CN103023544A - Low-complexity interference alignment method of multiple input multiple output (MIMO)interference channel system - Google Patents

Low-complexity interference alignment method of multiple input multiple output (MIMO)interference channel system Download PDF

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CN103023544A
CN103023544A CN201210562491XA CN201210562491A CN103023544A CN 103023544 A CN103023544 A CN 103023544A CN 201210562491X A CN201210562491X A CN 201210562491XA CN 201210562491 A CN201210562491 A CN 201210562491A CN 103023544 A CN103023544 A CN 103023544A
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王忠勇
朱政宇
高向川
王玮
肖岩
张传宗
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Zhengzhou University
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Abstract

The invention discloses a low-complexity interference alignment method of a multiple input multiple output (MIMO)interference channel system. The low-complexity interference alignment method includes: firstly, obtaining an interference channel matrix from other community base stations to local community users, and randomly initializing a pre-code matrix of base stations; secondly, obtaining an interference covariance matrix of users according to the pre-code matrix and the interference channel matrix, and then obtaining an orthogonal basis of an interference receiving subspace; thirdly, updating the pre-code matrix according to the orthogonal basis of the interference receiving subspace, and when an updated pre-code matrix dissatisfies conditions of convergence, recalculating the orthogonal basis of the interference receiving subspace, and if not, obtaining a final orthogonal basis of the interference receiving subspace according to the updated pre-code matrix which satisfies the conditions of the convergence; fourthly, obtaining a post-processing matrix according to the final orthogonal basis of the interference receiving subspace; and finally, performing zero forcing processing on a signal according to the post-processing matrix to obtain a signal with interference eliminated. The low-complexity interference alignment method of the MIMO interference channel system is simple in process and high in accuracy rate, and can reduce computation complexity on the premise of keeping system data throughout capacity.

Description

The low complex degree of MIMO interference channel system disturbs alignment schemes
Technical field
The present invention relates to communication technical field, the low complex degree that relates in particular to MIMO interference channel system disturbs alignment schemes.
Background technology
To high transfer rate more and more the pursuit of spectral efficient be the topic of a permanency of wireless communication field.Multi-antenna technology (Multiple Input Multiple Output, MIMO) is by at many antennas of transmitting terminal and receiving terminal configuration, for radio communication has been introduced the additional space degree of freedom, thereby greatly improved the availability of frequency spectrum and the throughput of system.In the wireless network, except noise and decline factor, disturb the impact for communication day by day to highlight.Now, the basic framework of 4G is established.Because its basic multi-access mode is based on OFDMA(OFDM access) frequency division multiple access, so the multi-user in the residential quarter no longer becomes research emphasis.And because neighbor cell subcarrier multiplexing, the interference of presence of intercell interference, particularly edge customer becomes outstanding problem.How effectively to eliminate interference effect and become important research topic.When introducing multi-antenna technology in the next generation communication system, and expect that generally the multiplexing factor of proportion is that 1 mode is carried out networking, inevitably can produce common-channel interference (Co-Channel Interference, CCI), the user of cell edge particularly, seriously weakened the spectral efficient that multi-antenna technology brings, existing interference mitigation technology, such as interference randomization, interference delete, interference management etc., can't address this problem well, the more advanced interference mitigation technology of an urgent demand research is in order to further promote spectrum efficiency.In LTE-Advanced, introduce cooperative multipoint transmission (Coordinated Multi Point, CoMP) technology, it suppresses the interference of minizone multiaerial system by the cooperation between each base station and the user, and interference alignment (Interference Alignment, IA) as in the COMP technology to a jamproof effective means, relatively traditional interference mitigation technology has demonstrated huge advantage and research potential.
Yet the channel condition information that traditional interference alignment techniques requires transmitting terminal to have the overall situation, and the needs that too do not gear to actual circumstances in theorizing; The channel condition information of imperfectization will make systematic function significantly descend, and can not reach the effect of reduce disturbance simultaneously.The defective of interference alignment techniques inherence is encouraging the development of the technology of some needs that more gear to actual circumstances.Reduce so as far as possible the computation complexity of real system, as disturbing alignment techniques research and development direction future.
