CN113329419A - Raptor code-based online joint control method for power and rate of energy collection communication system - Google Patents

Abstract

The invention discloses an energy collection communication system power and rate online combined control method based on Raptor codes. Aiming at a point-to-point energy collection wireless communication system combined with a Raptor code, under the conditions of energy arrival and random change of a channel state, a joint control method of transmitting power, a modulation mode and code word length under the constraint of available energy and aiming at maximizing a long-term average reachable transmission rate is provided, and an optimization problem is converted into a single-slot optimization problem with minimized drift and punishment by further utilizing a Lyapunov optimization framework. Finally, a low-complexity solution is then provided. The invention makes a decision only depending on the current battery state and channel state information, adopts Raptor coding and adaptive modulation technology for transmission, has the actual communication rate closer to the channel capacity, and is a method with high efficiency, low complexity and strong practicability.

Description

Raptor code-based online joint control method for power and rate of energy collection communication system

Technical Field

The invention relates to the field of information communication, in particular to a method for jointly controlling the transmission power, the modulation mode and the code word length of a communication system powered by collected energy.

Background

Wireless communication networks are continuously expanding in size, resulting in an increasing demand for power from transmission systems. In order to deal with the increasingly severe problem of energy consumption, the utilization of renewable energy sources to supply power to communication equipment will be an important direction for the development of future communication systems and networks. Energy Harvesting (EH) refers to a node in a communication network collecting energy (such as solar energy, wind energy, thermal energy, etc.) from a natural environment and converting the energy into electric energy for information transmission. Due to the instability of an environment energy source, the energy collectable by the energy collecting equipment has randomness and uncertainty, and a communication system introducing the energy collecting technology needs to design a reasonable energy scheduling and distributing algorithm, fully utilizes channels and energy resources and ensures the lasting and stable operation of the system. In the existing relevant research documents, energy scheduling strategies in an energy collection communication system can be divided into an offline scheduling strategy and an online scheduling strategy according to whether a sending end can know energy arrival and channel states in an information transmission process in advance.

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. The document [ Wang Zhe, Aggarwal V, Wang Xiao Dong, iterative dynamic Water-filling V, Wang Xiao odong, iterative dynamic Water-filling for multiple access channels with energy harvesting [ J ]. IEEE Journal of Selected Areas in communication, 2015,33(3):382 and 395 ] researches the energy scheduling algorithm in the multi-user multiple access system for energy collection, and under the condition of the known channel state and energy collection state of a plurality of time slots, the iterative dynamic water filling algorithm is adopted to maximize the sum rate of each time slot. Unlike off-line control algorithms, on-line 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. 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 method is a very practical optimization method. 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 virtual queue drift, 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 a 'queue drift plus penalty' as an optimized target function, and the target optimization is realized while the stability of the queue is achieved in the long-term time average sense 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-. 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 an actual system, it is also necessary to select an appropriate channel code (including a type of code, a code length, and a code rate) and a modulation scheme according to a channel state and a transmission power, and maximize a transmission rate (or throughput) while satisfying a requirement of an 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 an energy-harvesting wireless communication system, channel conditions, available energy, transmission power, etc. are constantly changing, so that a rate adaptive technique is more required to obtain higher channel and energy utilization efficiency. In a document [ Choi B J, Hando L, optimal mode-switched adaptive modulation [ C ]// IEEE Global communication Conference,2001:3316-3320 ], the influence of parameters such as transmitting power, modulation order and coding rate of a transmitting end on transmission performance is comprehensively considered, and the spectral efficiency of a multi-stage adaptive M-QAM modulation system under a fixed and variable power strategy is contrastively analyzed. Simulation results show that the self-adaptive technology after multi-parameter joint optimization can obviously improve the error code performance and the throughput of the system. A method for on-line resource allocation algorithm for weighting and rate maximization in an energy collection downlink multi-user multi-input multi-output system is provided in the documents [ Zeng Weiliang, Zheng Y R, Schober R. on-line resource allocation for generating downlink multi-user systems: coding rate and sub-channel selection [ J ]. IEEE Transactions on Wireless Communications,2015,14(10): 5780 and 5794 ], and a transmission power control problem during transmission with different modulation modes and coding rates in actual transmission is constructed into a stochastic dynamic programming problem for solving. The literature decomposes the high-dimensional random dynamic programming problem into an equivalent three-layer optimization problem, respectively gives the optimization algorithm solving process of each layer, and verifies the performance of the algorithm through simulation. In the literature [ Mota M P, Araujo D C, Costa F H, et al, adaptive modulation and coding based on recovery learning for 5G networks [ J ].2019 IEEE Global works, 2019:1-6 ], a coding and modulation selection scheme based on reinforcement learning is provided for a downlink multi-user transmission model, and a base station formulates a corresponding modulation and coding strategy according to a current channel state evaluation result and feeds back the evaluation result of a current time slot as an award to a formulation link of a next time slot sending strategy. The scheme can ensure that the base station can keep low bit error rate transmission and simultaneously improve the frequency spectrum utilization rate.

