KR20110003251A - Multiple input multiple output communication system for rotating reference codebook including codedwords of discrete fourier transformation codebook - Google Patents

Abstract

PURPOSE: A multiple input multiple output communication system for a rotating reference codebook including codedwords of a discrete Fourier transformation codebook is provided to calculate a rotating matrix calculated based on a certain codeword among the codewords included in a discrete Fourier transformation codebook. CONSTITUTION: A selection unit(823) selects a previous preference codeword based on vectorized channel information, and a calculation unit(824) calculates a rotating matrix based on the previous preference codeword. A generating unit(825) generates a new codebook by rotating a reference codebook through the rotating matrix. The generating unit uses the rotating matrix to create a new preference codeword by rotating at least one codeword included in the reference codebook.

Description

MULTIPLE INPUT MULTIPLE OUTPUT COMMUNICATION SYSTEM FOR ROTATING REFERENCE CODEBOOK INCLUDING CODEDWORDS OF DISCRETE FOURIER TRANSFORMATION CODEBOOK}

Embodiments of the present invention relate to codebooks used in multiple input / output communication systems.

Recently, various studies have been conducted to provide various multimedia services including voice services in a wireless communication environment and to support high quality and high speed data transmission. In particular, technology for a multi input multi output (MIMO) communication system using a plurality of channels in a spatial domain is rapidly developing.

In a MIMO communication system, base stations and terminals use codebooks to properly cope with the channel environment. The specific space may be quantized into a plurality of codewords, and the plurality of codewords generated by quantizing the space according to a predetermined criterion may be stored in the base station and the terminals. Here, each of the codewords may be a vector or a matrix.

For example, each of the terminals may select one of the matrices or vectors corresponding to the channel information among the matrices or vectors included in the codebook according to the channel formed between the base station and the respective terminals. By receiving the matrix or the vector selected by the terminal by using the channel information can be identified. The selected matrix or vector can then be used by the base station to perform precoding or to transmit via multiple antennas.

According to an embodiment of the present invention, a method of operating a receiver includes: recognizing a previous preferred codeword of the receiver; Calculating a rotation matrix based on any codeword of a previous preferred codeword of the receiver and codewords included in a discrete Fourier transform codebook; And generating a new codebook by rotating a reference codebook using the rotation matrix, or recognizing a new preferred codeword of the receiver by rotating at least one codeword included in the reference codebook using the rotation matrix. Include.

The calculating of the rotation matrix may be calculating the rotation matrix using the following equation.

[Equation]

는 상기 수신기의 이전 선호 코드워드고,

는 상기 이산 푸리에 변환 코드북에 포함된 코드워드들 중 임의의 코드워드이고,

는

와 관련된 유니터리 매트릭스이고,

는

와 관련된 유니터리 매트릭스로서 미리 정의된 것일 수 있고, H는 허미시안을 나타냄.R is the rotation matrix,

Is the previous preferred codeword of the receiver,

Is any codeword among the codewords included in the discrete Fourier transform codebook,

Is

Is the unitary matrix associated with

Is

A unitary matrix associated with may be predefined, where H stands for Hermian.

가 상기 이산 푸리에 변환 코드북에 포함된 코드워드들 중 임의의 코드워드인 경우, 상기

는 하기 수학식에 의해 정의될 수 있다.Previous preferred codeword of the receiver

Is a codeword of any of the codewords included in the discrete Fourier transform codebook,

Can be defined by the following equation.

[Equation]

은

의 n 번째 엘리먼트이고, n은 상기

의 n 번째 행을 나타내고, m은 상기

의 m 번째 열을 나타내고, n_t는 전송 안테나들의 개수를 나타냄.

silver

Is the n th element of, where n is

Represents the nth row of m, where

Where m is the n th column and n _t is the number of transmit antennas.

가 상기 이산 푸리에 변환 코드북의 코드워드들에 속하지 않는 경우, 상기

는 하기 수학식의 매트릭스를 직교화함으로써 생성될 수 있다.Previous preferred codeword of the receiver

Does not belong to codewords of the Discrete Fourier Transform codebook,

Can be generated by orthogonalizing the matrix of the following equation.

[Equation]

은

의 n 번째 엘리먼트이고, n은 상기 수학식의 매트릭스의 n 번째 행을 나타내고, m은 상기 수학식의 매트릭스의 m 번째 열을 나타내고, n_t는 전송 안테나들의 개수를 나타냄.

silver

Where n is the n th element, n represents the n th row of the matrix of equation, m represents the m th column of the matrix of equation, and n _t represents the number of transmit antennas.

를 기초로

를 생성하는 단계를 포함할 수 있다.Computing the rotation matrix may comprise a previous preferred codeword of the receiver using Gram-Schmidt orthogonalization.

Based on

It may include the step of generating.

If the previous preferred codeword of the receiver is any one of the codewords included in the discrete Fourier transform codebook,

The calculating of the rotation matrix may be calculating the rotation matrix in the form of a diagonal matrix.

The method of operation includes receiving information about the new preferred codeword from the receiver; And recognizing the new preferred codeword using the new codebook based on the information about the new preferred codeword, or recognizing the new preferred codeword among the codewords included in the rotation matrix and the reference codebook. The method may further include recognizing the new preferred codeword using a corresponding codeword.

The reference codebook may include codewords of a polar cap codebook that surrounds any reference codeword and codewords of the discrete Fourier transform codebook.

In the method of operating a receiver according to an embodiment of the present invention, when the previous preferred codeword is any one of the codewords of the discrete Fourier transform codebook, the codewords of the discrete Fourier transform codebook included in the reference codebook may be included in the new codebook. Calculating a rotation matrix so that; And generating the new codebook by rotating a reference codebook using the rotation matrix, or generating a new preferred codeword by rotating at least one codeword included in the reference codebook using the rotation matrix. .

The method may include determining a new preferred codeword using the new codebook or determining the new preferred codeword using at least one codeword included in the rotation matrix and the reference codebook; And feeding back information about the new preferred codeword to the transmitter, wherein the information about the new preferred codeword is information about an index of the new preferred codeword in the new codebook or the new code in the reference codebook. Information about an index of a codeword corresponding to the preferred codeword may be included.

According to an embodiment of the present invention, a transmitter includes a recognizer that recognizes a previous preferred codeword of a receiver; A calculation unit for calculating a rotation matrix based on any codeword among previous preferred codewords of the receiver and codewords included in a discrete Fourier transform codebook; And a generation unit for generating a new codebook by rotating a reference codebook using the rotation matrix, or recognizing a new preferred codeword of the receiver by rotating at least one codeword included in the reference codebook using the rotation matrix. Include.

According to an embodiment of the present invention, if the previous preferred codeword is any one of the codewords of the discrete Fourier transform codebook, the receiver may rotate the matrix so that the codewords of the discrete Fourier transform codebook included in the reference codebook may be included in the new codebook. Computing unit for calculating; And a generation unit generating the new codebook by rotating a reference codebook using the rotation matrix, or generating a new preferred codeword by rotating at least one codeword included in the reference codebook using the rotation matrix. .

According to an embodiment of the present invention, a method of operating a receiver includes: vectorizing information related to a previous explicit channel matrix between a transmitter and a receiver to obtain vectorized channel information; Selecting a previous preferred codeword based on the vectorized channel information; Calculating a rotation matrix based on the previous preferred codeword; And generating a new codebook by rotating a reference codebook using the rotation matrix, or generating a new preferred codeword by rotating at least one codeword included in the reference codebook using the rotation matrix.

