KR101456941B1 - Method for User Selection with Low Complexity - Google Patents

Method for User Selection with Low Complexity Download PDF

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KR101456941B1
KR101456941B1 KR1020140011433A KR20140011433A KR101456941B1 KR 101456941 B1 KR101456941 B1 KR 101456941B1 KR 1020140011433 A KR1020140011433 A KR 1020140011433A KR 20140011433 A KR20140011433 A KR 20140011433A KR 101456941 B1 KR101456941 B1 KR 101456941B1
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user
users
projection matrix
matrix
selecting
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KR1020140011433A
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Korean (ko)
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박현철
김기범
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한국과학기술원
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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
    • H04B7/0452—Multi-user MIMO systems
    • 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

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

Abstract

In particular, the present invention proposes a selection criterion having a low complexity in application of a greedy algorithm-based user selection scheme in a downlink MU-MIMO in a downlink multi-user environment. A method for selecting a low complexity multiple input multiple output (MU-MIMO) multiuser environment, comprising: calculating a projection matrix for each user; Selecting an initial user; Selecting a user having the largest Probenosis node among the unselected users; Updating the set of users including the unselected user and the selected user; And performing an update of the projection matrix.

Description

[0001] The present invention relates to a low complexity user selection method,

The present invention relates to a user selection method having low complexity. More particularly, the present invention relates to a method for proposing selection criterion having low complexity in application of a greedy algorithm-based user selection scheme in a downlink MU-MIMO in a downlink multi-user environment.

In general, it is known that a multi input multiple output (MIMO) channel can provide very high transmission efficiency, and in particular, can provide higher transmission efficiency in a multi-user environment.

1 is a multiple-input multiple-output (MU-MIMO) system in a general downward multi-user environment.

As shown in Figure 1,

Figure 112014009858818-pat00001
A base station (BS), and a base station
Figure 112014009858818-pat00002
Lt; / RTI > transmit antennas. And, the user
Figure 112014009858818-pat00003
And has an index < RTI ID = 0.0 >
Figure 112014009858818-pat00004
, And the channels
Figure 112014009858818-pat00005
The
Figure 112014009858818-pat00006
It is assumed that the complex matrix is completely known by the base station (BS).

Figure 112014009858818-pat00007
Of the users, some users who can maximize the sum rate are selected and data is transmitted.
Figure 112014009858818-pat00008
Lt; / RTI > The set of selected users
Figure 112014009858818-pat00009
, A set of unselected users
Figure 112014009858818-pat00010
. At this time,
Figure 112014009858818-pat00011
to be.

When comparing all combinations, as the number of users increases, the number of cases to be compared increases significantly. When selecting up to 4 users out of 20 users,

Figure 112014009858818-pat00012
It is necessary to calculate and compare the sum rate.

Greedy user selection is based on sequential criteria

Figure 112014009858818-pat00013
Select one user to maximize.

Figure 112014009858818-pat00014

At this time,

Figure 112014009858818-pat00015
User selected in the
Figure 112014009858818-pat00016
,
Figure 112014009858818-pat00017
to be.

If you select up to four users out of a total of 20 users who have fewer than all combinations

Figure 112014009858818-pat00018
Calculate and compare the sum rate of the cases.

That is, the overall complexity and performance of the greedy algorithm is determined according to the user selection criteria. Therefore, a user selection criterion with low complexity and high sum rate is required.

In the user selection method based on the Frobenius norm, which is a conventional user selection technique, a user using channel energy is selected and a user having the largest effective channel energy is selected.

Figure 112014009858818-pat00019

Table 1 shows the Provennius-based user selection technique.

Figure 112014009858818-pat00020

Figure 112014009858818-pat00021

Figure 112014009858818-pat00022
The matrix
Figure 112014009858818-pat00023
Selected in repeat
Figure 112014009858818-pat00024
Means a common row space of a user channel,
Figure 112014009858818-pat00025
In repetition
Figure 112014009858818-pat00026
excluding
Figure 112014009858818-pat00027
The user channel common column space
Figure 112014009858818-pat00028
Using
Figure 112014009858818-pat00029
Can be calculated.

