阅读说明：本技术 一种单跳移动的分子通信模型的信道容量和比特错误率分析方法 (Channel capacity and bit error rate analysis method of single-hop mobile molecular communication model ) 是由 程珍 涂宇淳 李燕君 池凯凯 夏明� 于 2019-09-20 设计创作，主要内容包括：一种单跳移动的分子通信模型的信道容量和比特错误率分析方法,包括以下步骤：第一步,利用泊松分布逼近二项分布得到当前时隙RN收到分子的个数；第二步,建立单跳移动的分子通信模型的假设检测信道模型；第三步,采用最小误差准则得到了最优决策阈值ξ<Sub>opt</Sub>的数学表达式；第四步,在最优决策阈值ξ<Sub>opt</Sub>基础上,获得最优的信道容量的和比特错误率。本发明为设计高信道容量和低比特错误率的单跳移动的分子通信系统提供了技术支撑。(A channel capacity and bit error rate analysis method for a single-hop mobile molecular communication model comprises the following steps of obtaining the number of molecules received by a current time slot RN by utilizing Poisson distribution to approach binomial distribution, establishing an assumed detection channel model of the single-hop mobile molecular communication model, and obtaining an optimal decision threshold ξ by adopting a minimum error criterion opt Fourth step, at the optimal decision threshold ξ opt On the basis, the optimal channel capacity and bit error rate are obtained. The invention provides technical support for designing a single-hop mobile molecular communication system with high channel capacity and low bit error rate.)

1. A channel capacity and bit error rate analysis method of a molecular communication model of single-hop mobility, the analysis method comprising the steps of:

firstly, obtaining the number of received molecules of the RN at the current time slot by utilizing the Poisson distribution to approach to binomial distribution;

secondly, establishing a hypothesis detection channel model of the single-hop mobile molecular communication model;

thirdly, the minimum error criterion is adopted to obtain the optimal decision threshold ξ_optThe mathematical expression of (a);

the fourth step is at the optimal decision threshold ξ_optOn the basis, the optimal values of the channel capacity and the bit error rate are obtained.

2. The method of claim 1, wherein the channel capacity and bit error rate of the molecular communication model of single hop mobility are analyzed by: in the first step, a one-dimensional diffusion molecular communication system composed of a sender nano machine TN, a receiver nano machine RN and a fluid medium is considered, and the environment is assumed to be large enough to enable the boundary not to limit the propagation, wherein the TN and the RN are separated by a certain distance and are positioned on the same straight line; assuming that TN and RN are completely synchronized in time, the transmission time of the molecules is divided into time slots of the same size, denoted as t ═ nT_s(ii) a Where T is the time of information transmission, T_sN is the number of divided slots for each slot duration, and at the beginning of each slot, the number of TN transmissions is Q_AThe information molecule of (1) represents bit 1, the non-transmitted molecule represents bit 0, the information molecule is released, freely diffuses to the detection range of RN via the fluid medium, is absorbed by RN, the motion of the molecule follows the Brownian motion rule, the distance between TN and RN does not change with time assuming the fixed positions of the TN and RN, and the collision effect between the molecules is not considered, then the probability density function f (t) describing the time t for any one molecule to reach RN from TN is expressed as:

wherein d is₀Distance between TN and RN, D_AThe diffusion coefficient of the type A information molecules in the fluid environment is represented, and the TN and the RN are not fixed and randomly change in position along with time, and the coordinates of the TN and the RN at the beginning of the kth time slot are respectively recorded as

in particular, the initial distance of TN and RN is

wherein the content of the first and second substances,

assuming that the motion of TN and RN are independent of each other and they cannot cross each other, the probability density distribution function satisfied by the time when the information molecule first enters the RN detection range after k time slots is as follows:

wherein D is_tot＝D_TN+D_RN，D_p,eff＝D_RN+D_AF (t) is a probability density distribution function defined by the formula (1), d₀For initial distances of TN and RN, erf (x) is a standard error function, i.e.

will slot cycle T_sDividing into M equal parts, and dividing the time interval t₀Called sample time, and assumes t₀Large enough to ensure mutual independence between the two samples, then there are:

t₀＝T_s/M (7)

by t_mRepresents the mth sample time in a bit gap, i.e. there is:

t_m＝mt₀(8)

the mth sample time t (n, m) for the RN to receive the nth bit slot is expressed as:

t(n,m)＝(n-1)T_s+t_m(9)

note N (t (N, m)) as the number of information molecules sent out by the TN in the current bit slot when the RN receives the TN at the mth sample time of the nth bit slot, since the motion of the information molecules follows the brownian motion law and is independent of each other, the molecules are only received and not received by the RN at a certain time, so N (t (N, m)) will obey the binomial distribution, and when the number of molecules released by the TN is large enough and the probability that the molecules are successfully received by the RN is small, the binomial distribution can be approximated by the poisson distribution, so N (t (N, m)) will obey the poisson distribution, and note the mean value thereof as the poisson distribution

as can be seen from the above formula, since the sum of the multiple Poisson random variables still obeys the Poisson distribution, N [ N ]]Is a Poisson random variable, the mean value of which is recorded as

