CN108282788A - A kind of resource allocation methods of the Energy Efficient based on quasi- newton interior point method - Google Patents
A kind of resource allocation methods of the Energy Efficient based on quasi- newton interior point method Download PDFInfo
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- CN108282788A CN108282788A CN201810071954.XA CN201810071954A CN108282788A CN 108282788 A CN108282788 A CN 108282788A CN 201810071954 A CN201810071954 A CN 201810071954A CN 108282788 A CN108282788 A CN 108282788A
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
- H04W16/14—Spectrum sharing arrangements between different networks
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L5/00—Arrangements affording multiple use of the transmission path
- H04L5/0001—Arrangements for dividing the transmission path
- H04L5/0003—Two-dimensional division
- H04L5/0005—Time-frequency
- H04L5/0007—Time-frequency the frequencies being orthogonal, e.g. OFDM(A), DMT
- H04L5/001—Time-frequency the frequencies being orthogonal, e.g. OFDM(A), DMT the frequencies being arranged in component carriers
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
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Abstract
The present invention proposes a kind of CR OFDM resource allocation methods of maximum energy efficiency.The process employs distributed algorithms to model object function, is optimization aim according to maximum energy efficiency, and the minimum required communication rate of cognitive system is added, will be converted into probability constraints based on the uncertain interference constraints to primary user of CSI.The calculating difficult point brought for introducing probability constraints, non-convex problem is carried out convex approximation by us using Bernstein approximations；When carrying out power distribution in distributed algorithm, we solve power distribution using newton interior point method is intended.Finally, the CR OFDM resource allocations based on energy efficiency are completed.Simulation results show under the MATLAB communication simulation environment low-complexity and accuracy of this method.
Description
Technical field
The present invention relates to a kind of cognitive radio technology more particularly to a kind of resource allocation methods of cognitive radio, more
Specifically, being related to a kind of Energy Efficient resource allocation methods based on quasi- newton interior point method.
Background technology
With the high speed development of wireless data service, the contradictions such as frequency spectrum resource shortage, underutilization of resources become increasingly conspicuous.Recognize
Know that the appearance of radio (CR) technology effectively improves the utilization rate of frequency spectrum resource.
Cognitive radio is by the instantaneous seizure condition of Intellisense frequency spectrum, in the premise for ensuring not influence primary user (PUs)
Under, the transmission band of time user (SUs) is determined according to ambient enviroment, and then the transmission of primary and secondary user is carried out in authorized spectrum band.
This access mechanism of waiting for an opportunity can make full use of frequency spectrum resource, and therefore, how reasonably to carry out resource allocation becomes current important
Research direction.
Orthogonal frequency division multiplexi (OFDM) has been widely used in the space access of CR systems, is become and is lining in bottom
Technology.But in systems in practice, do not ensure that primary and secondary user is all made of OFDM modulation, if so primary user and time user
The signal non-orthogonality of transmission will cause interference with generation.Research shows that：The secondary occupied subcarrier of user is done caused by primary user
It disturbs depending on power of the distribution in this subchannel and subcarrier to the spectrum intervals between primary user, is interfered with each other between user
An important factor for through becoming limitation system performance.
For macroscopic perspective, the resource allocation in CR-OFDM systems includes both sides content：First, according to difference
The characteristic of channel of OFDM subcarriers to wireless frequency spectrum reasonably utilize and distribute, this process is referred to as subcarrier distribution；The
Two, rational power distribution is carried out to the subcarrier of secondary user occupancy, while controlling the interference to primary user, realizes the height of resource
Effect utilizes, this process is known as power distribution.
It is maximized currently, lot of documents is absorbed in research CR-OFDM power system capacities.In recent years, with high speed data transfer
Service it is universal, the energy expenditure of wireless communication system also increases with surprising rapidity, cause a large amount of greenhouse gas emission with
And high running cost.Excessive energy expenditure is controlled, realizes that green communications are imperative.Therefore, the money based on energy efficiency
Source assignment problem has become the another research direction of academia.