The interference alignment problem of MIMO Gauss interference channel ascribes the formula of finding the solution in fact to, obtains one group of base station precoding and user's reprocessing matrix.Regrettably, solving equation group how
Figure BDA00002631500300021
Figure BDA00002631500300022
Remain academia's an open question.But, if having to take the second best, do not pursue accurately closed solutions, but seek a numerical solution that approaches very much, there is way to try to achieve.Numerical solution of distributed interference alignment schemes (EVD-IA method) random initializtion, utilize the reciprocity of communication system channel under the tdd mode, along with iteration between base station and the user is upgraded pre-coding matrix and reprocessing matrix, make numerical solution approach gradually accurately closed solutions, so that interference power reaches minimum, but this Technology Restriction is in 1) channel reciprocity of system, can only be operated in the communication system under the tdd mode, 2) used the Eigenvalues Decomposition algorithm of second order, made the computation complexity of whole system higher.Shortcoming for the EVD-IA method, propose alternating minimization and disturbed alignment schemes (AM-IA method), do not need to utilize the reciprocity of channel, utilize the distance between subspace-based and the matrix to be knowwhy, alternately iteration is upgraded transmitting terminal pre-coding matrix and user's interference space, so that the interference signal matrix must be aligned in interference space as far as possible, but this technical disadvantages is to have used the Eigenvalues Decomposition algorithm of second order, make the computation complexity of whole system higher, be unfavorable for that application and the hardware in real system is realized.
Summary of the invention
The technical problem that (one) will solve
The technical problem to be solved in the present invention is how in the keeping system throughput, to reduce the system-computed complexity in MIMO interference channel system.
(2) technical scheme
For solving the problems of the technologies described above, technical scheme of the present invention provides the low complex degree of a kind of MIMO interference channel system to disturb alignment schemes, it is characterized in that the method comprises:
S1: obtain other cell base stations to the interference channel matrix of this community user, and the pre-coding matrix of random initializtion base station;
S2: get user's interference covariance matrix according to described pre-coding matrix and interference channel Matrix Calculating, and then obtain receiving the orthogonal basis of interference space;
S3: the orthogonal basis according to described reception interference space upgrades pre-coding matrix, when the pre-coding matrix after upgrading does not satisfy the condition of convergence, returns step S2; Otherwise, obtain the orthogonal basis of final reception interference space according to the pre-coding matrix after the renewal of satisfying the condition of convergence;
S4: the orthogonal basis according to final reception interference space obtains the reprocessing matrix;
S5: by the reprocessing matrix signal is carried out ZF and process, the signal after the interference that is eliminated.
Described step S2 specifically comprises:
S21: the interference covariance matrix that obtains each user according to described pre-coding matrix and described interference channel matrix computations;
S22: described interference covariance matrix is decomposed, obtain the first unitary matrice;
S23: the orthogonal basis that receives interference space is classified in the appointment of choosing the first unitary matrice as.
Described step S3 specifically comprises:
S31: calculate the distance matrix between the orthogonal basis of described interference channel matrix and described reception interference space;
S32: described distance matrix is decomposed, obtain the second unitary matrice;
S33: the pre-coding matrix after the renewal is classified in the setting of choosing the second unitary matrice as;
S34: whether the pre-coding matrix that calculates after the described renewal satisfies the condition of convergence, when not satisfying the condition of convergence, replaces described pre-coding matrix with the pre-coding matrix after upgrading, and returns step S2; Otherwise, obtain the orthogonal basis of final reception interference space according to the pre-coding matrix after upgrading.
The computing formula of described interference covariance matrix is:
D k u = Σ k = 1 , k ≠ k u K H k u , k V k V k H H k u , k H
Wherein:
Figure BDA00002631500300041
Be interference covariance matrix;
Figure BDA00002631500300042
Be the interference channel matrix;
V kBe pre-coding matrix;
K is total number of base;
K is k base station;
k uBe k uIndividual user.
The described condition of convergence is:
Poor matrix between pre-coding matrix after the described renewal and the described pre-coding matrix is less than setting matrix.
The computing formula of described reprocessing matrix is:
W k u = I N k u - Q k u 1 : N k u - d k ( Q k u 1 : N k u - d k ) H
Wherein:
Be the reprocessing matrix;
Figure BDA00002631500300045
Be length
Figure BDA00002631500300046
Unit matrix;
Figure BDA00002631500300047
Orthogonal basis for final reception interference space;
Figure BDA00002631500300048
Number for reception antenna;
d kNumber of data streams for base station k emission.