Assuming that a bit sequence set transmitted by a TN is represented by S, S ═ S [1 ] is satisfied],S[2],...,S[n]}，S[n]E {0,1}, so a bit sequence has been sent at TNGiven the known premise, N [ N ]]The cumulative distribution function obeyed is expressed as follows:

wherein ξ represents the detection threshold of the RN;

due to the randomness of molecular brownian motion, the molecules released by the TN at the current time slot are not necessarily all absorbed by the RN in one signal period, and the type of the information molecules sent out by each time slot is the same, so that the current time slot is interfered by the molecules sent out by the TN at the previous time slot, i.e. intersymbol interference ISI, and if the total number of the molecules received by the RN from the TN at the current time slot N is N^C[n]The total number of molecules generated by ISI interference is N^ISI[n]Then the RN receives the total number of received numerators y [ n ] in the current time slot n]Expressed as:

y[n]＝N^C[n]+N^ISI[n](12)

suppose that the number of the molecules sent out by the TN in the ith bit slot and received by the RN at the mth sample time of the nth bit slot is N_i(n, m) is the mean value thereof

wherein Q is_ARepresenting the number of molecules released when TN transmits bit 1, F (t (n-i +1, m)) and F (t (n-i +1, m-1)) can be calculated by combining equation (6) and equation (10);

from the above analysis, the RN receives the message from N at the current nth time slot^C[n]Is a Poisson random variable, i.e. N^C[n]～Poisson(λ_C)，λ_CRepresents the mean of the Poisson distribution, if p is used₁Indicates the probability that TN sends bit 1 and the probability that TN sends bit 0 is (1-p)₁) Then, according to equation (13), the mean value λ_CThe following equation is satisfied:

similarly, since the sum of the multiple Poisson random variables still obeys Poisson distribution, N is^ISI[n]Satisfies N^ISI[n]～Poisson(λ_ISI) Mean value of λ_ISIComprises the following steps:

3. the method for analyzing channel capacity and bit error rate of a molecular communication model of single-hop mobility according to claim 1 or 2, wherein: in the second step, H₀And H₁Representing events assuming that TN transmits 0 and 1, respectively, in the current time slot, and that X_nIndicating the input of TN at the current nth time slot, Y_nThen represents the corresponding output of RN in the nth time slot, and supposing that TN input is 0 and RN output is 1, i.e. the probability of false alarm rate P_FRepresents; probability of TN input being 1 and RN output being 1, i.e. detection rate P_DIs expressed according to P_FAnd P_DThe definition of (1) is as follows:

by Z_nIndicating the number of received molecules in the current nth time slot, then combining with H₀And H₁Two cases whereby one takes into account a random variable Z_nBinary hypothesis test problem for observations:

wherein N is^ISI[n]And N^C[n]Can be obtained from the formula (13) by expressing the random variable Z by Z_nA value of (1), then Z_nAt H₀And H₁Both cases obey a poisson distribution, i.e. satisfy:

wherein λ is₀And λ₁Respectively expressed under the assumed condition H₀And H₁In this case, the number z of received numerators in the current nth slot of the RN follows the mean value of the poisson distribution, and the mean value of ISI interference obtained according to equations (14) and (15) and the mean value of the total number of received numerators in the current slot of the RN are calculated by combining the parameters of the poisson distribution of equation (18) as follows:

λ₀＝λ_ISI

4. the method for analyzing channel capacity and bit error rate of a molecular communication model of single-hop mobility according to claim 1 or 2, wherein: in the third step, according to the above hypothesis testing model, the optimal detection scheme is obtained by adopting the minimum error criterion:

wherein, P (H)₁)＝p₁Denotes the probability that TN sends bit 1, P (H)₀)＝1－p₁Representing the probability that TN sends bit 0, P (z | H)₁) And P (z | H)₀) The probability that the RN receives z molecules under the two events is represented by lambda (z) similarlyHowever, as can be seen from equation (20), the likelihood ratio calculation equation is:

wherein the content of the first and second substances,

therefore, we can get the likelihood ratio as:

combining with equation (23), taking the natural logarithm on both sides of the equation, we get:

by ξ_optRepresenting the best decision threshold, equation (24) is further solved:

