KR102230340B1 - Multiple input-output receiver based on gram-schmit qr decomposition and operation method thereof - Google Patents

Abstract

A Gram-Schmidt QR decomposition-based multiple input/output receiver according to an embodiment of the present application is a multiple input/output receiver that generates an intermediate matrix based on a channel matrix during a QR decomposition operation, wherein the column vector of the intermediate matrix Based on a first codec unit that performs an iterative vectoring codec operation for and a rotation direction rotated according to the vectoring codec operation, iteratively performs a rotation codec operation on the initial column vector corresponding to the column vector. It includes a second cordic part.

Description

Gram-Schmidt QR decomposition based multiple input/output receiver and its operation method {MULTIPLE INPUT-OUTPUT RECEIVER BASED ON GRAM-SCHMIT QR DECOMPOSITION AND OPERATION METHOD THEREOF}

The present application relates to a multiple input/output receiver based on Gram-Schmidt QR decomposition and a method of operation thereof.

In wireless communication, a MIMO receiver is essentially used. Here, MIMO (Multiple Input Multiple Output) may mean an antenna system capable of multiple inputs and outputs.

Recently, in order to implement a MIMO receiver in a mobile environment, it is very important to efficiently implement QR decomposition with high complexity. Here, QR decomposition may mean a matrix decomposition representing a real matrix as a product of an orthogonal matrix Q and an upper triangular matrix R.

Such QR decomposition is widely used as a preprocessing process for various types of MIMO detectors such as successive interference cancellation, V-BLAST, K-Best, and sphere decoding. Specifically, QR decomposition includes a Givens rotation method, a Householder transformation method, and a Gram-Schmidt method.

In particular, Gram-Schmidt QR decomposition, despite its low algorithmic complexity, is mobile due to the hardware implementation complexity of the square root and division operations used to find the vector size (norm) and unit vector (a vector of size 1). In the environment, it is not used well compared to Givens rotation or house holder conversion.

On the other hand, if Gram-Schmidt's square root and division operation can be simply implemented, compared to existing QR decomposition hardware with relatively low algorithmic complexity, it is possible to obtain almost the same coded/uncoded bit error rate performance and gain, and low latency area efficient. It is suitable for use in QR decomposition hardware implementation.

In addition, it is possible to show almost the same coded/uncoded bit error rate performance with less hardware complexity than the existing Gram-Schmidt QR decomposition using multiplication and division and Codex-based Givens rotation/Householder QR decomposition. It is suitable for use in disassembly hardware implementation. Such Gram-Schmidt's vector size operation can be obtained through Codec's vectoring mode operation, and the unit vector is obtained by the codeic rotation mode operation of a vector in which only the first element is 1 and all other element values are 0. I can.

The object of the present application is to provide a Gram-Schmidt QR decomposition-based multiple input/output receiver and an operation method that can replace the conventional complex operation of obtaining the standard element of the upper triangular matrix and the orthogonal column vector of the orthogonal matrix with a simple operation It is to do.

A Gram-Schmidt QR decomposition-based multiple input/output receiver according to an embodiment of the present application is a multiple input/output receiver that generates an intermediate matrix based on a channel matrix during a QR decomposition operation, wherein the column vector of the intermediate matrix Based on a first codec unit that performs an iterative vectoring codec operation for and a rotation direction rotated according to the vectoring codec operation, iteratively performs a rotation codec operation on the initial column vector corresponding to the column vector. It includes a second cordic part.

In an embodiment, the first codec unit outputs a first codec matrix through a shifting operation and an addition operation on the column vector, and the size of the first codeic matrix corresponds to the size of a standard element of the upper triangular matrix.

(1) 이고, 여기서, x는 상기 제1 코딕 행렬의 x축 크기이고, y는 상기 제1 코딕 행렬의 y축 크기이며, i는 상기 반복적인 벡터링코딕 동작의 i번째 순번을 나타내고, σ는 벡터링 회전 방향을 나타낸다. In an embodiment, the first codec unit determines, according to the iterative vectoring codec operation, a first codeic calculation equation (1) from a preset rotation equation, and the first codeic calculation equation (1),

(1), where x is the size of the x-axis of the first codec matrix, y is the size of the y-axis of the first codec matrix, i is the i-th order of the repetitive vectoring codec operation, σ Represents the vectoring rotation direction.

In an embodiment, the vectoring rotation direction is determined in one of a clockwise direction and a counterclockwise direction according to a sign of the y-axis size of the first codec matrix of the previous order.

를 누적하여, 상기 반복적인 벡터링코딕 동작의 마지막 벡터링 동작에서 한번에 스케일 팩터를 연산하고, 상기 스케일 팩터는,

이다. In an embodiment, the first cordic part is the constant

By accumulating, calculating a scale factor at once in the last vectoring operation of the iterative vectoring codec operation, and the scale factor is:

to be.

In an embodiment, the second codec unit outputs a second codeic matrix through a shifting operation and an addition operation on the initial column vector, and the second codeic matrix corresponds to an orthogonal column vector of an orthogonal matrix.

In an embodiment, the second codec unit derives a second codeic calculation equation (2) from a rotation equation preset according to the repetitive rotation codec operation, and the second codeic calculation equation (2),

(2)이고,

(2),

Here, x is the size of the x-axis of the second codeic matrix, y is the size of the y-axis of the second codeic matrix, i is the i-th order of the repetitive rotation codeic operation, and σ is the rotation direction of rotation. .

In an embodiment, the rotation direction is determined in one of a clockwise direction and a counterclockwise direction according to a direction in which the second codeic matrix of the previous order is located, based on a line constituting the initial column vector and the rotation angle.

A Gram-Schmidt QR decomposition-based multiple input/output receiver according to another embodiment of the present application is a multiple input/output receiver that generates an intermediate matrix based on a channel matrix during a QR decomposition operation, wherein the column vector of the intermediate matrix And at least one multiplier and at least one based on the standard elements of the upper triangular matrix and the orthogonal column vector of the orthogonal matrix obtained through the codeic unit for shifting and adding the initial column vector corresponding to the column vector, and the codeic unit. And a projection unit that calculates the remaining elements of the upper triangular matrix through an adder of and updates the remaining column vectors of the intermediate matrix.

In an embodiment, the codec unit includes a first codec unit including a plurality of vectoring codec modules sequentially performing an iterative vectoring codec operation in order to obtain the standard element, and to obtain the orthogonal column vector , A second codec unit including a plurality of rotation step modules sequentially performing a repetitive rotation codec operation, and a flip-flop unit that delays rotation direction and sign information obtained through the first codec unit and outputs it to the second codec unit. Includes.

