CN105429687A - Interference alignment method for minimizing interference power and dimension - Google Patents

Abstract

The invention discloses an interference alignment method for minimizing interference power and dimension. The method comprises the steps: 1, randomly generating an interference inhibition matrix, and setting an iteration number iter; 2, taking the nuclear norm of an interference mapping matrix as a target function, letting a desired signal matrix be a Hermitian positive definite matrix, and taking a condition that a minimum characteristic value is greater than or equal to 100 as a constraint condition, and solving a pre-coding matrix; 3, taking a received interference signal as the whole body, and solving an interference covariance matrix; 4, letting a characteristic vector corresponding to the minimum characteristic value of the interference covariance matrix be a column vector of the interference inhibition matrix; 5, judging whether all iterations are completed or not: carrying out the orthogonalization of the pre-coding matrix and the interference inhibition matrix if all iterations are completed, or else, returning to step 2. The method can improve the quality of received signals, enlarges the system capacity, and improves the utilization rate of frequency spectrum.

Description

The interference alignment schemes of a kind of minimise interference power and dimension

Technical field

The invention belongs to wireless communication technology field, particularly relate to the interference alignment schemes of a kind of minimise interference power and dimension.

Background technology

Multi-antenna technology (MultipleInputMultipleOutput, MIMO), because it can significantly improve the throughput of wireless communication system, and is subject to extensive concern.This technology is that communication system introduces the extra degree of freedom by configuring many antennas at transmitting terminal and receiving terminal, when without the need to increasing bandwidth sum antenna transmitted power, improve channel capacity and the availability of frequency spectrum.Although multi-antenna technology has opened up spatial domain resource, improve communication quality, improve the channel capacity of wireless communication system, decline and interference are that two in Information Communication hinders greatly always.When signal is propagated in the channel, can produce multipath effect, each is spatial flow by the signal reflected, and while introducing multiple antennas, system is also become interference-limited from noise limited.Existing interference treatment technology is as frequency division multiple access (FrequencyDivisionMultipleAccess, FDMA), time division multiple access (TimeDivisionMultipleAccess, and code division multiple access (CodeDivisionMultipleAccess TDMA), CDMA) etc., mainly the impact of interference signal on desired signal is eliminated by the orthogonalization of signal.In fact, when multiple users share frequency spectrum resource, this processing method can only accomplish frequency spectrum resource to distribute between K user.Such as, when interactional number of users is K, each user the 1/K of obtainable frequency spectrum resource when being unique user.Therefore, when number of users is very large, the obtainable frequency spectrum resource of each user institute is still very limited.The proposition of interference alignment techniques is exactly to address this problem, signal space is divided into desired signal space and two, interference signal space part by it, make interference overlapping at receiving terminal by precoding technique, thus the signal volume shared by compression interference, eliminate the impact of interference on desired signal, reach the object improving channel capacity.

CadambeVR and JafarSA is at IEEETrans.Inf.Theory, and 2008 " the InterferenceAlignmentandDegreesofFreedomoftheK-UserInter ferenceChannel " delivered propose interference alignment classical approach.Classical interference alignment algorithm gives the closed solutions of interference alignment, but its requires and number of transmit antennas is necessary identical with reception antenna number, which limits the design of transmitter and receiver.In addition, when number of users is greater than 3, constraints increases, and classical approach cannot obtain pre-coding matrix accurately.Therefore classical approach can only use in several specific situation.Iterative algorithm based on channel reciprocity replaces classical approach gradually, wherein comparatively typically CadambeVR and JafarSA at IEEEGlobalTelecommunicationsConference, the least interference that 2008 " the ApproachingtheCapacityofWirelessNetworksthroughDistribut edInterferenceAlignment " delivered propose leaks algorithm, and the people such as GomadamK is at IEEETrans.Inf.Theory, the maximize SINR algorithm that 2011 " the ADistributedNumericalApproachtoInterferenceAlignmentandA pplicationstoWirelessInterferenceNetworks " delivered propose.Although these two kinds of algorithms can obtain higher power system capacity, the noiseless dimension that both provide is very low, and maximize SINR algorithm even allows interference to leak at whole free space.DimitrisS.Papailiopoulos and AlexandrosG.Dimakis is at IEEETransactionsonSignalProcessing, 2012 " InterferenceAlignmentasaRankConstrainedRankMinimization " delivered utilize matrix nuclear norm be the convex closure network of order characteristic propose order constraint order minimization algorithm (RCRM), although solve the problem of target function non-convex, improve user's degree of freedom, but algorithm only limit the dimension of interference signal, if the interference power of leaking is very large, system still can not obtain very high capacity.