Currently, existing a small amount of document is explored in this respect.For example, there is document to consider undesirable frequency spectrum perception
Under the resource allocation problem based on energy efficiency, but interfering with each other between ignoring primary and secondary user do not account for sub- load yet
The allocation plan of wave.Have document consider under undesirable frequency spectrum perception how maximum efficiency energy, it is proposed that Newton method
Resource allocation problem is solved, but computation complexity is excessively high.Have and is based on undesirable frequency spectrum in literature research cognition ofdm system
The efficiency optimal resource allocation algorithm of perception it is assumed that channel state information (CSI) can be obtained accurately, but actual is recognized
Know in OFDM networks, tends not to obtain accurate CSI.Therefore, the present invention, will most in the case where that accurately cannot obtain CSI
Bigization energy efficiency target as an optimization, and the minimum required communication rate of cognitive system is added, it will be to the interference constraints of primary user
Probability constraints are converted into, non-convex problem is carried out by convex approximation using Bernstein approximations；Power point is carried out in multiple step format algorithm
Timing solves power distribution using quasi- newton interior point method.It is finally completed the CR-OFDM resource allocations based on energy efficiency.Emulation
The experiment proves that the low complex degree and accuracy of the invention.
Invention content
Goal of the invention：In view of the above-mentioned problems existing in the prior art, propose that a kind of energy based on quasi- newton interior point method has
Resource allocation methods are imitated, this method can realize the CR- of Energy Efficient with low complex degree under conditions of CSI cannot be obtained accurately
Ofdm system resource allocation.
Technical solution：Accurate CSI cannot be obtained as constraints, and convert this constraints to probability constraints,
Non- convex problem is subjected to convex approximation using Bernstein approximations；The process that quasi- newton interior point method is introduced to power distribution, due to mesh
Scalar functions inequality constraints containing there are six, so, first against the convex optimization problem with Prescribed Properties, solved using interior point method
Certainly, inequality constraints condition is implied by logarithmic function in object function, optimization problem reforms into unconstrained optimization problem.
During optimization object function, handled according to Newton iteration method, then in calculating process newton step-length solution meter
Calculating complexity can be very high.So in order to reduce calculation amount, solved using the BFGS algorithms in Quasi-Newton algorithm, introduces sea
The approximate matrix of gloomy matrix avoids each iteration and is required for calculating Hessian matrix and its inverse matrix, makes computational complexity significantly
It reduces.Foregoing invention is realized by the following technical programs：A kind of Energy Efficient resource based on quasi- newton interior point method point
Method of completing the square, including steps are as follows：
(1), consider in total transimission power limitation, to the interference limitation of primary user, the proportional fairness of secondary user and recognize
Know under the constraintss such as the minimum transmission rate of system, determines the system model of maximum energy efficiency；
(2), convex optimization is carried out to the system model of construction, it, will when accurate channel state information (CSI) can not be obtained
Probabilistic type constraints switched to the interference constraints condition of primary user in model, the degree of equitable proportion passes through fair door between user
It limits to weigh, for the nonconvex property in convex optimization process, non-convex problem is carried out by convex approximation using Bernstein approximations；
(3), subcarrier distribution is carried out to the object function after convex optimization, is carried using the son based on maximum energy efficiency
Wave allocation plan is completed subcarrier distribution, then is optimized to object function；
(4), power distribution is carried out using quasi- newton interior point method, is handled using interior point method, by inequality constrained optimization
Problem becomes unconstrained optimization problem；
(5), the optimal solution of no convex optimization of constraint can be approximated to be the minimization problem with obstruction factor t, calculate obstacle
Hessian matrix in factor t processing procedure and newton step-length dk, power distribution optimal solution is obtained using quasi-Newton method.
Further, the step (3) comprises the following specific steps that：
(3a), the setting of subcarrier initial power；
(3b) is based on maximum energy efficiency, completes subcarrier distribution.
Further, the step (4) comprises the following specific steps that：
(4a) carries out equivalent transformation, by mesh for the convex optimization problem with Prescribed Properties by Hypograph forms
Scalar functions are converted into convex optimization problem；
Inequality constraints condition is implied by logarithmic function in object function using interior point method, is become without about by (4b)
Beam optimization problem.
