CN105429687B - A kind of interference alignment schemes minimizing jamming power and dimension - Google Patents
A kind of interference alignment schemes minimizing jamming power and dimension 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
- H04B7/0426—Power distribution
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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
- H04B7/0486—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting taking channel rank into account
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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
Abstract
The invention discloses a kind of interference alignment schemes minimizing jamming power and dimension.Include the following steps, step 1：It is random to generate AF panel matrix, setting iterations iter；Step 2：Using the nuclear norm of interference map matrix as object function, it is Hermitian positive definite matrixes to enable desired signal matrix, and is constraints more than or equal to 100 with minimal eigenvalue, seeks pre-coding matrix；Step 3：As a whole by the interference signal of reception, interference covariance matrix is found out；Step 4：It is AF panel matrix column vector to enable the corresponding feature vector of characteristic value of interference covariance matrix minimum；Step 5：Judge whether to complete all iterations, if so, orthogonalization pre-coding matrix and AF panel matrix；Otherwise return to step two.The present invention can improve received signal quality, lifting system capacity and the availability of frequency spectrum.
Description
Technical field
The invention belongs to wireless communication technology fields more particularly to a kind of minimum jamming power to be aligned with the interference of dimension
Method.
Background technology
Multi-antenna technology (Multiple Input Multiple Output, MIMO), because it can be significantly improved wirelessly
The handling capacity of communication system, and receive significant attention.The technology is communication by configuring more antennas in transmitting terminal and receiving terminal
System introduces additional degree of freedom, and channel capacity and frequency are improved without increasing bandwidth and antenna transmission power
Compose utilization rate.Although multi-antenna technology has opened up spatial domain resource, communication quality is improved, improves the channel of wireless communication system
Capacity, but decline and interfere two in always information propagation to hinder greatly.When signal is propagated in the channel, multipath effect will produce
It answers, the signal each reflected is spatial flow, and while introducing multiple antennas, system also becomes interference-limited from noise limited.
Existing interference treatment technology such as frequency division multiple access (Frequency Division Multiple Access, FDMA), the time-division is more
Location (Time Division Multiple Access, TDMA) and CDMA (Code Division Multiple
Access, CDMA) etc., influence of the interference signal to desired signal is mainly eliminated by the orthogonalization of signal.In fact, when more
When users to share frequency spectrum resource, this processing method can only accomplish frequency spectrum resource being allocated between K user.For example,
When interactional number of users is K, each user can be obtained 1/K when frequency spectrum resource is single user.Therefore, when with
When amount amount is very big, it is still very limited that each user can be obtained frequency spectrum resource.It is exactly to be to interfere the proposition of alignment techniques
Solve the problems, such as this, signal space is divided into two parts of desired signal space and interference signal space by it, by prelisting
Code technology makes interference be overlapped in receiving terminal, to compress the shared signal volume of interference, eliminates influence of the interference to desired signal,
Achieve the purpose that improve channel capacity.
Cadambe V R and Jafar S A are delivered in IEEE Trans.Inf.Theory, 2008《Interference
Alignment and Degrees of Freedom of the K-User Interference Channel》It proposes dry
Disturb alignment classical approach.Classics interference alignment algorithm give interference alignment closed solutions, but it require and transmission antenna number with
Reception antenna number must be identical, and which limits the designs of transmitter and receiver.In addition, when number of users is more than 3, constraint
Condition increases, and classical approach is unable to get accurate pre-coding matrix.Therefore classical approach can only specifically be used in the case that several.
Iterative algorithm based on channel reciprocity gradually replaces classical approach, wherein being more typically Cadambe V R and Jafar S A
It is delivered in IEEE Global Telecommunications Conference, 2008《Approaching the
Capacity of Wireless Networks through Distributed Interference Alignment》It proposes
Least interference leakage algorithm, and Gomadam K et al. delivered in IEEE Trans.Inf.Theory, 2011《A
Distributed Numerical Approach to Interference Alignment and Applications to
Wireless Interference Networks》The maximum Signal to Interference plus Noise Ratio algorithm of proposition.Although both algorithms can obtain
Higher power system capacity is obtained, but the noiseless dimension that the two provides is very low, maximum Signal to Interference plus Noise Ratio algorithm even allows for interference to let out
Leakage is in entire free space.Dimitris S.Papailiopoulos and Alexandros G.Dimakis are in IEEE
Transactions on Signal Processing, 2012 deliver《Interference Alignment as a Rank
Constrained Rank Minimization》It is that the characteristic of the convex closure network of order proposes order constraint order most using matrix nuclear norm
Smallization algorithm (RCRM) improves user's free degree although solving the problems, such as that object function is non-convex, and algorithm only limits
The dimension of interference signal, if the jamming power of leakage is very big, system cannot still obtain very high capacity.
