CN112350789B - Cognitive IoV cooperative spectrum sensing power distribution algorithm based on energy efficiency maximization - Google Patents

Cognitive IoV cooperative spectrum sensing power distribution algorithm based on energy efficiency maximization Download PDF

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CN112350789B
CN112350789B CN202010427770.XA CN202010427770A CN112350789B CN 112350789 B CN112350789 B CN 112350789B CN 202010427770 A CN202010427770 A CN 202010427770A CN 112350789 B CN112350789 B CN 112350789B
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缪娟娟
宋晓勤
杜忠源
雷磊
陈文彬
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Nanjing University of Aeronautics and Astronautics
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/382—Monitoring; Testing of propagation channels for resource allocation, admission control or handover
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
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Abstract

The invention discloses a cognitive internet of vehicles cooperative spectrum sensing power distribution method with maximized energy efficiency. The method adopts a distributed algorithm to model an objective function, and adds the requirements of the lowest communication rate of a cognitive system, master user interference, transmitting power and the like according to an optimization objective of maximizing system energy efficiency. In the approximate optimal solution solving process, a fractal programming is adopted to convert a pseudo-concave problem into a convex function to obtain a new target function, two kinds of transmitting power required by adopting a mixed spectrum access mode are used as variables of the target function, an optimal Lagrange multiplier is obtained through a sub-gradient algorithm and substituted into an optimal solution, and finally, optimal power distribution is completed. Simulation verification in MATLAB communication simulation environment shows that the method can improve energy efficiency and ensure system perception performance.

Description

Cognitive IoV cooperative spectrum sensing power distribution algorithm based on energy efficiency maximization
Technical Field
The invention relates to a cognitive internet of vehicles technology, in particular to a spectrum sensing method of the cognitive internet of vehicles, and more particularly to a cognitive internet of vehicles cooperative spectrum sensing power distribution method based on energy efficiency maximization.
Background
The Internet of vehicles (IoV) refers to a huge network composed of information such as Vehicle position, speed and route. With the rapid development of information technology, people increasingly demand communication, and it is a hot issue to allocate wireless channel resources reasonably and efficiently. Currently, Resource Allocation (RA) in IoV faces many challenges. First, as IoV and the number of related application infrastructures are increasing, communication traffic is greatly increased, resulting in a shortage of Dedicated Short Range Communications (DSRC) spectrum resources; secondly, IoV is the basis of an Intelligent Transportation System (ITS), so in order to ensure the safety of the Transportation System, the real-time requirement of the System is stricter; thirdly, the internet of vehicles is applied to dense urban roads, and surrounding buildings are more, which causes serious interference among users.
In the cognitive car networking environment, due to the time-varying property of the position of a vehicle, the channel state information of frequency spectrum sensing is easily influenced by factors such as shadow fading and multipath effect, and the propagation environment is also complicated due to the fact that buildings around the car networking are complicated, and a user is only relied on to perform frequency spectrum sensing and is difficult to obtain a correct sensing result, so that the detection accuracy is greatly reduced, and communication of a master user is interfered and the frequency spectrum utilization rate is reduced. Therefore, multiple users need to be introduced for cooperative sensing, spectrum sensing information needs to be shared, and whether the authorized spectrum is in an idle state or not needs to be comprehensively judged. The process of cooperative spectrum sensing generally includes: firstly, a single secondary user carries out local spectrum sensing and transmits a sensing result to a Fusion Center (FC); then, the FC adopts different fusion rules to make decisions; and finally obtaining a global decision result.
