CN110380769B - A short packet communication transmission method based on multi-antenna energy harvesting - Google Patents

Abstract

The invention discloses a short packet communication transmission method based on multi-antenna energy capture. This method applies the multi-day wireless energy transmission technology to the short packet communication scenario for the first time, and uses the energy captured by the source node to send information; according to the spatial distribution of the source node and the user and the zero-forcing beamforming method, the energy of each user is obtained. The cumulative distribution function of signal-to-noise ratio and the approximate closed expression of each user's block error probability are deduced by using the method of Gaussian function approximation. By optimizing the number of time slots in the wireless energy transmission stage and the power allocation coefficient in the wireless information transmission stage, the minimum system block error probability is obtained.

Description

A short packet communication transmission method based on multi-antenna energy harvesting

technical field

The invention belongs to the field of wireless communication, and in particular relates to an ultra-reliable and low-delay application scenario in the fifth-generation cellular mobile communication.

Background technique

As wireless devices become smaller and more energy efficient, energy harvesting is emerging as a potential technology for powering low-power wireless devices. Because radio frequency signals can carry both information and energy, this makes wireless power transfer a particularly attractive technology. Today, most wireless devices are powered by cables or replaceable batteries, which limits energy sustainability and mobility of wireless communications. In practice, wired charging and battery replacement may not be feasible or incur high costs for many wireless applications, such as medical devices implanted in the human body. In addition, wired charging and battery refresh shorten the operating time of wireless mobile devices. Thus, wireless energy transfer serves as an auxiliary technology that enables energy-constrained nodes to harvest energy and send information in a relatively simple and reliable manner, allowing their lifetime to be extended almost indefinitely.

However, due to the inherently smaller data payloads, low latency requirements, and lack of energy resources to support longer transmissions, energy harvesting communication systems will exclusively use short data rates compared to most wireless systems designed for Internet access. Bag. Meanwhile, unlike conventional long packet transmission, machine type communication is realized by burst packets having a very short size. In order to meet the requirements of machine type communication, the fifth-generation cellular mobile communication proposes ultra-reliable and low-latency application scenarios.

The rapid development of the Internet of Things requires that the wireless communication system launched in the future must support more connected devices, and at the same time have strict requirements on delay and reliability. Due to the severe power loss of RF signals, the main challenge of wireless energy transfer based on RF signals is the significant attenuation of energy transfer efficiency over the distance from the energy transmitter to the energy receiver. How to power a potentially large number of IoT nodes and maintain their uninterrupted operation is a major challenge.

Contents of the invention

(1) Technical problems to be solved

In order to improve the reliability of the wireless energy harvesting system, the present invention discloses a short packet communication transmission method based on multi-antenna energy harvesting in the wireless communication system. Antenna to improve energy transfer efficiency. Multiple antennas on the energy transmitter help to focus the transmitted wireless energy in the direction of the energy receiver through digital beamforming or so-called energy beamforming technology, while multiple antennas at the energy receiver increase the received RF signal energy The effective aperture area of the collection, both leading to significantly improved energy transfer efficiency.

(2) Technical solution

In order to solve the above technical problems, the present invention discloses a short packet communication transmission method based on multi-antenna energy capture in a wireless communication system, which includes the following steps:

Step A, the present invention considers the multi-antenna energy capture short-packet communication system, configures multiple antennas for the energy transmitter and the source node, uses the energy captured by the source node to send information, builds a system model according to actual needs, and obtains channel gain matrix;

Step B, according to the system model and channel gain matrix in step A, calculate the energy captured by the source node and optimize it to obtain the maximum value of energy capture;

Step C, according to the energy captured by the source node in the energy capture phase, calculate the transmission power in the information transmission phase, and obtain the signal-to-noise ratio of the user;

Step D, calculating the error probability of the system;

In step E, the minimum system block error probability is obtained by optimizing the number of time slots in the wireless energy transmission phase and the power allocation coefficient in the wireless information transmission phase.

Wherein, step A specifically includes:

A1, the multi-antenna technology is applied to the wireless energy harvesting short packet transmission system. The system consists of an energy transmitter ET, a source node S and K users. Due to the limited energy of the nodes, the users are equipped with single antennas and are distributed in different locations, denoted by U ₁ , U ₂ ,…, U _K respectively; the number of antennas of the energy transmitter ET is M _E , and the number of antennas of the source node is N, where the energy collection and information transmission of the source node S share an antenna;

A2, for the system model of step A1, calculate the channel gain matrix of the energy harvesting stage and the wireless information transmission stage

Wherein, step B specifically includes:

其中，

是第i个传输波束成形向量，s_i是相应的能量信号。在ET处的传输协方差矩阵为

B1, first consider the energy beamforming at the ET, assuming that there are d energy beams at the ET, _1≤d≤ME . The energy signal transmitted at ET is

in,

is the i-th transmit beamforming vector and _si is the corresponding energy signal. The transmission covariance matrix at ET is

B2, from the covariance matrix obtained in step B1, the energy Q=ηTE(||Hx|| ² )=ηTtr(GS) captured by the source node can be obtained, wherein, η is the energy capture efficiency; T is the block length; H is the MIMO channel matrix between the energy transmitter and the source node,

B3. Estimate the length of the data packet according to the number of time slots for energy capture. Assuming that the approximate duration of a continuous-time signal is t and the approximate bandwidth is B, the length of the data packet is: T≈Bt. Therefore, T ≈ BmT _c ;

B4, according to the energy captured by the source node calculated in step B2 and the data packet length in step B3, the maximum value Q ^* = ηBmT _c Pλ ₁ of energy capture is obtained through an optimization method. λ ₁ is the largest eigenvalue of the matrix G, namely

Wherein, step C specifically includes:

C1, the source node uses the captured energy to transmit information with K users. K users communicate with the source node at the same time, and all users have the same block length M, M≈BnT _c , but have different power allocation coefficients β _k when each data packet is transmitted. ;

C2, according to the energy captured in the energy capture stage, calculate the transmission power of the source node

其中，h_k～CN(0_N,Ω_kI_N),k＝1,2,…,K为源节点与U_k之间的N×1信道矢量，Ω_k为源节点与U_k的平均信道功率增益；x_k为源节点给用户k传输的信息；

为加性高斯白噪声；

为源节点的1×N预编码矩阵；v_k,k＝1,2,…,K为信息x_k的一个1×N波束成形矢量，||v_k||＝1；C3, according to the information transmission between the source node and the user, the received signal of user k is obtained

Among them, h _k ～CN(0 _N ,Ω _k I _N ), k=1,2,…, K is the N×1 channel vector between the source node and U _k , Ω _k is the average of the source node and U _k Channel power gain; x _k is the information transmitted by the source node to user k;

is additive white Gaussian noise;

is the 1×N precoding matrix of the source node; v _k ,k=1,2,…,K is a 1×N beamforming vector of information x _k , ||v _k ||=1;

其中，

H_k＝[h₁,h₂,…,h_K]；C4, calculate the signal-to-noise ratio of U _k

in,

H _k = [h ₁ ,h ₂ ,...,h _K ];

Wherein, step D specifically includes:

D1, according to the spatial distribution of the source node and the user and the zero-forcing beamforming method, the cumulative distribution function of the signal-to-noise ratio of each user is obtained

D2, using the method of Gaussian function approximation, deduce the block error probability of each user

Wherein, step E specifically includes:

E1, according to the block error probability of user k obtained in the previous part, simplified and sorted to get

其中约束条件包括：功率分配系数的约束

最大的时延约束0＜δ≤δ_max；E2, by optimizing the number of time slots in the wireless energy transmission phase and the power allocation coefficient in the wireless information transmission phase, the optimization problem can be expressed as (P1):

The constraints include: constraints on the power distribution coefficient

The maximum delay constraint 0<δ≤δ _max ;

E3, the delay δ is directly affected by the number of time slots in the energy capture phase and wireless information transmission phase, therefore, the maximum delay constraint is transformed to 0<m+n≤s, s is a fixed value;

和(P1-b):

其中(P1-a)是给定β_k的m的优化子问题，(P1-b)是给定m的β_k的优化子问题；E4, we divide the problem (P1) into two sub-problems (P1-a):

and (P1-b):

Where (P1-a) is the optimization subproblem of m given β _k , and (P1-b) is the optimization subproblem of β _k given m;

E5, problem (P1-a) is optimized, and its optimal solution m is m ^* =sn, and wherein, s is the maximum total time slot number of WEI and WIT stage;

E6, optimize the problem (P1-b), and its optimal solution β ^* can be obtained by the following formula

E7, according to the optimal solution calculated by E5-E6, the minimum system block error probability is obtained through an iterative algorithm.

(3) Beneficial effects

The present invention improves energy transmission efficiency by equipping multiple antennas at either or both of the energy transmitter and the energy receiver. Multiple antennas on the energy transmitter help to focus the transmitted wireless energy in the direction of the energy receiver through digital beamforming or so-called energy beamforming technology, while multiple antennas at the energy receiver increase the received RF signal energy The effective aperture area of the collection, both leading to significantly improved energy transfer efficiency. That is to say, the present invention utilizes the characteristics of radio frequency signals and the space resources of multi-antenna technology to achieve multiplexing gain and diversity gain, which not only improves the energy transmission efficiency, shortens the energy collection time, but also reduces the error probability and improves the system efficiency. reliability.