5. the method for analyzing the channel capacity and the bit error rate of the molecular communication model with single-hop mobility as claimed in claim 1 or 2, wherein in the fourth step, the optimal decision threshold ξ is set_optOn the basis, the optimal information is obtainedValues of track capacity and bit error rate;

according to the optimum threshold ξ_optBy combining the definitions of the detection rate and the false alarm rate in the formula (16), P is not difficult to obtain_D，P_FThe calculation result of (a) is expressed as follows:

X_nand Y_nMutual information of I (Y)_n|X_n)Expressed as:

according to the knowledge of information theory, the calculation formula of the channel capacity C is obtained by combining the formula (27) as follows:

C＝max(I(X_n；Y_n)) (28)

according to the definition of the bit error rate, namely the ratio of the bits with transmission errors to the total number of the transmitted bits in a period of time, considering the probability of two error conditions of TN transmission 1, RN judgment 0 and TN transmission 0, RN judgment 1, combining the bit error rate of RN receiving information from TN obtained by formula (26), and using P_eExpressed as:

P_e＝p₁(1-P_D)+(1-p₁)P_F(29)。

6. the method for analyzing channel capacity and bit error rate of a molecular communication model of single-hop mobility according to claim 1 or 2, wherein: the method further comprises the steps of:

and fifthly, the influence of different parameters on mutual information and bit error rate is shown through experimental simulation.

Technical Field

The invention relates to biotechnology, nanotechnology and communication technology, in particular to a channel capacity and bit error rate analysis method of a single-hop mobile molecular communication model.

Background

Since molecular communication is distinguished from the characteristics of conventional communication technologies and is suitable for many specific application environments (e.g., in the human body), molecular communication based on biological elicitation is widely recognized by academia as one of the most feasible communication technologies to implement nano-networks. Currently, research on molecular communication is mainly focused on a static molecular communication model in which a transmitting-side nanomachine, a relaying nanomachine, and a receiving-side nanomachine are fixed. In mobile molecular communication, nanomachines are in a mobile state, which is more common in many practical applications (e.g., drug delivery in human body, health monitoring, target detection, etc.). Therefore, mobile molecular communication is the most important and practical molecular communication mode in the nano network. In a mobile molecular communication model, a sender nanomachine TN (transmitter nanomachine) and a receiver nanomachine RN (receiver nanomachine) respectively represent that the sender and the receiver in the model, and the TN and the RN are in a mobile state, and the position change of the TN and the RN is random. Therefore, the distance between the TN and the RN is in an uncertain state within one slot.

In the mobile molecular communication model, since the molecule follows the brownian motion rule, the nanomachines have mobility, and all the previous time slots are inevitably present for intersymbol interference of the receiving nanomachines in the current time slot. Therefore, the research of the mobile-based molecular communication model also faces more challenges, and one of the challenges is how to improve the channel capacity and reduce the bit error rate analysis method of the single-hop mobile molecular communication model under the condition of considering intersymbol interference and the mobility of the nanomachines.

Disclosure of Invention

In order to overcome the defects of low channel capacity and high bit error rate of a single-hop mobile molecular communication model of the existing channel analysis method and research the influence of the mobility of a nanometer machine on the channel capacity of the molecular communication model, the invention provides an analysis method for effectively improving the channel capacity of the single-hop mobile molecular communication model and reducing the bit error rate.

In order to solve the technical problems, the invention adopts the following technical scheme:

a channel capacity and bit error rate analysis method of a molecular communication model of single-hop mobility, the channel capacity optimization method comprising the steps of:

firstly, obtaining the number of molecules received by the RN at the current time slot by utilizing the Poisson distribution to approach to binomial distribution;

considering a one-dimensional diffusion molecular communication system composed of a sender nanomachine TN, a receiver nanomachine RN and a fluid medium, and assuming that the environment is large enough so that the boundary does not limit propagation, TN and RN are separated by a certain distance and are positioned on the same straight line; assuming that TN and RN are completely synchronized in time, the transmission time of the molecules is divided into time slots of the same size, denoted as t ═ nT_s(ii) a Where T is the time of information transmission, T_sFor each slot duration, n is the number of divided slots. At the beginning of each time slot, the number of TN transmissions is Q_AThe information molecule of (1) represents bit 1, and no molecule is transmitted represents bit 0; after the information molecules are released, the information molecules freely diffuse to the detection range of the RN through a fluid medium and are absorbed by the RN; the motion of the molecule follows the brownian rule of motion; assuming that the positions of TN and RN are fixed, the distance between them does not change with time, and the collision effect between molecules is not considered, the probability density function f (t) describing the time t for any one molecule to arrive at RN from TN is expressed as:

wherein d is₀Distance between TN and RN, D_ARepresenting the diffusion coefficient of the type A information molecules in the fluid environment; let TN and RN be unfixed and their positions vary randomly with time, let TN and RN coordinate at the beginning of k-th slot as