In the research literature of the power control problem of the energy collection system, the limit value of the transmission rate in theory is taken as an optimization target, and the influence of factors such as coding and modulation on the actual transmission performance is not considered. Some documents add a modulation scheme selection strategy on the basis of a power control strategy, but still do not consider channel coding, so that the actual communication rate and the channel capacity still have a gap, and the modulation schemes proposed in the documents are few, and the application scenarios are limited. In the above research literature for the transmission performance of the rateless code, when the Raptor code is used for transmission, situations in which the decoding codeword is too long, the decoding complexity is too high, or the upper limit exists in the amount of mutual information of the coded bits when the channel condition is good easily occur.

Disclosure of Invention

The invention researches the optimization problem of power and transmission rate in a point-to-point energy collection wireless communication system based on Raptor codes, which aims to maximize the long-term average throughput of the system. The source node is equipped with energy collection means and a rechargeable battery, the energy of the transmitted signal per time slot being derived from the energy collected from the surroundings. Under the conditions that the battery capacity is limited and the maximum decoding length of a decoder is restricted, a Lyapunov frame is utilized to solve the joint optimization problem of the transmitting power, the modulation mode and the code word 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, and solving a three-parameter optimization problem comprising transmission power, a modulation mode and codeword length to obtain an optimal solution.

The method comprises the following specific steps:

(1) deducing the relation between the decoding error probability of the Raptor code coding code word and the receiving signal-to-noise ratio and the code word length in a mutual information analysis mode;

(2) the source node collects energy from the surrounding environment in each time slot to be used for sending information to the destination node, and the transmission rate is maximized under the constraint of battery storage capacity and the constraint of the maximum code word length of the decoder;

(3) 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;

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

(5) 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 code word length, namely solving the optimal solution of the optimization objective function.

Specifically, in the step (1), the relationship between the decoding error probability of the Raptor code coding code word and the receiving signal-to-noise ratio and the code word length is deduced in a mutual information analysis mode. Firstly, deducing the relation between the decoding accumulated mutual information quantity and the decoding length, and calculating the signal-to-noise ratio and the accumulated mutual information quantity corresponding to different modulation modes under the condition of meeting the expected error code performance.

Specifically, the modeling of the communication system in the step (2) includes modeling and expressing the actual achievable transmission rate of the system and the battery power queue of the source node. And constructing an optimization problem by using the constraint conditions of maximum transmission power limit, limit of battery storage capacity to transmission power, maximum decoding length limit and battery capacity as the constraint conditions and taking the maximization of long-term time average transmission rate as the target.

Specifically, the Lyapunov optimization framework is used for solving the optimization problem in the step (3), 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 (4) indirectly realizes that the constraint condition is satisfied by minimizing the upper bound of the drift plus penalty, and the upper bound expression of the drift plus penalty term is obtained by the Lyapunov function and the Lyapunov drift expression.

Specifically, in step (5), the transmission power, modulation scheme, and codeword length should be appropriately adjusted according to the energy arrival and channel state. Since the 3 variables cannot be directly optimized in a combined manner, but the number of modulation modes is limited, the transmission power P (t) and the code word length N can be optimized from the highest order modulation mode_bM(t), if the obtained code word length meets the maximum decoding length constraint, stopping optimization; if not, the optimization is carried out under the modulation mode of lower order. Wherein, 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,maxTime counting to obtain code word length N_bM(t), if the obtained code word length does not exceed the maximum decoding length constraint, then P (t), N at the moment_bM(t) and modulation order M are the optimal solution; when X (t) < 0, the optimal solution of P (t) should be the extreme point of the objective function J (P (t) | M), and the optimal N obtained by calculation_bM(t) should satisfy N_bM(t)≤N_max。

Compared with the prior related research, the invention has the advantages 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 reaching and channel fading variation, and the method is an online low-complexity control algorithm; (2) compared with the literature adopting the Lyapunov method, 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-; (3) the algorithm provided by the invention has more available modulation modes, considers the rateless coding, performs combined optimization on three parameters of the transmission power, the modulation mode and the code word length, and has higher practicability.

