CN105577250B - Interference based on adaptive compound cost function in MIMO interference channel is aligned method for precoding - Google Patents
Interference based on adaptive compound cost function in MIMO interference channel is aligned method for precoding Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/0413—MIMO systems
- H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
Abstract
The invention discloses the interference based on adaptive compound cost function in a kind of MIMO interference channel to be aligned method for precoding, belong to wireless communication technology field, its core concept is that the optimization design of pre-coding matrix is realized using intermediate variable auxiliary, specifically includes the following steps: first, the weighted difference of residual interference and desired signal power in definition expectation subspace is cost function, and uses for reference the adaptive selection mode that maximum-ratio combing thought obtains weight coefficient；Then, auxiliary function is constructed according to receiving end decoding process, converts intermediate variable for AF panel matrix, realizes the Composite of cost function；Finally, realizing the Optimization Solution of adaptive compound cost function, using the gradient descent method in Grassmann manifold to obtain the optimal solution of pre-coding matrix.The present invention completes the double goal for inhibiting interference and retaining desired signal, to preferably improve system performance with lesser complexity cost；And realization mechanism is simple, has wide applicability.
Description
Technical field
The present invention relates to wireless communication technology fields, and in particular to multi-user's multiple-input and multiple-output (Multiple Input
Multiple Output, MIMO) in interference channel system a kind of interference based on adaptive compound cost function be aligned precoding
Method.
Background technique
Co-channel interference (Co-Channel Interference, CCI) is inevitably present in multi-user MIMO system,
And the presence of CCI seriously constrains the capacity of multi-user MIMO system.Interference alignment (Interference Alignment,
IA it) is concerned as most potential interference management techniques proposed in recent years, core concept is by precoding square
Interference signal is compressed in specific lower-dimensional subspace by battle array, to retain noiseless space as big as possible for desired signal
Transmission.
According to the difference of IA algorithm pre-coding matrix design mode, existing IA algorithm can be divided into two classes: direct method and repeatedly
Dai Fa.Direct method realizes complete IA by analytical Calculation, and complexity is lower, but usually to system antenna configuration and channel status
Information has strict requirements；And iterative method needs multiple loop iteration complexity is higher to approach complete IA, but tend to obtain compared with
Good system performance, and algorithm design is more flexible.Therefore, iterative method is focused primarily upon for the research of IA algorithm at present.
The mentality of designing of conventional iterative IA algorithm has following two: one is using the reciprocity of uplink and downlink channel, passing through
Transmitting-receiving both ends alternative optimization pre-coding matrix and AF panel matrix are eliminated to realize to interfere.It is calculated according to the IA that the thinking is designed
Method needs to receive and dispatch the tight fit at both ends, although can theoretically obtain preferable system performance, is dfficult to apply to practical system
System.Main cause includes: firstly, real system is difficult to meet the requirement fully synchronized to transmitting-receiving both ends of such algorithm；Secondly, receiving
Iterating for hair both ends can generate a large amount of feedback and synchronizing information, not only bring heavy redundancy to bear to communication system,
And the limited situation of the computing capabilitys such as mobile terminal is not suitable for it；Finally, algorithm excessively relies on channel reciprocity, it is only possible to answer
In time division duplex (Time Division Duplexing, TDD) system；The second is avoiding AF panel matrix completely
It calculates, using the methods of convex optimization, is updated by the iteration that transmitting terminal is independently performed pre-coding matrix.Based on thinking design
The transmitting-receiving many deficiencies of both ends alternating iteration bring are although overcome at IA algorithm, simplify the realization mechanism of IA algorithm, and will
The applicable scene of algorithm extends to frequency division duplex (Frequency Division Duplexing, FDD) system from TDD system
System, but its way for deliberately ignoring the influence of AF panel matrix not only limits the design flexibility of IA algorithm, also results in algorithm
During being aligned interference, the loss of desired signal cannot be effectively inhibited simultaneously, so that it is reachable to limit mimo system
The room for promotion of capacity.If the AF panel matrix in the first mentality of designing is only to assist only from mathematical angle
The tool of pre-coding matrix is designed, the contacting there is no certainty with receiving end is updated, only because the limitation of Design Thinking is
It must be calculated and be obtained by receiving end.And second of mentality of designing is simply considered that the optimization of AF panel matrix is only capable of by connecing
Receiving end is completed, thus directly simplifies the realization mechanism of IA algorithm to avoid the calculating of AF panel matrix, and such way is
It is extremely unadvisable.