Their motion is describedIs composed of a series ofConstructed so that the distance d between TN and RN at the beginning of the k-th slot_kIs represented as follows:

in particular, the initial distance of TN and RN is

By Δ x_uU e { TN, RN } indicates that TN and RN are in one time slot T_sRandom shift done internally, then the coordinates of TN and RN at the beginning of the k-th slot satisfy

Wherein, Δ x_uObedience mean 0, variance 2D_uT_sOf a Gaussian distribution, i.e. Δ x_u～(0,2D_uT_s)，D_uRepresents the diffusion coefficients of TN and RN in a fluid environment, and therefore, the variables

And d_kThe following gaussian distributions will be satisfied:

wherein the content of the first and second substances,

assuming that the motion of TN and RN are independent of each other and they cannot cross each other, the probability density distribution function satisfied by the time when the information molecule first enters the RN detection range after k time slots is as follows:

wherein D is_tot＝D_TN+D_RN，D_p,eff＝D_RN+D_AF (t) is a probability density distribution function defined by the formula (1), d₀For initial distances of TN and RN, erf (x) is a standard error function, i.e.

The cumulative distribution function F (t; k) of F (t; k) can be used to describe the probability that a molecule will reach RN from TN before starting from t ═ 0 to t, i.e.:

will slot cycle T_sDividing into M equal parts, and dividing the time interval t₀Called sample time, and assumes t₀Large enough to ensure mutual independence between the two samples, then there are:

t₀＝T_s/M (7)

by t_mRepresents the mth sample time in a bit gap, i.e. there is:

t_m＝mt₀(8)

the mth sample time t (n, m) for the RN to receive the nth bit slot is expressed as:

t(n,m)＝(n-1)T_s+t_m(9)

taking N (t (N, m)) as the number of information molecules sent out by the TN at the current bit slot when the RN receives the message at the mth sample time of the nth bit slot, since the motion of the information molecules follows the Brownian motion law and is independent of each other, the molecules are only received and not received by the RN at a certain time, so that N (t (N, m)) obeys a binomial distribution, and when the number of molecules released by the TN is large enough and the probability of successfully receiving the molecules by the RN is small, the binomial distribution can be approximated by a Poisson distribution; thus, N (t (N, m)) will be poisedThe loose distribution is recorded as

Then, the RN receives the total number of received numerators N [ N ] in the nth time slot]Is represented as follows:

as can be seen from the above formula, since the sum of the multiple Poisson random variables still obeys the Poisson distribution, N [ N ]]Is a Poisson random variable, the mean value of which is recorded as

Then there is

Assuming that a bit sequence set transmitted by a TN is represented by S, S ═ S [1 ] is satisfied],S[2],...,S[n]}，S[n]E {0,1}, so a bit sequence has been sent at TN

Given the known premise, N [ N ]]The cumulative distribution function obeyed is expressed as follows:

wherein ξ represents the detection threshold of the RN;

due to the randomness of molecular brownian motion, molecules released by the TN at the current time slot are not necessarily all absorbed by the RN in one signal period, and the types of information molecules sent out by each time slot are the same, so that the current time slot is interfered by the molecules sent out by the TN at the previous time slot, namely intersymbol interference ISI; if the total number of the molecules received by RN from TN at the current time slot N is recorded as N^C[n]The total number of molecules generated by ISI interference is N^ISI[n]Then the RN receives the total number of received numerators y [ n ] in the current time slot n]Expressed as:

y[n]＝N^C[n]+N^ISI[n](12)

suppose that the number of the molecules sent out by the TN in the ith bit slot and received by the RN at the mth sample time of the nth bit slot is N_i(n, m) is the mean value thereof

The calculation expression is as follows:

wherein Q is_ARepresenting the number of molecules released when TN transmits bit 1, F (t (n-i +1, m)) and F (t (n-i +1, m-1)) can be calculated by combining equation (6) and equation (10);

from the above analysis, the RN receives the message from N at the current nth time slot^C[n]Is a Poisson random variable, i.e. N^C[n]～Poisson(λ_C)，λ_CRepresents the mean of the Poisson distribution, if p is used₁Indicates the probability that TN sends bit 1 and the probability that TN sends bit 0 is (1-p)₁) Then, according to equation (13), the mean value λ_CThe following equation is satisfied:

similarly, since the sum of the multiple Poisson random variables still obeys Poisson distribution, N is^ISI[n]Satisfies N^ISI[n]～Poisson(λ_ISI) Mean value of λ_ISIComprises the following steps:

secondly, establishing a hypothesis detection channel model of the single-hop mobile molecular communication model;