Invention content
The object of the present invention is to provide one kind capable of improving received signal quality, lifting system capacity and the availability of frequency spectrum
, minimize the interference alignment schemes of jamming power and dimension.
A kind of interference alignment schemes minimizing jamming power and dimension, include the following steps,
Step 1：It is random to generate AF panel matrix, setting iterations iter；
Step 2：Using the nuclear norm of interference map matrix as object function, it is Hermitian positive definites to enable desired signal matrix
Matrix, and be constraints more than or equal to 100 with minimal eigenvalue, seek pre-coding matrix；
Step 3：As a whole by the interference signal of reception, interference covariance matrix is found out；
Step 4：The feature vector for enabling the characteristic value of interference covariance matrix minimum corresponding is AF panel matrix column
Vector；
Step 5：Judge whether to complete all iterations, if so, orthogonalization pre-coding matrix and AF panel square
Battle array；Otherwise return to step two.
The present invention it is a kind of minimize jamming power and dimension interference alignment schemes, can also include：
1, include K transmitting terminal, K receiving terminal, each transmitting terminal, receiving terminal configure MtRoot transmitting antenna, MrPiece-root grafting receives day
Line, the signal that k-th of receiving terminal receives are：
The signal that wherein base station k is sent is xk∈Cd×1,Representing matrix VkConjugate transposition,WithThe pre-coding matrix and AF panel matrix of receiving terminal k, H are indicated respectivelykjIt is independent same to indicate that each element is obeyed
The channel coefficient matrix being distributed between the base station j and user k of the multiple Gauss random distribution of zero mean unit variance,For clothes
From (0, σ2Id) white Gaussian noise, σ is variance, IdIndicate d rank unit matrix.
2, interference map matrix is：
Desired signal matrix is：
Advantageous effect：
The present invention considered interference leakage power and the influence received signal qualities of state no interference signal dimension two because
Element.Solve the jamming power for only minimizing leakage and the noiseless dimension brought reduces, and only minimize interference dimension and
Cause it is expected that space interference strength increases problem.The present invention reduces minizone by the double constraints of interference signal order and power
Interference effect, improve desired signal quality, improve power system capacity and the availability of frequency spectrum.
Description of the drawings
The algorithm flow chart of Fig. 1 present invention；
Fig. 2 multi-cell multi-antenna interference channel simplified models；
Figure d=1 compared with Fig. 3 present invention can utilize the space dimension number of degrees with other methods system；Fig. 3 (a) is that the present invention proposes
Method, Fig. 3 (b) is that least interference leaks algorithm, and Fig. 3 (c) is that order constraint order minimizes algorithm, and Fig. 3 (d), which is that maximum letter is dry, to make an uproar
Compare algorithm；
Figure d=3 compared with Fig. 4 present invention can utilize the space dimension number of degrees with other methods system；
Fig. 5 present invention figure d=1 compared with other methods system average total rate；
Fig. 6 present invention figure d=3 compared with other methods system average total rate.
Specific implementation mode
The present invention is described in further details below in conjunction with attached drawing.
The present invention proposes a kind of interference alignment algorithm minimizing jamming power and dimension, will interfere the constraint and interference of order
Power constraint is combined.The present invention relaxes the requirement to channel reciprocity, not only reduces the Spatial Dimension that interference signal occupies,
Reduce interference leakage power simultaneously.In addition, the present invention forces desired signal matrix for Hermitian positive definite matrixes, and addition pair
The constraint of desired signal power,
A kind of interference alignment algorithm minimizing jamming power and dimension, includes the following steps：
Step 1：It is random to generate AF panel matrix, choose suitable iterations iter；
Step 2：The nuclear norm of interference map matrix is calculated, pressure desired signal matrix is Hermitian positive definite matrixes,
And minimal eigenvalue is more than or equal to 100；
Step 3：Calculate pre-coding matrix；
Step 4：As a whole by the interference signal of reception, interference covariance matrix is found out；
Step 5：AF panel matrix column vector be interference covariance matrix minimum the corresponding feature of characteristic value to
Amount；
Step 6：Step 2~tetra- are repeated, until the complete all numbers of iteration；
Step 7：Orthogonalization pre-coding matrix and AF panel matrix；
The signal of the interference sections handled without interference suppression filter is known as interference map signal.It is dry by minimizing
The order of mapping matrix is disturbed, the dimension that interference signal occupies is reduced.Due to the object function by order as an optimization, not can prove that even
Whether the function is convex function, and because the nuclear norm of matrix is the convex closure network of rank of matrix, therefore the present invention is by minimizing square
The nuclear norm of battle array replaces minimizing rank of matrix.