In an embodiment, the number of vectoring codec modules and the number of rotation step modules are the same.

In an embodiment, the second codec unit includes a pair of multiplexers for operating a rotation step module having the highest priority among the plurality of rotation step modules and each multiplexer for operating each of the remaining rotation step modules, and the multiplexer The total number of is greater than the total number of the plurality of rotation step modules.

In an embodiment, a global control unit that generates a first control signal for controlling the codec unit and a second control signal for controlling the projection unit, based on the first control signal, among a vectoring codec mode and a rotation codec mode A codec control unit that determines one codec mode and a projection control unit that controls at least one of at least one multiplier and at least one adder based on the second control signal.

In an embodiment, the codec unit, when the one codec mode is determined as the vectoring codec mode, a first codec unit that performs a repetitive vectoring codec operation, and the one codec mode is determined as the rotation codec mode. In this case, it includes a second codec unit that performs a repetitive rotation codec operation, and at least one conversion unit that operates in any one of the first and second codec units according to an operation clock period.

In an embodiment, the number of the at least one transform module is less than the number of column vectors of the intermediate matrix.

In an embodiment, the projection unit comprises: a first input unit receiving each output information output through the codeic unit; a first calculation unit calculating first calculation information through a plurality of calculators based on the respective output information; A second input unit that receives and transmits the first calculation information, a second calculation unit that calculates second calculation information through a plurality of adders based on the first calculation information received through the second input unit, and the second input unit. And a summing unit for summing the first and second calculation information and outputting the remaining elements of the upper triangular matrix, the remaining column vectors of the intermediate matrix, and some column vectors of the channel matrix.

As a Gram-Schmidt QR decomposition-based multiple input/output receiver according to an embodiment of the present application, a multiple input/output receiver that generates an intermediate matrix based on a channel matrix during a QR decomposition operation, wherein the column vector of the intermediate matrix A codec unit that performs an iterative vectoring codec operation on and performs an iterative rotation codeic operation on an initial column vector corresponding to the column vector, and a standard element of an upper triangular matrix obtained through the codec unit and an orthogonal matrix. And a projection unit that calculates the remaining elements of the upper triangular matrix through at least one multiplier and at least one adder based on the orthogonal column vector, and updates the remaining column vectors of the intermediate matrix.

In an embodiment, the codec unit includes a first codec unit including a plurality of vectoring codec modules sequentially performing the repetitive vectoring codec operation, and a plurality of rotation steps sequentially performing the iterative rotation codeic operation And a second cordic unit including modules and a flip-flop unit for delaying rotation direction and sign information obtained through the first cordic unit and outputting the delayed information to the second cordic unit.

In an embodiment, the number of vectoring codec modules and the number of rotation step modules are the same.

In an embodiment, the second codec unit includes a pair of multiplexers for operating a rotation step module having the highest priority among the plurality of rotation step modules and each multiplexer for operating each of the remaining rotation step modules, and the plurality of The total number of rotation step modules of is less than the total number of multiplexers.

In an embodiment, a global control unit that generates a first control signal for controlling the codec unit and a second control signal for controlling the projection unit, based on the first control signal, among a vectoring codec mode and a rotation codec mode A codec control unit that determines one codec mode and a projection control unit that controls at least one of at least one multiplier and at least one adder based on the second control signal.

In an embodiment, the codec unit, when the one codec mode is determined as the vectoring codec mode, a first codec unit that performs a repetitive vectoring codec operation, and the one codec mode is determined as the rotation codec mode. In this case, a second codec unit that performs a repetitive rotation codec operation and at least one transform unit that converts to one of the first and second codec units and operates based on an operation period of the one codec mode.

In an embodiment, the number of the at least one transform unit is less than the number of column vectors of the intermediate matrix.

In an embodiment, the projection unit comprises: a first input unit receiving each output information output through the codeic unit; a first calculation unit calculating first calculation information through a plurality of calculators based on the respective output information; A second input unit that receives and transmits the first calculation information, a second calculation unit that calculates second calculation information through a plurality of adders based on the first calculation information received through the second input unit, and the second input unit. And a summing unit for summing the first and second calculation information and outputting the remaining elements of the upper triangular matrix, the remaining column vectors of the intermediate matrix, and some column vectors of the channel matrix.

A method of operating a multiple input/output receiver based on Gram-Schmidt QR decomposition according to an embodiment of the present application, wherein a first codec unit performs an iterative vectoring codec operation on a column vector of an intermediate matrix, and a second codec unit includes the And performing an iterative rotation codec operation on the initial column vector corresponding to the column vector based on the rotation direction rotated according to the vectoring codec operation.

In an embodiment, in the performing of the iterative vectoring codec operation, the first codec unit receives complex column vectors, the first codec unit removes imaginary vector vectors from the complex column vectors, and a real number Performing a first vectoring mode for acquiring sub-vectors, performing a second vectoring mode in which the first codec unit obtains the remaining real vector vectors from which half of the real vector is removed, and the first codeic unit And performing a third vectoring mode for obtaining one real part vector.

In an embodiment, the performing of the repetitive rotation codec operation comprises: receiving the initial column vector obtained by multiplying the second codeic unit by a first to third scale factor, and the second codeic unit receiving the third vectoring mode. Performing a first rotation mode for rotating the initial column vector based on a third rotation direction rotated according to, based on a second rotation direction in which the second cordic unit is rotated according to the second vectoring mode, Performing a second rotation mode in which the initial column vector rotated through the first rotation mode is rotated, the second rotational direction in which the second cordic unit is rotated according to the first vectoring mode, Performing a third rotation mode for rotating the initial column vector rotated through the rotation mode, and the second codeic unit outputting complex orthogonal column vectors through the third rotation mode, the complex orthogonal The column vectors include real orthogonal column vectors and imaginary orthogonal column vectors.

In an embodiment, the number of repetitive vectoring codec operations is greater than or equal to the number of repetitive rotation coded operations.

The Gram-Schmidt QR decomposition-based multiple input/output receiver and its operation method according to an embodiment of the present application can replace a conventional complex operation of obtaining a standard element of an upper triangular matrix and an orthogonal column vector of an orthogonal matrix with a simple operation. .

In addition, the Gram-Schmidt QR decomposition-based multiple input/output receiver and its operation method can reduce delay time, area, and energy consumption of hardware that performs computation.

