CN112788629A - Lyapunov optimization framework-based online combined control method for power and modulation mode in energy collection communication system - Google Patents

Abstract

The invention discloses an on-line joint control method of power and modulation mode in an energy harvesting communication system based on a Lyapunov optimization framework, aiming at a point-to-point energy harvesting wireless communication system equipped with an energy harvesting device at a source node, under the random change conditions of energy arrival and channel state , maximizing the long-term average transmission rate. This method uses the Lyapunov optimization framework to transform the long-term time control method under the constraints of battery operation and available energy into a joint control method of transmit power, modulation method and frame length with the goal of minimizing the virtual queue "drift plus penalty" per time slot. and solve. The present invention only relies on the current battery state and channel state information to make decisions, with low computational complexity and strong practicability.

Description

On-line joint control method of power and modulation mode in energy harvesting communication system based on Lyapunov optimization framework

technical field

The invention relates to the field of information communication, in particular to a method for joint control of transmission power and modulation mode of a communication system using collected energy to supply power.

Background technique

With the rapid development of wireless communication technology, its application fields are constantly expanding, the number of network users is increasing rapidly, and the problem of energy consumption is becoming more and more serious. The green communication technology based on the theory of "open source" and "cost saving" is one of the hotspot technologies in the current academic and industrial research. Energy harvesting (EH, energy harvesting) is an important technical means of "open source". Nodes in a communication network collect energy (such as solar energy, wind energy, thermal energy, etc.) from the natural environment and convert it into electrical energy for information transmission. Due to the instability of the environmental energy source, the amount of energy collected has obvious random variation characteristics, coupled with the randomness of the wireless channel state, it is necessary to dynamically control the signal transmission power and information transmission rate to efficiently utilize the collected energy. and channel resources. Among them, the transmission power control of the transmitter is a problem that has been researched more at present. The power control strategies proposed in the existing related literature can be divided into two categories: offline control strategies and online control strategies.

The offline management strategy is applied in the case where the collected energy, channel state and other information are known in advance. Although this assumption is unreasonable, offline strategies can achieve superior performance and are often used as an upper bound for evaluating the performance of other strategies. In the literature [REZAEE M, MIRMOHSENI M. Energy harvesting systems with continuous energy and data arrivals: The optimal offline and heuristic online algorithms[J]. IEEE Journal on Selected Areas in Communications, 2016, 34(12): 3739-3753.] For an energy harvesting communication system with continuous energy and data arrivals, a three-step optimal energy scheduling algorithm is presented to maximize single-user throughput. First, data arrival and energy harvesting are modeled as continuous functions, and then an offline power control algorithm is sought to maximize the average throughput of the system under a limited number of time slots. Literature [OZEL O, TUTUNCUOGLU K, ULUKUSS, et al. Transmission with energy harvesting nodes in fading wireless channels: Optimal policies[J]. IEEE Journal of Selected Areas in Communications, 2011, 29(8): 1732-1743.] for fading channels The energy harvesting system under the condition of energy harvesting system, a directional water injection algorithm is proposed, which controls the transmission power of each time slot, maximizes the amount of information transmission within a limited transmission time, or minimizes the transmission time under a certain amount of transmitted data. The directional water injection algorithm means that the energy collected in the current time slot can only be used for power water injection in the future time slot, and cannot be allocated to the water injection algorithm used in the previous time slot.

Unlike offline control algorithms, online algorithms mainly rely on statistical information such as energy and data arrivals, channel fading, etc., as well as current and past system states to make decisions. Under the condition that the transmitter can obtain statistical information reflecting the energy and data arrival process and channel fading process, the power control process is modeled as a Markov decision process (MDP, Markov decision process), and dynamic programming (DP, dynamic programming) is applied. Solving is the most studied online power control solution in the related literature. In the literature [WANG Z, AGGARWAL V, WANG X. Power allocation for energy harvesting transmitter with causal information [J]. IEEE Trans-actionson Communications, 2014, 62(11): 4080-4093.], the power allocation with the maximum transmit power constraint is studied. In the point-to-point communication system, a piecewise linear fitting function is defined based on the battery state, the optimal transmit power allocation problem under random channel conditions is constructed as an MDP, and the DP is used to solve the optimization problem. In order to have a more accurate description of the system state and obtain better performance, the MDP-based scheme needs to have a larger state and action space, and the computational complexity of the algorithm is usually very high. Lyapunov optimization technology is an optimization method that is widely used in cybernetics. This method does not need to know the statistical characteristics of the system state in application, but makes decisions based on the current system state. It is a very practical method. Optimization. The algorithm is particularly suitable for solving queuing problems, and the minimization of queue backlog is its basic goal and characteristic. When Lyapunov method is used to solve optimization problems with constraints, virtual queues can be constructed according to the constraints, and the virtual queues can be kept stable in the long-term time sense by minimizing the drift of the virtual queues, and the constraints can be met indirectly; and the optimization goal is used as a penalty. item, and construct "queue drift plus penalty" together with queue drift as the objective function of optimization. By minimizing the objective function, the optimization of the objective can be achieved while achieving the stability of the queue in the sense of long-term time average. The method transforms the long-term time-averaged optimization problem into a single-slot optimization problem, and can reduce the constraints and greatly reduce the complexity of solving the optimization problem. Reference [AMIMAVAEI F, DONG M. Online power control optimization for wireless transmission with energy harvesting and storage [J]. IEEE Transactionson Wireless Communications, 2016, 15(7): 4888-4901.] for the point-to-point communication where the source node is powered by the EH device In order to maximize the long-term average rate, an online power control algorithm using the Lyapunov optimization framework is proposed. To convert the battery power constraint into virtual queue stability, the negative number of the maximum transmission rate needs to be used as a penalty term, and a "drift plus penalty" is constructed. By minimizing its upper bound, the transmission rate is maximized while maintaining the battery power stability.