Summary of the invention

The object of this invention is to provide one and can improve received signal quality, capacity and the availability of frequency spectrum, the interference alignment schemes of minimise interference power and dimension.

An interference alignment schemes for minimise interference power and dimension, comprises the following steps,

Step one: stochastic generation AF panel matrix, setting iterations iter;

Step 2: with the nuclear norm of interference map matrix for target function, makes desired signal matrix be Hermitian positive definite matrix, and is more than or equal to 100 for constraints with minimal eigenvalue, ask for pre-coding matrix;

Step 3: by the interference signal of reception as a whole, obtain interference covariance matrix;

Step 4: the characteristic value making interference covariance matrix minimum corresponding characteristic vector be AF panel matrix column vector;

Step 5: judged whether all iterationses, if so, orthogonalization pre-coding matrix and AF panel matrix; Otherwise return step 2.

The interference alignment schemes of a kind of minimise interference power of the present invention and dimension, can also comprise:

1, K transmitting terminal is comprised, K receiving terminal, each transmitting terminal, receiving terminal configuration M _ttransmit antennas, M _rroot reception antenna, the signal that a kth receiving terminal receives is:

$y_k=U_k^H{H}_{kk}{V}_k+U_k^H\underset{j=1,j\≠k}{\overset{K}{\Σ}}{H}_{kj}{V}_j+U_k^H{n}_k,k=1,...,K$

The signal that wherein base station k sends is x _k∈ C ^{d × 1}, representing matrix V _kconjugate transpose, with represent pre-coding matrix and the AF panel matrix of receiving terminal k respectively, H _kjrepresent that each element all obeys the channel coefficient matrix between the base station j of the multiple gaussian random distribution of independent same distribution zero mean unit variance and user k, for obeying (0, σ ²i _d) white Gaussian noise, σ is variance, I _drepresent d rank unit matrix.

2, interference map matrix is:

Desired signal matrix is: $S_k=U_k^H{H}_{kk}{V}_k,k\∈K.$

Beneficial effect:

The present invention has considered the factor that interference leakage power and state no interference signal dimension two affect received signal quality.Solve the interference power of only minimum leaks and the noiseless dimension brought reduces, and only minimise interference dimension and cause expecting that space interference strength increases problem.The present invention passes through the double constraints of interference signal order and power, reduces the interference effect of minizone, improves desired signal quality, improve power system capacity and the availability of frequency spectrum.

Accompanying drawing explanation

Fig. 1 algorithm flow chart of the present invention;

Fig. 2 multi-cell multi-antenna interference channel simplified model;

Fig. 3 the present invention and additive method system can utilize space dimension number of degrees comparison diagram d=1; The method that Fig. 3 (a) proposes for the present invention, Fig. 3 (b) is least interference leakage algorithm, and Fig. 3 (c) is order constraint order minimization algorithm, and Fig. 3 (d) is maximize SINR algorithm;

Fig. 4 the present invention and additive method system can utilize space dimension number of degrees comparison diagram d=3;

Fig. 5 the present invention and the average total speed comparison diagram d=1 of additive method system;

Fig. 6 the present invention and the average total speed comparison diagram d=3 of additive method system.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further details.