Ideal interference alignment requirements expected matrix is non-singular matrix, and therefore, it is positive definite that the present invention, which forces desired signal matrix,
Matrix.Positive definite matrix also requires minimal eigenvalue to be more than zero, the present invention further constrains receiving terminal in addition to requiring matrix full rank
Desired signal matrix minimal eigenvalue is 100 (power 20dB).The case where this is less than 20dB to signal-to-noise ratio is also applicable.
Regard the interference signal of receiving terminal as a signal, is used in combination the form of trace of a matrix to find out its power expression, takes it
In the part comprising interference base station end pre-coding matrix and interference channel as interference covariance matrix.AF panel matrix i-th
The vector of row is the corresponding feature vector of i-th of minimal eigenvalue of interference covariance matrix.
The present invention is a kind of interference alignment algorithm minimizing jamming power and dimension, and algorithm flow is as shown in Figure 1, include
Following steps：
Step 1：It is random to generate AF panel matrix, choose suitable iterations iter；
The present invention considers that a flat Rayleigh fading channel, system include K transmitting terminal, and K receiving terminal is each to send
End, receiving terminal configure MtRoot transmitting antenna, MrRoot reception antenna.All mimo systems be all it is achievable, i.e.,
D is to send degree of freedom.Assuming that the signal that base station k is sent is xk∈Cd×1, xkFor the complex vector of d rows, power constraint is
Pk,For practical situation, the present invention enables
Representing matrix VkConjugate transposition,The precoding square of receiving terminal k is indicated respectively
Battle array and AF panel matrix, column vector are respectively to send the orthogonal standard base in space and reception space.Therefore k-th of receiving terminal
The signal received is
Wherein HkjIndicate that each element obeys the base of the multiple Gauss random distribution of independent same distribution zero mean unit variance
The channel coefficient matrix stood between j and user k,For obedience (0, σ2Id) white Gaussian noise, σ is variance, IdIndicate d ranks
Unit matrix.
The reason of iterations selection 10 of inventive algorithm, will illustrate in step 6.
Step 2：The nuclear norm of interference map matrix is calculated, pressure desired signal matrix is Hermitian positive definite matrixes,
And minimal eigenvalue is more than or equal to 100；
Fig. 2 is multi-cell multi-antenna interference channel simplified model.Multiple cell interference signal, the interference signal received are
Transmitting terminal j can be understood as the interference signal of user k the product of matrix and vector, matrix HkjVjIn complex field C
On through Cd→CMrLinear transformation CdIn vector xjA vector being mapped as in column vector subspace.Through AF panel square
Battle arrayAfter processing, MrThe vector of dimension is mapped to the vector of d dimensions again.Ideally, the vector of this d dimensions should be
One null vector.But all interference signals can only be allowed to snap to minimum dimension in practice, so that useful signal occupies bigger
Dimension.
Therefore, the signal of the interference sections handled without interference suppression filter is known as interference map signal by the present invention.
By minimizing interference mapOrder, reduce the dimension that occupies of interference signal.
Wherein,Indicate interference map rank of matrix.
Next, with the convex replacement rank of matrix of nuclear norm of matrix.It enables(5) formula can be of equal value
For
Wherein
The nuclear norm of representing matrix, σi(JJk) i-th of descending arrangement of representing matrix singular value.Assuming that M=||JJk
||, intuitively, in the limiting case, if interference order is zero, M=0,1/M is infinity, it is therefore to be understood that 1/M is (6) formula
The upper bound.
For desired signal, it is primarily upon " order maximizes and power maximizes ".Because when signal subspace can be turned into
When to all available dimensional spaces, the actually available degree of freedom of system is that the dimension that useful signal occupies subtracts interference signal and occupies
Dimension.The order of desired signal maximizes, and can receive signal by pressure and be realized for Hermitian positive definite matrixes.
Wherein, desired signal matrix(7) formula representing matrix is Hermitian positive definite squares
Battle array, i.e.,λmin(Sk) > 0, λmin(Sk) indicate desired signal matrix minimal eigenvalue.
It next it will be described for the reasonability of this compulsive means.If there is the precoding for meeting object function solution
Matrix and AF panel set of matrices, the new set of gained after all elements are multiplied with same arbitrary unitary matrice in set, should
All elements in set also can guarantee that meeting desired signal matrix is in the case where keeping cost equation constant
The condition of Hermitian positive definite matrixes.