In the above-mentioned literatures on the maximization of transmission rate or throughput, or the minimization of transmission time in energy harvesting communication systems, the channel capacity calculated by Shannon's formula is used as the transmission rate of the system. In the actual system, it is necessary to select the appropriate channel coding (including coding type, code length, code rate) and modulation method according to the channel state and transmission power, and maximize the transmission rate (or throughput under the requirement of error probability) quantity). The actual achievable transmission rate is lower than the channel capacity, and the choice of channel coding and modulation has a great influence on the final achievable transmission rate. Reference [MA R, ZHANG W. Adaptive MQAM for energy harvesting wire-less communications with 1-bit channel feedback [J]. IEEE Transactions on Wireless Communications, 2015, 14(11): 6459-6470.] In the communication system, according to the comparison result of the channel state represented by 1 bit at the receiving end and the threshold, the MDP problem is constructed, and the backward iterative algorithm is used to find the optimal combination of modulation mode and transmission power, so as to maximize the average throughput of the system in a finite time slot . The algorithm achieves good transmission performance, but the backward iterative algorithm has high computational complexity, and only uses 1 bit to represent the channel state, which cannot accurately reflect the randomness and diversity of the channel state. Proposed in [LI M Y, ZHAO X H, LIANG H, et al. Deep reinforcement learning optimal transmission policy for communication systems with energy harvesting and adaptive MQAM [J]. IEEE Transactions on Vehicular Technology. 2019, 68(6): 5782-5793.] An algorithm based on deep reinforcement learning is proposed. Under the premise of satisfying the bit error performance required by the system, the transmission power per time slot is optimized with the goal of maximizing the actual transmission rate, and the current channel quality and transmission power can be used. The highest order modulation method. The algorithm improves the traditional Q-learning algorithm and improves the convergence speed of the Q-learning algorithm. Simulation results show that the algorithm converges after a small number of iterations.

SUMMARY OF THE INVENTION

The invention studies the scheduling optimization problem of power and transmission rate aiming at maximizing the long-term average throughput of the system in a point-to-point energy harvesting wireless communication system. The source node is equipped with an energy harvesting device and a rechargeable battery, and the energy of the transmitted signal per time slot comes from the energy harvested from the surrounding environment. Under the condition of limited battery capacity, the Lyapunov framework is used to solve the joint optimization problem of transmit power, modulation mode and frame length to maximize the long-term time average throughput.

In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme: constructing an optimization problem aiming at maximizing the system transmission rate, converting the optimization problem into an optimization problem of long-term time average value, using the Lyapunov framework to solve it, and constructing a "drift plus penalty" , and convert the minimized "drift plus penalty" term to minimize the upper bound of this term to achieve the optimization purpose, solve the three-parameter optimization problem including transmit power, modulation mode, and frame length, and obtain the optimal solution.

Specific steps are as follows:

(1) Each time slot, the source node collects energy from the surrounding environment to send information to the destination node, and maximizes the transmission rate under the constraint of battery storage power;

(2) Using the Lyapunov optimization framework, the battery power of the source node is added to the offset to obtain a virtual queue, and then the negative value of the transmission rate is used as a penalty term to construct a "drift plus penalty" term to maximize the constrained long-term average transmission rate. The optimization problem is transformed into minimizing the "drift plus penalty" term;

(3) Convert minimizing the "drift plus penalty" term into an upper bound that minimizes the "drift plus penalty" term;

(4) Make decisions according to energy arrival and channel state, and find the optimal combination of transmit power, modulation mode, and frame length, that is, to solve the optimal solution of the optimization objective function.

Specifically, the communication system modeling described in step (1) includes modeling and expressing the actual reachable transmission rate of the system and the battery power queue of the source node. The optimization problem is constructed with the maximum transmission power limit, the limit of the battery storage power on the transmission power and the battery power change as constraints, and the goal of maximizing the long-term time average transmission rate;

Specifically, in step (2), the Lyapunov optimization framework is used to solve the optimization problem, that is, starting from the stability of the queue, adding an offset to the battery power of the source node as an energy virtual queue to keep the queue stable to meet the constraints , take the long-term average transmission rate of the optimization target as the penalty item, and construct and minimize the "drift plus penalty" item to achieve the optimization purpose

Specifically, in step (3), the constraint condition is indirectly achieved by minimizing the upper bound of "drift plus penalty", and the upper bound expression of the "drift plus penalty" term is obtained from the Lyapunov function and the Lyapunov drift formula;

Specifically, in step (4), appropriate adjustments should be made to transmit power, modulation mode, and frame length according to energy arrival and channel state. Since these three variables cannot be directly optimized jointly, but the number of modulation methods is limited, the transmit power P(t) and Frame length N. Among them, optimizing P(t) and N under a given modulation mode, when X(t)≥0, the objective function increases monotonically, and P(t) should take the maximum value P _d,max , when P(t)=P _{d , when max} is calculated to obtain the bit error rate P _eb , which is substituted into the partial derivative formula of the objective function to N, and the solution is found to be 0, that is, the optimal frame length N; when X(t)<0, the optimal P( The solution of t) and N should be the extreme point of the objective function J(P(t), N|M), that is, the solution of the system of equations composed of two partial derivatives of 0. Finally, the M that maximizes J(P(t), N|M) and its corresponding P(t) and N are selected as the optimal solutions.