The present invention proposes the interference alignment algorithm of a kind of minimise interference power and dimension, the constraint of interference order is retrained with interference power and combines.The present invention relaxes the requirement to channel reciprocity, not only reduces the Spatial Dimension that interference signal occupies, and reduces interference leakage power simultaneously.In addition, the present invention forces desired signal matrix to be Hermitian positive definite matrix, and adds the constraint to desired signal power,

An interference alignment algorithm for minimise interference power and dimension, comprises the following steps:

Step one: stochastic generation AF panel matrix, chooses suitable iterations iter;

Step 2: the nuclear norm calculating interference map matrix, force desired signal matrix to be Hermitian positive definite matrix, and minimal eigenvalue is more than or equal to 100;

Step 3: calculate pre-coding matrix;

Step 4: by the interference signal of reception as a whole, obtain interference covariance matrix;

Step 5: AF panel matrix column vector be the minimum characteristic value of interference covariance matrix corresponding characteristic vector;

Step 6: repeat step 2 ~ tetra-, until the complete all number of times of iteration;

Step 7: orthogonalization pre-coding matrix and AF panel matrix;

The signal of the interference sections without interference suppression filter process is called interference map signal.By the order of minimise interference mapping matrix, reduce the dimension that interference signal occupies.Due to using the target function of order as optimization, even can not prove whether this function is convex function, again because the nuclear norm of matrix is the convex closure network of rank of matrix, therefore the present invention replaces minimizing rank of matrix by the nuclear norm minimizing matrix.

Desirable interference alignment requirements expected matrix is non-singular matrix, and therefore, the present invention forces desired signal matrix to be positive definite matrix.Positive definite matrix, except requiring matrix full rank, also requires that minimal eigenvalue is greater than zero, and the desired signal matrix minimal eigenvalue that the present invention retrains receiving terminal is further 100 (power 20dB).This situation being less than 20dB to signal to noise ratio is also applicable.

The interference signal of receiving terminal is regarded as a signal, and obtains its power expression by the form of trace of a matrix, get wherein comprise interference base station end pre-coding matrix and interference channel part as interference covariance matrix.The vector that AF panel matrix i-th arranges is interference covariance matrix i-th minimal eigenvalue characteristic of correspondence vector.

The present invention is the interference alignment algorithm of a kind of minimise interference power and dimension, and algorithm flow as shown in Figure 1, comprises the following steps:

Step one: stochastic generation AF panel matrix, chooses suitable iterations iter;

The present invention considers a flat Rayleigh fading channel, and system comprises K transmitting terminal, K receiving terminal, each transmitting terminal, receiving terminal configuration M _ttransmit antennas, M _rroot reception antenna.All mimo systems are all attainable, namely

$d\≤\frac{Mt+Mr}{K+1}---\left(1\right)$

D is for sending the degree of freedom.Suppose that the signal that base station k sends is x _k∈ C ^{d × 1}, x _kfor the complex vector that d is capable, power constraint is P _k, for the situation of reality, the present invention makes

$V_k^H{V}_k=\frac{P}{d}{I}_d---\left(2\right)$

representing matrix V _kconjugate transpose, represent pre-coding matrix and the AF panel matrix of receiving terminal k respectively, its column vector is respectively the orthogonal Standard basis sending space and receive space.Therefore the signal that a kth receiving terminal receives is

$y_k=U_k^H{H}_{kk}{V}_k+U_k^H\underset{j=1,j\≠k}{\overset{K}{\Σ}}{H}_{kj}{V}_j+U_k^H{n}_k,k=1,...,K---\left(3\right)$

Wherein H _kjrepresent that each element all obeys the channel coefficient matrix between the base station j of the multiple gaussian random distribution of independent same distribution zero mean unit variance and user k, for obeying (0, σ ²i _d) white Gaussian noise, σ is variance, I _drepresent d rank unit matrix.

The iterations of algorithm of the present invention selects the reason of 10 will illustrate in step 6.

