CN112788629A

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

Info

Publication number: CN112788629A
Application number: CN202011628300.6A
Authority: CN
Inventors: 雷维嘉; 孙嘉琳; 付安琦
Original assignee: Chongqing University of Post and Telecommunications
Current assignee: Chongqing University of Post and Telecommunications
Priority date: 2020-12-31
Filing date: 2020-12-31
Publication date: 2021-05-11
Anticipated expiration: 2040-12-31
Also published as: CN112788629B

Abstract

The invention discloses a Lyapunov optimization framework-based online combined control method for power and modulation modes in an energy collection communication system. The method utilizes a Lyapunov optimization framework to convert a long-term time control method under the constraint of battery operation and available energy into a combined control method of transmitting power, a modulation mode and a frame length, wherein the combined control method is used for minimizing a virtual queue drift plus penalty as a target in each time slot, and solving is carried out. The invention makes decision only depending on the current battery state and channel state information, and has low calculation complexity and strong practicability.

Description

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

Technical Field

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

Background

With the rapid development of wireless communication technology, the application field thereof is continuously expanded, the number of network users is rapidly increased, and the problem of energy consumption is increasingly severe. The green communication technology based on the theory of "open source" and "throttling" is one of the hot techniques studied in academia and industry at present. Energy Harvesting (EH) is an important technology means of "open source", and nodes in a communication network collect energy (such as solar energy, wind energy, heat energy, etc.) from the natural environment and convert the energy into electric energy for information transmission. Due to instability of the environmental energy source, the energy collection amount has obvious random variation characteristics, and the randomness of the wireless channel state, the signal sending power and the information transmission rate need to be dynamically controlled, so that the collected energy and the channel resources are efficiently utilized. The transmission power control of the transmitter is a problem which is currently being studied. The power control strategies proposed in the related art can be classified into an offline control strategy and an online control strategy.

The offline management policy is applied to a case where information such as collected energy, channel state, and the like is known in advance. While this assumption is less than reasonable, offline policies achieve superior performance and are therefore often used as an upper bound for evaluating the performance of other policies. Energy harvesting communication systems with continuous energy and data arrival are considered in The literature [ REZAEE M, MIRMOSENSII M. energy harving systems with continuous energy and data arrival [ J ]. IEEE Journal on Selected Areas in communication, 2016,34(12): 3739-3753 ], giving a three-step optimal energy scheduling algorithm to achieve single-user throughput maximization. Data arrival and energy collection are modeled as continuous functions, and an offline power control algorithm is sought to maximize the average throughput of the system under a limited number of time slots. For an energy collection system under the condition of a fading channel, a directional water filling algorithm is proposed to control the sending power of each time slot, maximize the information Transmission in a limited Transmission time or minimize the Transmission time under the requirement of a certain Transmission data amount. The directional water filling algorithm refers to a water filling algorithm that the energy collected by the current time slot can only be used for power water filling of the later time slot, but can not be allocated to the previous time slot, namely, the use of the collected energy is causally restricted, and the energy can only flow directionally.

Unlike offline control algorithms, online algorithms rely primarily on statistical information of energy and data arrival, channel fading, etc., as well as current and past system states to make decisions. Under the condition that a transmitter can obtain statistical information reflecting an energy and data arrival process and a channel fading process, a power control process is modeled into a Markov Decision Process (MDP), and Dynamic Programming (DP) is applied to solve, so that the on-line power control solution which is researched more in related documents is provided. Point-to-point communication systems with maximum transmit power constraints are studied in the literature [ WANG Z, AGGARWAL V, WANG X. Power allocation for energy harnessing transmission with computational information [ J ]. IEEE transactions on Communications,2014, 62(11): 4080) 4093 ], a piecewise linear fitting function is defined based on battery status, the optimal transmit power allocation problem under random channel conditions is constructed as an MDP, and the optimization problem is solved using DP. In order to describe the system state more accurately and obtain better performance, the MDP-based scheme needs larger state and motion space, and the computational complexity of the algorithm is usually high. The Lyapunov optimization technology is an optimization method widely applied to the control theory, the statistical characteristics of the system state are not required to be known in the application, the decision is made according to the current system state, and the optimization method is very practical. The algorithm is particularly suited to solving the queuing problem, and queue backlog minimization is an essential goal and feature thereof. When the Lyapunov method is used for solving the optimization problem containing the constraint, a virtual queue can be constructed according to the constraint condition, the virtual queue is kept stable in the long-term time sense by minimizing the drift of the virtual queue, and the constraint condition is indirectly met; and the optimized target is used as a penalty item, the penalty item and the queue drift are combined to form 'queue drift plus penalty' as an optimized target function, and the target is optimized while the stability of the queue in the long-term time average sense is achieved by minimizing the target function. The method converts the long-term time-averaged optimization problem into a single-time-slot optimization problem, can reduce constraint conditions, and greatly reduces the complexity of solving the optimization problem. In the document [ AMIMAVAEI F, DONG M. Online power control optimization for Wireless transmission with energy transforming and storage [ J ]. IEEE Transactions on Wireless Communications,2016,15(7):4888 and 4901 ] for a point-to-point communication system in which a source node is powered by an EH device, an Online power control algorithm using a Lyapunov optimization framework is proposed to maximize a long-term average rate. The constraint of battery electric quantity is converted into virtual queue stability, the negative number of the maximized transmission rate is used as a penalty item, drift plus penalty is constructed, and the transmission rate is maximized while the battery electric quantity is kept stable by minimizing the upper bound of the 'drift plus penalty'.