Compared with the existing related research, the characteristics of the present invention are: (1) The present invention proposes to use the Lyapunov optimization framework to convert the long-term time-averaged optimization problem into a single-slot optimization problem, and convert the energy constraints into queue stability requirements, only Relying on the current battery state and channel state, it does not need to obtain statistical information on energy arrival and channel fading changes, and is an online, low-complexity control algorithm; (2) Compared with the literature that uses the same Lyapunov method, For example [AMIMAVAEI F, DONG M. Online power control optimization for wirelesstransmission with energy harvesting and storage [J]. IEEE Transactions on Wireless Communications, 2016, 15(7): 4888-4901.], the algorithm proposed in the present invention optimizes the transmission power At the same time, the modulation mode is optimized, and the goal of maximization is not the limit of the theoretical transmission rate, but the actual achievable transmission rate. The simulation results show that the actual achievable rate of the present invention is higher than that of the literature algorithm; (3) The present invention proposes There are many modulation modes available in the algorithm, and considering the necessary overheads such as check bits in the actual data frame, it is more practical to jointly optimize the three parameters of transmission power, modulation mode and frame length.

Description of drawings

Fig. 1 is the communication system model of the present invention;

Fig. 2 is the trajectory diagram of the algorithm proposed by the present invention and the average information transmission rate of the comparison algorithm changing with time;

FIG. 3 is a trajectory diagram of the battery power of the source node changing with time between the algorithm proposed by the present invention and the comparison algorithm;

Fig. 4 is the simulation parameter of the algorithm proposed by the present invention in some time slots in simulation;

Figure 5 shows the effect of the energy virtual queue offset A on the information transmission rate and the average battery power;

Figure 6 shows the influence of the weight V in the drift plus penalty term on the information transmission rate, the average battery power, and the standard deviation of the battery power;

Figure 7 shows the effect of the energy arrival rate λ on the information transfer rate and the average battery charge.

Detailed ways

Consider the transmission system model shown in Figure 1, the system includes a sending node S and a destination node D. The sending node is equipped with an energy harvesting device and a rechargeable battery with limited capacity, which can collect energy from the surrounding environment, store it in the battery, and use it to send data to the destination node. During the transmission process, the energy collected by the sending node and the wireless channel change randomly. The sending node dynamically adjusts the sending power, modulation method, and data frame length according to the instantaneous channel state information and energy collection to maximize the long-term time average system. speed and improve the efficiency of energy use.

Note that the unit power signal sent by the source node is x(t), the channel coefficient from the transmitter to the receiver is h(t), and the channel coefficient h(t) remains unchanged within a time slot. The received signal at the receiver can be expressed as

where P(t) is the transmit power of the source node, and n(t) is the additive white Gaussian noise with a bilateral power spectral density of N ₀ /2.

The capacity of the rechargeable battery of the source node is E _max (Jour, J), and the maximum charging rate is P _{c, max} W. The battery power at the beginning of time slot t is E _S (t) J, which satisfies

0≤E _S (t)≤E _max

The sending power of the sending node should not exceed the maximum discharge power P _d,max of the battery, that is

0≤P(t)≤P _d,max

The energy consumed by sending information in this time slot should not exceed the power stored in the battery at the beginning of the time slot, that is, the causal constraints of battery power usage should be satisfied:

0≤ΔtP(t)≤E _S (t)

where Δt is the length of a time slot. The energy collected by the energy harvesting device from the environment at the time slot t is E _a (t)J. Assuming that there is no energy loss during the charging and discharging of the battery, limited by the charging rate and the remaining capacity of the battery, the time slot t stores the energy stored in the battery. The electric quantity E _H (t) is

0≤E _H (t)≤min E _a (t),ΔtP _c,max ,E _S (t)-ΔtP(t)

The first item in the min function is the energy collected in this time slot, the second item is the maximum charging rate limit, and the third item is the battery remaining storage capacity limit. At the beginning of the next time slot, the battery level is updated to

E _S (t+1)=E _S (t)-ΔtP(t)+E _H (t)

(在无码间干扰时频带传输能达到的最高符号速率为R_s＝B(Baud)。)，其中T_S为符号周期，各调制方式下的符号速率相同。在数据传输中，为了使接收方能够判断接收到的数据是否有错，需要将待传输数据进行分组，并在每个分组附加上一定长度的校验比特形成帧，循环冗余校验(CRC,cyclical redundancy check)是最常用的校验码。接收端收到数据包后通过检查数据与校验比特间的校验关系是否满足对接收数据包是否正确进行判断，如有错则丢弃，并请求重发。假设数据帧的长度为N比特，CRC校验位长度为N_CRC比特，则信息数据序列的长度为 N-N_CRC比特(N≥N_CRC)。当采用M元调制时，每帧中的调制符号长度为

这里假设N为log₂M的整数倍。采用以上6种调制方式时的误比特率为Due to the random time-varying characteristics of the wireless channel state and the instability of energy harvesting, it is necessary to continuously adjust the transmit power and modulation method according to the channel state and available energy. Assuming that the set of optional modulation methods is Θ={BPSK, QPSK, 8PSK, 16QAM, 32QAM, 64QAM}, the transmission bandwidth of the channel is B Hz, and the symbol transmission rate on the corresponding channel is