It realizes that desired signal power maximizes, considers that the calculation formula of rate, the rate that user k is obtained are first
WhereinDet expressions take determinant of a matrix, log2It indicates to take the logarithm with 2 bottom of for,
Superscript " -1 " indicates to be to matrix inversion.Promoting transmission rate in above formula need to increase the value of determinant.By characteristic value and row
The relationship of column is it is found that for arbitrary matrix, it is assumed that the product of all characteristic values of matrix A, A is equal to the determinant of A.A
Add 1 with unit matrix and matrix characteristic value for the characteristic value of A.So (10) formula is finally to reach
(9) characteristic value of formula is maximum.However discuss that the characteristic value of the formula is highly difficult.Intuitively it is readily appreciated that the formula
Indicate Signal to Interference plus Noise Ratio (SINR).Therefore (9) formula can be replaced with (10) formula
Wherein Tr indicates to seek the mark of matrix.So (8) formula of maximization, exactly maximizes the power of receiving terminal desired signal.
By the property of Hermitian diagonalizables it is found thatWith SkCharacteristic value it is related.To be kept for the receiving terminal phase
The signal-to-noise ratio of signal is hoped not reduce, it is assumed that whenWhen,The scheme of proposition forces to be promoted
The desired signal matrix minimal eigenvalue of receiving terminal is Pk.But when noise is relatively high, when being higher than 20dB, the expectation letter of receiving terminal
Number matrix minimal eigenvalue is with PkIncrease, rate and degree of freedom be not obviously improved, this is because in iterative process,
Pre-coding matrix and AF panel matrix appear in desired signal and interference signal simultaneously, and desired signal power is excessive, accordingly
Interference can also enhance, so, the desired signal matrix minimal eigenvalue of receiving terminal is finally constrained to 100 (power by the present invention
20dB).The case where this is less than 20dB to signal-to-noise ratio is also applicable.
Step 3：Calculate pre-coding matrix；
The present invention utilizes the theory of convex optimization, using the nuclear norm of interference map matrix as object function, desired signal matrix
For Hermitian positive definite matrixes, and it is constraints that minimal eigenvalue, which is more than or equal to 100, seeks pre-coding matrix.
Step 4：As a whole by the interference signal of reception, interference covariance matrix is found out；
As a whole by interference signal, jamming power is defined as the power of the sum of receiving terminal interference signal to the present invention, receives
End k jamming power be
Step 5：AF panel matrix column vector be interference covariance matrix minimum the corresponding feature of characteristic value to
Amount；
In formula (12),Indicate the d row of the AF panel matrix of user k, vd[]D-th of minimal characteristic of homography
The feature vector of value.
Step 6：Step 2~five are repeated, until the complete all numbers of iteration；
The present invention is had to pass through successive ignition, could be kept using distributed interference alignment thereof, distribution interference alignment
Algorithmic statement.
After each iteration, the nuclear norm of interference map can all reduce.It, may finally by choosing suitable iterations
Function to achieve the objective is stablized in its minimum value.Order constraint order minimizes algorithm by analysis, and it is iterations that the present invention, which chooses 10,.
Step 7：Orthogonalization pre-coding matrix and AF panel matrix.
To avoid data inter-stream interference, pre-coding matrix and AF panel matrix are orthogonalized processing.
The invention will be further described below in conjunction with the accompanying drawings.
The present invention is aligned with existing various interference by way of experiment and realizes that algorithm compares by inventor.Experiment is set
It sets as follows：Assuming that system is a feasible system, base station end configures 8 antennas, and 4 antennas are respectively configured in 3 users, indicates
For (8 × 4, d)3, wherein d is degree of freedom obtained by system single user.It is zero that channel element, which obeys mean value, and variance is 1
Multiple Gauss is distributed.Simulation result is the average result of 200 independent identically distributed channels.The present invention is by matrix SkMore than 10-8's
The quantity of singular value subtracts matrix JkMore than 10-8Singular value quantity obtained by difference be defined as user and can utilize Spatial Dimension
Number, you can be used for transmission the noiseless Spatial Dimension quantity of desired signal data.The algorithm of comparison includes that order constraint order minimizes
Algorithm.Least interference leaks algorithm, maximum Signal to Interference plus Noise Ratio algorithm.