H₀and H₁Representing events assuming that TN transmits 0 and 1, respectively, in the current time slot, and that X_nIndicating the input of TN at the current nth time slot, Y_nThen represents the corresponding output of RN in the nth time slot, and supposing that TN input is 0 and RN output is 1, i.e. the probability of false alarm rate P_FTo represent(ii) a Probability of TN input being 1 and RN output being 1, i.e. detection rate P_DIs expressed according to P_FAnd P_DThe definition of (1) is as follows:

by Z_nIndicating the number of received molecules in the current nth time slot, then combining with H₀And H₁Two cases whereby one takes into account a random variable Z_nBinary hypothesis test problem for observations:

wherein N is^ISI[n]And N^C[n]Can be obtained from the formula (13) by expressing the random variable Z by Z_nA value of (1), then Z_nAt H₀And H₁Both cases obey a poisson distribution, i.e. satisfy:

wherein λ is₀And λ₁Respectively expressed under the assumed condition H₀And H₁In this case, the number z of received numerators in the current nth slot of the RN follows the mean value of the poisson distribution, and the mean value of ISI interference obtained according to equations (14) and (15) and the mean value of the total number of received numerators in the current slot of the RN are calculated by combining the parameters of the poisson distribution of equation (18) as follows:

λ₀＝λ_ISI

thirdly, the minimum error criterion is adopted to obtain the optimal decision threshold ξ_optThe mathematical expression of (a);

according to the hypothesis testing model, the optimal detection scheme is obtained by adopting a minimum error criterion:

wherein, P (H)₁)＝p₁Denotes the probability that TN sends bit 1, P (H)₀)＝1－p₁Representing the probability that TN sends bit 0, P (z | H)₁) And P (z | H)₀) And respectively corresponding to the probability that the RN receives z molecules under the two events, and expressing the likelihood ratio by using lambada (z), wherein the likelihood ratio is calculated by the formula (20):

wherein the content of the first and second substances,

and

respectively under the assumption condition H₀And H₁In this case, the probability density function of the poisson distribution to which the RN receives z molecules is expressed as follows:

therefore, the likelihood ratio is obtained from equations (21) and (22):

combining with equation (23), taking the natural logarithm on both sides of the equation, we get:

by ξ_optRepresenting the best decision threshold, equation (24) is further solved:

the fourth step is at the optimal decision threshold ξ_optOn the basis, obtaining the optimal values of the channel capacity and the bit error rate;

according to the optimum threshold ξ_optBy combining the definitions of the detection rate and the false alarm rate in the formula (16), P is not difficult to obtain_D，P_FThe calculation result of (a) is expressed as follows:

X_nand Y_nMutual information of I (Y)_n|X_n)Expressed as:

according to the knowledge of information theory, the calculation formula of the channel capacity C is obtained by combining the formula (27) as follows:

C＝max(I(X_n；Y_n)) (28)

according to the definition of the bit error rate, namely the ratio of the bits with transmission errors to the total number of the transmitted bits in a period of time, considering the probability of two error conditions of TN transmission 1, RN judgment 0 and TN transmission 0, RN judgment 1, combining the bit error rate of RN receiving information from TN obtained by formula (26), and using P_eExpressed as:

P_e＝p₁(1-P_D)+(1-p₁)P_F(29)。

further, the method comprises the following steps:

and fifthly, the influence of different parameters on mutual information and bit error rate is shown through experimental simulation.

The technical conception of the invention is as follows: the invention fully combines the random behavior of the movement of molecules in the biological environment in a mobile molecular communication model and the characteristic of the mobility of a nanometer machine, and researches the channel capacity optimization scheme of the single-hop mobile molecular communication model. In a mobile molecular communication system, the nanomachines are all in motion, and the distance between the nanomachines and the communication channel characteristics will vary over time. Therefore, it is important to study the influence of the mobility of the transmitting and receiving nanomachines on the communication capability of the mobile molecular communication system. Under the condition of considering intersymbol interference, it is important to study how to improve the channel capacity and reduce the bit error rate of the molecular communication model of single-hop mobility. The invention mainly develops the communication technology which can be used for the nano network and takes the molecular communication as the basis for the optimal channel capacity and the lowest bit error rate. Different system parameters are set, and a mathematical expression of an optimal decision threshold is obtained by adopting a minimum error criterion, so that the channel capacity and the bit error rate are optimized.