(The highest symbol rate that can be achieved by frequency band transmission when there is no intersymbol interference is R _s =B(Baud).), where T _S is the symbol period, and the symbol rates are the same in each modulation mode. In data transmission, in order to enable the receiver to judge whether the received data is wrong, it is necessary to group the data to be transmitted, and attach a certain length of check bits to each group to form a frame. Cyclic Redundancy Check (CRC) , cyclical redundancy check) is the most commonly used check code. After receiving the data packet, the receiving end judges whether the received data packet is correct by checking whether the check relationship between the data and the check bits is satisfied, and if there is an error, it will be discarded and retransmission is requested. Assuming that the length of the data frame is N bits and the length of the CRC check bit is N _CRC bits, the length of the information data sequence is NN _CRC bits (N≥N _CRC ). When M-ary modulation is used, the length of the modulation symbol in each frame is

It is assumed here that N is an integer multiple of log ₂ M. The bit error rate when using the above 6 modulation methods

E_b表示接收信号平均比特能量，N₀表示噪声功率谱密度、

表示接收比特信噪比，E_b与发送功率P(t)之间的关系为in the formula

E _b is the average bit energy of the received signal, N ₀ is the noise power spectral density,

Represents the signal-to-noise ratio of the received bits, and the relationship between E _b and the transmit power P(t) is

Here g(t)=|h(t)| ² is the channel power gain. Q( ) in the formula for calculating the bit error rate is a Gaussian Q function, and the expression is

Only when all bits in a frame are received correctly can the frame be verified as correct, and the probability that the data frame is correct is

P _cf = (1-P _eb ) ^N

The average number of information bits transmitted in one frame is

N _info = (NN _CRC )×(1-P _eb ) ^N (bit)

One frame contains L symbols, and the transmission duration of one data frame is

T _P =L×T _S (s)

In the present invention, the rate of correctly transmitted information data bits per unit bandwidth is used as an index to measure system performance, and its expression is:

It can be seen from the above formula that the information transmission rate of the system is related to the transmission power, modulation mode and frame length. The greater the transmit power, the higher the received signal-to-noise ratio, and the lower the error probability, but the transmit power is constrained by the collected energy, and the energy should be used reasonably according to the channel state. For the modulation method, if a higher-order modulation method is used, each symbol can carry more information bits, but the bit error rate is higher and the frame error rate is also higher; lower, but fewer bits are transmitted in the same amount of time. Therefore, it is necessary to select an appropriate modulation order according to the transmit power and channel fading conditions to maximize the information transmission rate. The choice of frame length also affects the information transmission rate. When a longer frame is used for transmission, the proportion of parity bits is smaller and the overhead is smaller, but under the same bit error rate, the frame error probability is higher; , when the frame length is small, the frame error probability is low, but the overhead such as parity bits is large. Therefore, the frame length also needs to be optimized. From this point of view, the actual achievable information transmission rate of the system is not a monotonic function of modulation order and frame length. The optimal modulation order and frame length are related to the transmission power and channel state, and the transmission power is affected by the available energy. constraint. Therefore, the optimization problem of the present invention is to jointly optimize the transmission power P(t), modulation order M and frame length N of each time slot to maximize the long-term average information transmission rate of the system:

st0≤P(t)≤P _d,max

0≤ΔtP(t)≤E _S (t)

E _S (t+1)=E _S (t)-ΔtP(t)+E _H (t)

M ∈ Θ

_N≥NCRC

In the constraints, E[·] represents the expected operation. Since the collected energy and channel state are random processes with random changes, P1 is a stochastic optimization problem.

Rewrite battery update to

E _S (t+1)-E _S (t)=E _H (t)-ΔtP(t)

Time slot t from 0 to T-1 has

Superimpose both ends of the above formula, and find the expected

Divide the left and right ends by T at the same time, and find the limit of T→∞ to obtain a long-term time-averaged relationship:

上式的含义是从长期看来，应将收集到的能量全部用于信息发送。将原约束问题中的单时隙的电池电量约束放松为长期时间电量约束，优化问题转换为in,

The meaning of the above formula is that in the long run, all the collected energy should be used for information transmission. The single-slot battery power constraint in the original constraint problem is relaxed to a long-term time power constraint, and the optimization problem is transformed into

st0≤P(t)≤P _d,max

0≤ΔtP(t)≤E _S (t)

M ∈ Θ

_N≥NCRC

Since the optimization objective is the optimization of the long-term time average, it can be solved by adopting the Lyapunov framework. By transforming the constraints into the problem of maintaining the stability of the virtual queue, and taking the optimization objective as the penalty item, the "drift plus penalty" item is constructed, and the performance optimization under the constraints is achieved by minimizing the "drift plus penalty". First construct the battery energy virtual queue of the sending node

X(t)= _ES (t)-A

where A is the offset. After Lyapunov optimization, the queue length will fluctuate around 0. Adding an offset to the energy virtual queue can keep the battery power around the offset value and fluctuate up and down. According to the battery power update formula E _S (t+1)=E _S (t)-ΔtP(t)+E _H (t), the update formula of the easy-to-obtain energy virtual queue is:

X(t+1)=X(t)-ΔtP(t)+E _H (t)

Define quadratic Lyapunov function

Lyapunov drift is defined as

The smaller the offset, the smaller the variation of the queue length between the two slots, and the queue length is approximately close to 0. Taking the negative value of the information transmission rate R _b to be maximized as the penalty term, the drift plus penalty is constructed as

Δ(X(t))-VE[R _b (t)|X(t)]

where V is the weight between the drift and the penalty term, which is a constant, and is used to make a trade-off between the queue stability and the maximization of the system transmission rate. If the "drift plus penalty" can be minimized, the information transfer rate is maximized while keeping the virtual queue (ie, battery power) stable. Further, there is an upper bound for "drift plus penalty", and changing the minimization of "drift plus penalty" to minimize its upper bound can further reduce the complexity of solving the optimization problem.