Step 2: the nuclear norm calculating interference map matrix, force desired signal matrix to be Hermitian positive definite matrix, 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 is

$J_k=U_k^H\[{\left\{H_{kj}{V}_j\right\}}_{j=1,j\≠k}^K\]---\left(4\right)$

The interference signal of transmitting terminal j to user k can be understood as matrix and vectorial product, matrix H _kjv _jthrough C on complex field C _d→ C _mrlinear transformation C _din vector x _jbe mapped as a vector in column vector subspace.Through AF panel matrix after process, M _rthe vector of dimension is mapped to again the vector of a d dimension.Ideally, the vector that this d ties up should be a null vector.But all interference signals can only be allowed in reality to snap to minimum dimension, occupy larger dimension to make useful signal.

Therefore, the signal of the interference sections without interference suppression filter process is called interference map signal by the present invention.Mapped by minimise interference order, reduce the dimension that occupies of interference signal.

$\begin{array}{cc}min& \underset{k=1}{\overset{K}{\Σ}}rank\left({\left\{H_{kj}{V}_j\right\}}_{j=1,j\≠k}^K\right)\end{array}---\left(5\right)$

Wherein, represent interference map rank of matrix.

Next, with the convex alternative rank of matrix of the nuclear norm of matrix.Order (5) formula can be equivalent to

$\begin{array}{cc}min& \frac{1}{M}\underset{k=1}{\overset{K}{\Σ}}\left|\right|{\mathrm{JJ}}_k|{|}_{*}\end{array}---\left(6\right)$

Wherein

$\left|\right|{\mathrm{JJ}}_k|{|}_{*}=\underset{i=1}{\overset{rank\left({\mathrm{JJ}}_k\right)}{\Σ}}{\mathrm{\σ}}_i\left({\mathrm{JJ}}_k\right)$

The nuclear norm of representing matrix, σ _i(JJ _k) singular value of representing matrix i-th descending arrangement.Suppose M=||JJ _k||, intuitively, in the limiting case, some orders of disturbing are zero, then M=0,1/M are infinitely great, are therefore appreciated that 1/M is the upper bound of (6) formula.

For desired signal, main concern " order maximizes and maximizes power ".Because when signal subspace can be opened into all available dimensionality spaces, the actual available degree of freedom of system is the dimension that dimension that useful signal occupies deducts interference signal and occupies.The order of desired signal maximizes, can by forcing Received signal strength to be that Hermitian positive definite matrix realizes.

Wherein, desired signal matrix (7) formula representing matrix is Hermitian positive definite matrix, namely λ _min(S _k) > 0, λ _min(S _k) represent the minimal eigenvalue of desired signal matrix.

Next the reasonability of this compulsive means will be described.If there is the pre-coding matrix and the AF panel set of matrices that meet target function solution, in set all elements be multiplied with same arbitrary unitary matrice after the new set of gained, all elements in this set also all can ensure that the signal matrix that meets the expectation is the condition of Hermitian positive definite matrix when keeping cost equation constant.

Realize desired signal power to maximize, first consider the computing formula of speed, the speed that user k obtains is

$R={\log }_2\det (I_d+{\left(I_d+J_k{J}_k^H\right)}^{-1}{S}_k{S}_k^H)---\left(8\right)$

Wherein det represents and gets determinant of a matrix, log ₂the logarithm that it is the end that expression is got with 2, superscript "-1 " represents is to matrix inversion.Promoting transmission rate in above formula, need increase the value of determinant.From the relation of characteristic value and determinant, for arbitrary matrix, hypothesis matrix is the determinant that the product of all characteristic values of A, A equals A.A and unit matrix be A with the characteristic value of matrix characteristic value adds 1.So (10) formula is finally to reach

${(I_d+J_k{J}_k^H)}^{-1}{S}_k{S}_k^H---\left(9\right)$

(9) characteristic value of formula is maximum.But the characteristic value that this formula is discussed is very difficult.Be readily appreciated that this formula represents Signal to Interference plus Noise Ratio (SINR) intuitively.Therefore (9) formula can be replaced by (10) formula

$Tr\left(S_k{S}_k^H\right)/Tr(I_d+J_k{J}_k^H)---\left(10\right)$

Wherein Tr represents and asks matrix trace.So (8) formula of maximization, be exactly the power maximizing receiving terminal desired signal.

