CN107302388A - A kind of combination treatment method of descending multi-user mimo system - Google Patents

A kind of combination treatment method of descending multi-user mimo system Download PDF

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CN107302388A
CN107302388A CN201710625035.8A CN201710625035A CN107302388A CN 107302388 A CN107302388 A CN 107302388A CN 201710625035 A CN201710625035 A CN 201710625035A CN 107302388 A CN107302388 A CN 107302388A
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msub
mrow
msup
msubsup
user
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仲涛
周红明
刀学龙
王俊峰
张苹珍
王蕊
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Yuxi FA science and Technology Development Co., Ltd.
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Yuxi Normal University
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B7/00Radio transmission systems, i.e. using radiation field
    • H04B7/02Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413MIMO systems
    • H04B7/0452Multi-user MIMO systems
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B7/00Radio transmission systems, i.e. using radiation field
    • H04B7/02Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413MIMO systems
    • H04B7/0456Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting

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  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Mobile Radio Communication Systems (AREA)

Abstract

The invention discloses a kind of combination treatment method of descending multi-user mimo system, the combination treatment method of the descending multi-user mimo system, using known channel condition information, precoding is carried out using BD algorithms in transmitting terminal to the signal of each user;In receiving terminal, according to MMSE criterions, the signal that each user receives is detected respectively by solving optimal weights matrix.The present invention carries out precoding in transmitting terminal using BD algorithms, eliminates the interference between user, uses MMSE algorithms in receiving terminal, further increases the accuracy of signal detection.The present invention considers the compromise of performance and complexity, and under the conditions of high SNR, puies forward the performances of BD MMSE algorithms close to optimal.Therefore, in actual downstream multi-user MIMO system, carrying BD MMSE algorithms has certain practical value.