Further, the step (5) comprises the following specific steps that：
(5a), for newton step-length dkSolution, using the BFGS algorithms in quasi-Newton method, construct Hessian matrix and its
The approximate matrix of inverse matrix avoids and directly calculates Hessian matrix and its inverse matrix, substantially reduces calculation amount；
(5b), the introducing correction matrix needed during solving Hessian matrix and its inverse matrix to BFGS algorithms, for
Object function is done Taylor expansion, takes Two-order approximation by the calculation processing of correction matrix, goes out to correct square using the method construct of iteration
Battle array；
(5c) is solved using the method for undetermined coefficients, is applied for calculating the correction matrix in iterative process each time
Sherman-Morrison formula obtain kth step and the relational expression between the approximate matrix and inverse matrix of+1 step of kth, complete school
The calculating of positive matrices.
Advantageous effect：A kind of resource allocation methods of Energy Efficient based on quasi- newton interior point method proposed by the present invention, are examined
Total transimission power limitation, interference limitation, the proportional fairness of secondary user and the minimum transmission of cognitive system to primary user are considered
The constraintss such as rate, it is ensured that the reasonability of resource allocation.In the case where accurate CSI cannot be obtained, by model to master
The interference constraints condition of user switchs to probabilistic type constraints, and the degree of equitable proportion is weighed by fair thresholding between user,
Reduce the difficulty in computation of model.Processing is non-convex with maximum energy efficiency target and the object function established as an optimization
Property, approximate, Hypograph form equivalent transformations are carried out using Bernstein, and there will be inequality constraints items using interior point method
The object function of part, becomes unconstrained optimization problem.Last calculating target function, using the method for fractional steps, first using based on maximization
The sub-carrier wave distribution method of energy efficiency carries out subcarrier distribution, then carries out power distribution.During power distribution, utilize
BFGS algorithms in quasi- newton interior point method are handled, and when solving newton step-length, are introduced the approximate matrix of Hessian matrix, are avoided
Each iteration is required for calculating Hessian matrix and its inverse matrix, and computational complexity is made to greatly reduce.
In conclusion in the case that ensureing that resource allocation is reasonable and result of calculation is accurate, one kind proposed by the present invention
The resource allocation methods of Energy Efficient based on quasi- newton interior point method effectively reduce the complexity of calculating.
Description of the drawings
Fig. 1 is the flow chart of the energy efficient process based on quasi- newton interior point method；
Fig. 2 is the variation diagram that system energy efficiency is limited with transimission power under different sub-carrier number；
Fig. 3 is the variation diagram that system energy efficiency is limited with transimission power under different ε；
Fig. 4 is system energy efficiency under different primary user's interference thresholds with the variation diagram of ε.
Specific implementation mode
Core of the invention thought is：Quasi-Newton method and interior point method are combined and carry out power distribution, by introducing Hai Sen
It is inverse can to obtain new Hessian matrix on the inverse approximate basic of the Hessian matrix that upper primary iteration obtains for the approximate matrix of matrix
Approximation, each iteration only need calculate gradient vector, obtain optimal solution while but greatly reduce computation complexity.
The present invention is described in further detail below.
Step (1) considers in total transimission power limitation, limits the interference of primary user, the proportional fairness of secondary user
Under the constraintss such as the minimum transmission rate of cognitive system, determines the system model of maximum energy efficiency, include the following steps：
Consider that the downlink of a cognition OFDM network, cognitive system have K users, with set κ=1,2 ..,
K } it indicates, while main system has L primary user, with setIt indicates, total authorized bandwidth W is divided into NallIt is a
OFDM subcarriers, and primary user not necessarily uses OFDM to modulate.Secondary user is with transmission of the unit power on subcarrier n to primary
Family l generate interference factor beSimilar, primary user l is to the secondary user k interference factors generated on subcarrier n
Transimission powers of the secondary user k on subcarrier n is pK, n.SNRs of the secondary user k on subcarrier n is HK, n, remember and do not accounted for by primary user
T easet ofasubcarriers areThen energy efficiency ηEEIt is defined as the ratio of power system capacity and total power consumption in per unit band
Value, accordingly, it is considered to which system model is represented by under carried constraints：
Wherein, PTTo recognize the maximum transmission power of AP,For the interference threshold of primary user l, { β1, β2..., βkIt is pre-
The one group of proportionality constant first set, RminIt is the minimum transmission rate of cognitive system.