Figure 112014009858818-pat00030

Figure 112014009858818-pat00031
Wow
Figure 112014009858818-pat00032
In the form of a connection of
Figure 112014009858818-pat00033
When configured,
Figure 112014009858818-pat00034
, And as the repetition increases
Figure 112014009858818-pat00035
And the actual common row space and
Figure 112014009858818-pat00036
.

Therefore,

Figure 112014009858818-pat00037
The calculation of the matrix reduces the accuracy of the user selection and also reduces the sum rate.

The complexity of the computation can be seen by analyzing with the flop count of known operations.

Table 2 shows the flop counts by the Probeenius method. The actual addition / multiplication / division is calculated by one flop,

Figure 112014009858818-pat00038
.

Figure 112014009858818-pat00039

Figure 112014009858818-pat00040

Figure 112014009858818-pat00041

The O-notation (Big-O notation)

Figure 112014009858818-pat00042
The complexity is determined by calculation,
Figure 112014009858818-pat00043
According to
Figure 112014009858818-pat00044
to be.

Therefore,

Figure 112014009858818-pat00045
There is a problem in that the complexity is greatly increased in a portion where all the valid channels of the already selected users are calculated.

That is, the Provenius method

Figure 112014009858818-pat00046
Matrix calculations do not accurately calculate the row space of selected users, and each candidate
Figure 112014009858818-pat00047
User selected for
Figure 112014009858818-pat00048
The calculation of the effective channel and the column matrix of the users is repeated.

SUMMARY OF THE INVENTION The present invention is directed to a low complexity user selection method that proposes a selection criterion having a low complexity in applying a user selection technique based on a greedy algorithm in a downlink MU-MIMO in a multi-input multiple output (MIMO) .

According to an embodiment of the present invention, in a selection method having a low complexity in a multiple input multiple output (MU-MIMO) of a multiuser environment proposed by the present invention, a step of calculating a projection matrix for each user ; Selecting an initial user; Selecting a user having the largest Probenosis node among the unselected users; Updating the set of users including the unselected user and the selected user; And performing an update of the projection matrix.

According to one aspect, the projection matrix (P m ) calculation for each user is obtained using the following equation,

Figure 112014009858818-pat00049

here,

Figure 112014009858818-pat00050
Is the number of transmission antennas of the base station,
Figure 112014009858818-pat00051
Is a group of unselected users, m is a user candidate, H m is a channel of user candidates
Figure 112014009858818-pat00052
A complex matrix,
Figure 112014009858818-pat00053
The subtraction matrix for
Figure 112014009858818-pat00054
.

According to another aspect, the user selection with the maximum Probenui norm is determined using the following equation,

Figure 112014009858818-pat00055

here,

Figure 112014009858818-pat00056
The
Figure 112014009858818-pat00057
Lt; th > iteration,
Figure 112014009858818-pat00058
The user with the maximum Probenui norm for the user,

The projection matrix

Figure 112014009858818-pat00059
Can be set.

According to another aspect, the updating of the user set uses the following equation,

Figure 112014009858818-pat00060

here,

Figure 112014009858818-pat00061
Is a group of unselected users,
Figure 112014009858818-pat00062
Is a group of selected users,
Figure 112014009858818-pat00063
The
Figure 112014009858818-pat00064
Lt; / RTI > iteration.

According to another aspect, the updating of the projection matrix is performed in a selected

Figure 112014009858818-pat00065
According to the following formula
Figure 112014009858818-pat00066
By doing a matrix update,

Figure 112014009858818-pat00067

here,

Figure 112014009858818-pat00068
The
Figure 112014009858818-pat00069
It is also possible that p = 1 to 3.

According to another aspect, it is possible to repeat the steps as many as the number of users desiring to transmit data at the same time.

According to embodiments of the present invention, more precise user selection can be performed using the approximation of the projection matrix.

In addition, since it has a low computational complexity, as the number of antennas at the transmission end and the total number of users increases, it has a greater performance improvement effect than the conventional one, and at the same time, a high total transmission rate can be obtained.