All in all

必为非负有限值，一定存在非负常数B满足Since both P(t) and E _S (t) are finite, then

must be a non-negative finite value, there must be a non-negative constant B that satisfies

then

Δ(X(t))≤B+X(t)E[E _H (t)-ΔtP(t)|X(t)]

Then the upper bound of "drift plus penalty" is

Δ(X(t))-VE[R _b (t)|X(t)]≤B+X(t)E[E _H (t)-ΔtP(t)|X(t)]-VE[R _b (t)|X(t)]

得到满足，就可将其从优化约束条件中移除。进一步去除“漂移加惩罚”上界中与P(t)、M、N无关的项，再乘以 -1，相应将最小化改为最大化，同时由于当前的信道状态和电池状态已知，上界中的均值运算可以去掉，优化问题重新表述为单时隙的优化问题：By keeping the virtual queue of energy stable, that is, the battery's charge fluctuates within a limited range and does not tend to infinity or zero over time, the energy collected in the long run is equal to the energy used for information transmission , so the constraints in P2

is satisfied, it can be removed from the optimization constraints. Further remove the items unrelated to P(t), M, and N in the upper bound of "drift plus penalty", and multiply by -1, and correspondingly change the minimization to maximization. At the same time, since the current channel state and battery state are known, The mean operation in the upper bound can be removed, and the optimization problem can be reformulated as a single-slot optimization problem:

M ∈ Θ

_N≥NCRC

The above formula has rewritten the maximum transmit power constraint and the battery power usage constraint in the P2 optimization problem.

Further solve the optimization problem. Let J(P(t),M,N)=P(t)X(t)+VR _b (t) be the optimization objective function, where R _b (t) is related to the modulation method (modulation order), frame length and related to transmit power. The optimization problem P3 is a 3-variable joint optimization problem, in which the optional modulation mode is one of BPSK, QPSK, 8PSK, 16QAM, 32QAM, and 64QAM, that is, only a limited number of values of M can be selected. Since these three variables cannot be directly optimized jointly, but the number of modulation methods is limited, the transmit power P(t) and The frame length is N, and then M that maximizes J(P(t), N|M) and its corresponding P(t) and N are the optimal solutions. The following first analyzes the solution of the optimal P(t) and N under a given M.

First, the partial derivative of the objective function with respect to N is:

P _eb in the formula is the bit error rate calculated by the previous formula. The partial derivative of the objective function to P(t) is

K in the above formula is always greater than 0, which is

in,

目标函数单调递增。显然，要使目标函数最大，P(t)应取最大值P_d,max。从实际物理意义看，X(t)≥0表示电池中有足够的电量，可采用最大发送功率进行传输。在P(t)＝P_d,max时计算得到误比特率P_eb，代入目标函数对N的偏导公式中，并求其为0的解，即最优帧长N。P_eb已知时，

为一个一元二次方程，其解为According to the partial derivative formula of the objective function to P(t), when X(t) ≥ 0,

The objective function is monotonically increasing. Obviously, to maximize the objective function, P(t) should take the maximum value P _d,max . From the actual physical point of view, X(t)≥0 indicates that there is enough power in the battery, and the maximum transmit power can be used for transmission. When P(t)=P _d,max , the bit error rate P _eb is calculated and substituted into the partial derivative formula of the objective function to N, and the solution of 0 is obtained, that is, the optimal frame length N. When P _eb is known,

is a quadratic equation in one variable whose solution is

Negative solutions have been discarded here.

When X(t) < 0, the optimal solution of P(t) and N should be the extreme point of the objective function J(P(t), N|M), that is, it should be composed of two partial derivatives of 0. Solution to the system of equations:

或记为 N(P(t))。再将N(P_eb)代入方程(b)中，得到一个仅含一个未知数P(t)的方程，最优P(t)可以采用数值方法求解该方程得到，但也可以在[0,P_d,max]内搜索使优化目标函数J(P(t)|M)(这里的目标函数中的变量没有帧长N，因为其已经用P(t)的函数N(P(t))代换)最大的P(t)得到。观察

的表达式，可以发现其非常复杂，还包含积分运算，采用数值计算方法求解

的解复杂度明显高于搜索优化目标函数J(P(t)|M)最大值的复杂度。因此本文采用搜索使优化目标函数J(P(t)|M)最大的方法获得最优的P(t)。在搜索到最优的P(t)后，将其代入N(P(t))的表达式中，就可获得最优的帧长N。Obviously, an analytical solution to this system of equations cannot be obtained. But if the bit error rate P _eb determined by the transmit power P(t) in equation (a) is regarded as a known number, then it is a quadratic equation of one variable about N, and its solution is

Or denoted as N(P(t)). Then substitute N(P _eb ) into equation (b) to get an equation with only one unknown P(t). The optimal P(t) can be obtained by numerically solving this equation, but it can also be obtained in [0,P The search within _d,max ] optimizes the objective function J(P(t)|M) (the variable in the objective function here has no frame length N, because it has been replaced by the function N(P(t)) of P(t). exchange) the largest P(t) is obtained. Observed

The expression of , it can be found that it is very complex, and also includes integral operations, which are solved by numerical calculation methods

The solution complexity of is significantly higher than that of searching for the maximum value of the optimization objective function J(P(t)|M). Therefore, this paper adopts the method of searching to maximize the optimization objective function J(P(t)|M) to obtain the optimal P(t). After searching for the optimal P(t), substitute it into the expression of N(P(t)) to obtain the optimal frame length N.