However, as the number of locally perceived secondary users increases, especially in the presence of high traffic density scenarios, the cooperative spectrum sensing may result in a large amount of additional energy consumption. Meanwhile, with the development of society and science and technology, the energy consumption of the information communication industry is continuously increasing at an incredible speed, and the environmental deterioration is further aggravated. Therefore, how to control the excessive energy consumption has become a new round of urgent solution, and the academia also proposes the concept of "green communication". For spectrum sensing for optimizing Energy Efficiency (EE), people also have some research results at present. The method comprises the following steps that a multi-channel cooperative spectrum sensing optimization problem for maximizing system energy efficiency is provided in literature, the influence of optimal transmission power, sensing time and the number of cooperative secondary users on system performance is jointly considered, but spectrum utilization rate is not considered; documents provide an OSA cooperative spectrum sensing model with maximized energy efficiency, the system energy efficiency is further improved by adopting an iterative algorithm and optimizing a detection threshold of a single secondary user, but the spectrum utilization rate is not considered; in the background mode, the literature proposes that the user interruption probability is taken as a constraint condition, and the constraint condition is jointly considered in a system model, but the interference to a main user is large. The above documents consider the OSA or spectrum access model of spectrum sharing. Therefore, the cooperative spectrum sensing model under the Hybrid spectrum access technology is adopted, the error probability is considered in the system model aiming at the condition that the report channel has the report error, the average transmission power of the sending end of the secondary user, the interference of the primary user, the system rate and the like are taken as constraint conditions, the energy efficiency maximization is taken as an optimization target, and the interference to the primary user is reduced while the energy efficiency of the system is improved.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, a cognitive IoV cooperative spectrum sensing power distribution method based on energy efficiency maximization is provided, and the method can realize energy efficiency maximization in a Hybrid spectrum access mode.
The technical scheme is as follows: in the cognition IoV based on energy efficiency maximization, the purposes of improving energy efficiency and ensuring system perception performance are achieved. And considering the error probability into a system model aiming at the condition that the report channel has report errors, and jointly optimizing the energy efficiency of the system by combining the constraint conditions such as the average transmission power of a secondary user sending end, the interference of a main user, the system rate and the like. And solving the optimal power distribution of the target function by modeling and adopting a fractional programming and Lagrange iteration method. The invention is realized by the following technical scheme: a cooperative spectrum sensing power distribution method based on energy efficiency maximization in cognitive Internet of vehicles is characterized by comprising the following steps:
(1) all secondary users perform cooperative spectrum sensing to obtain a false alarm probability and a detection probability of a global decision, and an expression of an average rate and an average total energy consumption is obtained by considering a spectrum sensing error probability in a system model;
(2) determining a system model for maximizing energy efficiency under the constraint conditions of average transmission power of a secondary user transmitting end, main user interference, system rate and the like to obtain a target function;
(3) adopting a fractional programming to convert the pseudo-concave problem into a convex function to obtain a new target function, and taking two transmitting powers required by adopting a mixed spectrum access mode as variables of the target function;
(4) constructing a Lagrangian function, and obtaining an optimal solution according to a KKT condition;
(5) and obtaining an optimal Lagrange multiplier by adopting a sub-gradient algorithm, and substituting the optimal Lagrange multiplier into an optimal solution to finish optimal power distribution.
Further, the step (1) comprises the following specific steps:
(1a) the secondary user carries out local spectrum sensing to obtain the false alarm probability and the detection probability of the local spectrum sensing;
(1b) the secondary users report the respective perception results to a fusion center, and the fusion center makes a decision by adopting an OR criterion to obtain the false alarm probability and the detection probability of the overall decision;
(1c) calculating the probability of detecting that the channel is idle and busy and the conditional probability that the actual channel is busy under the condition of detecting that the channel is idle or busy;
(1d) in order to improve the utilization rate of the frequency spectrum, a mixed frequency spectrum access mode is adopted, and when the idle channel is detected, the power P is used as the power of a secondary user0Transmitting data, when detecting the channel busy, the secondary user is powered up by power P1Transmitting data;
(1e) the average rate available in one slot of the secondary user is calculated as:
Figure GSB0000197742180000021
the average energy consumption within one frame of the secondary user is:
Figure GSB0000197742180000031
further, the step (5) comprises the following specific steps:
(5a) the initialized fractional programming coefficient α is α0Lagrange multiplier tau(0)＝τ0，υ(0)＝υ0，ε(0)＝ε0Iteration step delta > 0, error threshold theta1，2＞0，F(α0) Infinity, and given a maximum number of iterations Lmax；
(5b) Substituting the initial value into an optimal solution formula to obtain initial optimal transmitting power:
Figure GSB0000197742180000032
Figure GSB0000197742180000033
(5c) updating the Lagrange multiplier until the iteration error of the Lagrange multiplier is smaller than a preset error threshold, and then the algorithm is converged to obtain the Lagrange multiplier;
(5d) updating the fractional programming coefficient until F (alpha) is less than or equal to theta1Or the iteration times reach the iteration upper limit to obtain a fractional programming coefficient, namely the energy efficiency;
(5e) and substituting the Lagrange multiplier and the fractional programming coefficient into an optimal solution formula to obtain the optimal transmitting power of the secondary user.