In the documents introduced above regarding 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 an actual system, an appropriate channel code (including a type of code, a code length, and a code rate) and modulation scheme need to be selected according to a channel state and transmission power, so as to maximize a transmission rate (or throughput) while meeting the requirement of error probability. The actually achievable transmission rate is lower than the channel capacity, and the choice of channel coding and modulation has a very large influence on the final achievable transmission rate. In the document [ MA R, ZHANG W. Adaptive MQAM for energy transforming with-less communication with 1-bit channel feedback [ J ]. IEEE Transactions on Wireless communication, 2015,14(11): 6459 and 6470 ], a point-to-point energy collection Wireless communication system is constructed, and an MDP problem is constructed according to the comparison result of the channel state represented by 1 bit of a receiving end and a threshold value, and an optimal modulation mode and transmission power combination are sought by adopting a backward iteration algorithm, so that the average throughput of the system in a finite time slot is maximized. The algorithm realizes better transmission performance, but the backward iteration algorithm has high calculation complexity, only 1 bit is used for representing the channel state, and the randomness and diversity of the channel state cannot be accurately reflected. The document LI M Y, ZHAO X H, LIANG H, et al, deep re-initiation strategy polarization for communication systems with energy transforming and adaptive MQAM J. IEEE Transactions on Vehicular technology.2019,68(6):5782 and 5793 ] proposes an algorithm based on deep reinforcement learning to optimize the transmission power per slot with the goal of maximizing the actual transmission rate on the premise of satisfying the error performance required by the system, and to adopt the highest order modulation mode supportable under the current channel quality and transmission power. The algorithm improves the traditional Q learning algorithm, and improves the convergence rate of the Q learning algorithm. Simulation results show that the algorithm converges after a few iterations.

Disclosure of Invention

The invention researches the scheduling optimization problem of power and transmission rate in a point-to-point energy collection wireless communication system by taking the maximum long-term average throughput of the system as a target. The source node is equipped with an energy harvesting device and a rechargeable battery, and the energy of the transmitted signal per time slot is derived from the energy harvested from the surrounding environment. Under the condition that the battery capacity is limited, a Lyapunov framework is utilized to solve the joint optimization problem of the transmission power, the modulation mode and the frame length, and the long-term time average throughput is maximized.

In order to achieve the purpose, the invention adopts the following technical scheme: the optimization method comprises the steps of constructing an optimization problem with the maximum system transmission rate as a target, converting the optimization problem into an optimization problem of a long-term time average value, utilizing a Lyapunov framework to solve the optimization problem, constructing a 'drift plus penalty' item, converting a minimum 'drift plus penalty' item into an upper bound of the minimum 'drift plus penalty' item to achieve the optimization purpose, solving a three-parameter optimization problem comprising transmission power, a modulation mode and a frame length, and obtaining an optimal solution.

The method comprises the following specific 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 electric quantity of a source node to obtain a virtual queue, then using a negative value of a transmission rate as a penalty term to construct a 'drift plus penalty' term, and converting a constrained optimization problem of maximizing a long-term average transmission rate into a minimized 'drift plus penalty' term;

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

(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.