In a word, the method only depends on the current battery state and channel state information to make a decision, adopts Raptor coding and adaptive modulation technology to transmit, has the actual communication rate closer to the channel capacity, and is an efficient, low-complexity and strong-practicability method.

Drawings

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

FIG. 2 shows the frame error rate of a Raptor code on AWGN channel, with a code length of 19000;

FIG. 3 is a trace graph of the average information transfer rate over time for the algorithm and the comparison algorithm proposed by the present invention;

FIG. 4 is a trace graph of source node battery power changes over time for the algorithm and comparison algorithm proposed by the present invention;

FIG. 5 shows the effect of energy arrival rate λ on information transmission rate;

FIG. 6 shows the effect of virtual queue energy offset A on information transfer rate and battery level average;

FIG. 7 shows the influence of weight V in the drift plus penalty term on the information transmission rate, the average value of battery power, and the standard deviation of battery power;

fig. 8 shows the frame error rate when Raptor coding is adopted under different energy arrival rates.

Detailed Description

Considering the transmission system model shown in fig. 1, a transmitting node encodes information by a Raptor code, and then transmits data to a destination node by adopting a proper modulation mode and transmitting power; the decoder receives a sufficient number of encoded symbols and then performs Raptor code decoding. The transmitting node is equipped with an energy harvesting device and a rechargeable battery of limited capacity, where energy can be harvested from the surrounding environment and stored in the battery and used to transmit data to the destination node. In the transmission process, the energy collected by the sending node and the wireless channel are randomly changed, the sending node dynamically adjusts the sending power, the modulation mode and the code word length according to the instantaneous channel state information and the energy collection condition, the long-term time average system rate is maximized under the condition that the maximum decoding length limit of a decoder is not exceeded, and the energy use efficiency is improved.

The omega is recorded as a modulation mode set which can be adopted by the system, wherein the modulation mode set is { BPSK, QPSK,16QAM,64QAM or 256QAM }, and information to be transmitted is coded by a Raptor code and then is transmitted by selecting one appropriate modulation mode. The modulated unit power sends signal x (t), and the receiving end receives signal

Where h (t) is the channel coefficient, P (t) is the transmitted signal power, n (t) is the mean 0, and the variance σ is²White additive gaussian noise. Signal-to-noise ratio is gamma (t) ═ P (t) | h (t) |²/σ². The received signal is corrected in amplitude and phase to obtain

Wherein h is^*(t) represents the conjugate of the channel coefficient,

as equivalent noise, mean 0, variance

Raptor codes are decoded using soft information, so demodulation uses soft-decision demodulation, i.e., computing the LLR of each bit in the received symbol. When M-order modulation is employed, each symbol contains log₂M channel coding bits, let b_iIs the ith bit in the symbol x. Received symbol r superimposed with channel noise_iHas an LLR of

p(r|b_i＝0)，p(r|b_i1) respectively represents a bit b_iIs a conditional probability density function of r under the conditions of 0 and 1.

The receiving end can successfully decode with high enough probability after the code word length is long enough and the decoder can accumulate enough mutual symbol information. The mutual information of the received symbol r and the transmitted symbol x is

I_sM(r；x)＝h(r)-h(r|x)

In the formula I_sMFor the average mutual information content of a symbol when M-order modulation is used, h (r) is informationEntropy, h (r | s) is conditional entropy.

The calculation formula of the information entropy h (r) is

Wherein p (r) represents a probability density function

The expression is

Representing the equivalent noise variance, x_iRepresenting modulation symbols.

Substituting the above formula into the expression of h (r), and further deriving to obtain

The above formula needs to sum the exponential terms and then perform integral operation, and a closed expression cannot be obtained. The conditional entropy h (r | x) can be derived to yield a closed expression. When M-order modulation is used, the probability of transmission of each symbol under the prior equality is Pr (x ═ x)_i) 1/M. The conditional entropy h (r | x) is calculated by the formula

Wherein p (r | x ═ x)_i) For transmitting a symbol of x_iA conditional probability density function of the received signal r. Substituting h (r), h (r | x) into I_sMThe expression of (r; x) is that the symbol average mutual information quantity is

Under the condition of ensuring that the decoding error code performance expected by the system is met, the total quantity of mutual information accumulated by the decoder for decoding one code word modulated by M orders is I_wMThen the number of symbols to be entered into the decoder can be expressed as