Has the advantages that: the cognitive Internet of vehicles cooperative spectrum sensing power distribution algorithm based on energy efficiency maximization further improves energy efficiency by introducing a Hybrid spectrum access technology. Meanwhile, constraint conditions such as the error probability of a report channel, the average transmission power of the system, the interference threshold of a main user, the rate of a secondary user and the like are considered, and the energy efficiency of the system is jointly optimized. And solving the optimal power distribution of the target function by modeling and adopting a fractional programming and Lagrange iteration method. Simulation results show that the Hybrid model is superior to the traditional OSA model in the aspect of maximizing the system energy efficiency, and meanwhile, the influence of sensing time and the number of secondary users on the system energy efficiency is also simulated and analyzed, and the correctness of the conclusion is further proved.
Drawings
FIG. 1 is a secondary user frame structure;
FIG. 2 is a graph of system energy efficiency as a function of transmission power for different models;
FIG. 3 is a graph of system energy efficiency as a function of reported channel error for different models;
FIG. 4 is a graph of system energy efficiency as a function of sensed time under different models;
FIG. 5 is a graph showing the variation of system energy efficiency with the number of users under different models;
Detailed Description
The core idea of the invention is that: energy efficiency is further improved by introducing Hybrid spectrum access technology. Meanwhile, constraint conditions such as the error probability of a report channel, the average transmission power of the system, the interference threshold of a main user, the rate of a secondary user and the like are considered, and the energy efficiency of the system is jointly optimized. And solving the optimal power distribution of the target function by modeling and adopting a fractional programming and Lagrange iteration method. And obtaining the spectrum allocation based on the maximum energy efficiency.
The present invention is described in further detail below.
Step (1), all secondary users perform cooperative spectrum sensing to obtain a false alarm probability and a detection probability of a global decision, and an expression of an average rate and an average total energy consumption is obtained by considering a spectrum sensing error probability in a system model, wherein the expression comprises the following steps:
suppose that the system has 1 primary user and K secondary users, and the frame structure of the secondary users is shown in fig. 1, where T is the frame length; t issFor sensing time, finishing local spectrum sensing by secondary users in the time period, preliminarily judging whether a primary user exists and assuming that all secondary users adopt an energy detection technology for sensing simultaneously; t isrIn the time period, the secondary users finish reporting respective local sensing results to the fusion center, and then make global decision according to an OR fusion criterion; t isdAnd accessing the authorized frequency band for data transmission by the secondary user in the time period for data transmission time. Meanwhile, we consider the system model to beAll channels are independent and meet flat fading in each frame, defining the channel power gain from the secondary user transmitter to the secondary user receiver as GssThe channel power gain from the secondary user transmitter to the primary user receiver is denoted Gsp。
Since the energy detection technology is adopted for local spectrum sensing, the derivation shows that the local false alarm probability of the kth secondary user is expressed as:
Figure GSB0000197742180000041
wherein λ is an energy detection threshold;
Figure GSB0000197742180000042
is the variance of the noise; f. ofsIs the sampling frequency; the Q function is defined as:
Figure GSB0000197742180000043
meanwhile, the local detection probability of the kth secondary user is expressed as:
Figure GSB0000197742180000044
where γ is the average signal-to-noise ratio of the primary user. Further, if given
Figure GSB0000197742180000045
Then the relationship between expression 1 and expression 2 is expressed as:
Figure GSB0000197742180000046
wherein Q-1Is the inverse function of Q.