Specifically, the modeling of the communication system in the step (1) includes modeling and expressing an actual achievable transmission rate of the system and a battery power queue of the source node. Constructing an optimization problem by taking the maximum transmission power limit, the limit of battery storage capacity to the transmission power and the battery capacity as constraint conditions and taking the maximum long-term time average transmission rate as a target;

specifically, the optimization problem is solved by using the Lyapunov optimization framework in the step (2), namely starting from the stability of the queue, adding an offset to the battery capacity of the source node to be used as an energy virtual queue, keeping the queue stable to meet constraint conditions, using the long-term average transmission rate of the optimization target as a penalty item, and constructing and minimizing a 'drift plus penalty' item to achieve the optimization purpose

Specifically, the step (3) is realized by minimizing the upper bound of the drift plus penalty to satisfy the constraint condition indirectly, and an upper bound expression of the drift plus penalty term is obtained by a Lyapunov function and a Lyapunov drift formula;

specifically, in step (4), the transmission power, modulation scheme, and frame length should be appropriately adjusted according to the energy arrival and channel state. Since these 3 variables cannot be directly optimized jointly, but the number of modulation schemes is limited, the transmit power p (t) and the frame length N may be optimized with the maximum J (p (t), N | M) as the target under a given modulation scheme instead. Wherein, P (t) and N under the given modulation mode are optimized, when X (t) is more 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 objective function J (P (t), N | M)I.e. the solution of the system of equations that should be made up of two partial derivatives of 0. Finally, M with the maximum J (P (t) and N | M) and the corresponding P (t) and N are selected as the optimal solution.

Compared with the prior related research, the invention is characterized in that: (1) the invention provides a method for converting a long-term time-averaged optimization problem into a single-time slot optimization problem by adopting a Lyapunov optimization framework, converting energy constraint into a queue stability requirement, only depending on the current battery state and channel state, and not needing to obtain statistical information of energy arrival and channel fading variation, so that the method is an online low-complexity control algorithm; (2) compared with the Lyapunov method adopted by the literature, such as [ AMIMAVAEI F, DONG M. Online power control optimization for Wireless transmission with energy transforming and storing [ J ]. IEEE Transactions on Wireless Communications,2016,15(7):4888 + 4901 ], the algorithm provided by the invention optimizes the transmission power and simultaneously optimizes the modulation mode, the maximized target is not the limit of the transmission rate theoretically but the actually achievable transmission rate, and the simulation result shows that the actually achievable rate of the invention is higher than the literature algorithm; (3) the algorithm provided by the invention has more available modulation modes, considers the expenses such as necessary check bits and the like in the actual data frame, performs combined optimization on three parameters of the transmission power, the modulation mode and the frame length, and has higher practicability.

Drawings

FIG. 1 is a communication system model of the present invention;

FIG. 2 is a trace plot of average information transfer rate versus time for the algorithms proposed by the present invention and for the comparison algorithm;

FIG. 3 is a trace graph of source node battery power changes over time for the algorithm and comparison algorithm proposed by the present invention;

FIG. 4 is a simulation parameter of the algorithm proposed by the present invention during a portion of a time slot in a simulation;

FIG. 5 shows the effect of virtual queue energy offset A on information transfer rate and battery level average;

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

fig. 7 shows the effect of energy arrival rate λ on information transmission rate and battery level average.

Detailed Description

Consider a transmission system model as shown in fig. 1, the system comprising a sending node S and a destination node D. The transmitting node is equipped with an energy harvesting device and a rechargeable battery of limited capacity, which can harvest energy from the surrounding environment, store it in the battery and use it for transmitting data to the destination node. In the transmission process, the energy and the wireless channel collected by the sending node are randomly changed, and the sending node dynamically adjusts the sending power, the modulation mode and the data frame length according to the instantaneous channel state information and the energy collection condition, so that the long-term time average system rate is maximized, and the energy use efficiency is improved.

The unit power signal sent by the source node is recorded as x (t), the channel coefficient from the sending end to the receiving end is recorded as h (t), and the channel coefficient h (t) is kept unchanged in a time slot. The received signal at the receiving end can be expressed as

Where P (t) is the transmission power of the source node, and N (t) is the bilateral power spectral density N₀Additive white Gaussian noise of/2.