Description of drawings

The method flowchart of the embodiment of the present invention of Fig. 1;

System model in the method of the embodiment of the present invention in Fig. 2;

Fig. 3 is a relation diagram of the transmission power PS of the source node and the time slot number m of the _WET stage in the method of the embodiment of the present invention;

Fig. 4 is the block error probability _{ε k} corresponding to different transmission power PS in the method of the embodiment of the present invention;

Fig. 5 is a diagram of the relationship between the total block error probability and the transmission power ratio of the source node in the method of the embodiment of the present invention;

Fig. 6 is the relationship between the block error probability ε _k of user k and the number of time slots (m+n) in the whole process from WET to WIT in the method of the embodiment of the present invention;

Fig. 7 shows the relationship between the total block error probability ε ₀ of user k and the number of time slots (m+n) in the whole process from WET to WIT in the method of the embodiment of the present invention.

Detailed ways

In the short packet communication transmission method based on multi-antenna energy harvesting provided by the present invention, the wireless energy harvesting short packet transmission system is configured with multiple antennas, which can use the spatial dimension to improve energy transmission efficiency and effectively reduce time delay; the block error probability can be directly Characterize system reliability, availability, and energy capture efficiency. For this system, this research uses the energy captured by the source node to send information; according to the spatial distribution of the source node and users and the zero-forcing beamforming method, the cumulative distribution function of the signal-to-noise ratio of each user is obtained, and the method of Gaussian function approximation is used , deriving an approximate closed expression for the block error probability for each user. Theoretical analysis shows that the block error probability is inversely proportional to the block length and power distribution coefficient of information transmission. The simulation results verify the correctness of the derived closed expression of the block error probability, and according to the simulation data, it is obtained that: under the conditions of the given block length and the number of antennas for information transmission, there is an optimal value for the number of time slots used by WET and WIT.

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

The specific steps of the system modeling process are as follows:

Step A1, applying the multi-antenna technology to the wireless energy harvesting short packet transmission system, the system consists of an energy transmitter ET, a source node S and K users. Due to the limited energy of the nodes, the users are equipped with single antennas and are distributed in different locations, denoted by U ₁ , U ₂ ,…, U _K respectively; the number of antennas of the energy transmitter ET is M _E , and the number of antennas of the source node is N, where the energy collection and information transmission of the source node S share an antenna;

Step A2, for the system model of step A1, calculate the channel gain matrix of the energy harvesting stage and the wireless information transmission stage

The wireless energy harvesting process flow, the specific steps are as follows:

其中，

是第i个传输波束成形向量，s_i是相应的能量信号。在ET处的传输协方差矩阵为

Step B1, first consider the energy beamforming at the ET, assuming that there are d energy beams at the ET, _1≤d≤ME . The energy signal transmitted at ET is

in,

is the i-th transmit beamforming vector and _si is the corresponding energy signal. The transmission covariance matrix at ET is

Step B2, from the covariance matrix obtained in step B1, the energy Q=ηTE(||Hx|| ² )=ηTtr(GS) captured by the source node can be obtained, wherein, η is the energy capture efficiency; T is the block length; H is the MIMO channel matrix between the energy transmitter and the source node,

Step B3, estimate the data packet length according to the number of time slots for energy capture, assuming that the approximate duration of a continuous-time signal is t, and the approximate bandwidth is B, then the data packet length is: T≈Bt. Therefore, T ≈ BmT _c ;

Step B4, according to the energy captured by the source node calculated in step B2 and the data packet length in step B3, the maximum value Q ^* = ηBmT _c Pλ ₁ of energy capture is obtained by an optimization method. λ ₁ is the largest eigenvalue of the matrix G, namely

The wireless information transmission phase process, the specific steps are as follows:

Step C1, the source node uses the captured energy to transmit information with K users. K users communicate with the source node at the same time, and all users have the same block length M, M≈BnT _c , but have different power allocation coefficients β _k when each data packet is transmitted.

Step C2, according to the energy captured in the energy capture stage, calculate the transmission power of the source node

其中，h_k～CN(0_N,Ω_kI_N),k＝1,2,…,K为源节点与U_k之间的N×1信道矢量，Ω_k为源节点与U_k的平均信道功率增益；x_k为源节点给用户k传输的信息；

为加性高斯白噪声；

为源节点的1×N预编码矩阵；v_k,k＝1,2,…,K为信息x_k的一个1×N波束成形矢量，||v_k||＝1；Step C3, according to the information transmission between the source node and the user, the received signal of user k is obtained