The reference codebook may be determined based on codewords of a polar cap codebook surrounding the arbitrary reference codeword and codewords of the discrete Fourier transform codebook.

'이고, 여기서 N_t는 상기 송신기의 전송 안테나들의 개수일 수 있다.All elements included in the arbitrary reference codeword are '

', Where N _t may be the number of transmit antennas of the transmitter.

Each dimension of the codewords included in the reference codebook is N _t ² x 1, where N _t may be the number of transmit antennas of the transmitter.

The reference codebook may be determined in consideration of chordal distances between codewords of the polar cap codebook and codewords of the vectorized discrete Fourier transform codebook.

Vectorizing the information associated with the explicit channel matrix may include vectorizing the explicit channel matrix into a vector or processing the explicit channel matrix into a vector to obtain the vectorized channel information. Vectorizing.

The selecting of the previous preferred codeword may be selecting the previous preferred codeword from a plurality of codewords included in the previous codebook or the basic codebook.

The method may further include feeding back information about the new preferred codeword to a transmitter, wherein the information about the new preferred codeword is information about an index of the new preferred codeword or the reference codebook in the new codebook. May include information about an index of a codeword corresponding to the new preferred codeword.

Calculating the rotation matrix based on the arbitrary reference codeword and the previous preferred codeword.

According to an embodiment of the present invention, a method of operating a transmitter includes: recognizing a previous preferred codeword selected by the receiver based on a previous explicit channel matrix between a transmitter and a receiver; Calculating a rotation matrix based on the previous preferred codeword; And generating a new codebook by rotating a reference codebook using the rotation matrix, or generating a new preferred codeword by rotating at least one codeword included in the reference codebook using the rotation matrix.

According to an embodiment of the present invention, a receiver includes a vectorizer for vectorizing information related to a previous explicit channel matrix between a transmitter and a receiver to obtain vectorized channel information; A selection unit for selecting a previous preferred codeword based on the vectorized channel information; A calculator configured to calculate a rotation matrix based on the previous preferred codeword; And a generation unit generating a new codebook by rotating a reference codebook using the rotation matrix, or generating a new preferred codeword by rotating at least one codeword included in the reference codebook using the rotation matrix.

According to an embodiment of the present invention, a transmitter includes a recognizer that recognizes a previous preferred codeword selected by the receiver based on a previous explicit channel matrix between a transmitter and a receiver; A calculator configured to calculate a rotation matrix based on the previous preferred codeword; And a generation unit generating a new codebook by rotating a reference codebook using the rotation matrix, or generating a new preferred codeword by rotating at least one codeword included in the reference codebook using the rotation matrix.

According to an embodiment of the present invention, a method of operating a transmitter includes: recognizing a previous preferred codeword of a receiver; The reference codebook includes codewords of a polar cap codebook and codewords of the discrete Fourier transform codebook surrounding a reference codeword, which is one of the codewords of the discrete Fourier transform codebook, and is defined based on the reference codeword. Accessing a memory in which a product between a matrix and the reference codebook is stored in advance; And generating a new codebook from a product between the reference codebook and a matrix defined based on the reference codeword using the previous preferred codeword, or between the reference codebook and the reference codeword using the previous preferred codeword. Generating a new preferred codeword from the product of.

A method of operating a receiver according to an embodiment of the present invention includes codewords of a polar cap codebook and codewords of the discrete Fourier transform codebook in which a reference codebook surrounds a reference codeword which is one of the codewords of the discrete Fourier transform codebook. Accessing a memory in which a product between the reference codebook and a matrix defined based on the reference codeword is stored in advance; And generating a new codebook from a product between the reference codebook and a matrix defined based on the reference codeword using the previous preferred codeword, or between the reference codebook and the reference codeword using the previous preferred codeword. Generating a new preferred codeword from the product of.

The transmitter and the receiver according to an embodiment of the present invention are codewords included in the previous preferred codeword and discrete Fourier transform codebook so that the codewords of the DFT codebook included in the reference codebook can still be included in the new codebook as elements of the DFT codebook. It is possible to calculate a rotation matrix calculated based on any of the codewords.

According to an embodiment of the present invention, a transmitter and a receiver may select a preferred codeword based on information about a explicit explicit channel matrix, or update a reference codebook with a new codebook to determine the selected preferred codeword. Can be.

1 is a diagram illustrating a closed loop multiple input / output communication system according to an embodiment of the present invention.
2 illustrates a reference codebook including only a polar cap codebook and a new polar cap codebook generated by rotating the reference codebook.
FIG. 3 is a diagram illustrating a reference codebook according to an embodiment of the present invention including codewords included in a Discrete Fourier Transform codebook and codewords of a polar cap codebook.
4 illustrates a reference codebook and a new codebook generated by rotating the reference codebook according to an embodiment of the present invention.
5 is an operation flowchart illustrating a method of operating a base station and a terminal according to an embodiment of the present invention.
6 is a flowchart illustrating a method of operating a receiver and a transmitter for selecting a preferred codeword or recognizing a preferred codeword based on an explicit channel matrix.
7 is a block diagram illustrating a base station and a terminal according to an embodiment of the present invention.
8 is a block diagram illustrating a transmitter and a receiver according to another embodiment of the present invention.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings.

1 is a diagram illustrating a closed loop multiple input / output communication system according to an embodiment of the present invention.

Referring to FIG. 1, a closed loop multiple input / output communication system includes a base station 110 and users 120, 130, and 140. 1 is an example of a multi-user multi-input / output communication system, and the present invention may be applied to a single-user multi-input / output communication system. In addition, the term “closed loop” means that the users 120, 130, and 140 feed back feedback data including channel information to the base station 110, and the base station 110 generates a transmission signal based on the feedback data. Means that.

A plurality of antennas are installed in the base station 110, and one or a plurality of antennas may be installed in each of the users 120, 130, and 140. In addition, channels are formed between the base station 110 and the users 120, 130, and 140, and a signal is transmitted / received through each of the channels.

Base station 110 may transmit one or more data streams to users 120, 130, 140. In this case, the base station 110 may use a spatial division multiplexing access technique or a spatial division multiplexing technique. The base station 110 may generate a precoding matrix based on the codewords included in the codebook, and generate a transmission signal using the generated precoding matrix. Here, each of the codewords may be a matrix or a vector.

More specifically, as will be described again below, users 120, 130, and 140 may use explicit feedback. In this case, when the users 120, 130, and 140 feed back H ^H H, each of the codewords has a form of a matrix, and when feeding back H, each of the codewords is a vector according to the number of receiving antennas. Or in the form of a matrix. However, when each of the users 120, 130, and 140 feeds back the vectorized H ^H H or the vectorized H, each of the codewords has the form of a vector. In addition, when users 120, 130, and 140 use implicit feedback, each of the codewords may be a matrix or a vector according to a transmission rank.

The base station 110 may transmit pilot signals to the users 120, 130, and 140 through downlink channels. Here, the pilot signal is a well-known signal to the base station 110 and the users 120, 130, and 140.