1 is a block diagram of a multiple input/output system based on Gram-Schmidt QR decomposition according to an embodiment of the present application.
2 is a block diagram of the multiple input/output receiver of FIG. 1 according to an embodiment.
3 is a diagram for explaining the operation of the first and second cordic units of FIG. 2.
4A is an operation diagram of a vectoring codec repetitively of the first codec unit of FIG. 2 according to an exemplary embodiment.
4B is an operation diagram of a vectoring codec repetitively of the first codec unit of FIG. 2 according to another embodiment.
5A is a diagram illustrating an operation of repetitive rotation codecs of the second codec unit of FIG. 2 according to an exemplary embodiment.
5B is a diagram illustrating an operation of a rotation codec of the second codec of FIG. 2 repeatedly according to another exemplary embodiment.
6 is an operation process of the multiple input/output receiver of FIG. 2.
7 is a diagram showing in detail the operation of the first and second cordic units of FIG. 2.
8 is an operation process of the first cordic unit of FIG. 2.
9 is an operation process of the second cordic unit of FIG. 2.
10 is a block diagram of the multiple input/output receiver of FIG. 1 according to another embodiment.
11 is an example in which the multiple input/output receiver of FIG. 10 is applied in a semi-pipeline QR decomposition structure.
12 is a block diagram showing in detail each of the 0th to third codex stages of FIG. 11.
13 is a timing diagram of the second projection of FIG. 11.
14 is an example in which the multiple input/output receiver of FIG. 10 is applied in a repetitive QR decomposition structure.
15 is an operation timing diagram of the multiple input/output receiver of FIG. 14.

Specific structural or functional descriptions of the embodiments according to the concept of the present application disclosed in this specification are exemplified only for the purpose of describing the embodiments according to the concept of the present application, and the embodiments according to the concept of the present application are It may be implemented in various forms and is not limited to the embodiments described herein.

Since the embodiments according to the concept of the present application can apply various changes and have various forms, the embodiments will be illustrated in the drawings and described in detail in the present specification. However, this is not intended to limit the embodiments according to the concept of the present application to specific disclosed forms, and includes all changes, equivalents, or substitutes included in the spirit and scope of the present application.

Terms such as first or second may be used to describe various constituent elements, but the constituent elements should not be limited by the terms. The above terms are only for the purpose of distinguishing one component from other components, for example, without departing from the scope of the rights according to the concept of the present application, the first component may be referred to as the second component, and similarly The second component may also be referred to as a first component.

When a component is referred to as being "connected" or "connected" to another component, it is understood that it may be directly connected or connected to the other component, but other components may exist in the middle. It should be. On the other hand, when a component is referred to as being "directly connected" or "directly connected" to another component, it should be understood that there is no other component in the middle. Other expressions describing the relationship between components, such as "between" and "directly between" or "adjacent to" and "directly adjacent to" should be interpreted as well.

The terms used in this specification are only used to describe specific embodiments, and are not intended to limit the present application. Singular expressions include plural expressions unless the context clearly indicates otherwise. In the present specification, terms such as "comprise" or "have" are intended to designate the existence of implemented features, numbers, steps, actions, components, parts, or a combination thereof, but one or more other features or numbers It is to be understood that the possibility of addition or presence of, steps, actions, components, parts, or combinations thereof is not preliminarily excluded.

Unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. Terms as defined in a commonly used dictionary should be interpreted as having a meaning consistent with the meaning in the context of the related technology, and should not be interpreted as an ideal or excessively formal meaning unless explicitly defined in the present specification. Does not.

1 is a block diagram of a multiple input/output system 1000 based on Gram-Schmidt QR decomposition according to an embodiment of the present application.

Referring to FIG. 1, a multiple input/output system 1000 based on Gram-Schmidt QR decomposition may include a multiple input/output receiver 100 and a multiple input/output transmitter 500.

First, the multiple input/output transmitter 500 may transmit a transmission signal vector X to the multiple input/output receiver 100. In this case, the multiple input/output transmitter 500 may include Nt transmission antennas.

Next, the multiple input/output receiver 100 may receive a received signal vector Y from the multiple input/output transmitter 500. In this case, the multiple input/output receiver 100 may include Nt receiving antennas.

Here, the received signal vector (Y) is a value obtained by adding the noise vector (n) to the product between the channel matrix (H) and the transmission signal vector (X), and the channel matrix (H) is between each transmit antenna and each receive antenna pair. It may be a matrix based on the channel gain information of. For example, the (hj,i) element corresponding to the j-th row and the i-th column of the channel matrix H may mean signal gain information of a channel formed between the j-th receiving antenna and the i-th transmitting antenna. In this case, n may be an additional white Gaussian noise vector.

The multiple input/output receiver 100 may generate an intermediate matrix W through a QR decomposition operation in which the channel matrix H is decomposed by the product of the unit matrix Q and the upper triangular matrix R. . In this case, the multiple input/output receiver 100 may restore the transmission signal vector X from the received signal vector Y based on the upper triangular matrix R derived through the QR decomposition operation.

For example, since the channel matrix (H) is the product of the identity matrix (Q) and the upper triangular matrix (R). The upper triangular matrix R may be a product of the channel matrix H and the orthogonal matrix Q ^{H of the identity matrix Q.} Here, the orthogonal matrix Q ^H may be referred to as an Hermitian matrix of the identity matrix Q. In this case, the intermediate matrix W may be a matrix updated according to a QR decomposition operation from the channel matrix H.

Hereinafter, with reference to FIG. 2, a Gram-Schmidt QR decomposition-based multiple input/output receiver 100 according to an embodiment of the present application will be described in more detail.

FIG. 2 is a block diagram of the multiple input/output receiver 100 of FIG. 1 according to an embodiment, and FIG. 3 is a diagram for explaining the operation of the first and second cordic units 110 and 120 of FIG. 2.

1 to 3, the multiple input/output receiver 100 may include a first cordic unit 110 and a second cordic unit 120.

First, the first codec unit 110 may perform an iterative vectoring codec operation on the column vector wi of the intermediate matrix W.

Specifically, the first codec unit 110 may perform a shift operation and an addition operation on the column vector wi of the intermediate matrix W to output the first codec matrix. Here, the size of the X-axis of the first codec matrix may correspond to the size of the standard elements (ri,i) of the upper triangular matrix R. For example, the standard elements (ri,i) of the upper triangular matrix R may be elements (r ₁₁ , r ₂₂ , r ₃₃ , r ₄₄ ) located on the diagonal of the matrix.

That is, the first codec unit 110 may simply implement a conventional square operation and a square root operation for obtaining a standard element of the upper triangular matrix R by shifting and addition operations.