(3) beneficial effect
The present invention has adopted according to the ordering QR decomposition algorithm based on the Gram-Schmidt method of revising and has approached Eigenvalues Decomposition algorithm in the AM-IA algorithm, and adopted loop iteration base station pre-coding matrix and received the mode of reprocessing matrix, seek one very near the numerical solution of closed solutions.At first by channel estimating, obtain this cell base station to the channel information of this community user, and other residential quarters user's in this residential quarter interference channel matrix information, and the pre-coding matrix of each base station of random initializtion; The interference channel matrix information of user in this residential quarter is arrived in pre-coding matrix and other residential quarters according to each base station, obtains each user's interference covariance matrix; Afterwards, according to each user's interference covariance matrix, according to use ordering QR decomposition algorithm based on the Gram-Schmidt method of revising, obtain the upper triangular matrix that unitary matrice and diagonal entry increase progressively; According to unitary matrice, choose the most front
Figure BDA00002631500300051
Classify the orthogonal basis that receives interference space as; According to minimizing Euclid distance criterion, according to other residential quarters user's in this residential quarter interference channel matrix information with receive interference space, obtain the distance of the orthogonal basis of the interference channel matrix of each base station and interference space; Afterwards, the distance according to the orthogonal basis of the interference channel matrix of each base station and interference space according to use ordering QR decomposition algorithm based on the Gram-Schmidt method of revising, obtains the upper triangular matrix that unitary matrice and diagonal entry increase progressively; According to unitary matrice, choose last d kClassify each new base station pre-coding matrix as; Until convergence is final, according to the orthogonal basis that receives interference space, obtain user's reprocessing matrix.Owing to used the ordering QR decomposition algorithm based on the Gram-Schmidt method of revising, the process of search order is circulated in the calculating interference channel Matrix QR Decomposition process, before orthogonalizing process each time, row to channel matrix are arranged, the criterion of choosing is exactly that the column vector of column vector Norm minimum is carried out at first QR and decomposed, therefore reduced the dimension of each subscriber channel matrix of system, thereby the SQRD-IA scheme is calculated under low dimension, effectively reduced the computation complexity of traditional AM-IA scheme.In the increase along with iterations, further increased throughput of system and receive to disturb to have significantly and reduce, and the iteration effect that substantially is consistent with traditional AM-IA scheme, thereby promoted the method feasibility in actual applications.
Description of drawings
Fig. 1 is the flow chart that the low complex degree of MIMO interference channel of the present invention system disturbs alignment schemes;
Fig. 2 is the transmission schematic diagram that the low complex degree of MIMO interference channel of the present invention system disturbs the embodiment of alignment schemes;
Fig. 3 provided system and respectively held antenna configuration (8,8,3), and K=4 is under the different signal to noise ratio conditions, based on SQRD-IA method of the present invention and the AM-IA scheme comparative graph in power system capacity;
Fig. 4 has provided at each end antenna configuration
Figure BDA00002631500300052
K=4, SNR=30dB is under the condition of different iterationses, based on the convergence comparative graph of the power system capacity of SQRD-IA scheme of the present invention and AM-IA scheme;
Embodiment
For making purpose of the present invention, content and advantage clearer, embodiment of the present invention is described further in detail below in conjunction with accompanying drawing.