At this time, the terminal corresponding to each of the users (120, 130, 140) receives a well-known signal transmitted from the base station 110, the base station 110 and the users 120, 130, using a pilot signal Estimating a channel formed between the plurality of nodes 140, selecting at least one codeword from a codebook, and feeding back information on the selected at least one codeword to the base station. In this case, the codebook may be designed according to the contents described below, and may be changed according to the state of the channel. In particular, since at least one codeword selected by each of the users 120, 130, 140 is related to the state of the channel, the codebook is in accordance with at least one codeword selected by each of the users 120, 130, 140. can be changed.

Each of the users 120, 130, and 140 estimates a channel formed between the base station 110 and the users 120, 130, and 140 using the pilot signal. Each of the users 120, 130, and 140 selects a codeword of any one of the codewords included in a prestored codebook based on the estimated channel as a preferred codeword. Here, the preference codeword may also be called a preference vector or a preference matrix.

For example, each of users 120, 130, 140 is 2 ^B (B is the number of feedback bits in view of the data rate or signal to interference and noise ratio (SINR) that can be achieved. It is possible to select a preferred codeword among the) codewords. In addition, users 120, 130, 140 using intrinsic feedback can determine their respective preferred transmission rank. Here, the transmission rank corresponds to the number of data streams. For reference, when users 120, 130, 140 use explicit feedback, the transmission rank is determined by the base station 110.

In addition, each of the users 120, 130, and 140 feeds back information on the selected preferred codeword (hereinafter, referred to as channel information) to the base station 110. Here, the channel information used in the present specification may include channel state information, channel quality information, or channel direction information.

The base station 110 receives the channel information of each of the users 120, 130, and 140 to determine the precoding matrix. In addition, the base station 110 may select some or all of the users 120, 130, and 140 using various user selection algorithms such as semi-orthogonal user selection (SUS), greedy user selection (GUS), and the like.

That is, the base station 110 may store the same codebook as the codebook stored in the users 120, 130, and 140 in advance. Then, the base station 110 determines the precoding matrix based on the codewords in the codebook stored in advance using the channel information fed back from the users 120, 130, and 140. At this time, the base station 110 may determine the precoding matrix such that the total data rate is maximum.

The base station 110 also generates a transmission signal by precoding the data streams S ₁ , S _N using the determined precoding matrix. Here, the process of generating the transmission signal by the base station 110 is referred to as 'beam forming'.

In addition, the channel environment between the base station 110 and the users 120, 130, 140 may change over time. When the base station 110 and the users 120, 130, and 140 use a fixed codebook, it may be difficult to adaptively cope with the changing channel environment. However, as will be described in detail below, the base station 110 and the users 120, 130, and 140 according to an embodiment of the present invention may adaptively change the codebook.

In addition, the base station 110 may generate a precoding matrix using the changed new codebook. In particular, the base station 110 may change the old precoding matrix to the new precoding matrix using the changed new codebook.

The multiple input / output communication system includes information corresponding to a time correlation coefficient of a channel or a time correlation coefficient of a channel formed between each of the users 120, 130, and 140 and the base station 110. You can change the codebook according to the statistics. Here, the statistics on the change of the channel may be related to the rate of change of the channel, the amount of change of the channel or the pattern of change of the channel. In addition, since the preferred codeword selected by each of the users 120, 130, and 140 represents a change in channel, the codebook may be changed according to the preferred codeword selected by each of the users 120, 130, and 140. have.

The base station 110 and the terminals may use the basic codebook as a fixed codebook. The size of the basic codebook may vary, such as 4bit, 6bit, 8bit, etc., when the base station and the terminal uses the basic codebook, the terminal selects a preferred codeword from the fixed basic codebook, information about the preferred codeword (eg For example, the index information of the preferred codeword) is fed back to the base station. The base station also extracts the preferred codeword from the basic codebook based on the information about the fed back preferred codeword. Since the size of the basic codebook is limited, the basic codebook includes a limited number of codewords. However, since codewords of the basic codebook quantize a very large space, the basic codebook has a relatively high quantization error.

When the base station and the terminal can adaptively change the codebook, the base station and the terminal can adaptively generate and use a polar cap codebook. The polar cap codebook is generated by quantizing a relatively small space compared to the basic codebook, and thus has a relatively low quantization error.

For example, when there is a previous preferred codeword (channel vector or channel matrix between the base station and the terminal measured at the previous time) by the terminal, the base station and the terminal may configure a polar cap codebook around the previous preferred codeword. have. In this case, since the probability that the channel vector or channel matrix exists in a position adjacent to the codewords of the polar cap codebook in the next time is high, the base station and the terminal can be quantized by using a polar cap codebook that can be adaptively generated / modified. Reduce errors

At this time, the base station and the terminal can obtain the next polar cap codebook by rotating the reference codebook by an angle corresponding to the previous preferred codeword. Here, the reference codebook may include only a polar cap codebook or may further include other codebooks. The reference codebook according to the embodiments of the present invention may further include codewords of a discrete Fourier transform (DFT) codebook.

2 illustrates a reference codebook including only a polar cap codebook and a new polar cap codebook generated by rotating the reference codebook.

는 단말에 의해 선택된 이전 선호 코드워드를 나타낸다. 여기서, 이전 선호 코드워드는 기본 코드북의 코드워드들 중 어느 하나일 수 있다. Referring to Figure 2,

Denotes a previous preferred codeword selected by the terminal. Here, the previous preferred codeword may be any one of the codewords of the basic codebook.

가 결정되면, 이전 선호 코드워드

주변의 새로운 폴라 캡 코드북이 구성되어야 한다. 이 때, 기지국 및 단말은 새로운 폴라 캡 코드북을 구성하기 위하여 레퍼런스 코드북을 이전 선호 코드워드

및 레퍼런스 코드워드

사이 각도만큼 회전한다.Preferred Codeword

Is determined, the previous preferred codeword

A new polar cap codebook around should be constructed. At this time, the base station and the terminal previously used the reference codebook to configure a new polar cap codebook codeword

And reference codewords

Rotate by an angle in between.

를 이전 선호 코드워드

로 회전하는 회전 매트릭스를 R이라고 가정한다. 이러한 경우,

이다. 폴라 캡 코드북의 코드워드들만을 포함하는 레퍼런스 코드북의 코드워드들이

이고, 새로운 폴라 캡 코드북의 코드워드들을

라고 하는 경우, 레퍼런스 코드북과 새로운 폴라 캡 코드북은 하기 수학식 1의 관계를 갖는다.
Where the reference codeword

Previously preferred codeword

Assume that the rotation matrix rotating at In this case,

to be. Codewords in the reference codebook that contain only codewords in the Polar Cap codebook

Codewords from the new Polar Cap codebook

In this case, the reference codebook and the new polar cap codebook have a relationship of Equation 1 below.

[Equation 1]

을 이미 알고 있으므로, 새로운 폴라 캡 코드북을 구성하기 위해서는

로부터 R을 구해야 한다. 이 때, R은 하기 수학식 2와 같이 계산될 수 있다.
Referring to Equation 1, codewords of a reference codebook

As you already know, to configure a new Polar Cap codebook

R must be obtained from In this case, R may be calculated as in Equation 2 below.

[Equation 2]

는

와 관련된 유니터리 매트릭스이고,

는

와 관련된 유니터리 매트릭스이고, H는 허미시안을 나타낸다. In Equation 2,

Is

Is the unitary matrix associated with

Is

Is the unitary matrix associated with H.