Taking into account the fact that the reporting channel is not ideal, in the system model
Figure GSB0000197742180000047
Indicating the probability of error at the time of the kth user report. Since the fusion center employs the "OR" criterion, the expressions 1 and 2 are combined and the channel error probability is reported
Figure GSB0000197742180000048
At this time, the false alarm probability and the detection probability of the global decision are respectively expressed as:
Figure GSB0000197742180000049
Figure GSB0000197742180000051
wherein, introduced according to the spectrum sensing principle, the binary hypothesis sensing model has two conditions, H0Expressed as the case where PU is not present, H1Expressed as the presence of PU, and at the same time we redefine
Figure GSB0000197742180000052
Indicating that the fusion center detects the absence of a PU,
Figure GSB0000197742180000053
this indicates that the fusion center has detected the presence of a PU.
To simplify the analysis, assuming that all secondary users transmit in the same but independent reporting channel, expressions 5 and 6 can be simplified as:
Qf＝1-[(1-Pf)(1-Pe)+PfPe]K expression 7
Qd＝1-[(1-Pd)(1-Pe)+PdPe]K Expression 8
According to the real state of the master user and the result of frequency spectrum sensing, four combination conditions exist, which are respectively as follows:
case1：
Figure GSB0000197742180000054
i.e. PU is not present in both the detected and true cases, the probability in this case being P (H)0)(1-Qf) When SU is at power P0Carrying out data transmission;
case2：
Figure GSB0000197742180000055
that is, the presence of PU is detected but the actual condition is that PU is not present, and the probability in this case is P (H)0)QfWhen SU is at power P1Carrying out data transmission;
case3：
Figure GSB0000197742180000056
that is, it is detected that PU is not present but PU is present as a true case, and the probability in this case is P (H)1)(1-Qd) When SU is at power P0Carrying out data transmission;
case4：
Figure GSB0000197742180000057
i.e. PU exists in both the detected and true cases, the probability in this case being denoted as P (H)1)QdWhen SU is at power P1And carrying out data transmission.
Wherein P (H)0) Is H0Probability of situation, P (H)1) Is H1Probability of a situation, and P0＞P1。
Meanwhile, the transmit-receive model of the above four cases can be expressed as:
Figure GSB0000197742180000058
wherein, i is 1, 2d(ii) a x and y are transmitted and received signals, respectively; h is the channel gain between the secondary user transmitter to the secondary user receiver and Gss＝|h|2(ii) a n is a noise signal and satisfies a mean of 0 and a variance of
Figure GSB0000197742180000059
s is a fading signal received by a master user and satisfies that the mean is 0 and the variance is
Figure GSB0000197742180000061
Thereby, the probability of detecting the absence of the primary user is detected
Figure GSB0000197742180000062
And probability of existence
Figure GSB0000197742180000063
It can be calculated that:
Figure GSB0000197742180000064
Figure GSB0000197742180000065
in the same way, the method for preparing the composite material,
Figure GSB0000197742180000066
probability of situation
Figure GSB0000197742180000067
And
Figure GSB0000197742180000068
probability of situation
Figure GSB0000197742180000069
Respectively, it can be calculated that:
Figure GSB00001977421800000610
Figure GSB00001977421800000611
further, the rate R of the secondary user in one frame can be obtainedGExpressed as:
Figure GSB00001977421800000612
wherein
Figure GSB00001977421800000613
Given a sum of h
Figure GSB00001977421800000614
Mutual information between x and y; h ise(.) is differential entropy; ω is defined as:
Figure GSB00001977421800000615
by derivation, definition of RaveIs RGAt this time RaveCan be expressed as:
Figure GSB00001977421800000616
the average total energy consumption in one frame of the secondary user at this time is represented as:
Figure GSB00001977421800000617
wherein P issAnd PrPower consumed by the secondary user perception time slot and the reporting time slot respectively; pcIs the circuit power, i.e., the power consumed by the transmitter circuitry (mixers, filters, digital-to-analog converters, etc.).
Step (2), determining a system model for maximizing energy efficiency under the constraint conditions of average transmission power of a secondary user sending end, interference of a primary user, system rate and the like, and obtaining a target function:
energy efficiency is defined as the ratio of the average rate achievable over a time slot to the average total energy consumption, and can be expressed as:
Figure GSB0000197742180000071
expression 18 is our objective function by optimizing the power P0And P1The allocation of (c) reaches a maximum of the objective function.