In the formula (I), the compound is shown in the specification,

indicating rounding up. The code word length of the corresponding Raptor code is

According to the coding theory of the rateless code, assuming that the information length in one code word is K bits, the mutual information amount required by a decoder when the rateless code achieves the required error performance is I (1+ a) K bits, and a is the decoding overhead (a > 0), and is related to the characteristics, code length, modulation mode and the like of the code. Since the Raptor is random coding, the performance of the Raptor cannot be theoretically analyzed without a fixed coding structure. The invention adopts a method of combining simulation and theoretical analysis to obtain the mutual information quantity requirement. Firstly, simulating the error code performance of Raptor codes with fixed code length under different modulation modes under an Additive White Gaussian Noise (AWGN) channel, finding out the signal-to-Noise ratio under the error performance required, obtaining the mutual information of a next symbol of the signal-to-Noise ratio according to a calculation formula of the mutual information, and multiplying the mutual information by the code length to obtain the mutual information quantity required to be accumulated. The Raptor code used in the simulation of the invention has the information bit length of 9500, the outer code adopts the LDPC code with the code rate of 0.95, and the LT code as the inner code has the coding degree distribution of high-order polynomial, namely

Ω(x)＝0.0080x+0.4936x²+0.1662x³+0.0727x⁴+0.0826x⁵ +0.0560x⁸+0.0372x⁹+0.0556x¹⁹+0.025x⁶⁵+0.0031x⁶⁶

Fig. 2 shows simulation results of Word Error Rates (WER) (also referred to as frame Error rates and block Error rates) of Raptor code coded transmission under different modulation modes on AWGN channel. In simulation, the code word length of Raptor code is 19000, namely the code rate is 0.5; and decoding the LT code and the LDPC code by adopting a BP algorithm, wherein the maximum decoding iteration times are respectively 100 and 50.

The invention uses the frame error rate P_ef＝10^-3For decoding error performance goal, it can be estimated by analyzing fig. 2 that 5 modulation schemes achieve the snr required by the word error rate when the code length N is 19000. Then calculating the symbol mutual information I of different modulation modes in the signal-to-noise ratio_sMMultiplied by N to 10^-3The total amount of mutual information I required for the frame error rate_wMAs shown in table 1.

TABLE 15 modulation schemes P_ef＝10^-3Temporal SNR and accumulated mutual information required for decoding

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 that the battery is charged and dischargedIn the process, no energy loss exists, the charging rate and the residual capacity of the battery are limited, and the electric quantity E stored into the battery in 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)

Under the condition of unchanged transmission bandwidth, the symbol rate under each modulation mode is the same as

Baud. According to the above description, it can be determined that when the K bit information of one codeword is transmitted by using M-order modulation under the current channel state and given transmission power, the number of modulation symbols to be transmitted is N_sMThen the transmission duration of a codeword (or a frame) is

T_f＝N_sM×T_s(s)

Wherein T is_sRepresenting a symbol period.

The invention takes the rate of successfully transmitting information bits of one frame data on unit bandwidth as an index for measuring the system performance, and the expression is

In the above formula P_efIndicating a frame error rate.

The invention selects proper sending power and modulation mode under the constraint of available collected energy, determines the code length of code words, and maximizes the information transmission rate under the constraint of decoding complexity and decoding equivalent bit signal-to-noise ratio threshold. According to the relevant knowledge of the information theory, theoretically, the more the value quantity of the sent symbols is, the larger the mutual information quantity of each symbol in transmission is, namelyThat is, the higher the order of the modulation scheme, the larger the amount of information carried by each symbol. But under the same snr condition, the more the modulation order, the less the amount of information carried on each bit. If the selected modulation order is too high, the average mutual information amount of each bit is too small, the length of the code word required by decoding is too high, the decoding complexity is too high, and the decoder cannot work normally due to the fact that the average mutual information of the bits is too small (namely, the equivalent bit signal-to-noise ratio is too small). Therefore, the codeword length, here denoted as N, needs to be limited_max。

The invention jointly optimizes the sending power P (t) and the modulation order M of each time slot under the use constraint of collected energy and the constraint of maximum code word length, determines the code word length, and maximizes the long-term average actual achievable 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∈Ω

N_bM(t)≤N_max

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 content of the first and second substances,

the meaning of the above formula is that all the collected energy should be used for information transmission in a 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∈Ω

N_bM(t)≤N_max

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 Lyapunov optimization, the queue length can fluctuate around 0, and energyThe virtual queue plus an offset allows the battery charge to remain near the offset value, fluctuating up and down. Updating equation E based on 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_sM(t) negative value as penalty term, drift plus penalty constructed as