Step (2) carries out convex optimization to the system model of construction, can not obtain accurate channel state information (CSI)
When, probabilistic type constraints will be switched to the interference constraints condition of primary user in model, the degree of equitable proportion passes through between user
Fair thresholding is weighed, and for the nonconvex property in convex optimization process, is carried out non-convex problem using Bernstein approximations convex close
Seemingly.Then optimization problem can be converted into：
Where it is assumed thatCodomain be [an, bn], defconstant WithIt is to rely on the constant of given probability distribution, and is metσn>=0, ε ∈ (0,1) represent more than dry
Disturb the probabilistic upper bound of threshold value.Fairness is fair thresholding, is defined asWherein, fairness ∈
(0,1], with the increase of fairness, the fairness between user enhances therewith,Closer to equal.When fairness is equal to
When 1,Meet desired proportions condition at this time.
Step (3) carries out subcarrier distribution, using based on maximum energy efficiency to the object function after convex optimization
Subcarrier distribution scheme,
Subcarrier distribution is completed, including steps are as follows：
(3a), the setting of subcarrier initial power；
Assuming that assignable t easet ofasubcarriers areNumber is N, and joint considers power and interference constraints, then distributes to every
The initial power of a subcarrier is as follows：
(3b), subcarrier distribution；
Since optimization problem is to maximize system energy efficiency, according to the initial power obtained in (2a), then subcarrier n is answered
This is assigned to the secondary user k that can obtain highest energy efficiency, i.e.,：
(3c) completes distribution.
Enable Hn=HK, n, this process is repeated, until all subcarriers are all assigned.
Step (4) carries out power distribution using quasi- newton interior point method, includes the following steps：
(4a), object function conversion；
Equivalent transformation is carried out using Hypograph forms, and object function is subjected to convex transformation, is converted into：
Wherein,
(4b), interior point method optimization；
Expression formula 5 is converted to logarithmic function：
Wherein z={ p1, p2..., pN, x }, optimal solution can be approximated to be the minimization problem with obstruction factor t, expression
Formula is as follows：
minψt(z)=te-x+ φ (z) expression formulas 7
(4c), quasi-Newton method.
Expression formula 7 is that final goal function is indicated using in the BFGS algorithms in Quasi-Newton algorithm with matrix B after handling
To the approximation of Hessian matrix H, the inverse H to Hessian matrix is indicated with matrix D-1Approximation, i.e. B ≈ H, D ≈ H-1.It is clear in order to describe
It is clear, it is assumed that in kth time iterative process, gkRepresent gradient vector, HkRepresent Hessian matrix, BkIndicate HkApproximation, DkIndicate Hk -1
Approximation, dkIndicate newton step-length, zkIndicate solution.If obtaining z after k+1 iterationk+1, object function f (z) is existed at this time
zk+1Taylor expansion nearby is done, Two-order approximation is taken, obtains：
A gradient operator is acted on simultaneously on 8 both sides of expression formulaIt can obtain：
Enable z=zk, arrange：
gk+1-gk≈Hk+1·(zk+1-zk) expression formula 10
Introduce mark：
qk=zk+1-zk, yk=gk+1-gkExpression formula 11
Then expression formula 11 can be rewritten as：
yk≈Hk+1·qkExpression formula 12
According to Bk≈Hk, obtain：
yk=Bk+1·qkExpression formula 13
Using the method for iteration, it is assumed that Iteration is：
Bk+1=Bk+ΔBk, k=0,1,2 ... expression formula 14
B0Unit matrix I is taken, therefore emphasis is the correction matrix Δ B for constructing each stepk, using the method for undetermined coefficients, its is undetermined
For：
ΔBk=ω uuT+υvvTExpression formula 15
Expression formula 15 is substituted into 14, and combines expression formula 13, can be obtained：
yk=Bkqk+(ωuTqk)u+(υvTqk) v expression formulas 16