Summary of the invention
In view of this, carry out that essence is taken to abandon grain it is an object of the invention to two kinds of existing mentalities of designing to iteration IA algorithm,
It proposes a kind of design philosophy for assisting optimization pre-coding matrix using intermediate variable, both can guarantee that the unilateral of IA algorithm can be achieved
Property, and the unilateral IA algorithm of tradition can be broken through in design flexibility and system up to the limitation on capacity.According to the design philosophy, originally
Invention provides the IA method for precoding based on adaptive compound cost function under a kind of MIMO interference channel, it is intended to be aligned interference
Under the premise of, inhibit the loss of desired signal as much as possible, to further improve system performance.
In order to achieve the above objectives, the present invention adopts the following technical scheme that realization:
A kind of IA Precoding Design scheme based on adaptive compound cost function under multiuser MIMO interference channel is
System scene setting are as follows: number of users K, i.e., shared K transmitting terminal and receiving end, k-th of transmitting terminal are respectively configured with receiving end end
NkAnd MkRoot antenna transmits dkA data flow, meets dk≤min(Mk,Nk).This programme key step is as follows:
Step 1 constructs the optimization problem with particular constraints in Euclidean space, defines the weighting of optimization problem
Cost functionThe adjustable weight of the residual interference in shop sign in the form of a streamer space and desired signal power is poor by a definite date, defines weight system
Number αkThe nonnegative real number changed for one with desired signal, interference and noise intensity, value is with interference to systematic influence journey
The reinforcement of degree and reduce.
Step 2 constructs an auxiliary function according to the decoding process of receiving endBy 2KdkMember weighting cost letter
NumberBe converted to KdkThe compound cost function f (V) of member, i.e.,Wherein V={ V1,
V2,…,VK, U={ U1,U2,…,UKPre-coding matrix collection and AF panel matrix stack are respectively indicated, K indicates multiuser MIMO
The user of interference system is to number, dkIndicate the data flow number that k-th of transmitting terminal is sent.
Step 3 will minimize compound cost in conjunction with mathematics manifold, complex valued matrices derivation and gradient optimization algorithm
The restricted problem of function f (V) is converted to the unconstrained optimization problem in manifold, and then the solution procedure of the problem is gone to Ge La
It is executed in this graceful manifold, and completes the iteration optimization of pre-coding matrix collection V.
In a specific embodiment of the invention, with the optimization problem of particular constraints described in step 1 are as follows:
Wherein,Indicate weighting cost function,WithRespectively indicate that receiving end k receives from transmitting terminal
The interfering signal power of j and desired signal power from transmitting terminal k；αkForWeight coefficient, for adjust interference and the phase
The specific gravity for hoping signal shared in compound cost function；VkAnd UkRespectively indicate k-th of transmitting-receiving to corresponding pre-coding matrix and
AF panel matrix,WithRespectively indicate VkAnd UkConjugate transposition, K indicate multiuser MIMO interference system user couple
Number,Indicate dk×dkThe unit matrix of dimension.
The weight coefficient αkIt is defined as the nonnegative real number that can change with desired signal, interference and noise intensity,
Its value reduces the increase of systematic influence degree with interference, uses for reference the thought α of maximum-ratio combingkSelection mode it is as follows:
Wherein a is αkInitial value；b1And b2Respectively indicate αkWith γkWithReduction speed；Indicate transmitting terminal k
Transmission signal-to-noise ratio, γkIt indicates to send power allocation factor, the i.e. average transmission signal-to-noise ratio and desired transmitting terminal of interference transmitting terminal
Send the ratio of signal-to-noise ratio, calculating formula are as follows:
When transmission power averaging distributes to each transmitting terminal, γk=1；WhereinIndicate the transmission noise of transmitting terminal j
Than.