및

를 알고 있으므로,

및

를 계산할 수 있으며, 따라서, 회전 매트릭스 R을 계산할 수 있다. 그리고, 기지국 및 단말은 상기 수학식 1을 이용하여 새로운 폴라 캡 코드북을 얻을 수 있다.Base station and terminal

And

Since you know

And

Can be calculated and thus the rotation matrix R can be calculated. The base station and the terminal may obtain a new polar cap codebook using Equation 1.

가 하기 수학식 3과 같다고 가정한다.
Where the reference codeword of the reference codebook

Assume that Equation 3 is as follows.

&Quot; (3) "

는 4 x 4의 아이덴티티 매트릭스로 만들어질 수 있고, 이러한 경우, 회전 매트릭스 R은 하기 수학식 4와 같이 정의된다.
At this time,

Can be made of a 4 x 4 identity matrix, in which case the rotation matrix R is defined as

&Quot; (4) "

The rotation matrix R of Equation 4 may exhibit relatively good performance in spatially uncorrelated channels, but may not be suitable in spatially correlated channels.

Here, the DFT codebook will be described in detail below, but unlike FIG. 2, it is assumed that the reference codebook includes codewords of the DFT codebook. Codewords of the DFT codebook are often chosen as preferred codewords in spatially correlated channels.

가 회전 매트릭스 R을 통하여 회전되는 경우, 새로운 코드북의 원소로서 회전된 코드워드는 하기 수학식 5와 같이 표현된다.
One of the codewords in the DFT codebook

When is rotated through the rotation matrix R, the codeword rotated as an element of the new codebook is expressed as shown in Equation 5 below.

[Equation 5]

는 대각 매트릭스이어야 한다. 즉, 회전된 코드워드는 하기 수학식 6과 같이 표현되어야 회전된 코드워드는 새로운 코드북에서 여전히 DFT 코드북의 원소일 수 있다.
At this point, if the rotated codeword in the new codebook is still an element of the DFT codebook,

Must be a diagonal matrix. That is, the rotated codeword should be expressed as in Equation 6 below, so that the rotated codeword may still be an element of the DFT codebook in the new codebook.

&Quot; (6) "

는 언제나 상기 수학식 6에 표현된 형태의 대각 매트릭스일 수 없으므로, 상기 수학식 4의 회전 매트릭스 R을 DFT 코드북의 코드워드들에 적용하는 것은 부적절할 수 있다. 즉, 상기 수학식 4의 회전 매트릭스 R을 이용하여 DFT 코드북의 코드워드들을 회전하는 경우, 회전된 코드워드들은 새로운 코드북에서 DFT 코드북의 원소들이 아닐 수 있다. 이러한 것은 공간적으로 상관된 채널들에서 선호되는 DFT 코드북을 사용하지 못하게 할 수 있으므로, 효율적이지 못하다.
but,

Since may not always be a diagonal matrix of the form represented by Equation 6, it may be inappropriate to apply the rotation matrix R of Equation 4 to the codewords of the DFT codebook. That is, when the codewords of the DFT codebook are rotated using the rotation matrix R of Equation 4, the rotated codewords may not be elements of the DFT codebook in the new codebook. This may not be able to use the preferred DFT codebook in spatially correlated channels, which is not efficient.

FIG. 3 is a diagram illustrating a reference codebook according to an embodiment of the present invention including codewords included in a Discrete Fourier Transform codebook and codewords of a polar cap codebook.

Referring to FIG. 3, the reference codebook according to an embodiment of the present invention includes the codewords of the DFT codebook preferred in spatially correlated channels as well as the codewords of the polar cap codebook described with reference to FIG. 2. In FIG. 3, x denotes a codeword of a DFT codebook, and it is assumed that the reference codebook of FIG. 3 includes codewords of five DFT codebooks and codewords of eight polar cap codebooks.

가 2^B개의 DFT 매트릭스들을 포함하고, 기지국의 전송 안테나들의 개수가 n_t 개인 경우, DFT 코드북

은 하기 수학식 7과 같이 정의될 수 있다.
DFT codebook

Is 2 ^B DFT matrices and the number of transmit antennas of the base station is n _t , the DFT codebook

May be defined as in Equation 7 below.

[Equation 7]

As described above, the codewords of the DFT codebook have good line-of-site characteristics, so they have good performance in spatially correlated channels. Thus, when the reference codebook includes the codewords of the DFT codebook as shown in FIG. 3, in order for the new codebook to achieve good performance in spatially correlated channels, the codeword of the rotated DFT codebook in the new codebook. Must still be elements of the DFT codebook.

4 illustrates a reference codebook and a new codebook generated by rotating the reference codebook according to an embodiment of the present invention.

로 선택한다. 즉, 레퍼런스 코드워드

는

와 같이 선택된다.Referring to FIG. 4, the reference codebook includes codewords of the DFT codebook and codewords of the polar cap codebook. The base station and the terminal according to an embodiment of the present invention is any codeword of the codewords included in the DFT codebook reference codeword of the reference codebook

To select. That is, a reference codeword

Is

Is selected as follows.

가 하기 수학식 8과 같이 미리 정의되었다고 가정한다.
For convenience of explanation, reference codewords

Assume that is defined in advance as in Equation (8).

[Equation 8]

는 하기 수학식 9와 같이 계산된다.
At this time,

Is calculated as in Equation 9 below.

[Equation 9]

Here, F ⁽⁰⁾ is defined through the equation (7).

는 하기 수학식 9-1과 같이 계산된다.
More generally,

Is calculated as in Equation 9-1.

Equation 9-1

는 단위 벡터이고,

의 n 번째 엘리먼트는 x_n이다. 그리고,

의 n 번째 행, m 번째 열에 있는 (n, m)^th 원소는

이다.here,

Is a unit vector,

The nth element of is x _n . And,

The ^th element of the (n, m) ^th row of the nth row and mth column of

to be.

는 미리 정의될 수 있으므로, 코드북은 처음부터 미리 정의된

을 고려하여 설계될 수 있다.
And,

Can be predefined, so codebooks are predefined

It may be designed in consideration of.

는 DFT 코드북의 코드워드일 수 있고, 아닐 수도 있다. Preferred Codeword

May or may not be a codeword of the DFT codebook.

가 DTF 코드북의 코드워드인 경우, 이전 선호 코드워드

는

로 표현된다. 이 때,

는 하기 수학식 10과 같이 나타낼 수 있다.
Preferred Codeword

Is the codeword of the DTF codebook, the previous preferred codeword

Is

It is expressed as At this time,

Can be expressed as in Equation 10 below.

[Equation 10]

Here, diag (X) is a diagonal matrix containing elements of X as diagonal elements and 0 as remaining elements other than diagonal elements, for example, X = [1, 2, 3, 4] ^T If diag (X) is a diagonal matrix, the diagonal elements of diag (X) are 1, 2, 3, and 4.

가 DTF 코드북의 코드워드인 경우,

는 수학식 10에 의해 유니터리 매트릭스가 된다. 그리고, 회전 매트릭스 R은 하기 수학식 11과 같이 대각 매트릭스의 형태를 갖는다.
Preferred Codeword

Is the codeword of the DTF codebook,

Is a unitary matrix by equation (10). In addition, the rotation matrix R has a form of a diagonal matrix as shown in Equation 11 below.