Then, considering the constraint condition of the objective function, firstly, power constraint, in order to guarantee the power budget of the secondary user, it is necessary to constrain the average transmission power of the next user of the fading channel to be less than the power threshold, that is:
Figure GSB0000197742180000072
wherein, PaveAnd (4) averaging the transmission power threshold value for the sending end of the secondary user.
Secondly, considering interference constraint, in order to ensure that primary user communication is not affected, the interference of the secondary user must be smaller than the maximum interference threshold I tolerable by the primary userthExpressed as:
(T-Ts-KTr)E{[P(H1)(1-Qd)P0+P(H1)QdP1]|Gsp|}≤Ith expression 20
Given PTAnd IthThe value of (c).
Finally, in order to ensure normal communication of the secondary user, the rate thereof should reach a certain value, namely:
Rave≥Rminexpression 21
In summary, the system objective function can be modeled as:
Figure GSB0000197742180000073
wherein C1, C2, C3 represent the constraints in expression 19, expression 20, expression 21, respectively, and C4 ensures that the power is non-negative.
Step (3), the quasi-concave problem is converted into a convex function by adopting a fractional programming to obtain a new objective function, and two kinds of transmitting power required by adopting a mixed spectrum access mode are taken as variables of the objective function, and the method comprises the following steps:
firstly, a fractal programming is adopted to convert a simulated concave problem into a convex function, and a new objective function is defined:
g(P0，P1，α)＝Rave(P0，P1)-αEave(P0，P1) Expression 23
Where α is a positive coefficient, in this case, the optimization problem is expressed as:
Figure GSB0000197742180000081
the optimal value function of expression 24 is:
Figure GSB0000197742180000082
where S is the feasible fields of expressions 22 and 24.
Thus, the optimal solution for expression 24 can be calculated by:
Figure GSB0000197742180000083
dinkelbach lemination:
Figure GSB0000197742180000084
if and only if
Figure GSB0000197742180000085
When the condition in expression 27 is satisfied, expression 22 and expression 24 have the same optimal solution. Therefore, the original optimization problem is transformed into expression 24, for a fixed α, the optimal power allocation that maximizes the energy efficiency can be found, and α is updated until expression 27 is satisfied, at which time the optimal solution of expression 22 can be obtained.
And (4) constructing a Lagrangian function, and obtaining an approximate optimal solution according to a KKT condition, wherein the method comprises the following steps:
(4a) the lagrange function is expressed as:
Figure GSB0000197742180000086
wherein tau, upsilon and epsilon are Lagrangian multipliers of constraint conditions C1, C2 and C3 respectively, and none of the three are negative. Determination of P for formula (3.28)0And P1And let the derivative be 0, i.e.
Figure GSB0000197742180000087
(4b) According to the KKT condition, the optimal solution is obtained as follows:
Figure GSB0000197742180000088
Figure GSB0000197742180000089
wherein, [ x ]]+＝max{x，0}。
And (5) obtaining an optimal Lagrange multiplier by adopting a sub-gradient algorithm, substituting the optimal Lagrange multiplier into an optimal solution, and completing optimal power distribution, wherein the method comprises the following steps:
the invention adopts the sub-gradient algorithm, updates the Lagrange multiplier along the direction of the sub-gradient with a certain proper step length delta, and when the ith iteration is carried out,
the Lagrange multipliers tau, upsilon and epsilon are updated according to the following formulas respectively:
Figure GSB0000197742180000091
υi+1＝[υi-δi{Ith-(T-Ts-KTr)E{[P(H1)(1-Qd)P0+P(H1)QdP1]|Gsp|}}]+expression 32
εi+1＝[εi-δi(Rave-Rmin)]+Expression 33
Where δ is a sequence of steps greater than 0.
By iteratively calculating the formula (expression 29-expression 33) until F (α) ≦ θ1And if so, the optimal power allocation is obtained.