1 is a multiple-input multiple-output (MU-MIMO) system in a general downward multi-user environment.
2 is a flowchart illustrating a method of selecting a user having a low complexity according to an exemplary embodiment of the present invention.
3 is a graph illustrating the number of flaps for a number of users in accordance with an embodiment of the present invention.
FIG. 4 is a block diagram of a receive antenna according to an embodiment of the present invention.

Figure 112014009858818-pat00070
) ≪ / RTI > conditions.
FIG. 5 is a block diagram of a receiving antenna according to another embodiment of the present invention.
Figure 112014009858818-pat00071
) ≪ / RTI > conditions.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

The present embodiments are directed to a method for proposing a low-complexity selection criterion when a user selection scheme based on a greedy algorithm is applied to a downlink MU-MIMO in a downlink multi-user environment.

2 is a flowchart illustrating a method of selecting a user having a low complexity according to an exemplary embodiment of the present invention.

2, in a multi-input multi-output (MU-MIMO) selection method having a low complexity, a step 100 of calculating a projection matrix (Pm) for each user, , Selecting an initial user (110), and selecting a user having a maximum of the non-selected users (120), and selecting a user group including the selected user and the selected user A step 130 of updating the projection matrix and a step 140 of updating the projection matrix. At this time, the above steps are repeated by the number of users who want to transmit data at the same time.

first,

Figure 112014009858818-pat00072
Satisfy
Figure 112014009858818-pat00073
Combination
Figure 112014009858818-pat00074
in,
Figure 112014009858818-pat00075
Of the users belonging to
Figure 112014009858818-pat00076
, A specific user
Figure 112014009858818-pat00077
When a base station (BD) is applied to a precoding matrix
Figure 112014009858818-pat00078
The following characteristics are established.

Figure 112014009858818-pat00079

At this time,

Figure 112014009858818-pat00080
User
Figure 112014009858818-pat00081
Is an orthogonal projection matrix for a common null space of other user channel matrices.

Using the approximation of the projection matrix

Figure 112014009858818-pat00082
Can be calculated as follows.

Figure 112014009858818-pat00083

Each user's projection matrix

Figure 112014009858818-pat00084
Can be calculated as follows.

Figure 112014009858818-pat00085

At this time,

Figure 112014009858818-pat00086
And a sufficient accuracy can be obtained.

Using this, the conventional Probenus norm calculation method can be accurately calculated as a multiplication between matrices.

The method for reducing the complexity is as follows.

A collection of selected users

Figure 112014009858818-pat00087
Without the Provenius Nominal computation of
Figure 112014009858818-pat00088
The complexity is reduced as follows. ≪ tb >< tb >< tb >

Figure 112014009858818-pat00089
,
Figure 112014009858818-pat00090

At this time,

Figure 112014009858818-pat00091
Selects the least affected (orthogonal) user for the common null space of the users already selected in the iteration,
Figure 112014009858818-pat00092
The same projection matrix
Figure 112014009858818-pat00093
The complexity can be reduced.

In addition, unlike the conventional Provenius nominal matrix,

Figure 112014009858818-pat00094
In the update process, it is possible to improve the accuracy of the projection matrix and to select the correct user by considering the influence of newly added users at every repetition, rather than simply connecting them.

Figure 112014009858818-pat00095
By your channel
Figure 112014009858818-pat00096
The user selection performance is reduced because it does not take into account the influence of the users of the mobile terminal.

Table 3 shows the structure of the user selection method.

Figure 112014009858818-pat00097

The complexity of the calculation can be found in detail through the flop count in Table 4.

Figure 112014009858818-pat00098

Figure 112014009858818-pat00099

The O-

Figure 112014009858818-pat00100
The complexity is determined by the Probeenius norm calculation.

Figure 112014009858818-pat00101

Table 5 is a simulation element and compares the sum rate of the present invention with the conventional Provennus-based user selection.

Figure 112014009858818-pat00102

As described above, the flop count by the Provenius method is expressed by the following equation.