Enable ω uTqk=1, υ vTqk=-1 and u=yk, v=Bkqk, finally：
To sum up, correction matrix formula is obtained：
By applying Sherman-Morrison formula to expression formula 18, B can be obtainedk+1 -1And Bk -1Obtain relational expression：
In order to avoid there is matrix inversion symbol, D is enabledk+1=Bk+1 -1, Dk=Bk -1, then expression formula 19 become：
It is analyzed through step (4), in conjunction with Fig. 1, the algorithm flow of quasi- newton interior point method power distribution is：
(a) interior point method initializes, feasible solution z0∈RN+1, precision ε0＞ 0, t=t(0)＞ 0, μ ＞ 1；
(b) outer circulation judges (KN+L+3)/t ＜ ε0, wherein K, N, L is respectively time user, subcarrier and primary amount,
Cycle is jumped out if meeting, otherwise executes following circulation step；
(c) intend newton initialization, precision εn＞ 0, α ∈ (0,0.5), β ∈ (0,1), and enable D0=I, k=0；
(d) cycle in, calculates dk=-DkgkAnd λk=-gkdk；
(e) judge, if meeting λk 2/2≤εnCycle is then jumped out, following steps are otherwise executed；
(f) step factor s is obtained using backtracking line searchk, enable qk=skdk, zk+1=zk+qk, calculate yk=gk+1-gk, meter
It calculates
(g) k=k+1 is enabled；
(h) update t=μ t；
It is finally emulated, analyzes simultaneously comparison result.It is analyzed by emulation experiment more different based on Energy Efficient
The performance of resource allocation algorithm.A kind of optimization problem optimal solution upper bound algorithm is defined, referred to as " the optimal solution upper bound "；Pass through
The optimal solution upper bound carries out subcarrier distribution, then carries out power distribution with the quasi- newton interior point method proposed, referred to as " height is multiple
Miscellaneous+quasi- newton "；By it is above-mentioned carry based on maximum energy efficiency carry out subcarrier distribution, then with intend newton interior point method into
Row power distribution, referred to as " low complicated+quasi- newton ".Consider that a multi-user recognizes the downlink of ofdm system,
In all users (primary user and time user) be randomly dispersed in the region of a 3km × 3km, each user's receiver uniformly divides
Cloth is in the circle apart from its transmitter 0.5km.Assuming that channel will produce Rayleigh fading, the logarithm variance of shadow fading is 10dB.
Noise power N0=10-13W, OFDM symbol duration Ts=10-6s。
In fig. 2 it is described that under different sub-carrier number, variation diagram that system energy efficiency limits with transimission power.Its
In, primary amount is L=1, and secondary number of users is K=32, and the interference threshold to primary user is Ith=8 × 10-11W, static circuit work(
Rate Pc=0.25W, the minimum transmission rate request of system are Rmin=10bits/symbol, fair threshold parameter ξ=0.99, setting
More than probabilistic upper bound ε=0.8 of interference threshold, subcarrier number N is respectively 128,64, three kinds of method institute energy of comparative analysis
The energy efficiency of acquisition with transimission power rated value variation.
In figure 3, the variation diagram that system energy efficiency is limited with transimission power under different ε is described, wherein subcarrier
Number is N=128, and remainder values are as Fig. 2, and setting ε is respectively 0.8,0.4, and three kinds of algorithms of comparative analysis can obtain
Energy efficiency with transimission power rated value variation.
In Fig. 4, the variation diagram of system energy efficiency under different primary user's interference thresholds with ε is described, wherein secondary use
Family number K=32, subcarrier number N=256, static circuit power Pc=0.25W, the minimum transmission rate request of cognitive system are
10bits/symbol, transimission power rated value PT=1W, fair threshold parameter ξ=0.99 set IthRespectively 8 × 10-11W, 4
×10-11W, the energy efficiency that three kinds of algorithms of comparative analysis are obtained with ε variation diagram.