Δ(X(t))-VE[R_sM(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 level) 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 non-negative and limitedValue, must have a non-negative constant C

Then

Δ(X(t))≤C+X(t)E[E_H(t)-ΔtP(t)|X(t)]

The upper bound of "drift plus penalty" is

Δ(X(t))-VE[R_sM(t)|X(t)]≤C+X(t)E[E_H(t)-ΔtP(t)|X(t)]-VE[R_sM(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 removing items irrelevant to P (t) and M, N in the upper bound of 'drift plus penalty' and multiplying by-1, correspondingly changing minimization into maximization, meanwhile, because the current channel state and battery state are known, mean value operation in the upper bound can be removed, and the optimization problem is expressed as a single-time-slot optimization problem again:

M∈Ω

N_bM(t)≤N_max

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

As mentioned above, the higher the modulation order, the larger the amount of symbol mutual information, and therefore, should beWhen the length of code word does not exceed N_maxThe higher order modulation scheme is preferably selected under the constraint condition and the error word rate index. Let the optimization objective function be

J(P(t),M)＝P(t)X(t)+VR_sM(t)

Further derivation to obtain

Because the number of available modulation modes is limited and the modulation mode with the highest order should be selected, the optimization problem can be changed to the modulation mode with the highest order, and the maximum J (P (t) M) is used as the target to optimize the transmission power P (t) under the modulation mode to determine the code word length N_bM(t) of (d). If the obtained codeword length does not exceed the constraint N_maxThen p (t) and modulation order M at this time are the optimal solutions. If the code word length exceeds the constraint, the modulation order is reduced, and the sending power P (t) and the code word length N are obtained through optimization_bMAnd (t), judging whether the code word length meets the constraint, stopping if the code word length meets the constraint, and reducing the modulation order to perform similar optimization and judgment if the code word length does not meet the constraint. If the codeword length in the lowest-order BPSK modulation cannot meet the codeword constraint, which indicates that the current channel state is poor or the available energy is low, the transmission should be stopped in the timeslot.

The monotonicity of the objective function is analyzed below. As P (t) increases, the signal-to-noise ratio increases and the equivalent noise variance increases

Decreasing, in the target function expression after the denominator of item 2 is reduced

Increases the value of (2). When X (t) ≧ 0, the 1 st term of J (P (t) | M) is a monotonically increasing function of P (t). Therefore, the optimization objective function J (P (t) M) is a monotone increasing function P (t), and in order to maximize the objective function, P (t) should take the maximum value P_d,max. From the practical physical sense, X (t) is more than or equal to 0 to indicate that the battery has enough electric quantity, and canThe maximum transmit power is used for transmission.

When X (t) < 0, since the 1 st term of J (P (t) | M) is the monotonous decreasing function of P (t) and the 2 nd term is the increasing function of P (t), the optimization objective function is not the monotonous function of P (t), and it is necessary to find the monotonous function of P (t)

The extreme point within the range that maximizes the objective function J (p (t) | M), i.e., the optimal transmit power. Optimizing r (t) in the integral of the denominator of term 2 of the objective function,

The integral is related to the transmission power P (t), but the integral has no closed expression, so that the optimization objective function is not a closed expression, a solution of the optimal transmission power which enables the optimization objective function to be maximum cannot be obtained through a method of analyzing and solving, and only a method of linear search can be adopted for solving. Due to the limitation of the transmission power P (t)

In the range, power points can be taken at intervals of step length δ in the range, and the power points are substituted into the target function to calculate the target function J (p (t) | M) value corresponding to each power point, wherein the power value with the maximum target function value is the optimal power. When calculating the J (P (t) M) value at each power point, the integral needs to be calculated once

The integral can be obtained only by numerical calculation and is the part with the highest calculation amount in the optimization process.

Is the inverse of the received signal to noise ratio gamma (t), the integral being effectively a function of the signal to noise ratio. In order to reduce the calculation amount when solving the optimization problem, the integration of different signal-to-noise ratios can be firstly carried out within the range of possible receiving signal-to-noise ratios at certain intervals

The values of (a) are calculated and stored in a table. When the optimization objective function value under each power point is calculated, the signal-to-noise ratio value is obtained through conversion according to the channel state, the corresponding integral value is obtained through table lookup, and the value of the optimization objective function J (P (t) M) is obtained through substitution calculation. The integral values in the range of-2 to 25dB at intervals of 0.5dB are given in Table 4.1. Because the table is calculated under the on-line condition, the calculation can be carried out in advance, and no extra calculation amount is brought to the algorithm. If a more accurate integral value is needed and a wider signal-to-noise ratio range is adapted, only the signal-to-noise ratio interval needs to be reduced and the size of the table needs to be increased. The signal-to-noise ratio interval of the integrated value table in the simulation of the invention is 0.001 dB.

