the molecules released by TN _i in the first k time slots are received in the current time slot and the number of previous time slots.

与TN₁的先验概率p₁的关系。Figure 3 shows the achievable mutual information for different values of the distance d ₁ between TN ₁ and RN

Relationship to the prior probability p ₁ of TN ₁ .

与TN₁每个时隙发送的分子数Q₁的关系。Figure 4 shows the mutual information that can be achieved when the number of numerators Q _j (2≤j≤4) sent by the interfering nanomachine TN _j (2≤j≤4) per time slot takes different values

Relation to Q ₁ , the number of numerators sent per time slot by TN ₁ .

与外部噪声方差

的关系。Figure 5 shows the achievable mutual information for different values of the number of TNs M

variance with external noise

Relationship.

与TN₁的先验概率p₁的关系。Figure 6 shows the achievable mutual information when the number of TNs M takes different values and sets 3 different numbers of time slots for systems with different values of M

Relationship to the prior probability p ₁ of TN ₁ .

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings.

1 to 6 , a method for channel capacity optimization based on a diffusion-based molecular communication model includes the following steps:

The first step is to use the normal distribution to approximate the binomial distribution to obtain the number of molecules received by RN in the current time slot. The process is as follows:

In the binary diffusion-based multi-user molecular communication model, the input and output are both binary information bits 1 or 0, and OOK is used as the modulation technique, that is, the sender nanomachine TN expresses sending bit 1 by releasing a certain number of molecules, without releasing any Molecular means sending bit 0. Once the molecule is released into the biological environment, it will diffuse freely. When it moves to the detection range of the receiver's nanomachine RN, it will be absorbed immediately and no longer exist in the biological environment. The sender's nanomachine releases the molecule Then, the motion form of molecules in the medium will follow the law of Brownian motion, and the probability density distribution function f(t) of the time t required for a molecule to travel from the sender nanomachine TN _i to the receiver nanomachine with a distance d _i is, 1 ≤i≤M:

Among them, d is the distance from the sender's nanomachine to the center of the receiver's nanomachine, and D is the diffusion coefficient of the biological environment. The probability of arrival is expressed as F _i (t,d _i ) as follows:

Considering the time-slotted diffusion molecular communication model, it is assumed that all molecules received events occur at discrete time points, and the information transmission time is divided into time-slot intervals of equal size, denoted as T=nt _s , where T is the information transmission time time, _ts is the duration of each time slot, n is the number of divided time slots;

At the beginning of the nkth time slot, 1≤k≤n-1, TN _i releases Q _i numerators to send bit 1, no molecule to send bit 0, P _i (k) represents the release of the nkth time slot The probability that the numerator is received in the nth time slot is calculated as follows:

P _i (k)=Fi ₍ (k+1)t _s ) _{−Fi (kt s )}

Assuming that the number of molecules released by TN _i in the nk th time slot and received by the RN in the current n th time slot is represented by _Ni (k), _Ni (k) obeys the following binomial distribution:

N _i (k)～B(Q _i ,P _i (k))

Since the value of P _i (k) is around 0.1, the binomial distribution obeyed by the random variable N _i (k) can be approximated by a normal distribution. The approximate distribution formula is as follows:

Assuming that the optimal decision threshold of the current time slot is η, if Ni (k) _≥η , the RN outputs 1; if Ni ( _k )<η, the RN outputs 0.

表示，

服从的正态分布表示如下：Due to the randomness of Brownian motion, the remaining numerators not received by RN in the previous time slots will cause inter-symbol interference to subsequent bit receptions. Therefore, for the current time slot n, the (n-1) time slots generated by TN _i before The number of all interfering molecules is

express,

The normal distribution obeyed is expressed as follows:

服从的正态分布表示如下：For a diffusion-based multi-user molecular communication system, multiple sender nanomachines share the channel, and the RN will receive molecules from other TNs and cause inter-user interference. Therefore, for the current time slot n, TN _j (1≤j≤M , j≠i) The numerator sum of all interferences generated by the current time slot and the previous (n-1) time slot is denoted as

The normal distribution obeyed is expressed as follows:

的正态分布，其中μ_C和

分别为该噪声的均值和方差。Considering that RN makes some unavoidable errors in statistical information molecules, an external noise is introduced, which is usually assumed to obey

the normal distribution of , where μ _C and

are the mean and variance of the noise, respectively.