Description

A kind of combination treatment method of descending multi-user mimo system
Technical field
The invention belongs to multi-user MIMO system technical field, more particularly to a kind of joint of descending multi-user mimo system Processing method.
Background technology
For multiple-input and multiple-output (MIMO) system, being communicated using space division multiple access (SDMA) mode with multiple users can be real Throughput of system now higher than time division multiple acess (TDMA) mode.Therefore, in recent years to the research of MIMO technology just from single user Shifted to multi-user.For descending many family mimo systems, can cooperate transmitting between transmitting terminal antenna, and in receiving terminal, it is different User can not but cooperate.Therefore precoding technique turns into the key technology in descending multi-user mimo system.It is nonlinear Dirty paper code algorithm, it is possible to achieve the capacity of multi-user MIMO system, but be difficult in systems in practice because complexity is too high Using.As the compromise of performance and complexity, linear pre-coding method is increasingly becoming the focus of research.ZF (ZF) precoding is calculated Method is a kind of linear algorithm simple and easy to apply, for the scene of multi-user's single antenna, and ZF precoding process only needs a secondary channel Invert (or pseudoinverse), it is possible to isolate each user signal of oneself.BD algorithms are broken zero algorithm under multi-user multi-antenna Popularization, its main thought is that equivalent global channel matrix changed into block diagonalization matrix form, eliminates the interference between user. Corresponding with transmitting terminal pretreatment is how receiving terminal effectively detects signal.Compared with squeeze theorem algorithm, lowest mean square Error (MMSE) algorithm make use of the statistical property of channel, and with preferable detection performance, and robustness is stronger.
The content of the invention
It is an object of the invention to provide a kind of combination treatment method of descending multi-user mimo system, it is intended to solves ... The problem of.
The present invention is achieved in that a kind of combination treatment method of descending multi-user mimo system, described descending multi-purpose The combination treatment method of family mimo system channel condition information known in transmitting terminal, using BD algorithms to each user's Signal carries out precoding;In receiving terminal, according to MMSE criterions, each user is received respectively by solving optimal weights matrix Signal is detected.
Further, it is by H that the BD algorithms carry out precoding to the signal of each userS MSIt is block diagonal matrix HS MS Block diagonalization, finds the optimal transmission vector M for causing inter-user interference to be 0S;WhenWhen, it is Complete Diagonalization, directly Realized with the pseudoinverse of channel matrix.
Further, according to MMSE criterions,Wherein PjFor weight matrix, the mean square error of signal is now received MSE is expressed as:
Now solve optimal P1The problem of be changed into:
Wherein WjThe power distributed for base station to user j, optimal PjFor:
For j-th of user, now useful signal djEstimation signal be:
Another object of the present invention is to provide a kind of multi-user MIMO system using the multi-user MIMO system.
The combination treatment method for the descending multi-user mimo system that the present invention is provided, using block diagonalization (BD) algorithm and most The mode that small mean square error (MMSE) algorithm is combined carries out Combined Treatment to signal, significantly reduces common-channel interference, carries The high performance of system;Simulating, verifying puies forward the validity of algorithm.The present invention utilizes known channel status letter in transmitting terminal Cease (CSI), precoding is carried out to the signal of each user using BD algorithms, the interference between user is eliminated, in receiving terminal, according to MMSE criterions, are detected to the signal that each user receives respectively by solving optimal weights matrix;Theory analysis and experiment Show, significantly reduce the influence of the interference and channel mutation between user, improve the performance of system.The present invention is adopted in transmitting terminal Precoding is carried out with BD algorithms, the interference between user is eliminated, MMSE algorithms is used in receiving terminal, further increases signal detection Accuracy.The present invention considers the compromise of performance and complexity, and under the conditions of high SNR, puies forward the property of BD-MMSE algorithms Can be close to optimal.Therefore, in actual downstream multi-user MIMO system, carrying BD-MMSE algorithms has certain practical value.
Brief description of the drawings
Fig. 1 is the combination treatment method flow chart of descending multi-user mimo system provided in an embodiment of the present invention.
Fig. 2 is descending multi-user mimo system model schematic provided in an embodiment of the present invention.