Next, based on the rotation direction (σ) of the column vector (wi) of the intermediate matrix (W) rotated through the first codec unit (110), the second codeic unit (120), the initial of the column vector (wi). An iterative rotation codec operation may be performed on the column vector w0.

Specifically, the second codec unit 120 shifts and adds the initial column vector w0 based on the rotation direction σ rotated according to the repetitive vectoring codec operation through the first codec unit 110. The second codec matrix may be output by performing the operation. Here, the second codec matrix may correspond to an orthogonal column vector qi ^{of the orthogonal matrix Q H.}

That is, the second codec unit 120 may simply implement a conventional division operation for obtaining an orthogonal column vector qi by a shifting operation and an addition operation through the second codec unit 120.

The Gram-Schmidt QR decomposition-based multiple input/output receiver 100 according to an embodiment of the present application uses shifting and addition operations of the first and second codecs 110 and 120 sharing the rotation direction σ. It is possible to obtain a standard element (ri,i) and an orthogonal column vector (qi). Accordingly, the Gram-Schmidt QR decomposition-based multiple input/output receiver 100 obtains a standard element (ri,i) and an orthogonal column vector (qi). It can reduce consumption.

FIG. 4A is a repetitive vectoring codec operation diagram of the first codec unit 110 of FIG. 2 according to an embodiment, and FIG. 4B is an iterative vector of the first codec unit 110 of FIG. 2 according to another embodiment. This is a linkodic operation diagram.

First, referring to FIG. 4A, when the column vector wi of the intermediate matrix W is a vector (x, y), the first codec unit 110 is a vector ( Iterative rotations for x and y) may be sequentially performed. Here, iterative rotations may mean vectoring codec operations. For example, as shown in FIG. 4A, the first codec unit 110 may perform iterative rotations for vectors (x, y) in 1 to 4 order.

In addition, referring to FIG. 4B, when the column vector wi of the intermediate matrix W is a vector (x, y), the first codec unit 110 is preset so that the column vector wi is converged on the X axis. Iterative rotations for vectors (x, y) may be sequentially performed according to the time series rotation angle. For example, the first cordic unit 110 repetitively rotates a vector (x, y) according to a preset time series rotation angle such as 90 degrees, 45 degrees, 26.565 degrees, 14.036 degrees, ... (Iterative Rotations) can be performed sequentially.

The first codec unit 110 according to the embodiment calculates the first codeic calculation equation (4) from the preset rotation equation (1) according to iterative rotations performed according to a preset time series rotation angle. Can be derived.

(1)로서, 일반적인 벡터(x,y)의 회전에 대한 행렬식일 수 있다. 또한, 기설정된 회전 방정식(1)은 탄젠트 치환식(2)로 치환될 수 있다. Specifically, the preset rotation equation (1) is

As (1), it may be a determinant for the rotation of a general vector (x,y). In addition, the predetermined rotation equation (1) may be substituted with the tangent substitution equation (2).

Here, the tangent substitution formula (2) is,

(2)이고, 이때, θ가 90도, 45도, 26.565도, 14.036도, ...인 기설정된 시계열 회전 각도이므로, tan(θ)는 2^k로 치환될 수 있다.

(2), and at this time, since θ is a preset time series rotation angle of 90 degrees, 45 degrees, 26.565 degrees, 14.036 degrees, ..., tan(θ) can be replaced by ^{2 k.}

This tangent substitution equation (2) can be substituted with the following rotation angle equation (3) based on the number of iterative rotations.

Here, the rotation angle equation (3) is,

(3)일 수 있다.

It can be (3).

This rotation angle equation (3) can be replaced with the following first codeic equation (4) in order to apply the rotation direction (σ).

Here, the following first codec formula (4),

(4) 이고,

(4) is,

Here, x is the size of the x-axis of the first codec matrix, y is the size of the y-axis of the first codec matrix, i is the i-th order of the repetitive vectoring codec operation, and σ is the vectoring rotation direction. Can be indicated.

Specifically, the vectoring rotation direction (σ) is either clockwise or counterclockwise according to the sign of the y-axis information (y _{i-1 ) of the first codec matrix (x i-1} ,y _{i-1) of the previous order.} Can be determined by one.

For example, when the y-axis information (y _i-1 ) of the first codec matrix (x _i-1 ,y _i-1 ) of the previous order is a (-) sign, the vectoring rotation direction (σ) is counterclockwise. It may be +1, which is (Counter Clock-Wise). In addition, when the y-axis information (y _i-1 ) of the first codec matrix (x _i-1 ,y _i-1 ) of the previous order is a (+) sign, the vectoring rotation direction (σ) is clockwise (Clock- Wise) may be -1.

를 누적하여, 반복적인 벡터링코딕 동작의 마지막 벡터링 동작에서 스케일 팩터를 한번에 연산할 수 있다. Depending on the embodiment, the first codec unit 110 is a constant in the first codec calculation equation (1).

By accumulating, it is possible to calculate the scale factor at once in the last vectoring operation of the iterative vectoring codec operation.

Here, the scale factor is calculated through the following scale factor calculation equation (5),

(5)일 수 있다. At this time, the scale factor calculation formula (5) is

It can be (5).

5A is a repetitive rotation codec operation diagram of the second codec unit 120 of FIG. 2 according to an embodiment, and FIG. 5B is an iterative rotation codec operation of the second codec unit 120 of FIG. 2 according to another embodiment. It is an operation diagram.

First, referring to FIG. 5A, when the initial column vector w0 is a vector (x, y), the second cordic unit 120 is a line forming a θ angle with the vector (x, y) (hereinafter,'θ). Iterative Rotations on the vectors (x, y) may be sequentially performed so as to converge on a line'). Here, iterative rotations may mean a rotation codec operation. For example, as illustrated in FIG. 5A, the second codec unit 120 may perform iterative rotations for vectors (x, y) in 1 to 4 order.

In addition, referring to FIG. 5B, when the initial column vector w0 is a vector (x, y), the second cordic unit 120 is at a preset time series rotation angle such that the vector (x, y) converges on the θ line. Accordingly, iterative rotations for vectors (x, y) may be sequentially performed. For example, the second cordic unit 120 performs repetitive rotational motions for a vector (x, y) according to a time series rotation angle such as 90 degrees, 45 degrees, 26.565 degrees, 14.036 degrees, ... Rotations) can be performed sequentially.

The second codec unit 120 according to the embodiment calculates the second codeic calculation equation (6) from the preset rotation equation (1) according to iterative rotations performed according to a preset time series rotation angle. Can be derived. Hereinafter, since the second codeic calculation equation (6) is similar to the process of deriving the first codeic calculation equation (4), a detailed description of deriving the second codeic calculation equation (6) will be omitted.