After obtaining the optimal P(t) and N under all available modulation modes, compare the values of the objective function J(P(t), M, N) that can be obtained under all modulation modes, and select the modulation that maximizes the objective function The mode is the optimal modulation mode, which together with the corresponding transmit power and frame length constitutes the solution {P(t), M, N} of the optimization problem P3, and the optimization problem is solved. The optimized frame length should satisfy N>N _CRC . If the optimized N ≤ N _CRC , no data is transmitted in the current time slot, and P(t)=0, R _b (t)=0.

The optimization algorithm is summarized as shown in Algorithm 1.

次。由于X(t)≥0时的计算复杂度远小于X(t)＜0时，作为计算复杂度上限的估计，我们假设X(t)＜0。每个调制方式下的计算复杂度在于P_eb的计算，而P_eb的计算则是Q函数的计算，可以采用查表法等降低计算复杂度(与加法、乘法的计算复杂度相当)的方式实现。因此一个调制方式下的计算复杂度为

进一步，每个调制方式下都需要进行一次最优 {P(t),N}的求解，共6种调制方式，所以1个时隙的计算复杂度为

一般而言，在可用功率范围内选择1000个功率点的精度已经足够，因此算法的复杂度很低。Algorithm 1 solves the three-parameter joint optimization problem of transmit power, modulation mode, and frame length. Since the set of available modulation modes is a finite set, Algorithm 1 first performs steps 2. to 12. for each modulation mode to optimize { P(t),N}. When X(t)≥0, the main calculation is to calculate the bit error rate _Peb and the frame length N. When X(t)<0, it is necessary to calculate the objective function J(P(t)|M) and N once at each power point when searching for the optimal power. When calculating J(P(t)|M) The main complexity is to compute _Peb once; a common search is required within the available power range

Second-rate. Since the computational complexity when X(t)≥0 is much smaller than when X(t)<0, we assume that X(t)<0 as an estimate of the upper limit of computational complexity. The computational complexity of each modulation mode lies in the calculation of _Peb , and the calculation of _Peb is the calculation of the Q function, and methods such as table look-up can be used to reduce the computational complexity (equivalent to the computational complexity of addition and multiplication). accomplish. Therefore, the computational complexity of a modulation scheme is

Further, the optimal {P(t),N} needs to be solved once in each modulation mode, there are 6 modulation modes in total, so the computational complexity of one time slot is

In general, the accuracy of selecting 1000 power points within the available power range is sufficient, so the complexity of the algorithm is low.

如无特殊说明，电池电量虚队列的偏移量设置为A＝40，惩罚项权重V＝5，电池初始电量为50J。The present invention will be further described in detail below with reference to the accompanying drawings. Unless otherwise specified, the parameters in the simulation are set as follows: the energy arrival process of node S obeys the Poisson process of compound uniform distribution, the arrival rate is λ=0.7 units/slot, and each unit energy obeys [0, 0.4] (unit J) The battery capacity E _max = 50J, the maximum charging power P _c,max =0.8W, the maximum discharge power P _d,max =0.9W; the time slot length Δt = 1s; the channel is a Rayleigh fading channel, the channel The coefficient h(t) obeys a complex Gaussian distribution with zero mean and unit variance, and remains unchanged within a time slot; noise power spectral density N ₀ =10 ^-8 W/Hz; check bit length N _CRC =32 bits; symbol Rate R _s = 10 ⁶ Baud, bandwidth B = 10 ⁶ Hz. The search step size in the transmit power search algorithm is

Unless otherwise specified, the offset of the battery power virtual queue is set to A=40, the penalty item weight V=5, and the initial battery power is 50J.

In order to compare the performance of the present invention, four algorithms are compared.

(1) Greedy Algorithm (GA): The sending node of each time slot sets the sending power according to the maximum value of the available power in the battery. Under the limit of the maximum power, there are

(2) Half Power Algorithm (HPA): The sending node in each time slot sets the sending power by half of the available power in the battery. Under the limit of the maximum power, there are

(3) The online power control algorithm proposed by the literature [AMIMAVAEI F, DONG M. Online power control optimization for wireless transmission with energy harvesting and storage [J]. IEEE Transactionson Wireless Communications, 2016, 15(7): 4888-4901.]: In this paper, the channel capacity obtained by Shannon's formula is used as the transmission rate, and the Lyapunov framework is used to optimize the transmission power to maximize the long-term average transmission rate of the system. The battery power virtual queue offset A and penalty item weight V selected in the literature are relatively conservative. Here, the parameter settings that can obtain better performance are selected in the simulation, that is, A=40, V=4.

(4) Offline water injection algorithm: The transmitter has obtained the channel changes and energy collection in the entire transmission process before transmission, and obtains the average transmission power of the signal according to the total energy collected in the transmission process. Under the constraint of this average power, aiming at maximizing the average channel capacity, the water-filling algorithm is used to obtain the transmit power of each time slot. This algorithm does not consider the causality of data and energy, nor does it consider the overflow of the battery.

When simulating the actual achievable transmission rate of the algorithm, first obtain the transmit power according to the algorithm, then calculate the bit error rate P _eb of the six modulation modes, and then calculate the optimal frame length N under different modulation modes according to formula (c), and the achievable information transmission rate R _b (t), select the maximum value as the information transmission rate that the algorithm can achieve.