Among them, h _k ～CN(0 _N ,Ω _k I _N ), k=1,2,…, K is the N×1 channel vector between the source node and U _k , Ω _k is the average of the source node and U _k Channel power gain; x _k is the information transmitted by the source node to user k;

is additive white Gaussian noise;

is the 1×N precoding matrix of the source node; v _k ,k=1,2,…,K is a 1×N beamforming vector of information x _k , ||v _k ||=1;

其中，

H_k＝[h₁,h₂,…,h_K]；Step C4, calculate the signal-to-noise ratio of U _k

in,

H _k = [h ₁ ,h ₂ ,...,h _K ];

The system error probability calculation process, the specific steps are as follows:

Step D1, according to the spatial distribution of source nodes and users and the zero-forcing beamforming method, the SNR cumulative distribution function of each user is obtained

Step D2, using the method of Gaussian function approximation, deduce the block error probability of each user

The joint optimization algorithm process, the specific steps are as follows:

Step E1, according to the block error probability of user k obtained in the previous part, simplified and sorted

其中约束条件包括：功率分配系数的约束

最大的时延约束0＜δ≤δ_max；Step E2, by optimizing the number of time slots in the wireless energy transmission phase and the power allocation coefficient in the wireless information transmission phase, the optimization problem can be expressed as (P1):

The constraints include: constraints on the power distribution coefficient

The maximum delay constraint 0<δ≤δ _max ;

Step E3, the time delay δ is directly affected by the number of time slots in the energy capture phase and the wireless information transmission phase, therefore, the maximum time delay constraint is transformed into 0<m+n≤s, s is a fixed value;

和(P1-b):

其中(P1-a)是给定β_k的m的优化子问题，(P1-b)是给定m的β_k的优化子问题；Step E4, divide the problem (P1) into two sub-problems (P1-a):

and (P1-b):

Where (P1-a) is the optimization subproblem of m given β _k , and (P1-b) is the optimization subproblem of β _k given m;

Step E5, optimize the problem (P1-a), its optimal solution m is m ^* =sn, wherein, s is the maximum total number of time slots in WEI and WIT stages;

Step E6, optimize the problem (P1-b), and its optimal solution β ^* can be obtained by the following formula

In step E7, according to the optimal solution calculated in E5-E6, the minimum system block error probability is obtained through an iterative algorithm.

The present invention improves energy transmission efficiency by equipping multiple antennas at either or both of the energy transmitter and the energy receiver. Multiple antennas on the energy transmitter help to focus the transmitted wireless energy in the direction of the energy receiver through digital beamforming or so-called energy beamforming technology, while multiple antennas at the energy receiver increase the received RF signal energy The effective aperture area of the collection, both leading to significantly improved energy transfer efficiency. That is to say, the present invention utilizes the characteristics of radio frequency signals and the space resources of multi-antenna technology to achieve multiplexing gain and diversity gain, which not only improves the energy transmission efficiency, shortens the energy collection time, but also reduces the error probability and improves the system efficiency. reliability.

The inventors found that Ultra-reliable and Low-latency Communication (URLLC) needs to accurately transmit information under the condition of limited delay; therefore, short data packets need to be used for transmission; the traditional Shannon approximation The attainable error-free rate criterion is no longer applicable. The maximum attainable rate (MaximalAchievable Rate, MAR) is not only related to the channel distribution, but also related to the block error probability (Packet Error Probability, PEP). Restricted, it is necessary to use energy harvesting to obtain energy for data transmission. At the same time, because the system uses short data packet transmission, the efficiency of its energy harvesting is reduced, which in turn affects the transmission performance of the entire system.

Multi-antenna technology can use space resources to achieve multiplexing gain, improve the MAR of the short data packet transmission system, and thereby reduce transmission delay; at the same time, it can also achieve diversity gain, thereby reducing the PEP of the system. In terms of energy harvesting, the literature configures multiple antennas on the energy transmitter (Energy Transmitter, ET) and energy receiver (Energy Receiver, ER). ET uses multiple antennas to focus the transmitted wireless energy to the ER through beamforming technology. direction, and the multiple antennas of ER increase the receiving energy collection area, which can effectively improve the energy harvesting efficiency, thereby improving the data transmission performance of the short data packet transmission system.

The existing literature deduces the MAR and PEP of the system under the condition of finite block length and finite battery capacity, and gives the time delay of the wireless energy transmission (Wireless Energy Transmission, WET) and wireless information transmission (Wireless Information Transmission, WIT) phase of the system, From the relationship between MAR, PEP, system delay and captured energy, it can be seen that energy capture directly affects the transmit power of the sender, thereby affecting MAR and PEP, while MAR affects the transmission delay of WIT, but the limitation of PEP , directly affects the energy capture time, and then affects the delay of the system. Some literatures have studied the time delay of the energy harvesting URLLC system, which is inversely proportional to the PEP of the system, that is, the lower the PEP, the longer the time delay required; some literatures have studied the MAR performance of the system under the condition of limited energy PEP is related to channel divergence; it can be seen that PEP directly affects the MAR of short data packet transmission, thereby further affecting its transmission delay; at the same time, the amount of energy captured directly affects the size of the transmit power, which in turn affects PEP and MAR; Therefore, PEP can characterize the reliability, effectiveness and energy capture efficiency of the short data packet transmission system, and can also affect the delay of the entire system. However, the performance of PEP in multi-antenna energy harvesting short packet transmission systems has not been studied.