[Equation 11]

가 DTF 코드북의 코드워드인 경우, 회전 매트릭스 R은 대각 매트릭스의 형태를 가지며,

의 위상에 대한 정보(

)를 포함함을 알 수 있다. 따라서, 이러한 회전 매트릭스 R을 이용하여 레퍼런스 코드북에 포함된 DFT 코드북의 코드워드들을 회전하는 경우, 회전된 코드워드들은 상기 수학식 6에 표현된 것과 같이 DFT 코드북의 원소들로 표현된다. 물론, 레퍼런스 코드북에 포함된 폴라 캡 코드북의 코드워드들도 회전 매트릭스 R을 통하여 회전되며 폴라 캡 코드북의 성질이 그대로 유지된다.Preferred Codeword

Is a codeword of a DTF codebook, the rotation matrix R has the form of a diagonal matrix,

Information about the phase of (

It can be seen that the (). Therefore, when rotating the codewords of the DFT codebook included in the reference codebook using the rotation matrix R, the rotated codewords are represented by the elements of the DFT codebook as shown in Equation 6 above. Of course, the code words of the polar cap codebook included in the reference codebook are also rotated through the rotation matrix R, and the properties of the polar cap codebook are maintained.

가 DTF 코드북의 코드워드가 아닌 경우,

는 상기 수학식 10과 다소 다른 방식으로 계산된다. 즉,

에 그람-슈미트 직교화가 적용된다. x에 그람-슈미트 직교화를 적용하는 것을 Gram_Schmidt(x)라고 가정하는 경우,

는 하기 수학식 12와 같이 표현된다.
Preferred Codeword

Is not a codeword of the DTF codebook,

Is calculated in a somewhat different manner from Equation 10 above. In other words,

Gram-Schmid orthogonalization applies. Supposing Gram-Schmid orthogonalization to x is Gram_Schmidt (x),

Is expressed by Equation 12 below.

[Equation 12]

의 회전 매트릭스

는 하기 수학식 12-1과 같이 나타낼 수 있다.
Gram-Schmid orthogonalization can be implemented as Generally,

Rotation matrix

May be represented as in Equation 12-1.

Equation 12-1

및

각각은 유닛 놈(unit norm)을 갖는 컬럼들을 포함하며,

및

각각의 컬럼들은

및

각각의 컬럼들과 직교한다. 위 첨자(superscript H)는 벡터 혹은 매트릭스의 복소 전치(conjugate transpose)를 나타낸다.

And

Each contains columns with unit norm,

And

Each column is

And

Orthogonal to each column. Superscript H represents the conjugate transpose of a vector or matrix.

를 얻기 위하여

과

를 추출하는 과정은 다음과 같다.

과

중 임의의 하나를 일반적인 매트릭스

를 정의한다. 여기서 x는 유닛 벡터이며, x의 (n, m) 번째((n, m)^th) 엔트리는 하기 수학식 12-2와 같이 주어진다.
For four transmit antennas and transmit rank 1,

To get

and

The process of extracting is as follows.

and

Any one of the common matrix

Define. Where x is the unit vector and (n, m) of x The second ((n, m) ^th ) entry is given by Equation 12-2.

[Equation 12-2]

은 x의 n 번째 엘리먼트이다. 유닛 벡터 x의 엔트리들이 동일한 크기(magnitude)를 갖는다면,

는 유니터리 매트릭스이다. 그렇지 않다면, 유니터리 매트릭스를 구하기 위하여 그람-슈미트 직교화가

에 적용될 수 있다.

는 하기 수학식 12-3과 같이 쓰여질 수 있다.
Where n and m are natural numbers ranging from 1 to n _t . And,

Is the nth element of x. If the entries of the unit vector x have the same magnitude,

Is the unitary matrix. Otherwise, the Gram-Schmid orthogonalization

Can be applied to

May be written as in Equation 12-3.

Equation 12-3

가 고정되어 있고, x=w_b인 경우,

는 하기 수학식 12-4와 같이 쓰여질 수 있다.
The diag (x) operator produces a diagonal matrix, the diagonal entries of which are given by the vector x.

Is fixed and x = w _b ,

May be written as Equation 12-4.

Equation 12-4

의 엔트리들이 일한 크기를 갖는 다면,

의 회전 매트릭스

는 하기 수학식 12-5와 같이 구해진다.
Unit vector

If the entries of have the same size,

Rotation matrix

Is obtained as in Equation 12-5.

Equation 12-5

에 대하여, 그람-슈미트 직교화는

를 얻기 위하여

에 적용된다. 이 때,

는 하기 수학식 12-6과 같이 쓰여질 수 있다.
More common

Regarding Gram-Schmid Orthogonalization

To get

Applies to At this time,

May be written as Equation 12-6.

Equation 12-6

First, the Gram-Schmid orthogonalization is applied as in Equation 12-7 at c ₂ .

[Equation 12-7]

와 같이 적용된다. d₃ 및 d₄는 다음 프로시져에 따라 d₂의 함수로서 표현될 수 있다.After normalization, normalization

Is applied as d ₃ and d ₄ may be expressed as a function of d ₂ according to the following procedure.

는 하기 수학식 12-8과 같이 구해진다.
Rotation matrix

Is obtained as in Equation 12-8.

[Equation 12-8]

Gram-Schmid orthogonalization is described as described above, and more specific ones are related to the well-known principles of linear algebra and are omitted below.

The base station and the terminal calculate the rotation matrix R according to Equations 2 and 9, and rotate the reference codebook using the calculated rotation matrix R.

로 선택함으로써, DFT 코드북에도 잘 적용될 수 있다. 도 5에서 새로운 코드북의 삼각형들은 DFT 코드북의 원소들을 나타낸다.
As described above, the base station and the terminal according to an embodiment of the present invention is any codeword of the codewords included in the DFT codebook reference codeword of the reference codebook

By selecting, it can be well applied to the DFT codebook. In FIG. 5, the triangles of the new codebook represent elements of the DFT codebook.

5 is an operation flowchart illustrating a method of operating a base station and a terminal according to an embodiment of the present invention.

Referring to FIG. 5, the terminal estimates a channel based on a well-known signal and determines a preferred codeword from a basic codebook based on the estimated channel (511).

In addition, the terminal feeds back the information about the preferred codeword determined in step 511 to the base station (512).

The base station determines the preferred codeword determined in step 511 based on the information on the preferred codeword, and then generates a precoding matrix based on the preferred codeword. The base station precodes at least one data stream using the precoding matrix (521).

The base station transmits a transmission signal to the terminal through a plurality of transmission antennas.

)를 기초로 회전 매트릭스를 계산한다(530).In addition, the base station and the terminal is the preferred codeword (previous preferred codeword determined in step 511)

The rotation matrix is calculated based on the equation 530.

가 DFT 코드북의 원소인 경우, 기지국 및 단말은 하기 수학식 13을 이용하여

를 계산한다.
More specifically, previous preferred codeword

Is an element of the DFT codebook, the base station and the terminal using the following equation (13)

Calculate

[Equation 13]

은

의 n 번째 엘리먼트이고, n은 상기

의 n 번째 행을 나타내고, m은 상기

의 m 번째 열을 나타내고, n_t는 전송 안테나들의 개수를 나타낸다.here,

silver

Is the n th element of, where n is

Represents the nth row of m, where

Represents the m-th column of, and n _t represents the number of transmit antennas.