And finally, carrying out simulation analysis on the cooperative spectrum sensing power distribution algorithm through a simulation tool, comparing the simulation analysis with the traditional OSA model, and verifying the feasibility of a conclusion, wherein the simulation result is the average value of 1000 MonteCarlo experiments. When system model parameters are set, the number of primary users is considered to be 1, the number of secondary users K is 10, the time slot length of one frame of the secondary users T is 100ms, and T isr10 mus; with simultaneous power of Ps＝0.02w，Pr＝0.05w，Pc0.1 w; setting P (H)0)＝0.7，P(H1)＝0.3，Qd＝0.9，Qf0.1; and f iss＝6MHZ，
Figure GSB0000197742180000092
-20 dB; channel power gain GssAnd GspIs traversal smooth and satisfies exponential distribution. For convenience of analysis, an energy efficiency maximization algorithm under a traditional opportunistic spectrum access model is defined as 'OSA', and an energy efficiency maximization algorithm under a Hybrid spectrum access technology model provided by the invention is defined as 'Hybrid'.
In fig. 2, the relationship between system energy efficiency and transmission power under different models is depicted. It can be seen from the figure that the energy efficiency is a function of the transmission power PaveIs increasedIs increased when P isaveWhen the value of (1) is greater than-10 dB, the value of the energy efficiency is basically unchanged, because the larger the threshold value of the transmission power of the system is, the larger the feasible domain of the original optimization problem about the variables is, the higher the energy efficiency is, but when the transmission power is increased to a certain value, the condition for restricting the energy efficiency mainly depends on interference, and the energy efficiency tends to be stable. Meanwhile, it can be seen that when P isaveWhen a fixed value is taken, the Hybrid has the highest energy efficiency, namely under the same condition, the Hybrid model provided by the invention has the energy efficiency superior to that of the traditional OSA.
In fig. 3, the relationship between the energy efficiency and the probability of reporting channel error using the conventional OSA and Hybrid cooperative spectrum sensing model is described, and it is obvious from the graph that the energy efficiency of the system varies with PeThe error probability of the reporting channel is higher, the system energy efficiency is lower, and the influence of the error probability of the reporting channel on the system energy efficiency is proved; fix P simultaneouslyeIt can be seen that the Hybrid energy efficiency we propose is superior to that of the conventional OSA.
In fig. 4, the energy efficiency and sensing time T using the conventional OSA and Hybrid cooperative spectrum sensing model are describedsIn the graph, it can be seen that the energy efficiency increases first and then decreases with the increase of the sensing time, the optimal sensing time is about 8ms, and when the value is exceeded, the data transmission time is shortened with the continuous increase of the sensing time, more energy is consumed, and the energy efficiency is reduced. At the same time, the same model, the same T, can be seen from the figuresConditional, sub-user rate RminThe larger the energy efficiency, the lower the energy efficiency, since the secondary user needs to consume more energy to meet the high rate, resulting in energy efficiency with rate RminIs increased and decreased. Similarly, under the same condition, a certain interval exists between the Hybrid and the OSA, and the energy efficiency obtained by the Hybrid is greater than that obtained by the OSA under the same condition, so that the Hybrid is proved to be superior to the OSA in energy efficiency.
In fig. 5, the relationship between the energy efficiency and the number of secondary users using the conventional OSA and Hybrid cooperative spectrum sensing model is described, and it can be seen from the graph that the energy efficiency of the system increases first and then decreases as the number of secondary users increases, and the system has the optimal secondary userThe number K is 3. This is because, as the number of secondary users increases, the improvement of the spectrum sensing performance is better than the performance loss caused by the transmission time and the energy consumption of the system, but as the number of secondary users increases, the consumed energy is more but the spectrum sensing performance tends to be stable, so that the performance loss caused by the energy consumption is greater than the improvement of the spectrum sensing performance, and the overall energy efficiency of the system tends to decrease. At the same time, PeIn the same way, we can see that Hybrid is superior to conventional OSA in energy efficiency.
From the description of the present invention, it should be apparent to those skilled in the art that the Hybrid model of the present invention is superior to the conventional OSA model in maximizing system energy efficiency and guaranteeing system performance.
Details not described in the present application are well within the skill of those in the art.