Under the conditions of Fig. 3 is different channels provided in an embodiment of the present invention, the BER performance curve schematic diagrames of inventive algorithm.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to Limit the present invention.
The application principle of the present invention is explained in detail below in conjunction with the accompanying drawings.
As shown in figure 1, the combination treatment method of descending multi-user mimo system provided in an embodiment of the present invention is including following Step:
S101:In transmitting terminal using known channel condition information (CSI), the signal of each user is entered using BD algorithms Row precoding, eliminates the interference between user;
S102:In receiving terminal, according to MMSE criterions, by solving the letter that optimal weights matrix is received to each user respectively Number detected.
The application principle of the present invention is further described below in conjunction with the accompanying drawings.
1. system model
The potentiality of single user channel high power capacity are mainly realized by abreast sending the subchannel of multi-stream data, are realized and are held Measure the CSI that maximized best practice is namely based on whole link known to transmitting terminal.If in CSI complete known to transmitting terminal, By selecting the right singular vector of channel matrix H to be used as pre-coding matrix M, the power ratio sent per sub-channels reuses water flood Calculate distribution.Although water-filling algorithm can improve the performance of system, in multiuser MIMO channel, base station sends data simultaneously To multiple independent users, this will produce co-channel interference.In this case, CSI known to transmitting terminal has very big advantage, carries not It is that CSI known to transmitting terminal can eliminate common-channel interference in the case of high s/n ratio (SNR).BD algorithms are just built upon transmitting terminal Proposed on the basis of known CSI.Although BD algorithms are not optimal algorithm, it has considered the folding of performance and complexity In, therefore a kind of practical method of can yet be regarded as.
Consider a multiuser downstream channel, its system model is as shown in Fig. 2 have K user and a base station.Base station There is nTRoot antenna, and j-th of user haveRoot antenna, total transmitting antenna number isDefinition Such a channel, for example:{ 2,2 } X4 represents that there are 4 antennas base station, there are 2 users, each 2 antennas of user configuring.From Channel matrix H of the base station to j-th of userjRepresent, corresponding pre-coding matrix MjRepresent, j-th of user receives Signal be:
Wherein, MjAnd djIt is the pre-coding matrix and transmission data vector of j-th of user respectively..
WithIt is the pre-coding matrix and transmission data vector of other users respectively, its expression formula is as follows:
If each user configuring single antenna, and cooperation is not present between user.In this case, channel diagonalization must be Transmitting terminal is completed.Only work as nT>During K, perfect diagonalization could be completed with channel inversion, for example, selectWherein For H pseudoinverse.If each user configures many reception antennas, Complete Diagonalization will be a kind of scheme of suboptimization, because often Individual user can be in receiving terminal collaborative process received signal, and it is respectively H to define channel matrix and pre-coding matrixSAnd MS
MS=[M1M2…MK] (5)
Under certain power limit, optimal algorithm is by the interference vanishing between all users, wherein requiring HS MSIt is Block diagonal matrix.As channel inversion algorithm, BD algorithms imply two conditions:One is dimension, and another is channel matrix Independence.
2.BD precoding algorithms
The general principle of BD algorithms is exactly by HS MSBlock diagonalization, finds the optimal transmission for causing inter-user interference to be 0 Vector MS.Note working asWhen, this method is just reduced to Complete Diagonalization, can directly with the pseudoinverse of channel matrix come Realize.Complete diagonalization can also be appliedAnd can obtain simplify reception advantage (every antenna is only received One signal), but this will be to reduce handling capacity or to increase transmission power as cost.
In order to eliminate the interference between all users, that is, have:As i ≠ j, HjMj=0.Under total transmission power limitation, block pair The handling capacity that angle system can reach is:
Wherein CSThe total capacity of expression system, * represents conjugate transposition, definitionFor:
The limitation of zero interference causes MjMust beKernel on.This condition gives dimension scope, so as to limit Fixed all users can meet the condition of zero interference.Base station sends data to user j, ifDimension be more than zero, whenWhen, this condition is met.Assuming that dimension condition meets all users, if Singular value (SVD) is defined to decompose:
Wherein,Before expressionRow right singular vector,After expressionRow right singular vector.ThereforeIt is Kernel orthogonal basis, its row can be used as pre-coding matrix MjCandidate vector.Define matrix:
Power system capacity under the conditions of zero interference is represented by:
So that CBDThe key of maximum capacity is to find precoding square M'SSo that above-mentioned determinant is maximum.This and single user MIMO capacity problems it is the same, most direct solution is to allow M'SEqual to H'SRight singular vector, then according to corresponding Singular value passes through power water-filling algorithm distribution power.Therefore, M' is solvedSAlgorithm be zero interference limitation under, based on SVD decompose The total capacity of system is maximized with power water filling.H'SBlock structure cause each user each to carry out SVD decomposition, rather than Single maximum SVD is calculated to decompose.SVD is defined to be decomposed into:
Wherein ∑jDimension is Before expressionIndividual characteristic vector.WithMultiplication constitutes oneDimension Orthogonal basis, under the conditions of it is represented to user's j zero interferences, maximizes the vector of information rate.Therefore pre-coding matrix is defined:
Wherein, Λ is the element λ in diagonal matrix, ΛiFor controlling MSThe transmit power of each row.The now appearance of BD algorithms Amount is changed into from (6):
Wherein:
Optimal power partition coefficient L is calculated using power water-filling algorithm and obtained.
3.MMSE receiving algorithms
In receiving terminal, conventional algorithm is ZF receiving algorithms, and it is d that base station, which is sent to user j useful signal,j, base station is adopted BD pre-coding matrixes are MS, MSAs shown in formula (12).The signal that user j is received is represented by:
If using ZF receiving algorithms in receiving terminal, useful signal d can be now obtainedjEstimate be:
As channel HjWhen poor, the poor-performing of this detection algorithm is corresponding with BD algorithms in order to further improve Detection performance, the present invention proposes a kind of to be based on MMSE detection algorithms.According to MMSE criterions, ifWherein PjFor power Weight matrix, the mean square error (MSE) for now receiving signal is expressed as:
Now solve optimal P1The problem of be changed into:
Wherein WjThe power distributed for base station to user j, can be calculated by water-filling algorithm.Therefore when channel status is given When, WjFor certain value.Obviously (18) are a convex optimization problems, can pass through typical Optimization Method Pj.By solving formula (18) optimal P can, be obtainedjFor:
For j-th of user, now useful signal djEstimation signal be:
The application effect of the present invention is explained in detail with reference to emulation.
Carry out simulation analysis to bit error rate (BER) performances of carried BD-MMSE algorithms using computer, and with it is traditional BD-ZF algorithms are compared.In simulations, the number of antennas of transmitting terminal is 4, and receiving terminal has 2 users, the day of each user Line number mesh is all 2, using QPSK (QPSK) modulation system.The present invention considers uncorrelated channel, weak correlation respectively Under channel and strong correlation channel condition, the BER performances of algorithm are put forward.Fig. 3 shows BD-ZF algorithms and carries BD-MMSE algorithms BER curve.Fig. 3 shows that the BER for carrying BD-MMSE algorithms declines with the increase of signal to noise ratio (SNR), with existing BD-ZF Algorithm is compared, and carrying algorithm has preferable BER performances, for example, under uncorrelated channel condition, as BER=0.001, with BD-ZF algorithms are compared, and propose the gain that BD-MMSE algorithms obtain nearly 0.5dB.When the correlation of channel gradually strengthens, two The BER performances of kind of algorithm are all accordingly reduced, but carried BD-MMSE algorithms performance still better than BD-ZF algorithms.By being carried The robustness of BD-ZF algorithms is stronger, gradually strengthens with the correlation of channel, compared with BD-ZF algorithms, proposes BD-MMSE calculations The performance advantage of method has the trend gradually expanded.Under the conditions of Fig. 3 different channels, the BER performance curves of algorithm are carried.
The present invention proposes a kind of BD-MMSE algorithms, i.e., carried out in transmitting terminal using BD algorithms between precoding, elimination user Interference, receiving terminal use MMSE algorithms, further increase the accuracy of signal detection.The present invention considers performance and multiple The compromise of miscellaneous degree, and under the conditions of high SNR, puies forward the performances of BD-MMSE algorithms close to optimal.Therefore, it is many in actual downstream In user's mimo system, carrying BD-MMSE algorithms has certain practical value.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention Any modifications, equivalent substitutions and improvements made within refreshing and principle etc., should be included in the scope of the protection.