To solve this problem, the present invention configures multiple antennas for the ET and the source node in the multi-antenna energy capture short data packet multi-user system, and uses the energy captured by the source node to send information; according to the spatial distribution and forcing of the source node and the user The zero-beamforming method obtains the SNR cumulative distribution function of each user, and uses the method of Gaussian function approximation to deduce the approximate closed expression of the block error probability of each user. Theoretical analysis shows that the block error probability is inversely proportional to the block length and power distribution coefficient of information transmission. The simulation results verify the correctness of the derived closed expression of the block error probability, and according to the simulation data, it is obtained that: under the conditions of the given block length and the number of antennas for information transmission, there is an optimal value for the number of time slots used by WET and WIT.

The method provided by the invention is specifically as follows:

2 system model

The present invention applies the multi-antenna technology to the wireless energy capture short packet transmission system. The system is composed of an energy transmitter ET, a source node S and K users, as shown in FIG. 2 . Due to the limited energy of nodes, K users are equipped with single antennas and are distributed in different locations, denoted by U ₁ , U ₂ ,..., U _K respectively; the number of antennas of the energy transmitter ET is M _E , and the antennas of the source node The number is N, and the energy collection and information transmission of the source node S share one antenna. Assuming that the energy harvesting nodes use the store-then-transfer protocol for wireless communication, the whole process is divided into WET phase and WIT phase. First, the source node S collects energy through the RF signal sent by ET in m time slots, and stores it in the battery, that is, the WET stage; then, the source node uses the collected energy to communicate with the destination node through n time slots Transmission, that is, the WIT stage. Assume that the channel is a quasi-static fading channel, and in each transmission block, its fading coefficient is fixed. In addition, it is assumed that ET to S have perfect channel state information (Channel State Information, CSI), S and K users all know each other's CSI. The duration of each slot is T _c . The introduction of multi-antenna technology not only improves the energy transmission efficiency, shortens the energy collection time, but also improves the reliability of the system.

2.1 WET stage

其中，

是第i个传输波束成形向量，s_i是相应的能量信号。在ET处的传输协方差矩阵为First consider the energy beamforming at the ET, assuming that there are d energy beams at the ET, _1≤d≤ME . The energy signal transmitted at ET is

in,

is the i-th transmit beamforming vector and _si is the corresponding energy signal. The transmission covariance matrix at ET is

Energy captured by source node S

Q=ηTE(||Hx|| ² )=ηTtr(GS) (2)

Among them: η is the energy capture efficiency; T is the block length; H is the MIMO channel matrix between ET and S,

Known on the basis of the existing literature, if the approximate duration of a continuous-time signal is t, and the approximate bandwidth is B, then the length of the data packet is: T≈Bt. Therefore, T≈BmT _c . Formula (2) can be written as

Q≈ηBmT _c tr(GS) (3)

tr(S)≤P。通过优化的方法得到公式(3)的最大值Q^*＝ηBmT_cPλ₁。λ₁为矩阵G的最大的特征值，即

in,

tr(S)≤P. The maximum value Q ^* =ηBmT _c Pλ ₁ of the formula (3) is obtained by an optimization method. λ ₁ is the largest eigenvalue of the matrix G, namely

2.2 WIT stage

The source node S uses the captured energy to transmit information with K users. At this stage, a zero-forcing beamforming scheme is adopted. K users communicate with S at the same time, and all users have the same block length M, M≈BnT _c , but have different power allocation coefficients β _k when each data packet is transmitted. P _S is the transmission power of the source node S

Maximum transmission power

The received signal of user k

为加性高斯白噪声；Among them, h _k ～CN(0 _N ,Ω _k I _N ), k=1,2,…,K is the N×1 channel vector between S and U _k , Ω _k is the average channel power between S and U _k Gain; x _k is the information transmitted by source node S to user k;

is additive white Gaussian noise;

为S的1×N预编码矩阵；v_k,k＝1,2,…,K为信息x_k的一个1×N波束成形矢量，||v_k||＝1；β_k为x_k的功率分配系数，

在现有文献的基础上得到U_k的信噪比(Signal-to-Noise Ratio，SNR)为

is the 1×N precoding matrix of S; v _k ,k=1,2,…,K is a 1×N beamforming vector of information x _k , ||v _k || ₌ 1; β _k is the power distribution factor,

Based on the existing literature, the signal-to-noise ratio (SNR) of U _k is obtained as

H_k＝[h₁,h₂,…,h_K]。in,

H _k =[h ₁ , h ₂ , . . . , h _K ].