Auxiliary function described in step 2Must be corresponded with the decoding process of receiving end, by its with the most
Simple force zero decoding is mapped, that is, defines the preceding d that AF panel matrix is its corresponding interference covariance matrixkA minimum
Feature vector group corresponding to characteristic value, i.e.,
Wherein dk、QkK-th of transmitting-receiving is respectively indicated to the data fluxion and corresponding interference covariance matrix transmitted.
WhereinIndicate interference covariance matrix corresponding to k-th of sending and receiving end；Pj, dj,
VjAnd HkjRespectively indicate transmitting terminal j send power, send data fluxion, send pre-coding matrix and its to receiving end k letter
Road matrix.
The matrix U being calculated by above formulakAutomatically meet constraint condition:To which, step 2 is by step
The one optimization problem equivalent description with particular constraints are as follows:
WhereinWithThe interfering signal power from transmitting terminal j that respectively indicates that receiving end k receives and come spontaneous
The desired signal power of sending end k, αkForWeight coefficient,Indicate VkConjugate transposition, K indicate multiuser MIMO interference
The user of system to number,Indicate dk×dkThe unit matrix of dimension.
Unconstrained optimization problem is gone into Grassmann manifold described in step 3, by the unconstrained problem after recombination using ladder
Descent method iterative solution is spent, wherein iteration step length uses the Armijo step-length selection mechanism with automatic adjusument function.It should
Constraint condition can be removed in problem recombination to the Grassmann manifold of low-dimensional, solve difficulty reconciliation Spatial Dimension to reduce.
It is had the advantage that using technical solution of the present invention
(1) under the premise of being aligned interference, the loss of desired signal is farthest inhibited.It weights cost function f (V)
Interference signal and desired signal, adaptive weighting factor alpha are considered simultaneouslykIt can be according to interference to the influencing characterisitic of system performance
The reasonable specific gravity for adjusting interference and desired signal in f (V).
(2) realization mechanism is simple, and applicability is wide.The entire implementation procedure that the present invention is suggested plans is independently complete by transmitting terminal
At not needing the cooperation of receiving end, realization mechanism is relatively easy, not only avoids because of front and back caused by iterating to link
A large amount of synchronizations and feedback information are born to the redundancy of system bring, and it is poor to be applicable to the receiving ends such as mobile terminal computing capability
Scene；The requirement to channel reciprocity is also relaxed, TDD and FDD system can be suitable for simultaneously.
(3) the larger promotion of power system capacity is realized with lesser complexity cost.The present invention suggests plans
Optimization problem is recombinated in Grassmann manifold, and completes the Optimization Solution of cost function, significantly reduces searching for optimal solution
Plain difficulty conciliates Spatial Dimension, and rate of convergence is very fast, therefore complexity cost is relatively small.The present invention has combined interference
The inhibition of signal and the reservation of desired signal, are more conducive to the promotion of power system capacity.
Detailed description of the invention
Fig. 1 is K user MIMO interference system model schematic；
Fig. 2 is the IA principle and Contrast on effect schematic diagram of the method for the present invention；
Fig. 3 is the master-plan flow chart of IA pre-coding scheme provided by the invention；
Fig. 4 is the specific of the pre-coding scheme based on adaptive cost compound function on Grassmann provided by the invention
Implementation flow chart.
Specific embodiment
Implementing procedure of the invention is described in further detail below in conjunction with attached drawing.