The method has the advantages that 1, under the condition of considering the intersymbol interference of all the previous time slots to the current time slot, the probability that different sending party nanometer machines send 1 or 0 in each time slot is considered, the number of molecules received by RN of the current time slot is obtained by utilizing the Poisson distribution to approach to binomial distribution, 2, on the basis, a hypothesis detection channel model of a single-hop mobile molecular communication model is established, and 3, the optimal decision threshold ξ is obtained by adopting the minimum error criterion_opt4, at the optimal decision threshold ξ_optOn the basis, the optimal values of the channel capacity and the bit error rate are obtained. 5. The effect of different parameters on mutual information and bit error rate is shown. The larger the spreading factor of the TN and RN, i.e. the stronger their mobility, the lower the channel capacity of the system, and the greater the uncertainty in the position of the TN and RN over time (the increase in the number of slots k), which also leads to a reduction in the channel capacity of the system. Meanwhile, the initial distance between the TN and the RN is reduced, the time slot length is prolonged, and the number of molecules transmitted by each time slot is increased, so that the channel capacity of a system is improved, and the bit error rate is reduced. Therefore, parameter setting provides technical support for designing a single-hop mobile molecular communication system with high channel capacity and low bit error rate.

Drawings

Fig. 1 is a single hop mobile molecular communication system. Wherein d is₁And d₂Is the distance between TN and RN at the beginning of 1,2 time slots.

FIG. 2 shows the period length T_sTaking the number of molecules Q sent by the mutual information I (X, Y) of the TN and the RN along with each time slot of the TN under the three conditions of 0.01ms, 0.1ms and 1ms respectively_AIncreasing the tendency to change.

FIG. 3 shows the initial distance d between TN and RN₀When different, the prior probability p of mutual information I (X, Y) of TN and RN along with TN₁Increasing change relation graph.

FIG. 4 shows that_ATaking different values, the mutual information I (X, Y) and the prior probability p₁The relationship (2) of (c).

FIG. 5 shows the prior probability p of mutual information I (X, Y) of TN and RN with TN when the number k of time slots takes three different values of 3, 20 and 50₁Increasing the variation relationship.

FIG. 6 shows_TNTaking different values, the mutual information I (X, Y) and the prior probability p₁The relationship (2) of (c).

Fig. 7 shows a variation trend of the bit error rate of the single-hop mobile molecular communication network with an increase in the number of molecules released per bit gap of the TN when the detection thresholds are different.

FIG. 8 shows that_TNAt different values of the bit error rate P_eAnd Q_AThe relationship (2) of (c).

Detailed Description

The invention is further described below with reference to the accompanying drawings.

Referring to fig. 1 to 8, a channel capacity and bit error rate analysis method of a single-hop moving molecular communication model includes the following steps:

firstly, obtaining the number of molecules received by the RN at the current time slot by utilizing the Poisson distribution to approach to binomial distribution;

considering a one-dimensional diffusion molecular communication system composed of a sender nanomachine TN, a receiver nanomachine RN and a fluid medium, and assuming that the environment is large enough so that the boundary does not limit propagation, TN and RN are separated by a certain distance and are positioned on the same straight line; assuming that TN and RN are perfectly synchronized in time, the molecular transit times are divided to be of the same sizeTime slot (t) is expressed as nT_s(ii) a Where T is the time of information transmission, T_sFor each slot duration, n is the number of divided slots. At the beginning of each time slot, the number of TN transmissions is Q_AThe information molecule of (1) represents bit 1, and no molecule is transmitted represents bit 0; after the information molecules are released, the information molecules freely diffuse to the detection range of the RN through a fluid medium and are absorbed by the RN; the motion of the molecule follows the brownian rule of motion; assuming that the positions of TN and RN are fixed, the distance between them does not change with time, and the collision effect between molecules is not considered, the probability density function f (t) describing the time t for any one molecule to arrive at RN from TN is expressed as:

wherein d is₀Distance between TN and RN, D_ARepresenting the diffusion coefficient of the type A information molecules in the fluid environment; let TN and RN be unfixed and their positions vary randomly with time, let TN and RN coordinate at the beginning of k-th slot as

Their motion is described as consisting of a series of

Constructed so that the distance d between TN and RN at the beginning of the k-th slot_kIs represented as follows:

in particular, the initial distance of TN and RN is

By Δ x_uU e { TN, RN } indicates that TN and RN are in one time slot T_sRandom shift done internally, then the coordinates of TN and RN at the beginning of the k-th slot satisfy

Wherein, Δ x_uObedience mean 0, variance 2D_uT_sOf a Gaussian distribution, i.e. Δ x_u～(0,2D_uT_s)，D_uRepresents the diffusion coefficients of TN and RN in a fluid environment, and therefore, the variables

And d_kThe following gaussian distributions will be satisfied:

wherein the content of the first and second substances,

assuming that the motion of TN and RN are independent of each other and they cannot cross each other, the probability density distribution function satisfied by the time when the information molecule first enters the RN detection range after k time slots is as follows:

wherein D is_tot＝D_TN+D_RN，D_p,eff＝D_RN+D_AF (t) is a probability density distribution function defined by the formula (1), d₀For initial distances of TN and RN, erf (x) is a standard error function, i.e.