TABLE 4.1 integral values under 5 modulation modes at different SNR

The optimization algorithm is summarized as shown in algorithm 1.

The algorithm 1 solves the joint optimization problem of three parameters of sending power, modulation mode and code word length, when X (t) is more than or equal to 0, the battery power is sufficient, the transmission is carried out at the maximum power, and P (t) is P_d,max. Starting from the highest-order modulation scheme, P (t) ═ P is calculated_d,maxThen look-up table 4.1 to obtain integral value in target function, and calculate J (P (t) M) and code length N_bM(t) if N_bM(t) if the maximum code length limit is not exceeded, the optimization is ended, otherwiseSelecting a modulation mode with a lower first gear, and repeating the steps until the obtained code length N is obtained_bM(t)≤N_maxAnd finishing the optimization. When X (t) < 0, starting from the highest order modulation scheme, within the available power range

Calculating J (P (t) M once at each power point, finding P (t) which maximizes J (P (t) M), and calculating corresponding N_bM(t) until the code length N is found_bM(t)≤N_max. Since the computation complexity when X (t) ≧ 0 is much less than X (t) < 0, X (t) < 0 is assumed as an estimation of the upper limit of computation complexity. The computational complexity of finding the optimal P (t) is mainly in integration

And the integral value can be obtained by a table look-up 4.1, which reduces the computational complexity (equivalent to that of addition and multiplication). The other operations are algebraic operations of addition, subtraction, multiplication and division. Need to search under one modulation mode

The target function value under 5 modulation modes is calculated at most for each power point, so 1 time slot needs to be searched in total

And (4) a power point. 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: the energy arrival process of the sending node is subjected to a composite uniformly distributed Poisson process, the arrival rate is lambda-1 unit/time slot, and each unit energy is subjected to [0,0.4 ]](unit J) uniform distribution among; capacity of battery E_max50J, maximum charging power P_c,maxMaximum discharge power P of 0.4W_d,max0.6W; the time slot length delta t is 1 s; the channel being a Rayleigh fading channelThe channel coefficients h (t) are kept constant in a time slot, subject to zero mean and a variance of 2 x 10^-9The complex gaussian distribution of random variables, i.e. the path loss of the channel, is 87 dB; noise power spectral density N₀＝1×10^-17W/Hz; symbol rate R_s＝1×10⁶Baud, bandwidth B1 × 10⁶Hz. The search step in the optimum transmission power search is

If not specifically stated, the offset of the battery charge virtual queue is set to a-30, the weight of the penalty term is V-4, and the initial battery charge is 40J. The information length of a Raptor code word is K9500 bits, and the maximum code word length is N_max21100. The frame error rate target is P_ef＝10^-3。

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 electricity consumption in the battery, and under the limit 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 literature algorithm sets the weight V to 4 and the virtual queue offset a to 30 in the simulation, where the best performance is obtained.

(4) An offline water injection algorithm: the transmitting end obtains the channel change condition and the energy collection condition in the whole transmission process before transmission, and obtains the average signal transmitting power 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.

After the 4 kinds of comparison algorithms determine the sending power of each time slot, the optimal modulation mode and code word length are obtained in the same mode as the algorithm in the chapter. If the length of the obtained code word exceeds the limit in the BPSK modulation mode, the data transmission is not carried out in the current time slot, and the sending power and the transmission rate are 0.