Here, the second codeic calculation equation (6),

(6)이고,

(6),

In this case, x is the size of the x-axis of the second codec matrix, y is the size of the y-axis of the second codec matrix, i is the i-th order of the repetitive rotation codec operation, and σ is the rotation direction of rotation. I can.

Specifically, the rotational rotation direction (σ) of the second codeic calculation equation (6) is clockwise based on the θ line and the direction in which the second codeic matrix (x _i-1 ,y _i-1 ) of the previous sequence is located. And counterclockwise direction.

For example, when the second codeic matrix (x _i-1 ,y _i-1 ) of the previous sequence is located in the clockwise direction (Clock-Wise) with respect to the θ line, the rotation of the second codeic equation (6) The rotation direction σ may be -1, which is a counter clock-wise. Also, based on the θ line, when the second codeic matrix (x _i-1 ,y _i-1 ) of the previous sequence is located in the counterclockwise direction (Counter Clock-Wise), the rotation of the second codeic equation (6) The rotation direction (σ) may be +1, which is a clockwise direction (Clock-Wise).

6 is an operation process of the multiple input/output receiver 100 of FIG. 2.

Referring to FIG. 6, in step S110, the first codec unit 110 may perform an iterative vectoring codec operation on the column vector wi of the intermediate matrix W.

Then, in step S120, the second codec unit 120 may perform an iterative rotation codec operation on the initial column vector w0 based on a rotation direction rotated according to the vectoring codec operation. In this case, the number of repetitive vectoring codec operations may be greater than or equal to the number of repetitive rotation coded operations.

7 is a diagram specifically showing the operation of the first and second cordic units 110 and 120 of FIG. 2, FIG. 8 is an operation process of the first cordic unit 110 of FIG. 2, and FIG. 9 is This is the operation process of the second codec unit 120 of.

First, referring to FIGS. 7 and 8, in step S210, the first codec unit 110 may receive complex column vectors. Here, the complex column vectors are imaginary part vectors {Im(h1i), Im(h2i), Im(h3i), Im(h4i)} and real part vectors {Re(h1i), Re(h2i), Re(h3i). ), Re(h4i)}.

Then, in step S220, the first codec unit 110 removes the imaginary part vectors {Im(h1i), Im(h2i), Im(h3i), Im(h4i)} from the complex column vectors, and A first vectoring mode for obtaining sub-vectors (Re(h1i), Re(h2i), Re(h3i), Re(h4i)) may be performed. Here, the first vectoring mode may be an operation mode of the first codec unit 110 for outputting a codeic matrix including real part vectors by shifting and adding operations on complex column vectors. In this case, the first codec unit 110 may obtain _{a first scale factor K 1 calculated according to the first vectoring mode.}

Then, in step S230, the first codec part 110 removes half from the real part vectors {Re(h1i), Re(h2i), Re(h3i), Re(h4i)}, and the remaining real part vector A second vectoring mode for acquiring fields {Re(h1i), Re(h3i)} may be performed. Here, in the second vectoring mode, the real part vectors {Re(h1i), Re(h2i), Re(h3i), Re(h4i)} are shifted and added, and the remaining real part vectors {Re(h1i) ), Re(h3i)} may be an operation mode of the first codec unit 110 for outputting a codeic matrix. In this case, the first codec unit 110 may obtain _{a second scale factor K 2 calculated according to the second vectoring mode.}

Then, in step S240, the first codec unit 110 is a third vectoring mode in which one real part vector {Re(h1i)} is obtained from the remaining real part vectors {Re(h1i), Re(h3i)}. You can do it. Here, in the third vectoring mode, shifting and addition operations are performed on the remaining real part vectors {Re(h1i), Re(h3i)}, and a codeic matrix including one real part vector {Re(h1i)} is output. It may be an operation mode of the first codec unit 110 to perform the operation. In this case, the first codec unit 110 may obtain _{a third scale factor K 3 calculated according to the third vectoring mode.}

Thereafter, in step S250, the first codec part 110 is based on one real part vector {Re(h1i)} and the first to third scale factors (K ₁ , K ₂ , K ₃ ), and the upper triangular matrix The standard element (r _i,i ) of (R) can be obtained. Specifically, the first codec unit 110 includes one real part vector {Re(h1i)} acquired through the third vectoring mode and first to third scale factors acquired through the first to third vectoring modes ( By multiplying K ₁ , K ₂ , K ₃ ), the standard elements (r _{i, i} ) of the upper triangular matrix R can be calculated. Here, the first to third scale factors K ₁ , K ₂ , and K ₃ are for performing an error correction operation of the standard elements r _{i, i.}

Next, referring to FIGS. 7 and 9, in step S310, the second codec unit 120 is an initial column vector w0 multiplied by _{the first to third scale factors K 1} , K ₂ , and K _{3 in advance.} ) Can be entered.

Then, in step S320, the second cordic unit 120 is a first rotation mode for rotating the initial column vector w0 based _{on the third rotation direction (σ vec, 3) rotated according to the third vectoring mode.} The first rotation output may be obtained through. Here, the first rotation mode may be an operation mode for obtaining a first rotation output including at least two real part orthogonal sequence vectors by shifting and adding operations on the initial column vector w0.

Then, in step S330, the second cordic unit 120 is based on the second rotation direction (σ _{vec, 2} ) rotated according to the second vectoring mode, through a second rotation mode that rotates the first rotation output. A second rotation output can be obtained. Here, the second rotation mode may be an operation mode for obtaining a second rotation output including all of the real part orthogonal sequence vectors by performing a shift operation and an addition operation on at least two real part vectors.

Thereafter, in step S340, the second cordic unit 120 is based on the first rotation direction (σ _{vec, 1} ) rotated according to the first vectoring mode, through a third rotation mode that rotates the second rotation output. 3 Can acquire rotation output. Here, the third rotation mode may be an operation mode for obtaining a third rotation output including complex orthogonal sequence vectors by performing a shifting operation and an addition operation on real orthogonal sequence vectors. In this case, the complex orthogonal column vectors are real orthogonal column vectors {Re(q1i), Re(q2i), Re(q3i), Re(q4i)} and the imaginary orthogonal column vectors {Im(q1i), Im(q2i). ), Im(q3i), Im(q4i)}.

10 is a block diagram of the multiple input/output receiver 100_1 of FIG. 1 according to another embodiment.

Referring to FIG. 10, the multiple input/output receiver 100_1 may include a cordic unit 150 and a projection unit 200.