Multi-user's multiple-input and multiple-output (Multiple Input Multiple Output, MIMO) interference system in the present invention
Uniting, number of users is K to model as shown in Figure 1:, i.e., shared K transmitting terminal and receiving end, is received and dispatched for k-th to N is respectively configuredkAnd MkRoot
Antenna transmits dkA data flow, meets dk≤min(Mk,Nk).Each receiving end can also connect while receiving expectation number signal
Receive the interference signal from other K-1 unexpected transmitting terminals, therefore, the signal y that k-th of receiving end receiveskIt can indicate
Are as follows:
WhereinFor the flat fading channel matrix of transmitting terminal j to receiving end k,Indicate Nk×MjThe Euclidean space of dimension；Indicate k-th of transmitting-receiving to corresponding flat fading channel square
Battle array；It indicates to send signal phasor, through pre-coding matrixAfter processing, meet power constraint E | | Vksk|
|2}≤Pk/dk；Indicate the white complex gaussian noise vector that receiving end k is received, distribution meets nk~CN (0, σ2I).Signal ykReceived end AF panel matrixAfter processing, it may be expressed as:
Under the channel model, system is average and rate can be expressed from the next:
Wherein RkIndicate the average data transfer rate of user k；σ2Indicate noise power；I indicates unit matrix；QkFor with
The k interference covariance matrix at family, expression formula are as follows:
WhereinIndicate that dimension is the complex valued matrices of m × p；ImIndicate that dimension is the unit matrix of m × m；| | | | table
Show the 2- norm of vector；(·)HThe conjugate transposition of representing matrix；E { } indicates that mathematic expectaion is sought operating；Det { } is indicated
Determinant of a matrix.
In order to effectively decode desired signal, signal space is divided into interference signal son sky in receiving end by receiving matrix
Between and desired signal subspace, as shown in Fig. 2, inter-user interference signalInterference signal will be aligned to
SpaceIt is interior；Desired signalThen it is aligned to desired signal subspaceIt is interior, soDimension cannot be less than the data flow number d to be transmittedk.Thus it is linear to show that multiuser MIMO interference channel is realized
The condition of interference alignment (Interference Alignment, IA) is as follows:
The wherein order of rank { } representing matrix, the generated subspace of span () representing matrix, A⊥Representing matrix A is just
It hands over and mends matrix.
However, the interference difficult to realize of iteration IA algorithm is perfectly aligned, and in Fig. 2, interference signalThough
It is so most of to have snapped to interference signals subspaceIt is interior, but still there have fraction to remain in desired signal to be empty
BetweenIt is interior, and this part residual interference can be approached be zero be measure the whether feasible unique finger of iteration IA algorithm
Mark.The power of residual interference can be calculated with following formula:
WhereinThe residual interference power from transmitting terminal j received for receiving end k；||·||F
The Frobenius norm of representing matrix.
Fig. 3 show the master-plan flow chart of IA pre-coding scheme provided by the invention, specifically comprises the following steps:
Step 1: the optimization problem for there are particular constraints is constructed in Euclidean space, weights cost function
The adjustable weight of the residual interference and desired signal power that are defined as in expectation subspace is poor, and uses for reference maximum-ratio combing thought and obtain
Weight coefficient α outkOne kind adaptive choose mode；
Existing iteration IA algorithm is mostly to minimize residual interference as optimization aim, although as shown in Fig. 2, such algorithm
Most interference signals can be aligned inIt is interior, but also inevitably by desired signal HkkVkskOne
Leakage is divided to existIt is interior, it is low although causing such IA algorithm that can obtain preferable system performance under high s/n ratio
Performance under signal-to-noise ratio is poor.Principal element due under low signal-to-noise ratio, influencing system performance is not interfered instead of, noise with
Desired signal ignores the loss of desired signal if only pursuing the minimum of interference, necessarily will limit the promotion of system performance.Cause
This, in order to preferably improve system performance, the present invention considers interference and desired signal simultaneously, to interfere and desired signal power
The cost function that weighted difference is designed as IA algorithm optimizationAt this point, IA problem can be described as:
WhereinRespectively pre-coding matrix collection and AF panel matrix stack；
Represent the desired signal power that receiving end k is received, calculating formula are as follows:
αkForWeight coefficient, for adjust interference and desired signal in cost functionIn shared specific gravity,
The difference of residual interference and desired signal power on the order of magnitude can be balanced again.Due to interfering the influence degree meeting to power system capacity
Change with the variation of signal and noise power, actual conditions are not obviously met using fixed weighting value, therefore, the present invention is by αk
It is defined as the nonnegative real number that can change with desired signal, interference and noise intensity, value should be with interference to system shadow
Ring degree reinforcement and reduce.The thought for using for reference maximum-ratio combing, obtains αkA kind of selection mode it is as follows:
Wherein a is αkInitial value；b1、b2Respectively describe αkWith γkWithReduction speed；Indicate receiving end k
Transmission signal-to-noise ratio；γkIndicate the average transmission signal-to-noise ratio of interference transmitting terminal and the ratio of desired transmitting terminal transmission signal-to-noise ratio, table
Levy influence of the power distribution mode of transmitting terminal to system performance, expression formula are as follows:
When transmission power averaging distributes to each transmitting terminal, γk=1.Due to γkPresence so that αkValue energy root
It is adaptively adjusted according to different transmitting terminals in the gap sent on power.