Fig. 3 is a result of an average information transmission rate of 10000 slots, and the average information transmission rate per slot is an average value of transmission rates of slots from the start of simulation to the current slot. The dashed line in the figure represents the channel capacity at the same transmission power; the solid line is the actual highest transmission rate that can be achieved when Raptor codes are employed under 5 alternative modulation modes. Simulation results show that the algorithm in the chapter is obviously higher than the greedy algorithm and the half-power algorithm in both channel capacity and actually-achievable transmission rate. The algorithm of this chapter optimizes the sending power, modulation mode, code word code length of the source node according to the channel state and battery power, under the constraint of satisfying the maximum code word length, maximize the information transmission rate that can be achieved practically; the greedy algorithm and the half-power algorithm do not consider the influence of the channel state on the transmission performance of the system, so the performance of the algorithm in this chapter is obviously superior to that of the two algorithms. The offline water filling algorithm and the algorithms in the document [ AMIMAVAEI F, DONG M. Online power control optimization for Wireless transmission with energy harnessing and storage [ J ]. IEEE Transactions on Wireless Communications,2016,15(7): 4888) 4901 ] are optimized with the goal of maximizing the average channel capacity, so that the two algorithms are superior to the current algorithm in average channel capacity, wherein the water filling algorithm is optimal and has a performance advantage of 0.63% compared to the current algorithm, and the document algorithm has a performance advantage of about 0.26% compared to the current algorithm. Because the algorithm in this chapter jointly optimizes the transmission power, the modulation mode and the codeword length, although the channel capacity is lower than that of the offline water-filling algorithm and the literature algorithm, the actually achievable transmission rate is superior to those of the two algorithms, and the performance advantages are respectively 0.09% and 0.45%. Compared with a transmission strategy only optimizing power and a modulation mode, under the same simulation condition, the actual achievable transmission rate of the transmission system adopting the rateless coding is improved by 40.99%, and the transmission performance is closer to the channel capacity.

Fig. 4 is a trace diagram of battery capacity changes with time in 4 online algorithms in a simulation process, selection of transmission power in an offline water injection algorithm is not causally constrained by collected energy, and battery capacity changes have no practical significance, and therefore are not 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. 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.

Fig. 5 shows the effect of a change in the energy arrival rate lambda on the actual transmission rate. As the energy arrival rate λ increases, the average collected energy per slot increases, the corresponding average transmission power increases, and the transmission rate increases.

Fig. 6 shows the effect of varying the virtual queue offset a on the performance of the system. Fig. 6(a) shows that the average level of battery charge increases with a, and fig. 6(b) shows that the transmission rate of the system increases first and then decreases slightly with a. This is because as a increases, the average power level of the battery increases, and higher transmit power can be supported when channel conditions are good, increasing the average transmission rate. However, when a is too large, the average remaining storage space of the battery is reduced, the probability of battery power overflow and partial loss of collected energy is increased, and the transmission rate is slightly reduced.

Figure 7 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. 7(a) shows that as V increases, the average battery charge decreases and that after V is greater than 4.3, the average of the average battery charge is already very small; fig. 7(b) shows that as V increases, the average information transfer rate increases first and then decreases, reaching a maximum value when V is 4.3; fig. 7(c) shows that the standard deviation of the battery charge increases 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 (>4.3), increasing V will result in a low average battery power and a small maximum power, and when the channel condition is good, there is not enough battery power to support a 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 4.3 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.

The invention verifies the sending work determined by the proposed algorithmThe rate, modulation mode and whether the code word length can reach the frame error rate is P_ef＝10^-3Error performance target of. The channel and energy arrival amount are randomly changed 100 times at each energy arrival rate, and the simulation 10 is carried out at each channel and energy arrival amount⁴Transmission of a single codeword. Co-transmission 10 at each energy arrival rate⁶And counting bit error rates and frame error rates of all the decoded code words. The error performance was simulated for a total of 5 energy arrival rates, and the results are shown in table 3. FIG. 8 shows the simulation result of the frame error rate, and it can be seen that the frame error rate is very close to 10^-3The deviation is very small, which shows that the analysis of the relationship between the frame error rate, the signal-to-noise ratio and the code length in the scheme is correct.

TABLE 3 frame error Rate when Raptor coding is used at different energy arrival rates

Claims (10)

1. The method for online joint control of power and rate of an energy collection communication system based on Raptor codes is characterized by comprising the following steps:

(1) deducing the relation between the decoding error probability of the Raptor code coding code word and the receiving signal-to-noise ratio and the code word length in a mutual information analysis mode;

(2) the source node collects energy from the surrounding environment every time slot to be used for sending information to the destination node, and under the constraint of battery storage capacity and the constraint of maximum code word length of a decoder, the transmission rate is maximized, and a communication system is modeled;

(3) 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;

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

(5) 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 code word length, namely solving the optimal solution of the optimal objective function.

2. The Raptor code-based online joint control method for power and rate of an energy harvesting communication system according to claim 1, characterized in that: the step (1) specifically comprises: deducing the relation between the accumulated mutual information amount of decoding and the decoding length as

N_bMIndicating the codeword length, I, of the Raptor code_wMRepresenting the amount of mutual information accumulated in decoding, I_sMRepresenting the average symbol mutual information quantity;

and calculating the signal-to-noise ratio and the accumulated mutual information quantity corresponding to different modulation modes under the condition of meeting the expected error code performance.