3 Performance Analysis

The source node S transmits information at a fixed rate r, and the performance of the system is mainly described by the block error probability and time delay. Assuming that the information carried in the unit block is κ nett, the transmission rate is

Assume that the time delay of the system is δ during the entire process from the WET stage to the WIT stage, and δ ^* is the minimum time delay that satisfies a given error probability.

δ=(m+n)T _c (8)

The number of time slots m in the WET stage directly determines the energy Q captured by the source node _S ; through the system total block error probability formula, it is found that the greater the transmission power PS of the source node _S , the smaller the total block error probability, and the ratio of PS and Q Proportional relationship. In addition, the size of m directly affects the size of the delay.

For the total block error probability of the system, it is first necessary to obtain an approximate expression of the error probability of user k, assuming ε _k is the error probability of user k. When n>100, in a quasi-static fading channel, ε _k can be approximated as

为信道散度；

为高斯函数；E{·}为均值。由于高斯函数极为复杂，求解较难，因此从高斯函数的近似形式着手，求得ε_k的闭合表达式。在现有文献的基础上述得到高斯函数近似Wherein, C(γ _k )=log ₂ (1+γ _k ) is the channel capacity obtained by Shannon's theorem;

is the channel divergence;

is a Gaussian function; E{·} is the mean value. Since the Gaussian function is extremely complex, it is difficult to solve it, so starting from the approximate form of the Gaussian function, the closed expression of ε _k is obtained. Gaussian function approximation obtained above on the basis of existing literature

in,

Equation (7) has obtained the SNR of U _k , and the cumulative distribution function (Cumulative distribution function, CDF) of the SNR of user k is obtained on the basis of existing literature

Therefore, its probability density function (Probability density function, PDF) is

in,

Therefore, formula (9) can be expressed as

Substituting formula (9) into (13), we get

把公式(12)代入公式(14)中，得到in,

Substituting formula (12) into formula (14), we get

其中γ(·,·)为低阶不完全gamma函数。因此In formula (15), it is first necessary to calculate ∫x ⁿ exp(-μx)dx. from the existing literature

Where γ(·,·) is a low-order incomplete gamma function. therefore

and then

According to formula (19), it can be obtained in the same way

Then, substitute formulas (16)~(21) into formula (21) and perform simplification to get the approximate expression of block error probability of user k as

4 simulation analysis

其中Ω_k为源节点S到用户k之间的平均信道功率增益，d为源节点S到能量发射器ET的距离，d_k为源结点S到用户k之间的距离，ω为路径损耗系数。在此信道模型中，在1米的距离上平均有30dB的功率衰落。另外，假设带宽为1MHz，每个时隙的持续时间T_c＝1μs。To describe the effect of path fading, the channel fading model is

where Ω _k is the average channel power gain between source node S and user k, d is the distance from source node S to energy transmitter ET, d _k is the distance between source node S and user k, and ω is the path loss coefficient. In this channel model, there is an average power drop of 30dB over a distance of 1 meter. In addition, assuming that the bandwidth is 1 MHz, the duration of each time slot is T _c =1 μs.

In the WET phase, the transmission power PE of the energy transmitter ET is _30dBm . Energy capture efficiency η=0.5, path fading factor ω ₁ =2. It is assumed that the number of antennas of the ET is 4, the number of antennas of the source node S is 4, the distance between them is d=12m, and the number of time slots in the WIT stage is n=600. FIG. 3 is a relation diagram of the transmission power PS of the source node _S and the number m of time slots in the WET phase. It can be seen from Figure 3 that _PS is not only affected by the number of time slots m, but also affected by the number of receiving days N. Under the same time slot, PS increases with the increase of the number _N of antennas.