The cumulative distribution function F (t; k) of F (t; k) can be used to describe the probability that a molecule will reach RN from TN before starting from t ═ 0 to t, i.e.:

will slot cycle T_sDividing into M equal parts, and dividing the time interval t₀Called sample time, and assumes t₀Large enough to ensure mutual independence between the two samples, then there are:

t₀＝T_s/M (7)

by t_mRepresents the mth sample time in a bit gap, i.e. there is:

t_m＝mt₀(8)

the mth sample time t (n, m) for the RN to receive the nth bit slot is expressed as:

t(n,m)＝(n-1)T_s+t_m(9)

taking N (t (N, m)) as the number of information molecules sent out by the TN at the current bit slot when the RN receives the message at the mth sample time of the nth bit slot, since the motion of the information molecules follows the Brownian motion law and is independent of each other, the molecules are only received and not received by the RN at a certain time, so that N (t (N, m)) obeys a binomial distribution, and when the number of molecules released by the TN is large enough and the probability of successfully receiving the molecules by the RN is small, the binomial distribution can be approximated by a Poisson distribution; thus, N (t (N, m)) will obey a Poisson distribution, taking the mean as

Then, the RN receives the total number of received numerators N [ N ] in the nth time slot]Is represented as follows:

as can be seen from the above formula, since the sum of the multiple Poisson random variables still obeys the Poisson distribution, N [ N ]]Is a Poisson random variable, the mean value of which is recorded as

Then there is

Assuming that a bit sequence set transmitted by a TN is represented by S, S ═ S [1 ] is satisfied],S[2],...,S[n]}，S[n]E {0,1}, so a bit sequence has been sent at TN

Given the known premise, N [ N ]]The cumulative distribution function obeyed is expressed as follows:

wherein ξ represents the detection threshold of the RN;

due to the randomness of molecular brownian motion, molecules released by the TN at the current time slot are not necessarily all absorbed by the RN in one signal period, and the types of information molecules sent out by each time slot are the same, so that the current time slot is interfered by the molecules sent out by the TN at the previous time slot, namely intersymbol interference ISI; if the total number of the molecules received by RN from TN at the current time slot N is recorded as N^C[n]The total number of molecules generated by ISI interference is N^ISI[n]Then the RN receives the total number of received numerators y [ n ] in the current time slot n]Expressed as:

y[n]＝N^C[n]+N^ISI[n](12)

suppose that the number of the molecules sent out by the TN in the ith bit slot and received by the RN at the mth sample time of the nth bit slot is N_i(n, m) is the mean value thereof

The calculation expression is as follows:

wherein Q is_ARepresenting the number of molecules released when TN transmits bit 1, F (t (n-i +1, m)) and F (t (n-i +1, m-1)) can be calculated by combining equation (6) and equation (10);

from the above analysis, the RN receives the message from N at the current nth time slot^C[n]Is a Poisson random variable, i.e. N^C[n]～Poisson(λ_C)，λ_CRepresents the mean of the Poisson distribution, if p is used₁Indicates the probability that TN sends bit 1 and the probability that TN sends bit 0 is (1-p)₁) Then, according to equation (13), the mean value λ_CThe following equation is satisfied:

similarly, since the sum of the multiple Poisson random variables still obeys Poisson distribution, N is^ISI[n]Satisfies N^ISI[n]～Poisson(λ_ISI) Mean value of λ_ISIComprises the following steps:

secondly, establishing a hypothesis detection channel model of the single-hop mobile molecular communication model;