3. The Raptor code-based online joint control method for power and rate of an energy harvesting communication system according to claim 2, characterized in that: the specific steps of calculating the signal-to-noise ratios and the accumulated mutual information amounts corresponding to different modulation modes are as follows: simulating the error code performance of Raptor codes with fixed code length under different modulation modes under an additive white Gaussian noise channel, finding out the signal-to-noise ratio meeting the expected error code performance, obtaining the mutual information of a next symbol of the signal-to-noise ratio according to a calculation formula of the mutual information, and multiplying the mutual information by the code length to obtain the accumulated mutual information quantity; the calculation formula of the symbol mutual information under different modulation modes is

x_iRepresenting modulation symbols, r representing received symbols,

represent the equivalentThe variance of the noise is determined by the variance of the noise,

γ represents the signal-to-noise ratio.

4. The Raptor code-based online joint control method for power and rate of an energy harvesting communication system according to claim 1, characterized in that: the modeling of the communication system in the step (2) includes constructing an optimization problem with the maximum transmission power limit, the maximum decoding length limit of a decoder, the limit of battery storage capacity to the transmission power and the battery capacity as constraint conditions, and with the maximum transmission rate as a target.

5. The Raptor code-based online joint control method for power and rate of an energy harvesting communication system according to claim 4, characterized in that: the optimization problem is as follows:

s.t.0≤P(t)≤P_d,max

0≤ΔtP(t)≤E_S(t)

M∈Ω

N_bM(t)≤N_max

wherein the content of the first and second substances,

indicating the rate of correctly transmitted information data bits per unit bandwidth, E [ ·]For the desired operation, K is the amount of information carried by a codeword, P_efFor frame 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 modulation order, and omega is optionalA set of modulation schemes of (a); codeword length N_bM(t) satisfies N_bM(t)≤N_max，N_maxIs the maximum codeword length;

in order to achieve long-term power constraints,

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

6. The Raptor code-based online joint control method for power and rate of an energy harvesting communication system according to claim 1 or 5, characterized in that: the step (3) 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 [_sM(t)|X(t)]

In the formula E [ R ]_sM(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.

7. The Raptor code-based online joint control method for power and rate of an energy harvesting communication system according to claim 6, 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 (4)

8. The Raptor code-based online joint control method for power and rate of an energy harvesting communication system according to claim 7, characterized in that: the method for solving the optimal solution of the optimization objective function in the step (5) comprises the following steps:

let J (P) (t), M ═ P (t) X (t) + VR_sM(t) as an optimization objective function, changing the optimization problem into a modulation mode with the highest given order, optimizing the transmission power P (t) by taking the maximum J (P (t) M) as a target under the modulation mode, and determining the length N of the code word_bM(t); if the obtained codeword length does not exceed the constraint N_maxThen p (t) and modulation order M at this time are the optimal solutions; if the code word length exceeds the constraint, the modulation order is reduced, and the sending power P (t) and the code word length N are obtained through optimization_bM(t), judging whether the length of the code word meets the constraint, if so, stopping, otherwise, reducing the modulation order to carry out similar optimization and judgment; if the codeword length at the lowest modulation does not meet the codeword constraint, the slot should cease transmission.

9. The Raptor code-based online joint control method for power and rate of an energy harvesting communication system according to claim 8, characterized in that: the optimal solution is solved 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,max，P_d,maxRepresents the maximum discharge power of the battery,at P (t) ═ P_d,maxTime counting to obtain code word length N_bM(t), if the obtained code word length does not exceed the maximum decoding length constraint, then P (t), N at the moment_bM(t) and modulation order M are the optimal solution;

when X (t) < 0, the optimal solution of P (t) should be the extreme point of the objective function J (P (t) | M), and the optimal N obtained by calculation_bM(t) should satisfy N_bM(t)≤N_max。

10. The Raptor code-based online joint control method for power and rate of an energy harvesting communication system according to claim 9, characterized in that: when X (t) is less than 0, solving by adopting a linear search method: the transmission power P (t) is limited to

Within the range, power points are taken at intervals of step length delta in the range and are substituted into the target function to calculate the value of the target function J (P (t) M) corresponding to each power point, and when the value meets N_bM(t)≤N_maxUnder the constraint of (3), the power value with the maximum target function value is the optimal power.

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