가 DFT 코드북의 원소가 아닌 경우, 기지국 및 단말은 하기 수학식 14의 매트릭스를 직교화함으로써

를 계산한다.
On the other hand, the previous preferred codeword

Is not an element of the DFT codebook, the base station and the terminal by orthogonalizing the matrix of Equation 14

Calculate

[Equation 14]

로 설정한다. 그리고, 기지국 및 단말은 상기 수학식 9를 이용하여

를 계산한다.Also, the base station and the terminal refer to any codeword among the codewords included in the discrete Fourier transform codebook.

. And, the base station and the terminal using the equation (9)

Calculate

및

이 계산되면, 기지국 및 단말은 상기 수학식 2를 이용하여 회전 매트릭스 R을 계산한다.

And

When this is calculated, the base station and the terminal calculates the rotation matrix R using Equation (2).

을 회전 매트릭스 R을 이용하여 회전함으로써, 새로운 코드북

를 생성한다(540). When the rotation matrix R is calculated, the base station and the terminal codewords of the reference codebook as shown in Equation 1 above.

Is rotated using the rotation matrix R, so that the new codebook

Generate 540.

를 참조하여 새로운 선호 코드워드를 결정하고(513), 새로운 선호 코드워드에 관한 정보를 기지국으로 피드백한다(514).In addition, the terminal is a new codebook

A new preferred codeword is determined with reference to 513, and information about the new preferred codeword is fed back to the base station 514.

로부터 새로운 선호 코드워드를 추출하고, 새로운 프리코딩 매트릭스를 생성한다(523).In addition, the base station determines a new codebook based on the information about the new preferred codeword.

A new preferred codeword is extracted from and a new precoding matrix is generated (523).

In addition, the base station generates a new transmission signal by performing precoding using the new precoding matrix (524).

The process of steps 530 to 524 is repeated at least once. That is, the terminal and the base station generate a new codebook based on the previous preferred codeword, the terminal determines the new preferred codeword based on the new codebook, and the base station performs precoding using the new codebook.

If the processes of steps 530 to 524 are repeated a predetermined number of times or a predetermined time has passed, the codebooks used for the base station and the terminal are reset to the basic codebook (550). In this case, the base station and the terminal sequentially update the codebooks used according to the above-described process, and use the updated codebook.

의 코드워드들 중 어느 하나를 새로운 선호 코드워드로 선택할 수 있으며, 그 새로운 선호 코드워드에 관한 정보를 기지국으로 피드백할 수 있다. 이 때, 단말이 반드시 새로운 코드북

를 완전하게(fully) 만들어야 하는 것은 아닐 수 있다. 왜냐 하면, 아래와 같이, 단말은 새로운 선호 코드워드를 선택하는 것과 등가적으로 레퍼런스 코드북

의 코드워드들 중 어느 하나를 선택할 수 있기 때문이다.The terminal is a new codebook as described above

Any one of the codewords of may be selected as the new preferred codeword, and information about the new preferred codeword may be fed back to the base station. At this time, the terminal must be a new codebook

It may not be necessary to make. Because, as shown below, the terminal is equivalent to selecting a new preferred codeword reference codebook

This is because one of the codewords may be selected.

을 완전하게 만든 후, 새로운 코드북

의 코드워드들 중 어느 하나를 새로운 선호 코드워드로 선택할 수 있고, 새로운 코드북

을 완전하게 만들지 않고도 새로운 선호 코드워드를 레퍼런스 코드북

의 코드워드들 중 어느 하나로 표현할 수 있다. 그리고, 단말은 새로운 선호 코드워드에 관한 정보를 기지국으로 피드백한다. 여기서, 그 새로운 선호 코드워드에 관한 정보는 새로운 코드북

에서 새로운 선호 코드워드의 인덱스에 관한 정보이거나, 레퍼런스 코드북

에서 새로운 선호 코드워드에 대응하는 코드워드의 인덱스에 관한 정보일 수 있다. 즉,

가 성립하므로, 새로운 선호 코드워드는 새로운 코드북

에 포함된 코드워드들 중 어느 하나의 인덱스로 표현되거나, 레퍼런스 코드북

에 포함된 코드워드들 중 어느 하나의 인덱스로 표현될 수 있다. 단말이 새로운 선호 코드워드에 관한 정보를 새로운 코드북

에서 생성하는 경우, 또는 레퍼런스 코드북

에서 생성하는 경우 둘 다에 대하여, 기지국은 회전 매트릭스 R을 만들어낼 수 있으므로, 단말로부터 피드백된 새로운 선호 코드워드에 관한 정보를 기초로 그 새로운 선호 코드워드를 파악할 수 있다.That is, the terminal is a new codebook

After creating a new codebook

Select one of the codewords of the new preferred codeword, and the new codebook

New preferred codeword reference codebook without making a complete

It can be represented by any one of the codewords of. The terminal feeds back information about the new preferred codeword to the base station. Here, the information about the new preferred codeword can be found in the new codebook.

Information about the index of the new preferred codeword in the

May be information about an index of a codeword corresponding to a new preferred codeword. In other words,

Is established, the new preferred codeword is the new codebook.

Represented by an index of any one of the codewords included in the

It may be represented by an index of any one of the codewords included in the. New codebook for the terminal to provide information about the new preferred codeword

Generated by or from a reference codebook

For both cases, the base station can generate a rotation matrix R, so that the new preferred codeword can be grasped based on the information about the new preferred codeword fed back from the terminal.

The foregoing descriptions associated with FIGS. 1-5 may also apply well to 'explicit feedback' described below.

6 is a flowchart illustrating a method of operating a receiver and a transmitter for selecting a preferred codeword or recognizing a preferred codeword based on an explicit channel matrix.

Before describing the operation of the receiver and the transmitter with reference to FIG. 6, a downlink case is assumed. In the downlink, the base station acts as a transmitter and each of the terminals acts as a receiver.

In general, each of the terminals calculates an implicit channel matrix using a well-known signal such as a pilot signal transmitted from a base station, and selects a preferred codeword based on the intrinsic channel matrix. Here, the implicit channel matrix refers to the product of the explicit channel matrix and the reception beamforming matrix. For example, each of the terminals performing the zero forcing beamforming does not measure the explicit channel matrix itself, but measures the intrinsic channel matrix which is a product of the explicit beam matrix and the reception beamforming matrix corresponding to the zero forcing beamforming. do. Each of the terminals selects a preferred codeword from a codebook based on an inherent channel matrix, and feeds back information on the selected preferred codeword to the base station.

At this time, the base station knows the explicit channel matrix itself, and can adaptively change the transmission mode with a high degree of freedom. For example, if the base station can know the explicit channel matrix itself, then the base station has a high degree of freedom in single user multiple input / output (SU-MIMO) transmission mode or multi user multiple input / output (MU-MIMO) transmission mode, transmit diversity transmission. One of the modes can be selected.

Accordingly, in order to give the base station a high degree of freedom, each of the terminals should be able to select a preferred codeword based on an explicit channel matrix, and feed back information about the preferred codeword, and the base station also properly transmits the preferred codeword. Be aware of it. For the foregoing, embodiments of the present invention may change the codebook used by each of the terminals and the base station somewhat, and may also change the technique of updating the codebook.

For sharing explicit channel matrices reference  Codebook

The reference codebook used by each of the base station and the terminals for sharing the explicit channel matrix may be determined based on the codewords of the polar cap codebook and the codewords of the DFT codebook. This will be described in detail below.