The energy efficiency resource allocation algorithm of quasi- newton interior point method, key are to replace Newton method using quasi-Newton method, use
Approximation method constructs Hessian matrix and its approximate matrix of inverse matrix, constructs the correction matrix of each step, finds out newton step-length.
According to the description of the invention, those skilled in the art should be not difficult to find out, quasi- newton interior point method of the invention
It can be required for asking Hessian matrix and its inverse matrix to avoid each step iteration, greatly reduce the complexity of calculating.
The content not being described in detail in the present patent application book belongs to the prior art well known to professional and technical personnel in the field.
Claims (3)
1. a kind of resource allocation methods of the Energy Efficient based on quasi- newton interior point method, feature exist in cognitive radio networks
In, including steps are as follows：
(1), consideration interferes limitation, the proportional fairness of secondary user and cognition system in total transimission power limitation, to primary user
It unites under the constraintss such as minimum transmission rate, determines the system model of maximum energy efficiency；
(2), convex optimization is carried out to the system model of construction, when accurate channel state information (CSI) can not be obtained, by model
In probabilistic type constraints switched to the interference constraints condition of primary user, between user the degree of equitable proportion by fair thresholding come
It weighs, for the nonconvex property in convex optimization process, non-convex problem is carried out by convex approximation using Bernstein approximations；
(3), subcarrier distribution is carried out to the object function after convex optimization, using the subcarrier based on maximum energy efficiency point
With scheme, subcarrier distribution is completed, then optimize to object function；
(4), power distribution is carried out using quasi- newton interior point method, recycles interior point method to be handled, inequality constrained optimization is asked
Topic becomes unconstrained optimization problem；
(5), the optimal solution of no convex optimization of constraint can be approximated to be the minimization problem with obstruction factor t, calculate obstruction factor t
Hessian matrix in processing procedure and newton step-length dk, power distribution optimal solution is obtained using quasi-Newton method.
2. the Energy Efficient resource allocation methods according to claim 1 based on quasi- newton interior point method, which is characterized in that institute
It states in step (4), comprises the following specific steps that：
(4a) carries out equivalent transformation, by target letter for the convex optimization problem with Prescribed Properties by Hypograph forms
Number is converted into convex optimization problem；
(4b) is implied inequality constraints condition in object function by logarithmic function using interior point method, becomes excellent without constraining
Change problem.
3. the Energy Efficient resource allocation methods according to claim 1 based on quasi- newton interior point method, which is characterized in that institute
It states in step (5), comprises the following specific steps that：
(5a), for newton step-length dkSolution construct Hessian matrix and its inverse square using the BFGS algorithms in quasi-Newton method
The approximate matrix of battle array avoids and directly calculates Hessian matrix and its inverse matrix, greatly reduces computation complexity；
(5b) solves introduced correction matrix during Hessian matrix and its inverse matrix for BFGS algorithms, using by mesh
Scalar functions do Taylor expansion, take Two-order approximation, then go out correction matrix with the method construct of iteration；
(5c) is solved using the method for undetermined coefficients, is applied for calculating the correction matrix in iterative process each time
Sherman-Morrison formula obtain kth step and the relational expression between the approximate matrix and inverse matrix of+1 step of kth, complete correction
The calculating of matrix.
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| CN111130557A (en) * | 2019-12-31 | 2020-05-08 | 秦皇岛职业技术学院 | Data reconstruction method based on distributed quasi-Newton projection tracking |
| CN111130557B (en) * | 2019-12-31 | 2023-11-17 | 秦皇岛职业技术学院 | Data reconstruction method based on distributed quasi-Newton projection tracking |
| CN111225363A (en) * | 2020-01-20 | 2020-06-02 | 深圳以正科技有限公司 | Distributed D2D system power distribution method and device based on imperfect CSI |
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