The low complex degree of the MIMO interference channel system that the present invention proposes disturbs alignment schemes, is described as follows in conjunction with the accompanying drawings and embodiments:
As shown in Figure 1, the present invention includes following steps:
S1: by channel estimating, obtain this cell base station to the channel matrix of this community user, and other residential quarters user's in this residential quarter interference channel matrix, and the pre-coding matrix of random initializtion base station;
The turnkey of setting up departments is drawn together K base station and K uIndividual user, k base station transmit antennas number is M k, the number of data streams of k base station emission is d k, k uIndividual user's reception antenna number is
Figure BDA00002631500300061
System configuration is
Figure BDA00002631500300062
K base station is to k in the system uIndividual user's channel matrix is
Figure BDA00002631500300063
K=1 ..., K; k u=1 ..., K u, the noise factor of system is σ, base station k transmitted signal S k
By channel estimating, obtain this cell base station to the channel information of this community user K=1 ..., K; k u=1 ..., K u; K=k u, and the interference channel matrix information of user in this residential quarter is arrived in other residential quarters
Figure BDA00002631500300065
K=1 ..., K; k u=1 ..., K u; K ≠ k u, and the pre-coding matrix of each base station of random initializtion
Figure BDA00002631500300066
K uIndividual user's reception signal is y k u = H k u , k V k S k + Σ k = 1 , k ≠ k u K H k u , k V k S k + n k u ;
S2: get user's interference covariance matrix according to described pre-coding matrix and interference channel Matrix Calculating, and then obtain receiving the orthogonal basis of interference space;
S21: the interference covariance matrix that obtains each user according to described pre-coding matrix and described interference channel matrix computations;
Pre-coding matrix V according to each base station kArrive the interference channel matrix information of user in this residential quarter with other residential quarters
Figure BDA00002631500300071
K=1 ..., K; k u=1 ..., K u; K ≠ k u, obtain each user's interference covariance matrix:
D k u = Σ k = 1 , k ≠ k u K H k u , k V k V k H H k u , k H
Wherein:
Be interference covariance matrix;
Figure BDA00002631500300074
Be the interference channel matrix;
V kBe pre-coding matrix;
K is total number of base;
K is k base station;
k uBe k uIndividual user.
S22: described interference covariance matrix is decomposed, obtain the first unitary matrice;
Interference covariance matrix according to each user
Figure BDA00002631500300075
According to use ordering QR decomposition algorithm based on the Gram-Schmidt method of revising, obtain the first unitary matrice
Figure BDA00002631500300076
The first upper triangular matrix that increases progressively with diagonal entry
Figure BDA00002631500300077
The process of decomposing based on the ordering QR of the Gram-Schmidt method of revising comprises: based on the determinant criterion column vector in the interference covariance matrix is rearranged, allow the column vector of Norm minimum carry out at first the QR decomposition, and the Gram-Schmidt method of revising is carried out the QR decomposition to the interference covariance matrix after resequencing; Finally obtain the first unitary matrice
Figure BDA00002631500300078
The first upper triangular matrix that increases progressively with diagonal entry
Figure BDA00002631500300079
Program circuit based on the ordering QR decomposition algorithm of the Gram-Schmidt method of revising is:
Initialization: R=0, Q = Σ k = 1 , k ≠ k u K H k u , k V k V k H H k u , k H
Figure BDA000026315003000711
Wherein:
M kIt is the number of transmit antennas of k base station;
r μ, μBe matrix q μNorm;
q μBe the remaining μ row of Q;
r μ, vBe projection matrix;
k μ, q v, v and the μ intermediate variable for setting.
S23: the orthogonal basis that receives interference space is classified in the appointment of choosing the first unitary matrice as.
Because the data flow that the base station sends is d k, for the desired signal that makes user side separates as much as possible with interference signal, user k uInterference signal be aligned in a dimension and be at most Linear subspaces in, choose again the first unitary matrice
Figure BDA00002631500300083
The most front
Figure BDA00002631500300084
Classify as and receive the orthogonal basis that disturbs linear subspaces
Figure BDA00002631500300085
S3: the orthogonal basis according to described reception interference space upgrades pre-coding matrix, when the pre-coding matrix after upgrading does not satisfy the condition of convergence, returns step S2; Otherwise, obtain the orthogonal basis of final reception interference space according to the pre-coding matrix after the renewal of satisfying the condition of convergence;
S31: calculate the distance matrix between the orthogonal basis of described interference channel matrix and described reception interference space;
According to minimizing Euclid distance criterion, arrive the interference channel matrix information of user in this residential quarter according to other residential quarters
Figure BDA00002631500300091
K=1 ..., K; k u=1 ..., K u; K ≠ k uWith the orthogonal basis that receives the interference linear subspaces
Figure BDA00002631500300092
Obtain the distance matrix of the orthogonal basis of the interference channel matrix of each base station and interference space
Figure BDA00002631500300093
S32: described distance matrix is decomposed, obtain the second unitary matrice;
Distance matrix according to the orthogonal basis of the interference channel matrix of each base station and interference space
Figure BDA00002631500300094
According to use ordering QR decomposition algorithm based on the Gram-Schmidt method of revising, obtain the second unitary matrice Q kThe the second upper triangular matrix R that increases progressively with diagonal entry k
S33: the pre-coding matrix after the renewal is classified in the setting of choosing the second unitary matrice as;
Then, be d owing to desired signal occupies reception subspace dimension k, according to the second unitary matrice Q k, choose the pre-coding matrix V after last dk classifies renewal as k, computing formula is V k = Q k M k - d k + 1 : M k .