)
(1) Polar cap codebook (

)

로 정의한다. 즉, 레퍼런스 코드워드 w_b의 모든 원소들은

이다. 여기서, 레퍼런스 코드워드 w_b를 둘러싸고 있는 여러 벡터들 중 미리 설정된 개수의 벡터들이 폴라 코드북(

)의 코드워드들로 선택된다. 특히, 폴라 캡 코드북(

)의 코드워드들 사이의 최소 거리가 최대화될 수 있도록 미리 설정된 개수의 벡터들이 선택될 수 있다.
N _t ² if the number of transmit antennas of the transmitter (base station in the downlink) is N _t the reference codeword w _b with dimension x 1

. That is, all elements of the reference codeword w _b

to be. Here, a preset number of vectors among the various vectors surrounding the reference codeword w _b is a polar codebook (

) Are selected. Specifically, Polar Cap Codebook (

A predetermined number of vectors may be selected so that the minimum distance between the codewords of λ may be maximized.

))
(2) DFT-like codebook (DFT-like codebook)

))

)은 상술한 DFT 코드북의 코드워드들을 기초로 정해질 수 있다. N_t = 4 인 경우, DFT-like 코드북(

)을 생성하기 위하여 DFT 코드북의 코드워드들 중 어느 하나의 트랜스포즈(transpose)인

의 형태와 동일한 형태를 갖는 여러 벡터들이 하기 수학식 15와 같이 정의될 수 있다.
DFT pseudo-codebook (

) May be determined based on the codewords of the above-described DFT codebook. If N _t = 4, then the DFT-like codebook (

Transpose one of the codewords of the DFT codebook to

Several vectors having the same shape as may be defined as in Equation 15 below.

[Equation 15]

는 미리 정의된 값이다.
here,

Is a predefined value.

After the vectors of the DFT codebook described in Equation 15 are defined, each of the vectors and the Hermisian of each of the vectors are multiplied with each other as shown in Equation 16 below.

[Equation 16]

는 벡터화된다. 즉, 상기 매트릭스의 모든 컬럼 벡터들은 하기 수학식 17과 같이 하나의 벡터로 통합된다.
At this time,

Is vectorized. That is, all column vectors of the matrix are integrated into one vector as shown in Equation 17 below.

[Equation 17]

Here, vec (X) is an operation of integrating all the column vectors of the matrix X into one vector.

)은 상기 수학식 17에 기재된 16x1의 벡터들의 집합으로 정의된다.
In this case, the DFT pseudo codebook (

) Is defined as the set of 16x1 vectors described in Equation 17 above.

) 또는 DFT 유사 코드북(

) 중 적어도 하나에 기반하는 레퍼런스 코드북
(3) Polar cap codebook (

) Or DFT pseudocodebook (

Reference codebook based on at least one of

) 및 DFT 유사 코드북(

)이 독립적으로 사용될 수 있다. 뿐만 아니라, 레퍼런스 코드북은 폴라 캡 코드북(

)과 DFT 유사 코드북(

)이 통합된 것일 수 있다. 특히, 레퍼런스 코드북은 폴라 캡 코드북(

)의 코드워드들 및 DFT 유사 코드북(

)(벡터화된 DFT 코드북의 코드워드들) 사이의 코달 거리(chordal distance)들을 고려하여 결정될 수 있다. 예를 들어, 레퍼런스 코드북은 상기 코달 거리들이 최대가 되도록 결정될 수 있다.
As a reference codebook, polar cap codebook (

) And DFT pseudocodebook (

) Can be used independently. In addition, the reference codebook is a polar cap codebook (

) And DFT pseudocodebook (

) May be integrated. In particular, the reference codebook is a polar cap codebook (

Codewords and DFT-like codebook (

) May be determined in consideration of the chordal distances between the (word codes of the vectorized DFT codebook). For example, a reference codebook may be determined such that the codal distances are maximum.

- reference  Codebook based codebook update  Method and Updated  How to use the codebook

), DFT 유사 코드북(

) 또는 폴라 캡 코드북(

) 및 DFT 유사 코드북(

)의 통합 중 적어도 하나를 포함할 수 있다. 이러한 레퍼런스 코드북(C)은 수신기 및 송신기 사이의 명시적 채널 매트릭스에 따라 업데이트된다.
The reference codebook C is stored in advance in the receiver and the transmitter. At this time, as described above, the reference codebook C is a polar cap codebook (

), DFT pseudocodebook (

) Or Polar Cap Codebook (

) And DFT pseudocodebook (

) May include at least one of. This reference codebook C is updated according to an explicit channel matrix between the receiver and the transmitter.

Referring to FIG. 6, a receiver (terminal in downlink) calculates an explicit channel matrix H, rather than an implicit channel matrix, using a well-known signal transmitted from a transmitter (611). In this case, the receiver may select a preferred codeword based on information generated by processing H or H (eg, H ^H H).

In addition, the receiver vectorizes the calculated H or H ^H H to obtain vectorized channel information (612). That is, H or H ^H H may be vectorized to vec (H) or vec (H ^H H) which is vectorized channel information. In addition, the vectorized channel information may be U _i vec (H) or U _i vec (H ^H H). Where U _i is the i th element of the set of unitary matrices. In the following, it is assumed that the vectorized channel information generated by the receiver is vec (H ^H H). In particular, the dimensions of the vec (H) according to the number of reception antennas of the receiver is varied, while, since the dimension of the vec (H ^H H) is fixed may be more efficient to use a ^(H H H) vec.

를 선택한다(613). 그리고, 수신기는 이전 선호 매트릭스

에 관한 정보(인덱스 등)를 송신기로 피드백한다(614). 송신기는 이전 선호 매트릭스

에 관한 정보를 기초로 적절히 프리코딩 매트릭스를 생성한 이후에, 적어도 하나의 데이터 스트림을 프리코딩 매트릭스를 이용하여 프리코딩함으로써, 전송 신호를 생성한다(622).If the previous explicit channel matrix between the transmitter and receiver is H, and the vectorized channel information based on the previous explicit channel matrix is vec (H ^H H), then the receiver uses the previous codebook or the currently applied codebook to make the previous preference. matrix

Select (613). And, the receiver is the previous preference matrix

Information about the index (index, etc.) is fed back to the transmitter (614). Transmitter Preferred Matrix

After appropriately generating a precoding matrix based on the information about, the transmission signal is generated by precoding at least one data stream using the precoding matrix (622).

를 기초로 업데이트되고, 수신기 및 송신기는 레퍼런스 코드북을 업데이트하기 위하여 회전 매트릭스를 계산한다(630).At this point, the reference codebook is the previous preference matrix.

And the receiver and transmitter compute a rotation matrix to update the reference codebook (630).

를 정의한다. 여기서,

의 n 번째 행, m 번째 열에 있는 (n, m)^th 원소는

이고,

은 X의 n 번째 원소이다. X의 원소들이 모두 동일한 크기(magnitude)를 갖는다면,

는 유니터리 매트릭스이다. 그렇지 않다면,

에 그람-슈미트 직교화가 적용될 수 있다.First, the matrix based on the unit vector X

Define. here,

The ^th element of the (n, m) ^th row of the nth row and mth column of

ego,

Is the nth element of X. If the elements of X all have the same magnitude,

Is the unitary matrix. otherwise,

Eg-Schmid orthogonalization may be applied.