The capacity of the rechargeable battery of the source node is recorded as E_max(Jour, J) maximum charge rate of P_c,maxW is added. Note that the battery power at the beginning of time slot t is E_S(t) J, satisfy

0≤E_S(t)≤E_max

The transmission power of the transmitting node should not exceed the maximum discharge power P of the battery_d,maxI.e. by

0≤P(t)≤P_d,max

The energy consumed for transmitting information in the time slot should not exceed the amount of power stored in the battery at the beginning of the time slot, i.e. the causal constraint on battery power usage should be satisfied:

0≤ΔtP(t)≤E_S(t)

where at is the length of one slot. The energy collected by the energy collecting device from the environment in time slot t is E_a(t) J, assuming no energy loss during the charging and discharging of the battery, limited by the charging rate and the remaining capacity of the battery, the amount of electricity E stored in the battery during the time slot t_H(t) is

0≤E_H(t)≤min E_a(t),ΔtP_c,max,E_S(t)-ΔtP(t)

The 1 st term in the min function is the energy collected in this time slot, the 2 nd term is the maximum charge rate limit, and the 3 rd term is the battery remaining storage capacity limit. At the beginning of the next time slot, the battery power is updated to

E_S(t+1)＝E_S(t)-ΔtP(t)+E_H(t)

Due to the random time-varying characteristic of the wireless channel state and the instability of energy collection, the transmission power and modulation mode need to be adjusted continuously according to the channel state and the available energy condition. Assume that the set of selectable modulation schemes 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 B Hz

(the highest symbol rate that can be achieved for transmission of the frequency band without intersymbol interference is R_sB (baud). ) Wherein T is_SThe symbol rate in each modulation mode is the same for the symbol period. In data transmission, in order to enable a receiving side to determine whether received data has errors, the data to be transmitted needs to be grouped, and each group is attached with a check bit with a certain length to form a frame, and Cyclic Redundancy Check (CRC) is the most commonly used check code. And after receiving the data packet, the receiving end judges whether the received data packet is correct or not by checking whether the check relation between the data and the check bit meets the requirement, if so, the receiving end discards the data packet and requests to retransmit the data packet. Assuming that the data frame has a length of N bits and the CRC check bit has a length of N_CRCBits, the length of the information data sequence is N-N_CRCBit (N is more than or equal to N)_CRC). When in useWhen M-ary modulation is used, the length of the modulation symbol in each frame is

It is assumed here that N is log₂An integer multiple of M. The bit error rate when the above 6 modulation modes are adopted is

In the formula

E_bRepresenting the mean bit energy, N, of the received signal₀Represents the noise power spectral density,

Representing the received bit signal-to-noise ratio, E_bWith a relation to the transmission power P (t) of

Here g (t) ═ h (t) & gtdoes not smoke²Is the channel power gain. Q (-) in the formula for calculating the bit error rate is a Gaussian Q function, and the expression is

A frame can only be verified as correct if all bits in the frame have been received correctly, with a probability of the data frame being correct

P_cf＝(1-P_eb)^N

The number of information bits transmitted in an average frame is

N_info＝(N-N_CRC)×(1-P_eb)^N(bit)

One frame comprises L symbols, and one data frame has a transmission time length of

T_P＝L×T_S(s)

The invention takes the rate of correctly transmitted information data bits in unit bandwidth as an index for measuring the system performance, and the expression is

As can be seen from the above formula, the information transmission rate of the system is related to the transmission power, the modulation scheme and the frame length. The larger the transmission power, the higher the received signal-to-noise ratio and the lower the error probability, but the transmission power is constrained by the collected energy, and the energy should be reasonably used according to the channel state. For the modulation mode, if a higher-order modulation mode is adopted, each symbol can carry more information bits, but the bit error rate is higher, and the frame error rate is also higher; when a lower-cost modulation scheme is used, the number of bits transmitted in the same time period is small although the error rate is low. Therefore, it is necessary to select an appropriate modulation order to maximize the information transmission rate according to the transmission power and the channel fading condition. The selection of the frame length also affects the information transmission rate, when a longer frame is adopted for transmission, the proportion of check bits is smaller, the cost is smaller, but under the same bit error rate, the frame error probability is higher; on the contrary, when the frame length is small, the frame error probability is low, but the overhead such as check bits is large. Therefore, optimization of the frame length is also required. From this point of view, the information transmission rate actually achievable by the system is not a monotonic function of the modulation order and the frame length, and the optimal modulation order and frame length are related to the transmission power and the channel state, and the transmission power is constrained by the available energy. Therefore, the optimization problem of the present invention is to jointly optimize the transmission power p (t), the modulation order M and the frame length N of each time slot, so as to maximize the long-term average information transmission rate of the system:

s.t.0≤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≥N_CRC

in the constraints, E [. cndot. ] represents the desired operation. Since the energy collection and channel state are random processes which change randomly, P1 is a random optimization problem.