Fig. 2 is the trajectory diagram of the average information transmission rate of different algorithms changing with time in the simulation process of 4000 time slots. The average information transmission rate per time slot is the average of the transmission rates of each time slot from the start of the simulation to the current time slot. The dotted line in the figure is the theoretical maximum rate that can be achieved under the same transmission power, that is, the channel capacity; the solid line is the actual maximum transmission rate that can be achieved under the six optional modulation modes. It can be seen from the simulation results that the present invention is significantly higher than the greedy algorithm and the half-power algorithm in terms of the theoretically achievable highest transmission rate and the actual achievable transmission rate. The greedy algorithm and the half-power algorithm only make decisions on the transmit power based on the battery state of the current time slot. The transmit power of each time slot of the greedy algorithm is determined by the energy collected in the previous time slot, and there is no energy scheduling between time slots, so the performance is the best. Poor; the half-power algorithm reserves half of the energy in the current battery for use in subsequent time slots, and to a certain extent averages the transmit power of different time slots, so the performance is better than the greedy algorithm. However, neither of the two algorithms considers the influence of the channel state on the transmission performance of the system. The present invention optimizes the source node's transmit power, modulation mode and frame length according to the channel state and battery power. Compared with the greedy algorithm and the half-power algorithm, it has obvious advantages. performance advantage. The offline water-filling algorithm knows the channel state and energy collection before transmission, and performs global power allocation with the goal of maximizing the theoretical transmission rate according to the channel state, and is not limited by the causality of energy and data, so it can obtain the highest theoretical Compared with the theoretical maximum transmission rate under the transmission power of the present invention, the transmission rate has a performance advantage of about 7.7%. The algorithm in the literature [AMIMAVAEI F, DONG M.Online powercontrol optimization for wireless transmission with energy harvesting and storage[J].IEEE Transactions on Wireless Communications,2016,15(7):4888-4901.] optimizes the channel capacity as the objective function , the theoretical maximum transmission rate supported by the obtained power control strategy is also better than that of the present invention, with a performance advantage of about 5.9%. However, if the actual available modulation mode and the overhead in the data frame are considered, the transmission power determined by the offline water-filling algorithm and the literature algorithm is not optimal. When determining the transmission power, the present invention has considered the modulation mode and the overhead in the data frame at the same time, and jointly optimized the transmission power, modulation mode and frame length. Therefore, the actual transmission rate that can be achieved is higher than the offline water injection algorithm and the literature algorithm.

Figure 3 shows the trajectories of the battery power changes over time for the four online algorithms during the simulation process. The selection of the transmission power in the offline water injection algorithm is not constrained by the causality of the collected energy, and the battery power changes have no practical significance, so they are not given here. The simulation results show that the battery power of the algorithm proposed in the present invention and the algorithm in the literature can fluctuate up and down at a certain level, and each time slot can ensure that there is enough storage power for data transmission and enough remaining storage space to store and collect data. energy of. The greedy algorithm and the half-power algorithm consume the pre-stored power in a very short time, and then the power stabilizes at a very low level.

Fig. 4 shows the variation of transmission power, modulation mode, frame length, etc. with channel gain and battery power in the present invention in the 150th to 200th time slots in the simulation. From top to bottom in the figure are channel gain g(t), battery power E _S (t), transmit power P(t), modulation order M, frame length N, and transmission rate R _b (t). It can be seen from the figure that the present invention adaptively adjusts the transmit power, modulation mode and frame length according to the channel condition and the battery state. When the channel state is good and the battery power is sufficient, a larger transmission power, a higher-order modulation method and a larger frame length will be used for transmission, and a high transmission rate can be obtained, such as time slot 180; when the channel fading is serious, When the storage energy of the battery is small, a lower transmission power and a lower-order modulation method will be selected, or even stop transmission, such as time slot 155, to reserve more energy for use after the channel state improves; When the battery power is sufficient, or the channel condition is good, but the battery power is low, or both are at a general level, the appropriate transmit power, modulation method and frame length will be selected for transmission, taking into account the effective use of channel resources and energy resources. , such as time slots 163, 189.

Figures 5-7 analyze the effects of algorithms and battery parameters on system performance. The results given in the simulation figures are the average of the simulation results for 10,000 time slots.

Figure 5 shows the effect of energy virtual queue offset change on the performance of the system. The offset A can control the average charge level in the battery to ensure that there is enough energy and storage space in the battery to adapt to random changes in channel state and energy harvesting. As can be seen from the figure, when A increases, the average level of battery storage power increases, and the transmission rate of the system increases first and then decreases slightly. This is because when A increases, the average power level of the battery increases, and each time slot has a wider range of adjusting the transmission power according to the channel state. When the channel condition is good, it can support a higher transmission rate and utilize the channel more fully. Therefore, the average The transfer rate increases. However, when A is too large, the average remaining storage space of the battery decreases, and the probability of battery overflow and partial loss of collected energy increases, resulting in a slight decrease in the transmission rate.

Figure 6 shows the effect of weight V changes in the drift plus penalty function on the system performance. The weight V is used to trade off between the maximization of the objective function and the stability of the energy virtual queue. The stability of the battery power is measured by the standard deviation of the battery power throughout the simulation period, and the formula is

显然，标准差越小，电池电量的稳定性越好。in

Obviously, the smaller the standard deviation, the better the stability of the battery power.