First, the codec unit 150 sequentially performs an iterative vectoring codec operation on the column vector wi of the intermediate matrix W, and outputs _{the standard elements r i, i of the upper triangular matrix R.} can do. In addition, the codec unit 150 may sequentially perform a rotation codec operation repetitively on the initial column vector w0 based on the rotation direction of the column vector wi rotated according to the repetitive vectoring codec operation. . In this case, the codec unit 150 may output an orthogonal column vector qi ^{of the orthogonal matrix Q H through an iterative rotation codec operation.}

Here, the initial column vector w0 may be a vector corresponding to the column vector wi of the intermediate matrix W. For example, when the column vector wi of the intermediate matrix W is (3, 5), the initial column vector w0 may be (3, 0).

The cordic unit 150 includes the first and second cordic units 110 and 120 described in FIGS. 2 to 5, and the first and second cordic units 110 and 120 described in FIGS. 2 to 5. ) Can perform the same function. Hereinafter, a redundant description of the cordic unit 150 including the first and second cordic units 110 and 120 described in FIGS. 2 to 5 will be omitted.

Next, the projection unit 200 _{responds to the standard element (r i,i} ) and the orthogonal column vector (qi), _{and the remaining elements (r i,j≠} ) located in the same row as the _{standard element (r i,i) i} ) and the remaining column vectors (w _j≠i ) of the intermediate matrix W may be output.

Specifically, the projection unit 200 based on the Hermit matrix (q _i ^H ) of the orthogonal column vector (qi) and the remaining column (h _j≠i ) of the channel matrix (H), the standard elements (r _{i, i) The remaining elements (r i,j≠i} ) located in the same row as) can be obtained. Here, the remaining elements (r _i,j≠i ) may be right elements located in the same row of the standard element (r _{i,i ).} In this case, the projection unit 200 may calculate the Hermitian matrix (q _i ^H ) of the orthogonal column vector (qi) and the remaining column (h _j≠i ) of the channel matrix (H) using a multiplier and an adder.

In addition, the projection unit 200 based on the remaining column (h _j≠i ), the remaining elements (r _i,j≠i ) and the orthogonal column vector (qi) of the channel matrix (H), the intermediate matrix (W) The remaining column vectors (w _j≠i ) of may be updated. In this case, the projection unit 200 may calculate the remaining column (h _j≠i ), the remaining elements (r _i,j≠i ), and the orthogonal column vector qi of the channel matrix H through a multiplier and an adder. .

11 is an example in which the multiple input/output receiver 100_1 of FIG. 10 is applied in a semi-pipe line QR decomposition structure.

Referring to FIG. 11, the multiple input/output receiver 100_1 may include 0th to third codex stages 151 to 154 and 0 to 3 projections 201 to 204.

First, each of the 0th to 3rd codec stages 151 to 154 is a module that performs the same function as the codec unit 150 described in FIG. 10, and each of the 0th to 3rd projections 201 to 204 is shown in FIG. It may be a module that performs the same function as the projection unit 200 described in FIG. 10. In the following, operation of the 0th to 3rd codec stages 151 to 154 overlapping with the codec unit 150 of FIG. 10 and the 0th to 3rd projections 201 overlapping with the projection unit 200 of FIG. 10 ~204) will be omitted.

_{For example, the 0th codec stage 151 outputs a first standard element (r 1,1} ) and a first orthogonal column vector (q1) based on a first column vector (h1) of a 4×4 channel matrix. can do. Here, the first column vector h1 may be the same as the first column vector w1 of the intermediate matrix W.

Then, the 0th projection 201 and the first projection 202 are the first orthogonal column vector (q1), the Hermitt matrix (q ₁ ^H ) of the first orthogonal column vector (q1), and the channel matrix (H). Based on the remaining column vectors (h ₂ , h ₃ , h _{4 ), the remaining elements (r 1,2} , r _1,2 , r _1,4 ) located in the same row as the first standard element (r _1,1) ) Can be obtained.

In this case, the zeroth projection 201 is based on one of the remaining column vectors (h ₂ ) of the channel matrix (H), one of the remaining elements (r _1,2 ), and the first orthogonal column vector (q1), The remaining column vectors w ₂ , w ₃ , and w ₄ of the matrix W may be updated.

_{Then, the first codec stage 152 is based on the second column vector (w 2} ) of the intermediate matrix (W) updated through the 0th projection 201, the second standard element (r ₂ , 2) and A second orthogonal column vector q2 may be output.

At this time, the second projection 201 is the second orthogonal column vector (q2), the Hermitian matrix (q ₂ ^H ) of the second orthogonal column vector (q2), and the third and fourth column vectors ( Based on w ₃ , w _{4 ), the remaining elements (r 2,3} , r _2,4 ) located in the same row as the second standard element (r _2,2 ) are obtained, and the fourth of the intermediate matrix (W) is obtained. The third and fourth column vectors (w ₃ , w ₄ ) may be updated.

_{Then, the second codec stage 153 is based on the third column vector (w 3} ) of the intermediate matrix (W) updated through the second projection (203), the third standard element (r ₃ , 3) and A third orthogonal column vector q3 may be output.

In this case, the third projection 204 is a third orthogonal column vector (q3), a Hermitian matrix (q ₃ ^H ) of the third orthogonal column vector (q3), and a third column vector (w ₄ ) of the intermediate matrix (W) _{Based on, the remaining elements (r 3} , 4) located in the same row as the third standard element (r ₃ , 3) may be obtained, and the fourth column vector (w ₄ ) of the intermediate matrix W may be updated. .

_{Thereafter, the third codex stage 154 is based on the fourth column vector (w 4} ) of the intermediate matrix (W) updated through the third projection 204, the fourth standard element (r ₄ , 4) and the fourth 4 Orthogonal column vectors (q4) can be output.

According to an embodiment, the multiple input/output receiver 100_1 may continuously output an orthogonal column vector qi for each column by making one codextage and at least two projections as a pair.

12 is a block diagram specifically showing each of the 0th to third codec stages 151 to 154 of FIG. 11, and FIG. 13 is a timing diagram of the second projection 120 of FIG. 11.

Referring to FIGS. 12 and 13, each of the 0th to third cordic stages 151 to 154 may include a first cordic portion 110, a second cordic portion 120, and a flip-flop portion 130. .

First, the first codec unit 110 may include a plurality of vectoring step modules that sequentially perform an iterative vectoring _{codec operation in order to obtain a standard element (r i, i ).} Here, the plurality of vectoring step modules (Vec.Step1 to Vec.Step3) may perform a repetitive vectoring codec operation step by step according to the first to third operation periods. In this case, each of the first to third operation periods may have a clock time of 4 units.