Step 2: an auxiliary function is constructed according to the decoding process of receiving endAnd by the functional relation
Intermediate variable is converted by AF panel matrix stack U, thus can be by 2KdkFirst cost functionBe converted to KdkMember is compound
Function f (V), i.e.,It lays the foundation for transmitting terminal complete independently Precoding Design；
Due to cost functionIn contain AF panel matrix UkIf continuing to use traditional unilateral IA mentality of designing,
It is summed with characteristic value and replaces Uk, not ensuring that makes to interfere the smallest subspace to weigh just with the maximum subspace of desired signal is made
It is folded, it just not can guarantee cost function yetOptimization.Therefore,Optimization process necessarily involve UkMeter
It calculates.In previous IA algorithm, UkIt can only be updated in receiving end, if simply following traditional IA design philosophy,Optimization must receive and dispatch both ends cooperation complete.The present invention has broken this thinking limitation, by AF panel matrix UkIt sees
Make the function of pre-coding matrix collection V, then UkIt can directly be sought according to the functional relation by transmitting terminal, both can guarantee algorithm unilateral
It realizes, in turn, ensures thatOptimal solution.
UkIt can flexibly be set with system scenarios according to actual needs with the functional relation of V, but must be with the solution of receiving end
Code mode corresponds, and the present invention in order to reduce complexity cost as much as possible, by itself and the most simply interference force zero decoding
It is mapped, it may be assumed that
WhereinThe preceding d of representing matrix AkFeature vector corresponding to a minimal eigenvalue, therefore matrix UkAutomatically
Meet constraint condition:After designing pre-coding matrix according to the functional relation, it is only necessary in receiving end using interference
Force zero decoding.
It, can be by 2KM according to above formulakdkMeta-functionBe converted to KMkdkFirst compound function, i.e.,To which above-mentioned IA optimization problem can equivalent description are as follows:
Step 3: in conjunction with the relevant knowledge of mathematics manifold, complex valued matrices derivation and gradient descent method, cost will be minimized
The restricted problem of function f (V) is converted to the unconstrained optimization problem in manifold, and then the solution procedure of the problem " translation " is arrived
The iteration optimization of pre-coding matrix collection V is executed and completed in Jim Glassman (Grassmann) manifold.
Step 2 defines an Euclidean spaceInterior constrained optimization problem.In order to convert the problem to
Unconstrained optimization problem, present invention introduces matrix manifolds to recombinate to optimization aim.Due to any unitary matrice G, interference association
Variance matrix QkAll meet:
Then utilize QkThe AF panel matrix stack U acquired also meets U (VG)=U (V), therefore to cost function f (V), must
So have:
I.e. compound cost function f (V) meets tenth of the twelve Earthly Branches invariance, this inspires the present invention to flow using Jim Glassman (Grassmann)
Optimization algorithm in shape solves the problem.Since Grassmann manifold is to be embedded in a set of more dimensional Euclidean Space,
It may be defined as:
Its dimension is far below corresponding Euclidean space dimension, therefore can not only remove cost letter using Grassmann manifold
Several constraint condition, moreover it is possible to the dimension of its solution space is substantially reduced, to greatly reduce the complexity that algorithm is realized.