传输距离d_k＝100，传输的信息量υ＝600bit，路径损耗系数ω₂＝3、噪声功率

图5为总块错误概率与源节点S的传输功率比关系图，其中，d₁＝100，d₂＝80，d₃＝130，源节点S与每个用户传输的信息量分别为υ₁＝600，υ₂＝800，υ₃＝1000。从图4-5中，可以发现随着源节点S的传输功率P_S的增大，用户k的块错误概率ε_k越小。同时，发现源节点S的天线数量N和数据包的长度M都会影响到ε_k。当传输功率P_S、数据包长度M一定时，天线数量N越多，块错误概率ε_k越小；当传输功率P_S、天线数量N一定时，数据包长度M越长，块错误概率ε_k越小。因此，可以通过增加传输功率P_S、天线数量N和数据包长度M来减少块错误概率ε_k，提高系统的可靠性。Fig. 4 shows block error probabilities _{ε k} corresponding to different transmission powers PS. Among them, total users K=3, power allocation coefficient

Transmission distance d _k = 100, transmitted information υ = 600bit, path loss coefficient ω ₂ = 3, noise power

Figure 5 is a graph showing the relationship between the total block error probability and the transmission power ratio of the source node S, where d ₁ =100, d ₂ =80, d ₃ =130, and the amount of information transmitted between the source node S and each user is υ ₁ =600, v ₂ =800, v ₃ =1000. From Figure 4-5, it can be found that with the increase of the transmission power PS of the source node _S , the block error probability ε _k of the user k becomes smaller. At the same time, it is found that the number N of antennas of the source node S and the length M of the data packet will both affect ε _k . When the transmission power PS and the data packet length _M are constant, the more the number of antennas N, the smaller the block error probability ε _k ; when the transmission power PS and the number of antennas _N are constant, the longer the data packet length M, the smaller the block error probability ε _k is smaller. Therefore, the block error probability ε _k can be reduced by increasing the transmission power PS , the number of antennas _N and the data packet length M, and the reliability of the system can be improved.

In Figure 4-5, it is found that when the number of antennas of the source node S is 8, the reliability of information transmission is better. Therefore, let N=8, and keep other parameters unchanged. Figure 6 and Figure 7 respectively show the relationship between the block error probability ε _k of user k, the total block error probability ε ₀ and the number of time slots (m+n) in the whole process from WET to WIT, that is, δ/T _c .

From Figure 6-7, it can be clearly observed that as the number of time slots δ/T _c increases, the block error probability and the total block error probability of user k decrease continuously, which means that the greater the system delay, the greater the error rate. The smaller the probability, the higher the reliability of information transmission. When the time delay is constant, the length of the data packet can be increased by increasing the number of time slots in the WIT phase, reducing the user's block error probability, thereby improving the reliability of the system. According to the requirements of the actual situation, the system delay and reliability can be traded off to obtain the best state. At the same time, under the given block length and number of antennas for information transmission, there is an optimal value for the number of time slots used by WET and WIT.

It can be seen that the present invention studies the block error probability of a multi-user wireless energy transmission system in a short-packet communication scenario. An approximate closed-form expression for the block error rate for each user is derived and verified for accuracy. According to the closed expression, the factors affecting the block error probability are analyzed, and it is obtained that the block error probability of the user can be improved by optimizing the number of transmitting antennas, the length of the data packet and the transmission power, and at the same time, the power allocation coefficient of the system can be optimized to improve the block error probability of the system . In addition, the relationship between block error probability and delay is verified by simulation, and the results show that the stricter the reliability, the higher the required delay, which also increases the time invested in WET. At the same time, it is found that when the delay is constant, the block error probability of the system can be reduced by increasing the length of the data packet, which provides a theoretical basis for the trade-off between delay and reliability of the system.

Each part in this manual is described in a progressive manner, and each part focuses on the difference from other parts, and the same and similar parts of each part can be referred to each other.

The above description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined in this application may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention will not be limited to the embodiments shown in this application, but will conform to the widest scope consistent with the principles and novel features disclosed in this application.

Claims (1)

1. A short packet communication transmission method based on multi-antenna energy capture specifically comprises the following steps:

step A, configuring a plurality of antennas for an energy emitter and a source node in a multi-antenna energy capture short packet communication system, transmitting information by using energy captured by the source node, constructing a system model according to actual requirements, and obtaining a channel gain matrix;

b, calculating energy captured by the source node according to the system model and the channel gain matrix in the step A, and optimizing the energy to obtain the maximum value of energy capture;

step C, calculating the transmitting power of the information transmission stage according to the energy captured by the source node in the energy capture stage, and obtaining the signal-to-noise ratio of the user;

step D, calculating the error probability of the system;

e, optimizing the time slot number of the wireless energy transmission stage and the power distribution coefficient of the wireless information transmission stage to obtain the minimum error probability of the system block;

wherein, step A specifically includes:

a1, applying multi-antenna technology to wireless energy capture short packet transmission system, the system is composed of energy emitter ET, source node and K users, because node energy is limited, users are equipped with single antenna and distributed at different positions, and U is used respectively ₁ ,U ₂ ,…,U _K Represents; number of antennas M of energy emitter ET _E The number of the antennae of the source node is N, wherein the energy collection and the information transmission of the source node share one antenna；

A2, calculating channel gain matrixes of an energy capture stage and a wireless information transmission stage for the system model in the step A1, wherein the channel gain matrix of the energy capture stage is