Claims (4)

1. a kind of combination treatment method of descending multi-user mimo system, it is characterised in that the descending multi-user mimo system Combination treatment method in transmitting terminal using known channel condition information, the signal of each user is carried out using BD algorithms pre- Coding;In receiving terminal, according to MMSE criterions, the signal that each user receives is examined respectively by solving optimal weights matrix Survey.
2. the combination treatment method of descending multi-user mimo system as claimed in claim 1, it is characterised in that the BD algorithms Signal progress precoding to each user is by HS MSIt is block diagonal matrix HS MSBlock diagonalization, finds and to do between user Disturb the optimal transmission vector M for 0S;WhenWhen, it is Complete Diagonalization, is directly realized with the pseudoinverse of channel matrix.
3. the combination treatment method of descending multi-user mimo system as claimed in claim 1, it is characterised in that accurate according to MMSE Then,Wherein PjFor weight matrix, the mean square error MSE for now receiving signal is expressed as:
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>MSE</mi> <mi>j</mi> </msub> <mo>=</mo> <mi>E</mi> <mo>&amp;lsqb;</mo> <mi>t</mi> <mi>r</mi> <mrow> <mo>(</mo> <mo>(</mo> <mrow> <msub> <mover> <mi>d</mi> <mo>~</mo> </mover> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>d</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mover> <mi>d</mi> <mo>~</mo> </mover> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>d</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>*</mo> </msup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mi>E</mi> <mo>&amp;lsqb;</mo> <mi>t</mi> <mi>r</mi> <mrow> <mo>(</mo> <mo>(</mo> <mrow> <msubsup> <mi>P</mi> <mi>j</mi> <mo>*</mo> </msubsup> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>d</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> <msup> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>P</mi> <mi>j</mi> <mo>*</mo> </msubsup> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>d</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>*</mo> </msup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
Now solve optimal P1The problem of be changed into:
<mrow> <mtable> <mtr> <mtd> <mrow> <munder> <mi>min</mi> <msub> <mi>P</mi> <mi>j</mi> </msub> </munder> <mi>E</mi> <mo>&amp;lsqb;</mo> <mi>t</mi> <mi>r</mi> <mrow> <mo>(</mo> <mo>(</mo> <mrow> <msubsup> <mi>P</mi> <mi>j</mi> <mo>*</mo> </msubsup> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>d</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> <msup> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>P</mi> <mi>j</mi> <mo>*</mo> </msubsup> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>d</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>*</mo> </msup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> <mi>t</mi> <mi>r</mi> <mrow> <mo>(</mo> <mo>(</mo> <mrow> <msub> <mi>M</mi> <mi>J</mi> </msub> <msub> <mi>d</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>M</mi> <mi>J</mi> </msub> <msub> <mi>d</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mi>H</mi> </msup> <mo>)</mo> </mrow> <mo>&amp;le;</mo> <msub> <mi>W</mi> <mi>j</mi> </msub> </mrow> </mtd> </mtr> </mtable> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>K</mi> <mo>;</mo> </mrow>
Wherein WjThe power distributed for base station to user j, optimal PjFor:
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>j</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mo>(</mo> <mrow> <msub> <mi>H</mi> <mi>j</mi> </msub> <msub> <mi>M</mi> <mi>j</mi> </msub> <msub> <mi>d</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>H</mi> <mi>j</mi> </msub> <msub> <mi>M</mi> <mi>j</mi> </msub> <msub> <mi>d</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>*</mo> </msup> <mo>+</mo> <mi>E</mi> <mo>&amp;lsqb;</mo> <msub> <mi>n</mi> <mi>j</mi> </msub> <msubsup> <mi>n</mi> <mi>j</mi> <mo>*</mo> </msubsup> <mo>&amp;rsqb;</mo> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>H</mi> <mi>j</mi> </msub> <msub> <mi>M</mi> <mi>j</mi> </msub> <msub> <mi>d</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <msubsup> <mi>d</mi> <mi>j</mi> <mo>*</mo> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mo>(</mo> <mrow> <msub> <mi>H</mi> <mi>j</mi> </msub> <msub> <mi>M</mi> <mi>j</mi> </msub> <msub> <mi>d</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>H</mi> <mi>j</mi> </msub> <msub> <mi>M</mi> <mi>j</mi> </msub> <msub> <mi>d</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>*</mo> </msup> <mo>+</mo> <msubsup> <mi>&amp;rho;</mi> <mi>j</mi> <mn>2</mn> </msubsup> <mi>I</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> <mrow> <mo>(</mo> <msub> <mi>H</mi> <mi>j</mi> </msub> <msub> <mi>M</mi> <mi>j</mi> </msub> <msub> <mi>d</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <msubsup> <mi>d</mi> <mi>j</mi> <mo>*</mo> </msubsup> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
For j-th of user, now useful signal djEstimation signal be:
<mrow> <msub> <mover> <mi>d</mi> <mo>~</mo> </mover> <mi>j</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msup> <mrow> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>H</mi> <mi>j</mi> </msub> <msub> <mi>M</mi> <mi>j</mi> </msub> <msub> <mi>d</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>H</mi> <mi>j</mi> </msub> <msub> <mi>M</mi> <mi>j</mi> </msub> <msub> <mi>d</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>*</mo> </msup> <mo>+</mo> <msubsup> <mi>&amp;rho;</mi> <mi>j</mi> <mn>2</mn> </msubsup> <mi>I</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>(</mo> <mrow> <msub> <mi>H</mi> <mi>j</mi> </msub> <msub> <mi>M</mi> <mi>j</mi> </msub> <msub> <mi>d</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> <msup> <msub> <mi>d</mi> <mi>j</mi> </msub> <mo>*</mo> </msup> <mo>)</mo> </mrow> <mo>*</mo> </msup> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>.</mo> </mrow>
4. the multi-user MIMO system of multi-user MIMO system described in a kind of any one of utilization claims 1 to 33.
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