Optimization space is determined, followed by the Solve problems of compound cost function f (V).Since f (V) there is no bumps
Characteristic, cannot be by analytical Calculation direct solution, therefore, and come Step wise approximation, its is optimal using classical gradient descent method by the present invention
Solution.Gradient descent method refers to the test point of cost function in its constraint set, along a certain rail of its steepest descent on direction
Mark constantly moves, until gradient be zero linear optimization method.The key of this method is that the gradient of cost function calculates.Due to fixed
The value of compound cost function f (V) of the justice in Grassmann manifold is real number, therefore its gradient calculating formula is as follows:
Wherein ()*The complex conjugate of representing matrix converts；Indicate f to matrix Vi *Partial derivative；
Respectively indicate compound cost function f (V) and its k-th of component part fk(V) gradient；IiExpression and ViVi HWith the unit of dimension
Matrix.
For convenience of expression, two operators are defined:And trv(mp)(·)。Representing matrix column vector
The inverse operation of operation vec (), i.e., by column vector lmp×1It is transformed into the matrix of m × p dimension, such as:
trv(mp)(An×mp) it is expressed as follows operation: by matrix An×mpRow vectorIt is changed by column
MatrixIt again will by columnIt is converted into as row vector
Finally by n biReassemble into a new matrix.Such as:
According to the auxiliary function defined above it is found that value by interference covariance
Matrix determines, only related with the interference pre-coding matrix of transmitting terminal,
So must have as k ≠ i:Then gradient as a result,
Two parts that must be split under k=i and k ≠ i calculate, i.e.,
Due toSo that
WhereinIndicate the residual interference power from transmitting terminal j that receiving end k is received；Indicate that receiving end k is received
The desired signal power arrived.
As k=i, according to Matrix Formula Tr (X+Y)=Tr (X)+Tr (Y), Tr (XY)=Tr (YX), d [Tr (X)]=Tr
(dX) and vec (dX)=dvec (X), d [Tr (XTY)]=vecT(X) vec (Y) can be calculated:
As k ≠ i, matrix operation formula Tr (XdY is utilizedH)=Tr (XTdY*),
Anddvec[F(X,X*)]=DXFdvec(X)+DX*Fdvec(X*) can
:
Wherein
Then when k ≠ i, have
The wherein mark of tr () representing matrix；The column vector of vec () representing matrix；(·)TThe transposition of representing matrix；The Kronecker product of representing matrix；The determinant of det { } representing matrix；The Moore-Penrose of representing matrix A
Generalized inverse matrix；Respectively indicate interference covariance matrix QkR-th of minimal eigenvalue and its corresponding feature to
Amount.
To sum up, the final result that gradient calculates are as follows:
Since the value of differentiable function is most fast along the reduction of negative gradient direction, the steepest descent of gradient descent method is along direction
Are as follows:
Next, solve the last one critical issue, i.e. the selection of iteration step length.Step-length is one in gradient descent method
Important parameter, if the too small cost function that will lead to of value reduced slowly, so that algorithmic statement rate is influenced, and the excessive pole of value
It is possible that missing the optimal solution of cost function, and optimal step value often constantly changes as iteration carries out.Therefore
This programme uses the Armijo step-length selection mechanism with automatic adjusument function.Under the mechanism, algorithm can be according to cost function
The variation of value automatically selects most suitable step-length.
Above-mentioned analysis is summarized, the unilateral IA finally obtained based on adaptive compound cost function in Grassmann manifold is pre-
Code Design scheme, shown in specific implementation flow chart 4, following table is that each step elaborates in Fig. 4.