Wherein h is _a,b ，a＝1,…,M _E N, which is a channel from the a-th transmitting antenna to the b-th receiving antenna; the channel gain matrix of the wireless information transmission stage is

Wherein h is _u,χ U =1, \8230;, N, χ =1, \8230;, K, is the channel from the u-th transmitting antenna to the χ -th receiving antenna;

wherein, step B specifically includes:

b1, first consider energy beam forming at ET, assuming there are a total of d energy beams at ET, 1 ≦ d ≦ M _E The energy signal transmitted at ET is

Wherein,

is the ith transmit beamforming vector, s _i Is the corresponding energy signal, the transmit covariance matrix at ET is

B2, solving the energy Q = eta TE (| | Hx | | | sweet wind) captured by the source node according to the covariance matrix obtained in the step B1 ² ) = η Ttr (GS), where η is energy capture efficiency; t is the block length; h is the MIMO channel matrix between the energy transmitter to the source node,

tr (·) is the trace of the matrix, and tr (GS) is the transmitted power;

and B3, estimating the length of the data packet according to the time slot number of energy capture, and assuming that the approximate duration of a continuous time signal is t and the approximate bandwidth is B, the length of the data packet is as follows: t ≈ Bt, where T = mT _c M is the number of time slots needed for transmitting data packets, T _c The length of a time slot for channel stability;

b4, obtaining the maximum value Q of energy capture through an optimization method according to the energy captured by the source node obtained through calculation in the step B2 and the data packet length in the step B3 ^* ＝ηBmT _c Pλ ₁ ，λ ₁ Is the largest eigenvalue of the matrix G, i.e.

Is the minimum eigenvalue of the matrix G, P is the maximum power transmitted;

wherein, step C specifically includes:

c1, the source node transmits information with K users by using the captured energy, the K users communicate with the source node at the same time, and all the users have the same block length M when each data packet is transmitted, wherein M is approximately equal to BnT _c N is the number of slots for energy capture, but with a different power distribution coefficient β _k ；

C2, calculating to obtain the transmission power of the source node according to the energy captured in the energy capturing stage

C3, obtaining the receiving signal of user k according to the information transmission between the source node and the user

Wherein h is _k ～CN(0 _N ,Ω _k I _N ) K =1,2, \8230, K is a source node and U _k N × 1 channel vector of, 0 _N Is an NxN zero matrix, U _k For user k, Ω _k Is a source node and U _k Average channel power gain of (a); x is the number of _k Information transmitted to user k for the source node;

is additive white gaussian noise;

a1 × N precoding matrix that is a source node; v. of _k K =1,2, \ 8230;, K, information x _k A1 xn beamforming vector, | v | | v _k ||＝1；

C4, calculating U _k Signal to noise ratio of

Wherein,

H _k ＝[h ₁ ,h ₂ ,…,h _K ]，I _N is an NxN unit matrix;

wherein, step D specifically includes:

d1, obtaining the signal-to-noise cumulative distribution function of each user according to the space distribution of the source node and the user and the zero forcing beam forming method

D2, deducing the block error probability of each user by using a Gaussian function approximation method

Wherein,

γ (·,) is a low order incomplete gamma function;

γ _k SINR for user k;

wherein, step E specifically includes:

e1, obtaining the block error probability of the user k according to the step D2, and simplifying and sorting the block error probability to obtain

E2, optimizing the time slot number in the wireless energy transmission stage and the power distribution coefficient in the wireless information transmission stage, wherein the optimization problem is expressed as P1 by a formula:

wherein the constraint conditions include: constraint of power distribution coefficient

Maximum time delay constraint 0 & ltdelta & lt delta & gt _max ，δ＝(m+n)T _c ，δ _max Is the maximum value of the preset delta;

e3, the time delay delta is directly influenced by the time slot number of the energy capture stage and the wireless information transmission stage, therefore, the maximum time delay constraint is converted into 0-less m + n ≦ s, and s is the maximum total time slot number of the WEI stage and the WIT stage;

e4, we divide the problem P1 into two sub-problems P1-a:

and P1-b:

wherein P1-a is a given value of beta _k P1-b is beta for a given m _k The optimization sub-problem of (2);

e5, optimizing the problem P1-a to obtain m as the optimal solution of m ^* = s-n, where s is the maximum total number of time slots in the WEI and WIT phases, WET is the wireless energy transmission phase, and WIT is the wireless information transmission phase;

e6, optimizing the problem P1-b and obtaining the optimal solution beta _k Is obtained by the following formula

Wherein,

minimum signal-to-noise ratio for the kth user;

and E7, obtaining the minimum error probability of the system block through an iterative algorithm according to the optimal solution calculated by the E5-E6.

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