Figure 6(a) shows that when V increases, the average battery power decreases, and when V is greater than 7, the average value of the average battery power is very small; Figure 6(b) shows that with the increase of V, the average information transmission The rate increases first and then decreases, and reaches the maximum value when V=6; Figure 6(c) shows that the standard deviation of battery power first increases and then decreases with the increase of V. These simulation results show that when V increases, the algorithm focuses more on maximizing the transmission rate, and tends to use higher transmit power for transmission, so that the power in the battery decreases, and the battery power stability decreases. When V is small, the information transfer rate can be reduced. It increases as V increases. However, after V is too large (>6), and then increase V, the average battery power will be very low, and the maximum power that can be supported is too small. When the channel conditions are good, whether there is enough power to support higher information transmission rates, on the contrary resulting in reduced transmission performance. The reason why the standard deviation of the battery power decreases with the increase of V after V is greater than 6 is that the battery power is already very low at this time, and the possible fluctuation range of the battery power is already small, which does not mean that the stability of the battery power has changed. All right.

Figure 7 shows the effect of energy arrival rate λ variation on system performance. With the increase of the energy arrival rate λ, the average value of the energy arriving at the energy harvesting node in each time slot increases, and the energy that can be collected increases, so the average level of battery power increases, as shown in Figure 7(a). As the available energy increases, the average transmission power per time slot increases, and the transmission rate increases accordingly, as shown in Figure 7(b).

Claims (7)

1. The method for online combined control of power and modulation mode in the energy collection communication system based on the Lyapunov optimization framework is characterized by comprising the following steps:

(1) the source node collects energy from the surrounding environment every time slot to be used for sending information to the destination node, and the transmission rate is maximized under the constraint of the electric quantity stored by a battery;

(2) utilizing a Lyapunov optimization framework, adding offset to the battery power of a source node to obtain a virtual queue, taking a negative value of a transmission rate as a penalty term, constructing the drift and penalty term, and converting the constrained optimization problem of the maximized long-term average transmission rate into the minimized drift and penalty term;

(3) converting the minimum drift plus penalty term into an upper bound of the minimum drift plus penalty term;

(4) and making a decision according to the energy arrival and the channel state, and searching the optimal combination of the transmission power, the modulation mode and the frame length, namely solving the optimal solution of the optimal objective function.

2. The Lyapunov optimization framework-based online combined control method for power and modulation mode in the energy collection communication system according to claim 1, characterized in that: in the step (1), a communication system is modeled, and an optimization problem is constructed by taking maximum transmission power limit, limit of battery storage capacity to transmission power and battery capacity as constraint conditions and taking maximization of a transmission rate as a target.

3. The Lyapunov optimization framework-based online combined control method for power and modulation mode in the energy collection communication system according to claim 2, characterized in that: the optimization problem is as follows:

s.t.0≤P(t)≤P_d,max

0≤ΔtP(t)≤E_S(t)

M∈Θ

N≥N_CRC

wherein,

indicating the rate of correctly transmitted information data bits per unit bandwidth, E [ ·]For the desired operation, P_ebFor bit error rate, P_d,maxIs a maximum transmit power constraint; delta tP is more than or equal to 0 and less than or equal to (t) E_S(t) is battery storage capacity constraint, Δ t is a time slot length; m is a modulation order, and theta is a set of selectable modulation modes; the length N of the data frame satisfies that N is more than or equal to N_CRC；

In order to achieve long-term power constraints,

the average stored energy per time slot into the battery and the average transmitted power, respectively.

4. The Lyapunov optimization framework-based online combined control method for power and modulation mode in the energy collection communication system according to claim 1, characterized in that: the step (2) is specifically as follows:

adding an offset to the battery power of the source node to be used as an energy virtual queue:

X(t)＝E_S(t)-A

wherein A is an offset and E_S(t) is the battery power at the beginning of time slot t;

a quadratic Lyapunov function of

Then Lyapunov drifts to

The drift plus penalty term is Δ (X (t)) -VE [ R [_b(t)|X(t)]

In the formula E [ R ]_b(t)]Is the target of optimization, i.e. the average transmission rate, with negative values as penalty terms, and V is the weight between drift and penalty terms;

the optimization problem translates into minimizing drift plus a penalty term, i.e.

5. The Lyapunov optimization framework-based online combined control method for power and modulation mode in the energy collection communication system according to claim 1, characterized in that: converting the minimum drift plus penalty term into an upper bound of the minimum drift plus penalty term and converting the optimization problem into a lower bound of the minimum drift plus penalty term in the step (3)

6. The Lyapunov optimization framework-based online combined control method for power and modulation mode in the energy collection communication system according to claim 1, characterized in that: the method for solving the optimal solution of the optimization objective function in the step (4) comprises the following steps:

let J (P) (t), M, N) ═ P (t) X (t) + VR_b(t) is an optimization objective function, and the optimization problem is changed to the optimization objective function with the maximization J (P) (t), N | M) under the given modulation mode according to the limited number of the modulation modesOptimizing the transmission power P (t) and the frame length N; finally, M with the maximum J (P (t), M and N) and the corresponding P (t) and N are selected as the optimal solution.

7. The Lyapunov optimization framework-based online combined control method for power and modulation mode in the energy collection communication system according to claim 6, characterized in that: the optimized transmission power p (t) and the frame length N are specifically as follows:

when X (t) is greater than or equal to 0, the objective function is monotonously increased, and P (t) should take the maximum value P_d,maxIn P (t) ═ P_d,maxCalculating to obtain the bit error rate P_ebSubstituting the obtained value into a partial derivative formula of the objective function to N, and solving the solution of the partial derivative formula to be 0, namely the optimal frame length N;

when x (t) < 0, the optimal solution for p (t), N should be the extreme point of the objective function J (p (t), N | M), i.e. the solution of the system of equations that should consist of two partial derivatives of 0.

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