Rewriting battery updates to

E_S(t+1)-E_S(t)＝E_H(t)-ΔtP(t)

The time slot T has from 0 to T-1

Superposing the two ends of the above formula and obtaining the expected value

The left and right ends are simultaneously divided by T and the limit of T → ∞ is found to yield a long-term time-averaged relationship:

wherein,

the meaning of the above equation is that the collected energy should be used for information transmission in the long term. The battery electric quantity constraint of a single time slot in the original constraint problem is relaxed into the long-term electric quantity constraint, and the optimization problem is converted into the long-term electric quantity constraint

s.t.0≤P(t)≤P_d,max

0≤ΔtP(t)≤E_S(t)

M∈Θ

N≥N_CRC

Since the optimization goal is the optimization of the long-term time average, it can be solved using the Lyapunov framework. The constraint condition is converted into the problem of keeping virtual queue stability, the optimization target is used as a penalty item, a 'drift plus penalty' item is constructed, and performance optimization under the constraint condition is achieved by minimizing the 'drift plus penalty'. Firstly, a battery energy virtual queue of a sending node is constructed

X(t)＝E_S(t)-A

Wherein A is an offset. After the Lyapunov optimization, the queue length can fluctuate around 0, and the energy virtual queue is added with an offset, so that the battery capacity can be kept around the offset value and fluctuates up and down. Updating formula E according to battery power_S(t+1)＝E_S(t)-ΔtP(t)+E_H(t) the update formula of the available energy virtual queue is

X(t+1)＝X(t)-ΔtP(t)+E_H(t)

Defining a quadratic Lyapunov function

Lyapunov drift is defined as

The smaller the offset, the less the change in queue length for the two slots, and the queue length is approximately 0. Information transmission rate R to be maximized_bIs used as a penalty term, and 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 penalty terms, which is a normal number, used to trade off queue stability against system transmission rate maximization. If "drift plus penalty" can be minimized, the information transfer rate is maximized while keeping the virtual queue (i.e., battery charge) stable. Further, there is an upper bound on "drift plus penalty", and minimizing "drift plus penalty" instead of minimizing its upper bound may further reduce the complexity of the optimization problem solution.

In conclusion, the following results

Due to P (t) and E_S(t) are all finite values, then

Must be a non-negative limit value, and must have a non-negative constant B satisfying

Then

Δ(X(t))≤B+X(t)E[E_H(t)-ΔtP(t)|X(t)]

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)]

By keeping the virtual queue of energy stable, i.e. the charge of the battery fluctuates within a limited range and does not tend to infinity or to 0 over time, the energy collected in the long term is equal to the energy used for information transmission, so the constraint in P2

If satisfied, it can be removed from the optimization constraints. Further elimination of "drift plus penalty" upper bound from P (t), M, N noneThe related item is multiplied by-1, the corresponding minimization is changed into maximization, meanwhile, since the current channel state and the current battery state are known, the mean value operation in the upper bound can be removed, and the optimization problem is restated as a single-slot optimization problem:

M∈Θ

N≥N_CRC

the above equation has been rewritten for the maximum transmit power constraint and the battery power usage constraint in the P2 optimization problem.

The optimization problem is further solved. Let J (P) (t), M, N) ═ P (t) X (t) + VR_b(t) is an optimization objective function, where R_b(t) is related to the modulation scheme (modulation order), frame length, and transmission power. The optimization problem P3 is a 3-variable joint optimization problem, in which the selectable modulation scheme is one of BPSK, QPSK,8PSK,16QAM,32QAM, and 64QAM, i.e., M can only select a limited number of values. Since these 3 variables cannot be directly optimized jointly, but the number of modulation schemes is limited, the transmit power p (t) and the frame length N may be optimized with the maximum J (p (t), N | M) as the target under a given modulation scheme, and then M with the maximum J (p (t), N | M) and its corresponding p (t), N are selected as the optimal solutions. The solution for the optimal P (t), N given M is analyzed below.