Specifically, the first vectoring step modules Vec. Step1 may include at least four modules for simultaneously performing a vectoring codec operation in the first operation period. In addition, the second vectoring step modules Vec. Step2 may include at least two modules for simultaneously performing a vectoring codec operation in the second operation period. In addition, the third vectoring step module (Vec.Step3) may include at least one module for performing a vectoring codec operation in the third operation period.

Next, the second codec unit 120 includes a plurality of rotation step modules (Rot.Step1 to Rot.Step3) that sequentially perform an iterative rotation codec operation in order to obtain an orthogonal column vector qi. I can. Here, the plurality of rotation step modules Rot.Step1 to Rot.Step3 may perform a repetitive rotation codec operation step by step according to the first to third operation sections. In this case, each of the first to third operation periods may have 4 clock cycles.

In addition, since the number of the plurality of rotation step modules (Rot.Step1 to Rot.Step3) and the number of the plurality of vectoring step modules (Vec.Step1 to Vec.Step3) are the same, the number of vectoring codec operations and the rotation are the same. The number of codec operations may be the same. For example, when a plurality of vectoring step modules (Vec.Step1 to Vec.Step3) perform eight vectoring codec operations, the plurality of rotation step modules (Rot.Step1 to Rot.Step3) rotate eight times. You can perform a codec operation.

In an embodiment, the second codec unit 120 may further include a plurality of multiplexers 170,175_1 to 175_6. Specifically, a pair of multiplexers 170 among the plurality of multiplexers 170,175_1 to 175_6 is the first rotation step module (Rot.Step1) having the highest priority among the plurality of rotation step modules (Rot.Step1 to Rot.Step3). ) Can be operated. For example, the pair of multiplexers 170 responds to the rotation direction (σ _Vec.Step3,1 ) and the sign bit (sign_a) output through the third vectoring step module (Vec.Step3), and the first rotation step module It is possible to operate the repetitive rotation codec operation of (Rot.Step1).

In addition, each of the remaining multiplexers 175_1 to 175_6 among the plurality of rotation step modules (Rot.Step1 to Rot.Step3) may operate each of the remaining rotation step modules (Rot.Step2 to Rot.Step3). For example, the remaining multiplexers 175_1 to 175_6 respond to a sign bit output through the first and second vectoring step modules (Vec.Step1, Vec.Step2), and the remaining rotation step modules (Rot.Step2 to). Rot.Step3) repetitive rotation codec operation can be operated.

In an embodiment, as shown in FIG. 13, when the third vectoring step module (Vec.Step3) performs one vectoring codec operation and then performs the remaining 7 vectoring codec operations, the first rotation The step module (Rot.Step1) may perform a rotation codec operation. Accordingly, the delay time of the sign bit output through the third vectoring step module (Vec.Step3) may be reduced.

Next, the flip-flop unit 130 includes a rotation direction σ of the column vector hi rotated through a plurality of vectoring step modules Vec.Step1 to Vec.Step3 and a plurality of vectoring step modules Vec. By delaying the sign bit determined through Step1~Vec.Step3), it can be output to a plurality of rotation step modules (Rot.Step1~Rot.Step3).

14 is an example in which the multiple I/O receiver 100_1 of FIG. 10 is applied in a repetitive QR decomposition structure, and FIG. 15 is an operation timing diagram of the multiple I/O receiver 100_1 of FIG. 14.

14 and 15, the multiple input/output receiver 100_1 may include a cordic unit 150, a projection unit 200, a global control unit 310, a cordic control unit 320, and a projection control unit 330. . Hereinafter, a redundant description of the cordic unit 150 and the projection unit 200 having the same reference numerals described in FIG. 10 will be omitted.

First, the global controller 310 may generate a first control signal for controlling the cordic unit 150 and a second control signal for controlling the projection unit 200.

Next, the codec controller 320 may determine one of the vectoring codec mode and the rotation codeic mode based on the first control signal generated through the global controller 310.

Next, the projection control unit 330 may control at least one of at least one multiplier and at least one adder based on the second control signal generated through the global control unit 310.

Next, the cordic unit 150 may include a first cordic unit 110, a second cordic unit 120, a zeroth input unit 111, and at least one conversion unit 161 to 163.

Specifically, when one codec mode is determined as the vectoring codec mode through the codec control unit 320, the first codec unit 110 may sequentially perform a repetitive vectoring codec operation. In addition, when one codec mode is determined to be a rotation codec mode through the codec control unit 320, the second codec unit 120 may sequentially perform a repetitive rotation codec operation.

In an embodiment, the at least one conversion unit 161 to 163 may convert to any one of the first and second codec units 110 and 120 based on the operation period of one codec mode. At this time, the 0th input unit 111 is shown as a separate configuration for receiving the first to fourth column vectors h1i to h4i of the 4×4 channel matrix H, but according to the embodiment ) May be included in the configuration.

Next, the projection unit 200 may include a first input unit 211, a first calculation unit 210, a second input unit 221, a second calculation unit 220, and a summing unit 230.

Specifically, the first input unit 211 may transmit each output information (out_0 to out_4) output through the cordic unit 150 to the first calculation unit 210 under the control of the projection control unit 330. In this case, the first calculation unit 210 may output the first calculation information calculated through a plurality of multipliers to the summing unit 230 and the second input unit 221 based on each output information (out_0 to out_4). have. Here, the number of the plurality of multipliers may be 16.

Then, the second input unit 221 may transmit the first calculation information output through the first calculation unit 210 to the second calculation unit 220 under the control of the projection control unit 330. In this case, the second calculation unit 220 may output second calculation information calculated through a plurality of adders to the summing unit 230 based on the first calculation information. Here, the number of the plurality of adders may be 16.