表示；3)IUI产生的分子，用

表示；4)外部噪声，用

表示。假设TN_i受到干扰的分子总数用

表示，则有

因此：To sum up, the total number of numerators _yi [n] received by TN _i in the current time slot n consists of four parts: 1) the numerators sent by TN _i in the nth time slot, denoted by _Ni [n]; 2) ISI-generated molecules, with

Representation; 3) The molecule produced by IUI, with

means; 4) External noise, with

express. Assuming that the total number of molecules disturbed by T _i is given by

means, there is

therefore:

The second step is to establish the hypothesis detection channel model of the diffusion-based multi-user molecular communication model;

和Y_n分别代表当前时隙的输入和输出，

表示误报率，即TN_i输入为0，RN输出为1的概率；

表示检测率，即TN_i输入为1，RN输出为1的概率。它们分别定义如下：make

and Y _n represent the input and output of the current slot, respectively,

Indicates the false alarm rate, that is, the probability that the input of TN _i is 0 and the output of RN is 1;

Represents the detection rate, that is, the probability that the input of TN _i is 1 and the output of RN is 1. They are respectively defined as follows:

表示RN当前第n个时隙收到TN_i发送的分子数。H₀和H₁分别表示当前时隙发送0和1的情况。以连续型随机变量

为观测值的二元假设检验问题：use

Indicates the number of numerators sent by TN _i received by the RN in the current nth time slot. H ₀ and H ₁ respectively represent the case of sending 0 and 1 in the current time slot. continuous random variable

A binary hypothesis testing problem for observations:

Therefore, this binary hypothesis testing model can be transformed into:

Among them, the parameters of the above normal distribution are as follows:

μ ₀ =μ _i,I

μ ₁ =Q _i P _i (0)+μ ₀

The third step is to use the minimum error probability criterion to realize the optimal detection scheme, thereby obtaining the optimal decision threshold η;

The minimum error probability judgment criterion is:

Wherein, P(H ₀ ) and P(H ₁ ) are the probabilities of sending 0 and 1 in the current time slot, respectively, that is, P(H ₁ )= _pi , P(H ₀ )=1- _pi . p(z|H ₀ ) and p(z|H ₁ ) represent the probability that the RN receives z molecules when 0 and 1 are sent in the current time slot, respectively; Λ(z) is used to represent the likelihood ratio, which is determined by the minimum The calculation formula of the likelihood ratio can be obtained from the error probability judgment criterion:

和

分别为H₀和H₁所服从的正态分布的概率密度函数。则可得似然比满足：in,

and

are the probability density functions of the normal distributions obeyed by H ₀ and H ₁ , respectively. Then the likelihood ratio satisfies:

Taking the natural logarithm on both sides of the equation, we get:

According to the above equation obtained according to the minimum error probability judgment criterion, and further solve z, we can get:

Among them, η is the best threshold, and the parameters A, B, and C are:

和检测率

计算公式如下：The fourth step is to obtain the optimal channel capacity value based on the optimal decision threshold η. Calculate the false alarm rate using the cumulative distribution function of the normal distribution

and detection rate

Calculated as follows:

in,

Through the above calculation formula, the channel capacity of the diffusion molecular communication model can be optimized. The calculation formula of the channel capacity is as follows:

C=max I(X;Y)

in

In the fifth step, the experimental simulation shows that different parameters include the distance from the nanomachine TN to the center of RN, the number of molecules released by the sender nanomachine in each time slot, the number of time slots, and the magnitude of external noise to the mutual information. Impact. We can obtain better mutual information values, and at the same time, the number of molecules used in each time slot is far less than the existing molecular communication models.