Figure 112014009858818-pat00103

FIG. 3 is a graph comparing a conventional Provenius method and a number of users according to an embodiment of the present invention. At this time,

Figure 112014009858818-pat00104
to be. As shown in FIG. 3, it can be seen that the present invention has a much lower number of flops, and the greater the number of users, the greater the reduction in the flop counts relative to the Provenius noun. Therefore, when the number of users is 20, a calculation amount of about 87% is reduced.

FIG. 4 is a block diagram of a conventional Provennus-Nom method and a receiving antenna according to an embodiment of the present invention.

Figure 112014009858818-pat00105
) Condition of the number of users. At this time, FIG. 4 shows the sum rate (
Figure 112014009858818-pat00106
, Rayleigh channel,
Figure 112014009858818-pat00107
)to be.

5 is a block diagram of a conventional Provennus-Nom method and a receiving antenna according to another embodiment of the present invention.

Figure 112014009858818-pat00108
) ≪ / RTI > conditions. At this time, FIG. 5 shows the sum rate (
Figure 112014009858818-pat00109
, Rayleigh channel,
Figure 112014009858818-pat00110
)to be.

As shown in Figs. 4 and 5,

Figure 112014009858818-pat00111
The performance of the present invention increases, and the performance increase rate is less than 1% with respect to the Provennus norm. Also, by calculating the common null space of the users whose projection matrices are already selected, it is possible to obtain a result closer to the effective channel of each user when applying the real base station (BD).

Also, in terms of complexity, the O-notation

Figure 112014009858818-pat00112
It can be confirmed that the present invention is advantageous.

Therefore, we reduced the complexity due to the inaccuracy and SVD (Singular Value Decomposition) of the conventional Probenui norm and increased the accuracy by using the approximation of the projection matrix.

And, as the number of receive antennas of a user increases, the sum rate that can be obtained with respect to the Probe Beanoid is improved, and numerical evaluation has much lower computational complexity under the same conditions.

In addition, the present invention can be applied to most communication systems using MU-MIMO, and is easy to apply because it maintains the form of the greedy algorithm that is conventionally used. In addition, it can be applied to MIMO-OFDM system after a slight deformation, and the range of application and application is wide.

The apparatus described above may be implemented as a hardware component, a software component, and / or a combination of hardware components and software components. For example, the apparatus and components described in the embodiments may be implemented within a computer system, such as, for example, a processor, a controller, an arithmetic logic unit (ALU), a digital signal processor, a microcomputer, a field programmable array (FPA) A programmable logic unit (PLU), a microprocessor, or any other device capable of executing and responding to instructions. The processing device may execute an operating system (OS) and one or more software applications running on the operating system. The processing device may also access, store, manipulate, process, and generate data in response to execution of the software. For ease of understanding, the processing apparatus may be described as being used singly, but those skilled in the art will recognize that the processing apparatus may have a plurality of processing elements and / As shown in FIG. For example, the processing apparatus may comprise a plurality of processors or one processor and one controller. Other processing configurations are also possible, such as a parallel processor.

The software may include a computer program, code, instructions, or a combination of one or more of the foregoing, and may be configured to configure the processing device to operate as desired or to process it collectively or collectively Device can be commanded. The software and / or data may be in the form of any type of machine, component, physical device, virtual equipment, computer storage media, or device , Or may be permanently or temporarily embodied in a transmitted signal wave. The software may be distributed over a networked computer system and stored or executed in a distributed manner. The software and data may be stored on one or more computer readable recording media.

The method according to an embodiment may be implemented in the form of a program command that can be executed through various computer means and recorded in a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, and the like, alone or in combination. The program instructions to be recorded on the medium may be those specially designed and configured for the embodiments or may be available to those skilled in the art of computer software. Examples of computer-readable media include magnetic media such as hard disks, floppy disks and magnetic tape; optical media such as CD-ROMs and DVDs; magnetic media such as floppy disks; Magneto-optical media, and hardware devices specifically configured to store and execute program instructions such as ROM, RAM, flash memory, and the like. Examples of program instructions include machine language code such as those produced by a compiler, as well as high-level language code that can be executed by a computer using an interpreter or the like. The hardware devices described above may be configured to operate as one or more software modules to perform the operations of the embodiments, and vice versa.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. For example, it is to be understood that the techniques described may be performed in a different order than the described methods, and / or that components of the described systems, structures, devices, circuits, Lt; / RTI > or equivalents, even if it is replaced or replaced.