First, the partial derivative of the objective function to N is

In the formula P_ebThe bit error rate calculated for the above formula. The partial derivative of the objective function pair P (t) is

K in the above formula is constantly greater than 0 and is

Wherein,

as can be seen from the partial derivative formula of the objective function for P (t), when X (t) is greater than or equal to 0,

the objective function monotonically increases. Obviously, to maximize the objective function, P (t) should take the maximum value P_d,max. From a practical physical sense, x (t) ≧ 0 indicates that there is sufficient charge in the battery and that maximum transmit power can be used for transmission. At P (t) ═ P_d,maxCalculating to obtain the bit error rate P_ebAnd substituting 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. P_ebWhen the information is known, the information is transmitted to the mobile terminal,

is a quadratic equation of one element, the solution of which is

Negative solutions have been discarded here.

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:

obviously, the solution of this system of equationsThe analysis is not available. But if the bit error rate P determined by the transmission power P (t) in equation (a) is used_ebWhen viewed as a known number, it is a quadratic equation of one-element with respect to N, the solution of which is

Or as N (P (t)). Then N (P) is added_eb) Substituting into equation (b) to obtain an equation containing only one unknown P (t), and solving the optimal P (t) by numerical method, but also in [0, P ]_d,max]The intra-search results in the maximum P (t) of the optimization objective function J (P (t) M) (where the variables in the objective function have no frame length N, since they have been replaced by the function N (P (t)) of P (t)). Observation of

The expression of (A) can be found to be very complex, and also comprises integral operation, and the numerical calculation method is adopted to solve

The complexity of the solution is significantly higher than the complexity of searching the maximum value of the optimization objective function J (p (t) M). Therefore, the optimal p (t) is obtained by searching the maximum optimization objective function J (p (t) M). After the optimal P (t) is searched, the optimal P (t) is substituted into the expression of N (P (t)), and the optimal frame length N can be obtained.

After obtaining the optimal P (t) and N under all available modulation modes, comparing the values of the objective functions J (P (t), M and N) obtained under all modulation modes, selecting the modulation mode which enables the objective function to be the maximum as the optimal modulation mode, forming the solution { P (t), M and N } of the optimization problem P3 together with the corresponding transmission power and frame length, and completing the solution of the optimization problem. The optimized frame length should satisfy N > N_CRCIf the optimized N is less than or equal to N_CRCThe current time slot does not transmit data, let p (t) be 0, R_b(t)＝0。

The optimization algorithm is summarized as shown in algorithm 1.

The algorithm 1 solves a joint optimization problem of three parameters of sending power, modulation modes and frame length, and because the available modulation mode set is a finite set, the algorithm 1 firstly executes the steps 2-12 for each modulation mode, and optimizes the { P (t), N } under the given modulation mode. When X (t) is greater than or equal to 0, the main calculation is to calculate the bit error rate P_ebFrame length N. When X (t) < 0, the objective function J (P (t) | M) and N are calculated once at each power point when the optimal power is searched, and the main complexity in calculating J (P) (t) | M) is to calculate P once_eb(ii) a Common need search within available power range

Next, the process is carried out. Since the computational complexity is much less for X (t) ≧ 0 than for X (t) < 0, we assume that X (t) < 0 as the upper limit of computational complexity. The computational complexity of each modulation mode is P_ebIs calculated by P_ebThe calculation of (2) is the calculation of the Q function, and can be realized by a method of reducing the calculation complexity (equivalent to the calculation complexity of addition and multiplication) by using a table look-up method and the like. The computational complexity in one modulation scheme is thus

Furthermore, the optimal { P (t), N } needs to be solved once under each modulation mode, and 6 modulation modes are total, so the computational complexity of 1 time slot is

Generally speaking, the accuracy of selecting 1000 power points within the available power range is sufficient, and therefore the complexity of the algorithm is low.