与TN₁的先验概率p₁的关系。可以看到TN₁到RN中心的距离d₁越小，互信息的值越大。Figure 3 shows the achievable mutual information for different values of the distance d ₁ from TN ₁ to the center of RN

Relationship to the prior probability p ₁ of TN ₁ . It can be seen that the smaller the distance d ₁ from TN ₁ to the center of RN, the greater the value of mutual information.

与TN₁每个时隙发送的分子数Q₁的关系。当Q₁越大，Q_j(2≤j≤4)越小，互信息的值越大。Figure 4 shows the mutual information that can be achieved when the number of numerators Q _j (2≤j≤4) sent by the interfering nanomachine TN _j (2≤j≤4) per time slot takes different values

Relation to Q ₁ , the number of numerators sent per time slot by TN ₁ . When Q ₁ is larger, Q _j (2≤j≤4) is smaller, and the value of mutual information is larger.

与外部噪声方差

的关系。可以看到，外部噪声越大，互信息就越小；TN的数量越少，用户间干扰越小，外部噪声所占总干扰的比重越大，对互信息的影响也就越大。Figure 5 shows the achievable mutual information for different values of the number of TNs M

variance with external noise

Relationship. It can be seen that the larger the external noise, the smaller the mutual information; the smaller the number of TNs, the smaller the interference between users, the greater the proportion of the external noise in the total interference, and the greater the impact on the mutual information.

与TN₁的先验概率p₁的关系。在M相同的系统中，n的增大会导致ISI和IUI的干扰变大，互信息因此而有小幅度地降低，但这种幅度随着系统用户的增多而越来越小。Figure 6 shows the achievable mutual information when the number of TNs M takes different values and sets 3 different numbers of time slots for systems with different values of M

Relationship to the prior probability p ₁ of TN ₁ . In a system with the same M, the increase of n will cause the interference of ISI and IUI to become larger, and the mutual information will therefore decrease slightly, but this magnitude will become smaller and smaller as the number of system users increases.

Claims (1)

1. a channel capacity optimization method based on a multi-user molecular communication model of diffusion, is characterized in that: described optimization method comprises the following steps: The first step is to use the normal distribution to approximate the binomial distribution to obtain the number of molecules received by the nanomachine at the receiver of the current time slot; The second step is to establish the hypothesis detection channel model of the diffusion-based multi-user molecular communication model; In the third step, the mathematical expression of the optimal decision threshold is obtained by using the normal distribution, so as to obtain the optimal decision threshold η; The fourth step is to obtain the optimal channel capacity value based on the optimal decision threshold η; In the first step, in the binary diffusion-based multi-user molecular communication model, the input and output are both binary information bits 1 or 0, and OOK is used as the modulation technique, that is, the sender nanomachine TN is expressed by releasing a certain number of molecules. Sending bit 1 and not releasing any molecule means sending bit 0. Once the molecule is released into the biological environment, it will diffuse freely. When it moves to the detection range of the receiving nanomachine RN, it will be immediately absorbed and no longer exist in the biological environment. , after the transmitter nanomachine releases the molecule, the motion form of the molecule in the medium will follow the Brownian motion law, the probability density distribution function of the time t required for a molecule to travel from the transmitter nanomachine TN _i to the receiver nanomachine with a distance d _i f(t) is, 1≤i≤M:

Among them, d is the distance from the sender's nanomachine to the center of the receiver's nanomachine, and D is the diffusion coefficient of the biological environment. The probability of arrival is expressed as F _i (t,d _i ) as follows:

Considering the time-slotted diffusion molecular communication model, it is assumed that all molecules received events occur at discrete time points, and the information transmission time is divided into time-slot intervals of equal size, denoted as T=nt _s , where T is the information transmission time time, _ts is the duration of each time slot, n is the number of divided time slots; At the beginning of the nkth time slot, 1≤k≤n-1, TN _i releases Q _i numerators to send bit 1, no molecule to send bit 0, P _i (k) represents the release of the nkth time slot The probability that the numerator is received in the nth time slot is calculated as follows: P _i (k)=Fi ₍ (k+1)t _s ) _{−Fi (kt s )} Assuming that the number of molecules released by TN _i in the nk th time slot and received by the RN in the current n th time slot is represented by _Ni (k), _Ni (k) obeys the following binomial distribution: N _i (k)～B(Q _i ,P _i (k)) Since the value of P _i (k) is around 0.1, the binomial distribution obeyed by the random variable N _i (k) can be approximated by a normal distribution. The approximate distribution formula is as follows:

Assuming that the optimal decision threshold of the current time slot is η, if Ni (k) _≥η , then RN outputs 1; if Ni ( _k )<η, then RN outputs 0; Due to the randomness of Brownian motion, the remaining numerators not received by RN in the previous time slots will cause inter-symbol interference to subsequent bit receptions. Therefore, for the current time slot n, the (n-1) time slots generated by TN _i before The number of all interfering molecules is

express,

The normal distribution obeyed is expressed as follows:

For a diffusion-based multi-user molecular communication system, multiple sender nanomachines share the channel, and the RN will receive molecules from other TNs and cause inter-user interference. Therefore, for the current time slot n, TN _j , the current time slot and the previous ( The molecular sum of all interferences generated by n-1) time slot is denoted as

1≤j≤M, j≠i, the normal distribution obeyed is expressed as follows:

Considering that RN makes some unavoidable errors in statistical information molecules, an external noise is introduced, which is usually assumed to obey

the normal distribution of , where μ _C and

are the mean and variance of the noise, respectively; The total number of numerators _yi [n] received by TN _i in the current time slot n consists of four parts: 1) numerators sent by TN _i in the nth time slot, denoted by _Ni [n]; 2) numerators generated by ISI, use

Representation; 3) The molecule produced by IUI, with

means; 4) External noise, with

represents, assuming that the total number of molecules disturbed by _TNi is given by

means, there is

therefore:

In the second step, let

and Y _n represent the input and output of the current slot, respectively,

Indicates the false alarm rate, that is, the probability that the input of TN _i is 0 and the output of RN is 1;

represents the detection rate, that is, the probability that the input of _TN is 1 and the output of RN is 1; they are respectively defined as follows:

use

Represents the number of numerators sent by TN _i in the current nth time slot of the RN, H ₀ and H ₁ represent the situation of sending 0 and 1 in the current time slot respectively, with continuous random variables

A binary hypothesis testing problem for observations:

Therefore, this binary hypothesis testing model can be transformed into:

The parameters of the above normal distribution are as follows:

In the third step, the optimal detection scheme is realized by using the minimum error probability criterion, and the minimum error probability judgment criterion is:

Among them, P(H ₀ ) and P(H ₁ ) are the probabilities of sending 0 and 1 respectively in the current time slot, that is, P(H ₁ )= _pi , P(H ₀ )=1- _pi , p(z |H ₀ ) and p(z|H ₁ ) represent the probability that the RN receives z molecules when 0 and 1 are sent in the current time slot, respectively; the likelihood ratio is represented by Λ(z), which is determined by the minimum error probability above. The formula for calculating the likelihood ratio of the criterion is:

in,

and

are the probability density functions of the normal distributions obeyed by H ₀ and H ₁ , respectively, then the likelihood ratio satisfies:

Taking the natural logarithm on both sides of the equation, we get:

To solve z further, we get:

Among them, η is the best threshold, and the parameters A, B, and C are:

In the fourth step, the false alarm rate is calculated using the cumulative distribution function of the normal distribution

and detection rate

Calculated as follows:

in

Through the above calculation formula, the channel capacity of the diffusion molecular communication model can be optimized. The calculation formula of the channel capacity is as follows: C=maxI(X;Y) in

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