IA pre-coding scheme based on adaptive compound cost function in Grassmann manifold
In table, qfp{ } then indicates that Euclidean space is calculated to the projection of corresponding Grassmann manifold, i.e.,
Due to failing edge direction ZiIn the tangential space of Grassmann manifold, so that Vi+βmZiIt is free in Grassmann
Except manifold.In order to ensure the independent variable V of cost functioniIt remains in Grassmann manifold and moves, it is necessary to utilize space
Projection operation qfp{ } is by Vi+βmZiConstraint reflux shape；The inner product of<>representing matrix calculates, since this programme exists
It is executed in Grassmann manifold, therefore meets relationship
Claims (7)
- Interference based on adaptive compound cost function in 1.MIMO interference channel is aligned method for precoding, which is characterized in that packet Include following steps:Step 1 constructs the optimization problem with particular constraints in Euclidean space, defines the weighting cost of optimization problem FunctionThe adjustable weight of the residual interference in shop sign in the form of a streamer space and desired signal power is poor by a definite date, defines weight coefficient αkFor One nonnegative real number changed with desired signal, interference and noise intensity, value add systematic influence degree with interference Reduce by force；Step 2 constructs an auxiliary function according to the decoding process of receiving endBy 2KdkMember weighting cost functionBe converted to KdkThe compound cost function f (V) of member, i.e.,Wherein V={ V1,V2,…, VK, U={ U1,U2,…,UKPre-coding matrix collection and AF panel matrix stack are respectively indicated, K indicates multiuser MIMO interference system The user of system is to number, dkIndicate the data flow number that k-th of transmitting terminal is sent；Step 3 will minimize compound cost function in conjunction with mathematics manifold, complex valued matrices derivation and gradient optimization algorithm The restricted problem of f (V) is converted to the unconstrained optimization problem in manifold, and then the solution procedure of the problem is gone to Jim Glassman It is executed in manifold, and completes the iteration optimization of pre-coding matrix collection V.
- 2. the interference based on adaptive compound cost function in MIMO interference channel is aligned precoding side according to claim 1 Method, it is characterised in that: with the optimization problem of particular constraints described in step 1 are as follows:Wherein,Indicate weighting cost function,WithRespectively indicate that receiving end k receives from the residual of transmitting terminal j Stay jamming power and the desired signal power from transmitting terminal k；αkFor weight coefficient, VkAnd UkK-th of transmitting-receiving is respectively indicated to institute Corresponding pre-coding matrix and AF panel matrix,WithRespectively indicate VkAnd UkConjugate transposition, K indicate multi-user The user of MIMO interference system to number,Indicate dk×dkThe unit matrix of dimension.
- 3. the interference alignment in MIMO interference channel according to claim 1 or claim 2 based on adaptive compound cost function prelists Code method, it is characterised in that: the weight coefficient αkSelection mode it is as follows:Wherein a is αkInitial value；b1And b2Respectively indicate αkWith γkWithReduction speed；Indicate the transmission of transmitting terminal k Signal-to-noise ratio, γkIt indicates to send power allocation factor, i.e., the average transmission signal-to-noise ratio of interference transmitting terminal and desired transmitting terminal, which are sent, believes It makes an uproar the ratio of ratio.
- 4. the interference based on adaptive compound cost function in MIMO interference channel is aligned precoding side according to claim 3 Method, it is characterised in that: the γkTo send power allocation factor, calculating formula are as follows:When transmission power averaging distributes to each transmitting terminal, γk=1；WhereinIndicate the transmission signal-to-noise ratio of transmitting terminal j,Indicate the transmission signal-to-noise ratio of transmitting terminal k.
- 5. the interference based on adaptive compound cost function in MIMO interference channel is aligned precoding side according to claim 1 Method, it is characterised in that:Auxiliary function described in step 2Must be corresponded with the decoding process of receiving end, by its with it is the simplest Force zero decoding be mapped, that is, define AF panel matrix be its corresponding interference covariance matrix preceding dkA minimal characteristic The corresponding feature vector group of value, i.e.,Wherein dk、QkK-th of transmitting-receiving is respectively indicated to the data fluxion and corresponding interference covariance matrix transmitted.
- 6. the interference alignment in the according to claim 1 or 2 or 5 MIMO interference channels based on adaptive compound cost function is pre- Coding method, it is characterised in that: step 2 will have particular constraints optimization problem equivalent description described in step 1 are as follows:WhereinWithThe interfering signal power from transmitting terminal j that respectively indicates that receiving end k receives and from transmitting terminal k's Desired signal power, αkForWeight coefficient,Indicate VkConjugate transposition, K indicate multiuser MIMO interference system use Family to number,Indicate dk×dkThe unit matrix of dimension.
- 7. the interference based on adaptive compound cost function in MIMO interference channel is aligned precoding side according to claim 1 Method, it is characterised in that: unconstrained optimization problem is gone into Grassmann manifold described in step 3, by the unconstrained problem after recombination It is iteratively solved using gradient descent method, wherein iteration step length uses the Armijo step-length with automatic adjusument function to select machine System.
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