The present invention will be described in further detail below with reference to the accompanying drawings. Unless otherwise indicated, the parameter settings in the simulation are as follows: node (C)The arrival process of the energy of the point S is subjected to a composite uniformly distributed Poisson process, the arrival rate is lambda which is 0.7 unit/time slot, and each unit energy is subjected to [0,0.4 ]](unit J) uniform distribution among; capacity E of battery_max50J, maximum charging power P_c,max0.8W, maximum discharge power P_d,max0.9W; the time slot length delta t is 1 s; the channel is a Rayleigh fading channel, and the channel coefficient h (t) obeys the complex Gaussian distribution of zero mean and unit variance and keeps unchanged in a time slot; noise power spectral density N₀＝10^-8W/Hz; check bit length N_CRC32 bits; symbol rate R_s＝10⁶Baud, bandwidth B10⁶Hz. The search step size in the transmission power search algorithm is

If not specifically stated, the offset of the battery charge virtual queue is set to a-40, the penalty term weight V-5, and the battery initial charge is 50J.

To compare the performance of the present invention, a comparison was made with 4 algorithms.

(1) Greedy Algorithm (Greedy Algorithm, GA): each time slot transmitting node sets the transmitting power according to the maximum value of the available electric quantity in the battery, and under the limiting condition of the maximum power, the transmitting power is set

(2) Half Power Algorithm (Half Power Algorithm, HPA): each time slot transmitting node sets the transmitting power by half of the available electric quantity in the battery, and under the limitation condition of the maximum power, the transmitting power is

(3) The on-line power control algorithm proposed in the document [ AMIMAVAEI F, DONG M. on line power control optimization for Wireless transmission with energy harving and storage [ J ]. IEEE Transactions on Wireless Communications,2016,15(7):4888 + 4901 ]: the literature takes the channel capacity obtained by a shannon formula as a transmission rate, and optimizes the transmission power by using a Lyapunov framework to maximize the long-term average transmission rate of the system. The battery capacity virtual queue offset A and the penalty term weight V selected in the simulation are conservative, and parameter settings which can obtain better performance are selected during the simulation, namely A is equal to 40, and V is equal to 4.

(4) An offline water injection algorithm: the transmitting end obtains the change situation of the channel and the energy collection situation in the whole transmission process before transmission, and obtains the average transmitting power of the signal according to the total energy collected in the transmission process. Under the constraint of the average power, the water filling algorithm is adopted to obtain the transmission power of each time slot by taking the maximum average channel capacity as a target. This algorithm does not consider the causality of data and energy, nor the overflow of the battery.

When the actually achievable transmission rate of the comparison algorithm is simulated, the sending power is firstly obtained according to the algorithm, and then the bit error rate P of 6 modulation modes is calculated_ebThen, according to the formula (c), the optimal frame length N under different modulation modes and the achievable information transmission rate R are obtained by calculation_bAnd (t), selecting the maximum value as the information transmission rate which can be achieved by the algorithm.

Fig. 2 is a trace graph of average information transfer rate over time for different algorithms during a 4000-slot simulation. The average information transmission rate per time slot is the average of the transmission rates of the time slots from the start of the simulation to the current time slot. The dotted line in the figure is the theoretical highest rate, i.e. channel capacity, that can be achieved at the same transmit power; the solid line is the highest transmission rate that can be achieved in practice with 6 alternative modulation schemes. From the simulation results, it can be seen that the transmission rate of the present invention, whether the theoretically highest transmission rate or the actually achievable transmission rate, is significantly higher than the greedy algorithm and the half-power algorithm. The greedy algorithm and the half-power algorithm only make a decision of transmitting power according to the battery state of the current time slot, the transmitting power of each time slot of the greedy algorithm is determined by the energy collected by the previous time slot, and energy scheduling between time slots is completely avoided, so that the performance is the worst; the half-power algorithm reserves half of the energy in the current battery for the use of the following time slots, and averages the transmission power of different time slots to a certain extent, so that the performance is better than that of the greedy algorithm. However, the two algorithms do not consider the influence of the channel state on the transmission performance of the system, and the invention optimizes the sending power, the modulation mode and the frame length of the source node according to the channel state and the battery power, and has obvious performance advantages compared with a greedy algorithm and a half-power algorithm. The offline water-filling algorithm knows the channel state and the energy collection condition before transmission, performs global power distribution by taking the maximum theoretical transmission rate as a target according to the channel state, and is not limited by causality of energy and data, so that the offline water-filling algorithm can obtain the highest theoretical transmission rate, and has a performance advantage of about 7.7% compared with the theoretical highest transmission rate under the transmission power of the invention. The algorithm of the document [ AMIMAVAEI F, DONG M. Online power control optimization for Wireless transmission with energy transforming and storage [ J ]. IEEE Transactions on Wireless Communications,2016,15(7): 4888-. However, if the actually available modulation scheme 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. The invention considers the overhead in the modulation mode and the data frame when determining the sending power, and optimizes the sending power, the modulation mode and the frame length in a combined manner, so that the actually achievable transmission rate is higher than the offline water filling algorithm and the literature algorithm.