S34: whether the pre-coding matrix that calculates after the described renewal satisfies the condition of convergence, when not satisfying the condition of convergence, replaces described pre-coding matrix with the pre-coding matrix after upgrading, and returns step S2; Otherwise, obtain the orthogonal basis of final reception interference space according to the pre-coding matrix after upgrading.
The condition of convergence is that pre-coding matrix after the described renewal and the poor matrix between the described pre-coding matrix are less than setting matrix.Set matrix and set flexibly according to actual conditions, reveal as long as satisfy to disturb Less than 10 -8Get final product.
Described interference is revealed
Figure BDA00002631500300097
Computing formula be:
IL k u = trace ( W k u H D k u W k u )
Wherein:
Figure BDA00002631500300099
Be the reprocessing matrix; Matrix trace is asked in trace () expression.
S4: the orthogonal basis according to final reception interference space obtains the reprocessing matrix;
Orthogonal basis according to the reception interference space after the convergence
Figure BDA00002631500300101
Obtain user's reprocessing matrix:
W k u = I N k u - Q k u 1 : N k u - d k ( Q k u 1 : N k u - d k ) H
Wherein:
Figure BDA00002631500300103
Be the reprocessing matrix;
Be length
Figure BDA00002631500300105
Unit matrix
Figure BDA00002631500300106
Orthogonal basis for final reception interference space;
Figure BDA00002631500300107
Number for reception antenna;
d kNumber of data streams for base station k emission.
S5: by the reprocessing matrix signal is carried out ZF and process, the signal after the interference that is eliminated.
Reach the condition of disturbing alignment by the reprocessing matrix:
W k u H H k u , k V k = 0 , k u ≠ k
rank ( W k u H H k u , k V k ) = d k
The signal of eliminating after disturbing is:
S ^ k u = W k u H y k u = W k u H H k u , k V k S k + Σ k = 1 , k ≠ k u K W k u H H k u , k V k S k + W k u H n k u
= W k u H H k u , k V k S k + W k u H n k u
So far finished the work of disturbing alignment optimizes.
In sum, the present invention proposes that low complex degree disturbs alignment schemes in a kind of MIMO interference channel system, have the advantage of low complex degree, all applicable for the system of any antenna configuration, number of users.Owing to used the ordering QR decomposition algorithm based on the Gram-Schmidt method of revising, the process of search order is circulated in the calculating interference channel Matrix QR Decomposition process, before orthogonalizing process each time, row to channel matrix are arranged, the criterion of choosing is exactly that the column vector of column vector Norm minimum is carried out at first QR and decomposed, therefore reduce the dimension of each subscriber channel matrix of system, effectively reduced the computation complexity that disturbs alignment techniques.
The below will provide the comparison of SQRD-IA scheme of the present invention and AM-IA scheme, so that advantage of the present invention and feature are more obvious.
For easy, can be similar to and think that the complexity of complex matrix operation is 6 times of real number matrix corresponding operating complexity.Wherein 1 flop is expressed as a floating-point operation.Be the real matrix of m * n to size
Figure BDA00002631500300111
, the computation complexity of matrix sum operation is: 2mn (flops) is 2mnp (flops) to the computation complexity of m * n and n * p matrix multiplication, matrix norm || G|| FThe computation complexity of computing is: 4mn (flop), and for m * m be matrix, the computation complexity of the Eigenvalues Decomposition of broad sense is 4m 3/ 3+17m 3(flops), the computation complexity of QR decomposition algorithm is: 2m 3(flops), wherein, with respect to the QR decomposition method of broad sense, the row ordering of matrix Q that the operand of this algorithm is only many.Be 2m based on the computation complexity of the ordering QR decomposition algorithm of the Gram-Schmidt method of revising a little more than the QR decomposition algorithm of broad sense 3+ m (m-1)/2 (flops).
The below is more as shown in table 1 to the computation complexity of SQRD-IA scheme and AM-IA scheme.