H₀and H₁Representing events assuming that TN transmits 0 and 1, respectively, in the current time slot, and that X_nIndicating the input of TN at the current nth time slot, Y_nThen represents the corresponding output of RN in the nth time slot, and supposing that TN input is 0 and RN output is 1, i.e. the probability of false alarm rate P_FRepresents; probability of TN input being 1 and RN output being 1, i.e. detection rate P_DIs expressed according to P_FAnd P_DThe definition of (1) is as follows:

by Z_nIndicating the number of received molecules in the current nth time slot, then combining with H₀And H₁Two cases whereby one takes into account a random variable Z_nBinary hypothesis test problem for observations:

wherein N is^ISI[n]And N^C[n]Can be obtained from the formula (13)By Z is meant the random variable Z_nA value of (1), then Z_nAt H₀And H₁Both cases obey a poisson distribution, i.e. satisfy:

wherein λ is₀And λ₁Respectively expressed under the assumed condition H₀And H₁In this case, the number z of received numerators in the current nth slot of the RN follows the mean value of the poisson distribution, and the mean value of ISI interference obtained according to equations (14) and (15) and the mean value of the total number of received numerators in the current slot of the RN are calculated by combining the parameters of the poisson distribution of equation (18) as follows:

λ₀＝λ_ISI

thirdly, the minimum error criterion is adopted to obtain the optimal decision threshold ξ_optThe mathematical expression of (a);

according to the hypothesis testing model, the optimal detection scheme is obtained by adopting a minimum error criterion:

wherein, P (H)₁)＝p₁Denotes the probability that TN sends bit 1, P (H)₀)＝1－p₁Representing the probability that TN sends bit 0, P (z | H)₁) And P (z | H)₀) And respectively corresponding to the probability that the RN receives z molecules under the two events, and expressing the likelihood ratio by using lambada (z), wherein the likelihood ratio is calculated by the formula (20):

wherein the content of the first and second substances,

and

respectively under the assumption condition H₀And H₁In this case, the probability density function of the poisson distribution to which the RN receives z molecules is expressed as follows:

therefore, the likelihood ratio is obtained from equations (21) and (22):

combining with equation (23), taking the natural logarithm on both sides of the equation, we get:

by ξ_optRepresenting the best decision threshold, equation (24) is further solved:

the fourth step is at the optimal decision threshold ξ_optOn the basis, obtaining the optimal values of the channel capacity and the bit error rate;

according to the optimum threshold ξ_optBy combining the definitions of the detection rate and the false alarm rate in the formula (16), P is not difficult to obtain_D，P_FThe calculation result of (a) is expressed as follows:

X_nand Y_nMutual information of I (Y)_n|X_n)Expressed as:

according to the knowledge of information theory, the calculation formula of the channel capacity C is obtained by combining the formula (27) as follows:

C＝max(I(X_n；Y_n)) (28)

according to the definition of the bit error rate, namely the ratio of the bits with transmission errors to the total number of the transmitted bits in a period of time, considering the probability of two error conditions of TN transmission 1, RN judgment 0 and TN transmission 0, RN judgment 1, combining the bit error rate of RN receiving information from TN obtained by formula (26), and using P_eExpressed as:

P_e＝p₁(1-P_D)+(1-p₁)P_F(29)。

further, the method comprises the following steps:

and fifthly, the influence of different parameters on mutual information and bit error rate is shown through experimental simulation.

FIG. 2 shows the period length T_sTaking the number of molecules Q sent by the mutual information I (X, Y) of the TN and the RN along with each time slot of the TN under the three conditions of 0.01ms, 0.1ms and 1ms respectively_AIncreasing the tendency to change.

FIG. 3 shows the initial distance d between TN and RN₀When different, the prior probability p of mutual information I (X, Y) of TN and RN along with TN₁Increasing change relation graph. Reducing the distance between the TN and the RN will result in a greater probability of the RN receiving the numerator transmitted by the current slot of the TN while reducing ISI, thereby increasing mutual information.

FIG. 4 shows that_ATaking different values, the mutual information I (X, Y) and the prior probability p₁The relationship (2) of (c). D_AThe larger the mutual information of the TN and the RN.

FIG. 5 shows the prior probability p of mutual information I (X, Y) of TN and RN with TN when the number k of time slots takes three different values of 3, 20 and 50₁Increasing the variation relationship.

FIG. 6 shows_TNTaking different values, the mutual information I (X, Y) and the prior probability p₁The relationship (2) of (c). D_TNResults in increased mobility of TN and RN, and D_TNThe smaller the mutual information I (X, Y) is.

FIG. 7 shows the variation trend of the bit error rate of the single-hop mobile molecular communication network with increasing number of molecules released per bit gap of TN when the detection thresholds are different, and Q required to reach the lowest bit error rate when the detection threshold ξ becomes larger_AAnd becomes larger, and the corresponding bit error rate becomes smaller.

FIG. 8 shows that_TNAt different values of the bit error rate P_eAnd Q_AThe relationship (2) of (c). Bit error rate P_eDecreases with increasing number of transmitted molecules per time slot of TN, D_TNThe smaller, the bit error rate P_eThe smaller.