From the character of Hermitian diagonalizable, with S _kcharacteristic value relevant.For keeping the signal to noise ratio of receiving terminal desired signal not reduce, suppose to work as time, the scheme proposed forces the desired signal matrix minimal eigenvalue promoting receiving terminal to be P _k.But when signal to noise ratio is higher, during higher than 20dB, the desired signal matrix minimal eigenvalue of receiving terminal is along with P _kincrease, speed and the degree of freedom significantly do not promote, this is because in iterative process, pre-coding matrix and AF panel matrix appear in desired signal and interference signal simultaneously, desired signal power is excessive, corresponding interference also can strengthen, so the desired signal matrix minimal eigenvalue of the present invention's receiving terminal is the most at last constrained to 100 (power 20dB).This situation being 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, and with the nuclear norm of interference map matrix for target function, desired signal matrix is Hermitian positive definite matrix, and minimal eigenvalue is more than or equal to 100 for constraints, asks for pre-coding matrix.

Step 4: by the interference signal of reception as a whole, obtain interference covariance matrix;

By interference signal as a whole, interference power is defined as the power of receiving terminal interference signal sum in the present invention, and the interference power of receiving terminal k is

$P_{ki}=Tr\left(U_k^H\underset{j=1,j\≠k}{\overset{K}{\Σ}}{H}_{kj}{V}_j{\left(\underset{j=1,j\≠k}{\overset{K}{\Σ}}{H}_{kj}{V}_j\right)}^H{U}_k\right)---\left(11\right)$

Step 5: AF panel matrix column vector be the minimum characteristic value of interference covariance matrix corresponding characteristic vector;

$U_{*d}^k=v_d\[\underset{j=1,j\≠k}{\overset{K}{\Σ}}{H}_{kj}{V}_j{\left(\underset{j=1,j\≠k}{\overset{K}{\Σ}}{H}_{kj}{V}_j\right)}^H\],d=1,...,d_k---\left(12\right)$

In formula (12), represent the d row of the AF panel matrix of user k, v _dthe characteristic vector of [] homography d minimal eigenvalue.

Step 6: repeat step 2 ~ five, until the complete all number of times of iteration;

The present invention adopts distribute amplification alignment thereof, and distribute amplification alignment has to pass through successive ignition, could keep algorithmic statement.

After each iteration, the nuclear norm of interference map all can reduce.By choosing suitable iterations, finally function to achieve the objective its minimum value can be stabilized in.Order constraint order minimization algorithm by analysis, the present invention chooses 10 for iterations.

Step 7: orthogonalization pre-coding matrix and AF panel matrix.

For avoiding disturbing between data flow, pre-coding matrix and AF panel matrix are carried out orthogonalization process.

Below in conjunction with accompanying drawing, the invention will be further described.

Inventor's mode by experiment implementation algorithm that the present invention alignd with existing various interference contrasts.Setup Experiments is as follows: supposing the system is a feasible system, and base station end configures 8 antennas, and 3 users configure 4 antennas respectively, be expressed as (8 × 4, d) ³, wherein d is the obtainable degree of freedom of system single user.It is zero that channel element all obeys average, and variance is the multiple Gaussian Profile of 1.Simulation result is the average result of 200 independent identically distributed channels.The present invention is by matrix S _kbe greater than 10 ^-8the quantity of singular value deduct matrix J _kbe greater than 10 ^-8the difference definition of quantity gained of singular value can utilize the space dimension number of degrees for user, namely can be used for the noiseless Spatial Dimension quantity that transmission period hopes signal data.The algorithm of contrast comprises the minimized algorithm of order constraint order.Least interference leaks algorithm, maximize SINR algorithm.