The computation complexity of two kinds of algorithms of table 1 relatively
Figure BDA00002631500300112
As shown in Table 1, compare with the interference alignment schemes of AM-IA scheme, the computation complexity of SQRD-IA scheme of the present invention has reduced by 51%, and this will be conducive to the application of method of the present invention in practical communication system.
In addition, as shown in Figure 3, at system configuration (M k, N k, d k)=(8,8,3), K=4, under different signal to noise ratio conditions, the comparative graph of the power system capacity of SQRD-IA scheme of the present invention and AM-IA scheme; As can be seen from Figure, SQRD-IA scheme of the present invention is compared with the AM-IA scheme, descends slightly to some extent under the power system capacity.
As shown in Figure 4, at system configuration (M k, N k, d k)=(8,8,3), K=4, under different signal to noise ratios and the condition of iterations, the system iterative convergence rate comparative graph of SQRD-IA scheme of the present invention and AM-IA scheme; As can be seen from Figure, SQRD-IA scheme of the present invention is compared with the AM-IA scheme, and two kinds of algorithmic statement speed decrease slightly before 500 iteration, and two kinds of algorithms reach convergence when 500 iteration, and performance tends towards stability and substantially is consistent;
The above only is preferred implementation of the present invention, for the those of ordinary skill of present technique, under the prerequisite that does not break away from the technology of the present invention principle, can also make some improvement and distortion, and these improvement and distortion also should be considered as protection scope of the present invention.

Claims (6)

1.MIMO the low complex degree of interference channel system disturbs alignment schemes, it is characterized in that the method comprises:
S1: obtain other cell base stations to the interference channel matrix of this community user, and the pre-coding matrix of random initializtion base station;
S2: get user's interference covariance matrix according to described pre-coding matrix and interference channel Matrix Calculating, and then obtain receiving the orthogonal basis of interference space;
S3: the orthogonal basis according to described reception interference space upgrades pre-coding matrix, when the pre-coding matrix after upgrading does not satisfy the condition of convergence, returns step S2; Otherwise, obtain the orthogonal basis of final reception interference space according to the pre-coding matrix after the renewal of satisfying the condition of convergence;
S4: the orthogonal basis according to final reception interference space obtains the reprocessing matrix;
S5: by the reprocessing matrix signal is carried out ZF and process, the signal after the interference that is eliminated.
2. method according to claim 1 is characterized in that, described step S2 specifically comprises:
S21: the interference covariance matrix that obtains each user according to described pre-coding matrix and described interference channel matrix computations;
S22: described interference covariance matrix is decomposed, obtain the first unitary matrice;
S23: the orthogonal basis that receives interference space is classified in the appointment of choosing the first unitary matrice as.
3. method according to claim 2 is characterized in that, described step S3 specifically comprises:
S31: calculate the distance matrix between the orthogonal basis of described interference channel matrix and described reception interference space;
S32: described distance matrix is decomposed, obtain the second unitary matrice;
S33: the pre-coding matrix after the renewal is classified in the setting of choosing the second unitary matrice as;
S34: whether the pre-coding matrix that calculates after the described renewal satisfies the condition of convergence, when not satisfying the condition of convergence, replaces described pre-coding matrix with the pre-coding matrix after upgrading, and returns step S2; Otherwise, obtain the orthogonal basis of final reception interference space according to the pre-coding matrix after upgrading.
4. method according to claim 2 is characterized in that, the computing formula of described interference covariance matrix is:
D k u = Σ k = 1 , k ≠ k u K H k u , k V k V k H H k u , k H
Wherein:
Figure FDA00002631500200022
Be interference covariance matrix;
Figure FDA00002631500200023
Be the interference channel matrix;
V kBe pre-coding matrix;
K is total number of base;
K is k base station;
k uBe k uIndividual user.
5. method according to claim 2 is characterized in that, the described condition of convergence is:
Poor matrix between pre-coding matrix after the described renewal and the described pre-coding matrix is less than setting matrix.
6. method according to claim 2 is characterized in that, the computing formula of described reprocessing matrix is:
W k u = I N k u - Q k u 1 : N k u - d k ( Q k u 1 : N k u - d k ) H
Wherein:
Figure FDA00002631500200025
Be the reprocessing matrix;
Figure FDA00002631500200026
Be length Unit matrix;
Figure FDA00002631500200028
Orthogonal basis for final reception interference space;
Number for reception antenna;
d kNumber of data streams for base station k emission.
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