Then, the summing unit 230 may sequentially output an orthogonal column vector qi for each column, based on the first and second calculation information during the first to fourth clock periods. In addition, the summing unit 230 is based on the first and second calculation information during the first to fourth clock periods, the remaining elements (r _1,2 , r _{1, 3} , r _{1) of the upper triangular matrix R , 4} , r _{2, 3} , r _{2, 4} , r _{3, 4} ), the remaining column vectors (w2, w3, w4) of the intermediate matrix (W), and some column vectors (h3, h4) of the channel matrix (H) ) Can be printed.

to the next,

100: multiple input/output receiver
110: first cordic part
120: second cordic part
150: Cordic part
200: projection unit

Claims (20)

As a Gram-Schmidt QR decomposition-based multiple input/output receiver that generates an intermediate matrix based on a channel matrix during a QR decomposition operation,
A first codec unit for performing an iterative vectoring codec operation on the column vector of the intermediate matrix; And
A second codec unit that performs an iterative rotation codec operation on an initial column vector corresponding to the column vector based on a vectoring rotation direction rotated according to the vectoring codec operation,
The first codec unit outputs a first codeic matrix through a shifting operation and an addition operation on the column vector,
The size of the first codec matrix corresponds to the size of the standard element of the upper triangular matrix,
The vectoring rotation direction is determined in one of a clockwise direction and a counterclockwise direction according to a sign of a y-axis size of a first codec matrix of a previous order output through the first codec unit. delete The method of claim 1,
The first codec unit, according to the iterative vectoring codec operation, determines a first codec calculation equation (1) from a preset rotation equation,
The first codeic calculation equation (1),

(1) is,
Here, x is the size of the x-axis of the first codec matrix, y is the size of the y-axis of the first codec matrix, i is the i-th order of the repetitive vectoring codec operation, and σ is the vectoring rotation direction. Indicating, multiple input and output receivers. delete The method of claim 3,
The first cordic part, corresponding to a constant

By accumulating, calculating a scale factor at once in the last vectoring operation of the iterative vectoring codec operation,
The scale factor is,

Phosphorus, multiple input/output receiver. The method of claim 1,
The second codec unit outputs a second codec matrix through a shifting operation and an addition operation on the initial column vector,
The second codec matrix corresponds to an orthogonal column vector of an orthogonal matrix. The method of claim 6,
The second codec unit derives a second codeic calculation equation (2) from a rotation equation preset according to the repetitive rotation codec operation,
The second codeic calculation equation (2),

(2),
Here, x is the size of the x-axis of the second codec matrix, y is the size of the y-axis of the second codec matrix, i is the i-th order of the repetitive rotation codec operation, and σ is the rotation direction of rotation. , Multiple input/output receiver. The method of claim 7,
The rotation rotation direction is determined in one of a clockwise direction and a counterclockwise direction based on a line in which the initial column vector converges according to a preset time series rotation angle, and according to a direction in which the second codeic matrix of the previous order is located. I/O receiver. As a Gram-Schmidt QR decomposition-based multiple input/output receiver that generates an intermediate matrix based on a channel matrix during a QR decomposition operation,
A codec unit performing an iterative vectoring codec operation on the column vector of the intermediate matrix and performing an iterative rotation codeic operation on an initial column vector corresponding to the column vector; And
Based on the standard elements of the upper triangular matrix obtained through the codec unit and the orthogonal column vector of the orthogonal matrix, the remaining elements of the upper triangular matrix are calculated through at least one multiplier and at least one adder, and the remaining columns of the intermediate matrix Includes a projection unit for updating vectors,
The codec unit may include: a first codec unit including a plurality of vectoring codec modules sequentially performing the repetitive vectoring codec operation;
A second codec unit including a plurality of rotation step modules sequentially performing the repetitive rotation codec operation; And
A flip-flop unit for delaying rotation direction and sign information obtained through the first codec unit and outputting the delayed rotation direction and sign information to the second codec unit,
The second codec unit may include a pair of multiplexers for operating a rotation step module having a highest priority among the plurality of rotation step modules; And
Including each multiplexer for operating each of the remaining rotation step modules,
A total number of the plurality of rotation step modules is less than the total number of the multiplexers. delete The method of claim 9,
A multiple input/output receiver, wherein the number of the plurality of vectoring codec modules and the number of the plurality of rotation step modules are the same. delete The method of claim 9,
A global control unit that generates a first control signal for controlling the cordic unit and a second control signal for controlling the projection unit;
A codec controller configured to determine one of a vectoring codec mode and a rotation codec mode based on the first control signal; And
Further comprising a projection control unit for controlling at least one of at least one multiplier and at least one adder based on the second control signal. The method of claim 13,
The codec unit may include: a first codec unit for performing a repetitive vectoring codec operation when the one codec mode is determined as the vectoring codec mode;
A second codec unit for performing a repetitive rotation codec operation when the one codec mode is determined as the rotation codec mode; And
And at least one conversion unit converting and operating into any one of the first and second codeic units based on the operation period of the one codec mode. The method of claim 14,
The number of the at least one transform unit is less than the number of column vectors of the intermediate matrix. The method of claim 13,
The projection unit may include: a first input unit receiving each output information output through the codec unit;
A first calculation unit that calculates first calculation information through a plurality of calculators based on the respective output information;
A second input unit for receiving and transmitting the first calculation information;
A second calculation unit that calculates second calculation information through a plurality of adders based on the first calculation information received through the second input unit; And
And a summing unit for summing the first and second calculation information and outputting the remaining elements of the upper triangular matrix, the remaining column vectors of the intermediate matrix, and some column vectors of the channel matrix. As a method of operation of a multiple input/output receiver based on Gram-Schmidt QR decomposition,
Performing, by the first codec unit, a repetitive vectoring codec operation on the column vector of the intermediate matrix; And
Comprising the step of performing an iterative rotation codec operation on an initial column vector corresponding to the column vector based on a rotation direction in which a second codec unit is rotated according to the vectoring codec operation,
The performing of the iterative vectoring codec operation may include: receiving, by the first codec unit, complex column vectors;
Performing a first vectoring mode in which the first codeic unit removes imaginary part vectors from the complex column vectors and obtains real part vectors;
Performing a second vectoring mode in which the first codeic unit obtains remaining real part vectors from which half of the real part vectors are removed; And
And performing a third vectoring mode in which the first codec unit obtains one real part vector,
The performing of the iterative rotation codec operation may include: receiving the initial column vector obtained by multiplying the first to third scale factors by the second codeic unit;
Performing a first rotation mode for rotating the initial column vector based on a third rotation direction in which the second cordic unit is rotated according to the third vectoring mode;
Performing a second rotation mode of rotating the initial column vector rotated through the first rotation mode based on a second rotation direction in which the second cordic unit is rotated according to the second vectoring mode;
Performing a third rotation mode for rotating the initial column vector rotated through the second rotation mode based on a first rotation direction in which the second cordic unit is rotated according to the first vectoring mode; And
The second codec unit further comprises the step of outputting complex orthogonal column vectors through the third rotation mode,
The complex orthogonal column vectors include real orthogonal column vectors and imaginary orthogonal column vectors. delete delete The method of claim 17,
The number of repetitive vectoring codec operations is greater than or equal to the number of repetitive rotation coded operations.

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