Therefore, other implementations, other embodiments, and equivalents to the claims are also within the scope of the following claims.

100: step of calculating a projection matrix for each user
110: Step of selecting the initial user
120: Step of selecting a user having the maximum number of Probenui beans among the unselected users
130: Updating a set of users, including unselected users and selected users
140: Performing the update of the projection matrix

Claims (6)

In a multi-input multi-output (MU-MIMO) multi-user environment with low complexity,
Computing a projection matrix for each user;
Selecting an initial user;
Selecting a user having a maximum Frobenius norm among unselected users;
Updating the set of users including the unselected user and the selected user; And
And performing an update of the projection matrix. ≪ Desc / Clms Page number 20 > The method according to claim 1,
The projection matrix P m for each user is calculated using the following equation,
Figure 112014009858818-pat00113

here,
Figure 112014009858818-pat00114
Is the number of transmission antennas of the base station,
Figure 112014009858818-pat00115
Is a group of unselected users, m is a user candidate, H m is a channel of user candidates
Figure 112014009858818-pat00116
A complex matrix,
Figure 112014009858818-pat00117
The subtraction matrix for
Figure 112014009858818-pat00118
And selecting a user with a low complexity. 3. The method of claim 2,
The user selection with the maximum Probenui norm is obtained using the following equation,
Figure 112014009858818-pat00119

here,
Figure 112014009858818-pat00120
The
Figure 112014009858818-pat00121
Lt; th > iteration,
Figure 112014009858818-pat00122
The user with the maximum Probenui norm for the user,
The projection matrix
Figure 112014009858818-pat00123
Is set to a low complexity value. The method according to claim 1,
The updating of the user set uses the following equation,
Figure 112014009858818-pat00124

here,
Figure 112014009858818-pat00125
Is a group of unselected users,
Figure 112014009858818-pat00126
Is a group of selected users,
Figure 112014009858818-pat00127
The
Figure 112014009858818-pat00128
Th < / RTI > iteration. ≪ RTI ID = 0.0 > 31. < / RTI > 3. The method of claim 2,
The update of the projection matrix may be performed
Figure 112014009858818-pat00129
According to the following formula
Figure 112014009858818-pat00130
By doing a matrix update,
Figure 112014009858818-pat00131

here,
Figure 112014009858818-pat00132
The
Figure 112014009858818-pat00133
Th user, and p = 1 to 3. The method of claim 1, The method according to claim 1,
And repeating the steps as many as the number of users desiring to transmit data at the same time.
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR20090023879A (en) * 2007-09-03 2009-03-06 삼성전자주식회사 Apparatus and method for signal processing to eliminate interference in multi-user multiple input multiple output wireless communication system
JP2009303224A (en) 2008-06-13 2009-12-24 Ntt Docomo Inc Apparatus and method for simultaneous transmission user selection
KR20120126572A (en) * 2011-05-12 2012-11-21 한국전자통신연구원 Cognitive radio base station and communication method of the cognitive radio base station in a multi-user multiple-input multiple output cognitive radio network system

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR20090023879A (en) * 2007-09-03 2009-03-06 삼성전자주식회사 Apparatus and method for signal processing to eliminate interference in multi-user multiple input multiple output wireless communication system
JP2009303224A (en) 2008-06-13 2009-12-24 Ntt Docomo Inc Apparatus and method for simultaneous transmission user selection
KR20120126572A (en) * 2011-05-12 2012-11-21 한국전자통신연구원 Cognitive radio base station and communication method of the cognitive radio base station in a multi-user multiple-input multiple output cognitive radio network system

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
논문:IEICE *

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