Fig. 3 is a trace diagram of battery power changes of 4 online algorithms along with time in a simulation process, selection of transmission power in an offline water-filling algorithm is not causally constrained by collected energy, and battery power changes have no practical significance, so that no representation is given here. Simulation results show that the battery power of the algorithm and the literature algorithm provided by the invention can fluctuate up and down at a certain level, and each time slot can ensure that enough storage power is used for transmitting data and enough residual storage space is used for storing collected energy. The greedy algorithm and the half-power algorithm consume the pre-stored electric quantity in a short time, and then the electric quantity is stabilized at a low level.

Fig. 4 shows the variation of the transmission power, modulation mode, frame length, etc. with the channel gain and battery power in the 150 th to 200 th time slots in the simulation. The channel gain g (t) and the battery power E are shown from top to bottom_S(t), transmission power P (t), modulation order M, frame length N, transmission rate R_b(t) of (d). It can be seen from the figure that the present invention adaptively adjusts the transmission power, modulation scheme, and frame length according to the channel condition and the battery status. When the channel state is good and the battery power is sufficient, the transmission can be carried out by adopting larger sending power, a higher-order modulation mode and a larger frame length, and a high transmission rate, such as a time slot 180, can be obtained; when the channel fading is severe and the battery energy is less, a lower transmission power and a lower-order modulation mode are selected, and even transmission is stopped, such as a time slot 155, and more energy is reserved for the use after the channel state is improved; when the channel condition is general but the battery power is sufficient, or the channel condition is good but the battery power is low, or both are at a general level, an appropriate transmission power, modulation scheme and frame length are selected for transmission, and effective use of channel resources and energy resources is considered, such as time slots 163 and 189.

Fig. 5-7 analyze the effect of the algorithm and battery parameters on system performance. The results given in the simulation chart are the average of the simulation results for 10000 time slots.

Figure 5 shows the impact of energy virtual queue offset changes on the performance of the system. The offset A can control the average electric quantity level in the battery, ensure that the battery has enough energy and storage space, and adapt to the random change of the channel state and the energy collection amount. As can be seen from the figure, as a increases, the average level of battery charge 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, the range in which the transmission power is adjusted in each slot according to the channel state is wider, a higher transmission rate can be supported when the channel condition is good, and the channel is more fully utilized, so the average transmission rate increases. However, when a is too large, the average remaining storage space of the battery is reduced, the probability that the battery capacity overflows and the collected energy is partially lost is increased, and the transmission rate is slightly reduced.

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

Wherein

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

FIG. 6(a) shows that as V increases, the average battery charge decreases, and after V is greater than 7, the average of the average battery charge is already very small; fig. 6(b) shows that as V increases, the average information transfer rate increases first and then decreases, reaching a maximum value when V is 6; fig. 6(c) shows that the standard deviation of the battery charge increases first and then decreases with increasing V. These simulation results show that the algorithm is more concerned with maximizing transmission rate when V increases, and tends to transmit with higher transmit power, so that the amount of power in the battery decreases, the battery power stability decreases, and the information transmission rate can increase with V increase when V is smaller. However, if V is too large (>6), increasing V will result in low average battery power and too small maximum power, and when the channel condition is good, there is not enough battery power to support higher information transmission rate, and the transmission performance will be reduced. 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 low, the possible fluctuation range of the battery power is already small, and the stability of the battery power is not improved.

Fig. 7 shows the effect of energy arrival rate λ variation on system performance. As the energy arrival rate λ increases, the average of the energy arriving at the energy harvesting node per slot increases, the collectable energy increases, and thus the average level of battery charge increases, as shown in fig. 7 (a). As the available energy increases, the average transmission power per slot increases and the transmission rate increases accordingly, as shown in fig. 7 (b).

Claims

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:

(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;

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.