Fig. 3, Fig. 4 are respectively d=1, and when 3, the present invention and additive method system single user can utilize space dimension number of degrees comparison diagram.Except maximize SINR algorithm can utilize dimension to be except 0, when the degree of freedom is 1, algorithm can reach the maximum degree of freedom; When the degree of freedom is 3, go owing to needing certain dimension to eliminate interference so all algorithms all can not reach the degree of freedom most, but can find out, algorithm can reach the degree of freedom still higher than other two kinds of algorithms.

Fig. 5, Fig. 6 are respectively d=1, when 3, and the present invention and the average total speed comparative result of additive method system.For convenience of drawing, the rate value in figure is 1/2 of former result.As d=1, average total speed that the present invention can obtain and maximize SINR are similar to, and higher than order constraint order minimization algorithm, are 1.5 times that least interference leaks algorithm.During d=3, the present invention is better than the three kinds of algorithms contrasted, and it is the poorest that order constraint order minimizes effect, this is because when signal to noise ratio is lower, power constraint method is better.As can be seen from the figure, along with the increase of signal to noise ratio, the present invention can obtain higher throughput.

The invention provides a kind of interference alignment algorithm method of minimise interference power and dimension.Interference alignment because signal dimension shared by interference can be compressed, obtain the maximum degree of freedom, the advantage such as lifting channel capacity, paid close attention to widely.But most interference alignment algorithm cannot balance the impact of interference leakage power and noiseless dimension two factors, cause received signal quality to be deteriorated, and power system capacity reduces.The present invention proposes the interference alignment algorithm of a kind of minimise interference power and dimension, and the constraint achieving interference order combines with power constraint.First the method utilizes the order of minimise interference signal matrix, calculates pre-coding matrix, then by minimizing the interference power of leakage, draws AF panel matrix.The invention solves the interference power of only minimum leaks and the noiseless dimension brought reduces, and only minimise interference dimension and cause expecting that space interference strength increases problem.By the double constraints of interference signal order and power, reduce the interference effect of minizone, improve received signal quality, improve power system capacity and the availability of frequency spectrum.

Claims (3)

1. an interference alignment schemes for minimise interference power and dimension, is characterized in that: comprise the following steps,

Step one: stochastic generation AF panel matrix, setting iterations iter;

Step 2: with the nuclear norm of interference map matrix for target function, makes desired signal matrix be Hermitian positive definite matrix, and is more than or equal to 100 for constraints with minimal eigenvalue, ask for pre-coding matrix;

Step 3: by the interference signal of reception as a whole, obtain interference covariance matrix;

Step 4: the characteristic value making interference covariance matrix minimum corresponding characteristic vector be AF panel matrix column vector;

Step 5: judged whether all iterationses, if so, orthogonalization pre-coding matrix and AF panel matrix; Otherwise return step 2.

2. the interference alignment schemes of a kind of minimise interference power according to claim 1 and dimension, is characterized in that: comprise K transmitting terminal, K receiving terminal, each transmitting terminal, receiving terminal configuration M _ttransmit antennas, M _rroot reception antenna, the signal that a kth receiving terminal receives is:

$y_k=U_k^H{H}_{kk}{V}_k+U_k^H\underset{j=1,j\≠k}{\overset{K}{\Σ}}{H}_{kj}{V}_j+U_k^H{n}_k,k=1,...,K$

The signal that wherein base station k sends is x _k∈ C ^{d × 1}, representing matrix V _kconjugate transpose, with represent pre-coding matrix and the AF panel matrix of receiving terminal k respectively, H _kjrepresent that each element all obeys the channel coefficient matrix between the base station j of the multiple gaussian random distribution of independent same distribution zero mean unit variance and user k, for obeying (0, σ ²i _d) white Gaussian noise, σ is variance, I _drepresent d rank unit matrix.

3. the interference alignment schemes of a kind of minimise interference power according to claim 1 and dimension, is characterized in that: described in

Interference map matrix be:

Desired signal matrix is: k ∈ K.