Claims (1)

1. A cooperative spectrum sensing power distribution method based on energy efficiency maximization in cognitive Internet of vehicles is characterized by comprising the following steps:
(1) assuming that the system has 1 primary user and K secondary users, all the secondary users perform cooperative spectrum sensing to obtain the false alarm probability and the detection probability of the global decision, and considering the spectrum sensing error probability in the system model to obtain an expression of average rate and average total energy consumption;
(2) determining a system model for maximizing energy efficiency under the conditions of average transmission power, main user interference, system rate and power constraint at a secondary user transmitting end to obtain a target function:
Figure FSB0000196787530000011
Figure FSB0000196787530000012
wherein, PaveFor the transmitting end average transmission power threshold of the secondary user, RaveAnd RminRespectively representing the average and minimum transmission rates, I, of the secondary usersthRepresenting the maximum interference threshold value which can be tolerated by the master user;
(3) and converting the pseudo-concave problem into a convex function by adopting fractional programming to obtain a new objective function, and taking two transmitting powers required by adopting a mixed spectrum access mode as variables of the objective function:
Figure FSB0000196787530000013
(4) and constructing a Lagrangian function, and obtaining an optimal solution according to a KKT condition:
Figure FSB0000196787530000014
Figure FSB0000196787530000015
wherein tau, upsilon and epsilon are Lagrangian multipliers of constraint conditions C1, C2 and C3 respectively;
(5) obtaining an optimal Lagrange multiplier by adopting a sub-gradient algorithm, substituting the optimal Lagrange multiplier into an optimal solution, and completing optimal power distribution;
the step (1) comprises the following specific steps:
(1a) the secondary user carries out local spectrum sensing to obtain the false alarm probability of the local spectrum sensing
Figure FSB0000196787530000016
And probability of detection
Figure FSB0000196787530000017
(1b) The secondary users report the respective perception results to the fusion center, and the situation that the report channel is not ideal is considered for use
Figure FSB0000196787530000018
And (3) representing the error probability when the kth secondary user reports, the fusion center adopts an OR criterion to make a decision, and assuming that all secondary users transmit in the same but independent reporting channel, the false alarm probability and the detection probability of the global decision can be obtained:
Figure FSB0000196787530000021
Figure FSB0000196787530000022
(1c) adopting a mixed spectrum access mode, and when detecting that a channel is idle, the secondary user uses power P0Transmitting data, when detecting the channel busy, the secondary user is powered up by power P1Transmitting data;
(1d) calculating the probability of detecting the channel being free
Figure FSB0000196787530000023
And probability of channel busy
Figure FSB0000196787530000024
And conditional probability that the actual channel is busy in case it is detected that the channel is free
Figure FSB0000196787530000025
And conditional probability of actual channel being busy in the case of busy
Figure FSB0000196787530000026
(1e) Calculating the average rate obtainable in one time slot of the secondary user, wherein T is the frame length and TSFor sensing time, TrTo report time, TdFor data transmission time, GssFor the channel power gain from the secondary-user transmitter to the secondary-user receiver, GspIs the channel power gain from the secondary user transmitter to the primary user receiver, n is the noise signal and satisfies the mean 0 and the variance
Figure FSB0000196787530000027
s is a fading signal received by a master user and satisfies that the mean is 0 and the variance is
Figure FSB0000196787530000028
Figure FSB0000196787530000029
(1f) And calculating the average energy consumption of one frame of the secondary user:
Figure FSB00001967875300000210
Psand PrPower consumed for the secondary user sensing and reporting slots, P, respectivelycCircuit power, i.e., the power consumed by the transmitter circuit;
wherein, the step (5) comprises the following specific steps:
(5a) the initialized fractional programming coefficient α is α0Lagrange multiplier tau(0)＝τ0，υ(0)＝υ0，ε(0)＝ε0Iteration step delta > 0, error threshold theta1And theta2Satisfy theta respectively1> 0 and theta2＞0，F(α0) Infinity, and given a maximum number of iterations Lmax；
(5b) Substituting the initial value into an optimal solution formula to obtain initial optimal transmitting power;
(5c) updating the Lagrange multiplier until the iteration error of the Lagrange multiplier is smaller than a preset error threshold, and then the algorithm is converged to obtain the Lagrange multiplier;
(5d) updating the fractional programming coefficients until
Figure FSB00001967875300000211
Or the iteration times reach the iteration upper limit to obtain a fractional programming coefficient, namely the energy efficiency;
(5e) and substituting the Lagrange multiplier and the fractional programming coefficient into an optimal solution formula to obtain the optimal transmitting power of the secondary user.
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