Fig. 3, Fig. 4 are respectively d=1, when 3, compared with the present invention can utilize the space dimension number of degrees with other methods system single user
Figure.In addition to maximum Signal to Interference plus Noise Ratio algorithm can be 0 using dimension, when degree of freedom is 1, algorithm can reach maximum free
Degree；When degree of freedom is 3, due to needing certain dimension to go to eliminate interference so all algorithms, which cannot all reach, most freedom
Degree, it can be seen that algorithm remains above other two kinds of algorithms up to degree of freedom.
Fig. 5, Fig. 6 are respectively d=1, when 3, the present invention and other methods system average total rate comparison result.For convenience of picture
Scheme, the rate value in figure is the 1/2 of former result.As d=1, average total rate and maximum that the present invention can obtain believe dry make an uproar
Than approximation, algorithm is minimized higher than order constraint order, is 1.5 times of least interference leakage algorithm.When d=3, the present invention is better than comparison
Three kinds of algorithms, order constraint order minimize effect it is worst, this is because when noise is relatively low, power constraint method is preferable.From
It can be seen from the figure that, with the increase of signal-to-noise ratio, the present invention can obtain higher handling capacity.
The present invention provides a kind of interference alignment algorithm methods minimizing jamming power and dimension.Interference alignment is because can be with
The shared signal dimension of compression interference obtains maximum degree of freedom, promotes the advantages that channel capacity, is widely paid close attention to.However,
Majority interference alignment algorithm can not balance the influence of interference two factors of leakage power and noiseless dimension, cause to receive signal matter
Quantitative change is poor, and power system capacity reduces.The present invention proposes a kind of interference alignment algorithm minimizing jamming power and dimension, realizes dry
The constraint for disturbing order is combined with power constraint.This method calculates precoding first with interference signal rank of matrix is minimized
Matrix obtains AF panel matrix then by minimizing the jamming power of leakage.The present invention, which solves, only minimizes leakage
Jamming power and the noiseless dimension brought reduces, and only minimize interference dimension and cause it is expected that space interference strength increases
Problem.By the double constraints of interference signal order and power, the interference effect of minizone is reduced, received signal quality is improved,
Improve power system capacity and the availability of frequency spectrum.
Claims (3)
1. a kind of interference alignment schemes minimizing jamming power and dimension, it is characterised in that：Include the following steps,
Step 1：It is random to generate AF panel matrix, setting iterations iter；
Step 2：Using the nuclear norm of interference map matrix as object function, it is Hermitian positive definite squares to enable desired signal matrix
Battle array, is known as interference map signal by the signal of the interference sections handled without interference suppression filter, is reflected by minimizing interference
Rank of matrix is penetrated, the dimension that interference signal occupies is reduced, the nuclear norm by minimizing matrix replaces minimizing rank of matrix, by force
Desired signal matrix processed is positive definite matrix, and minimal eigenvalue is required to be more than zero, further constrains the desired signal square of receiving terminal
Battle array minimal eigenvalue is 100, and is constraints more than or equal to 100 with minimal eigenvalue, seeks pre-coding matrix；
Step 3：As a whole by the interference signal of reception, interference covariance matrix is found out；
Step 4：It is AF panel matrix column vector to enable the corresponding feature vector of characteristic value of interference covariance matrix minimum；
Step 5：Judge whether to complete all iterations, if so, orthogonalization pre-coding matrix and AF panel matrix；
Otherwise return to step two.
2. a kind of interference alignment schemes minimizing jamming power and dimension according to claim 1, it is characterised in that：Packet
Containing K transmitting terminal, K receiving terminal, each transmitting terminal, receiving terminal configure MtRoot transmitting antenna, MrRoot reception antenna, k-th of reception
The signal that receives is held to be：
The signal that wherein base station k is sent is xk∈Cd×1,Representing matrix UkConjugate transposition,With
The pre-coding matrix and AF panel matrix of receiving terminal k, H are indicated respectivelykjIt is equal to indicate that each element obeys independent same distribution zero
The channel coefficient matrix being worth between the base station j and user k of the multiple Gauss random distribution of unit variance,For obedience (0, σ2Id)
White Gaussian noise, σ is variance, IdIndicate d rank unit matrix.
3. a kind of interference alignment schemes minimizing jamming power and dimension according to claim 1, it is characterised in that：Institute
The interference map matrix stated is：
Desired signal matrix is：k∈K。
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| CN103166685A (en) * | 2013-02-04 | 2013-06-19 | 重庆邮电大学 | Interference aligning method based on combined power distribution in LTE |
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| CN103580745A (en) * | 2013-10-10 | 2014-02-12 | 电子科技大学 | Iteration interference alignment method |
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