는 하기 수학식 18과 같이 표현될 수 있다.
For example, if x is a unit vector of 4x1 dimension,

May be expressed as in Equation 18 below.

Equation 18

및 레퍼런스 코드워드 w_b를 기초로 새로운 코드북으로 업데이트된다(640). 이 때, 새로운 코드북을 생성하기 위하여 레퍼런스 코드북(C)을 회전하는 '회전 매트릭스

'는 하기 수학식 19와 같이 이전 선호 매트릭스

및 레퍼런스 코드워드 w_b(여기서, w_b는 상술한 바와 같이

임)를 기초로 계산된다. 그리고, 회전 매트릭스

및 레퍼런스 코드북(C)을 곱함으로써, 새로운 코드북이 생성된다.
Reference codebook (C) is the previous preference matrix

And a new codebook based on the reference codeword w _b (640). At this time, the rotation matrix that rotates the reference codebook (C) to generate a new codebook.

'Is the previous preference matrix as shown in Equation 19

And a reference codeword w _b , where w _b is as described above.

Is calculated on the basis of And rotation matrix

And by multiplying the reference codebook (C), a new codebook is generated.

[Equation 19]

의 n 번째 행, m 번째 열에 있는 (n, m)^th 원소는

이고,

은

의 n 번째 원소이다. 그리고,

의 n 번째 행, m 번째 열에 있는 (n, m)^th 원소는

이고, w_n은 w_b의 n 번째 원소이다. 여기서,

는 미리 정의될 수 있으므로, 코드북에 미리 곱해질 수 있다.
here,

The ^th element of the (n, m) ^th row of the nth row and mth column of

ego,

silver

Is the nth element of. And,

The ^th element of the (n, m) ^th row of the nth row and mth column of

And w _n is the n th element of w _b . here,

Since can be predefined, the codebook can be premultiplied.

가 계산된 이후에, 새로운 코드북이 생성되면, 수신기 및 송신기는 생성된 새로운 코드북을 사용한다. 즉, 수신기는 명시적 채널 매트릭스를 다시 측정한 이후에, 새로운 코드북을 이용하여 새로운 선호 코드워드를 선택한다(651). 그리고, 수신기는 새로운 코드북 내에서 새로운 선호 코드워드의 인덱스에 관한 정보를 포함하는 새로운 선호 코드워드에 관한 정보를 송신기(652)로 피드백한다. 이 때, 송신기는 새로운 선호 코드워드에 관한 정보를 기초로 프리코딩 매트릭스를 생성하고, 프리코딩을 수행한다(661). 그리고, 프리코딩이 수행됨으로써 생성된 전송 신호는 수신기로 전달된다(662).Rotation matrix through Equation 19

After is calculated, if a new codebook is generated, the receiver and transmitter use the generated new codebook. That is, after the receiver measures the explicit channel matrix again, the receiver selects a new preferred codeword using the new codebook (651). The receiver then feeds back information to the transmitter 652 about the new preferred codeword, including information about the index of the new preferred codeword in the new codebook. At this time, the transmitter generates a precoding matrix based on the information about the new preferred codeword and performs precoding (661). In operation 662, the transmission signal generated by the precoding is transmitted to the receiver.

The above-described process is repeated for a preset number of times or time, and the codebook used by the transmitter and the receiver is reset (670). In other words, the transmitter and the receiver repeat the above-described process again using the basic codebook that was originally used.

As described with reference to FIG. 5, the terminal may select one of the codewords of the new codebook as a new preferred codeword, and may feed back information about the new preferred codeword to the base station. At this time, the terminal may not necessarily make a new codebook completely. This is because the terminal may select any one of the codewords of the reference codebook C equivalent to selecting a new preferred codeword.

을 만들어낼 수 있으므로, 단말로부터 피드백된 새로운 선호 코드워드에 관한 정보를 기초로 그 새로운 선호 코드워드를 파악할 수 있다.
That is, after the terminal completes the new codebook, one of the codewords of the new codebook may select one of the new preferred codewords, and the new preferred codeword without making the new codebook completely. It can be expressed as either. The terminal feeds back information about the new preferred codeword to the base station. The information about the new preferred codeword may be information about an index of a new preferred codeword in a new codebook or information about an index of a codeword corresponding to a new preferred codeword in a reference codebook C. That is, the new preferred codeword may be represented by the index of any one of the codewords included in the new codebook, or the index of any one of the codewords included in the reference codebook C. For both cases where the terminal generates information about a new preferred codeword in a new codebook, or when generating in reference codebook C, the base station determines the rotation matrix.

Since it is possible to generate the new preferred codeword based on the information about the new preferred codeword fed back from the terminal.

를 생성한 후, 그 회전 매트릭스 R 또는 회전 매트릭스

를 이용하여 새로운 코드북을 생성하거나 새로운 선호 코드워드를 생성하는 케이스에 대하여 설명하였다. 이러한 케이스에서, 수신기 및 송신기가 미리 저장된 레퍼런스 코드북

또는 레퍼런스 코드북 C를 회전 매트릭스를 이용하여 회전함으로써 새로운 코드북을 생성하거나 새로운 선호 코드워드를 생성한다.5 and 6, the receiver and transmitter are rotated matrix R or rotated matrix

After generating, its rotation matrix R or rotation matrix

The case of generating a new codebook or generating a new preferred codeword using the above has been described. In this case, the reference codebook pre-stored the receiver and transmitter

Alternatively, the reference codebook C is rotated using the rotation matrix to generate a new codebook or generate a new preferred codeword.

However, according to various embodiments of the present disclosure, not only the reference codebook but also the product between the reference codebook and the matrix defined based on the reference codeword may be stored in the memory of the receiver and the transmitter in advance. In this case, the receiver and transmitter can generate a new codebook or generate a new preferred codeword with less complexity.

에 대하여, 레퍼런스 코드북 레퍼런스 코드북을

로 나타낸다고 가정한다. 그리고, 이전 선호 코드워드를

로 나타낸다고 가정한다. 이 때, 새로운 코드북

은 상술한 수학식 1과 같이 회전 매트릭스 R과

의 내적인

로 표현될 수 있으며, 회전 매트릭스 R은 상술한 수학식 2와 같이

로 표현될 수 있다. 따라서, 새로운 코드북

=

로 표현될 수 있다. 이 때, 레퍼런스 코드워드

를 기초로 정의되는 매트릭스인

와 레퍼런스 코드북

는 고정되어 있으므로, 새로운 코드북

은

만의 함수로 간주될 수 있다. 송신기 및 수신기는 레퍼런스 코드워드

를 기초로 정의되는 매트릭스

와 레퍼런스 코드북

사이의 곱(product)인

를 미리 메모리에 저장해둘 수 있으며, 변화하는 이전 선호 코드워드

만을 공유함으로써 적응적으로 새로운 코드북

을 만들어낼 수 있다.For example, given a reference codeword

About the Reference Codebook Reference Codebook

Assume that And the previous preferred codeword

Assume that At this time, the new codebook

Is the rotation matrix R and

Internal

The rotation matrix R may be represented by Equation 2

It can be expressed as. Thus, the new codebook

=

It can be expressed as. At this time, the reference codeword

Is a matrix defined based on

And reference codebook

Is fixed, so the new codebook

silver

Can be regarded as a function of Transmitter and Receiver Reference Codewords

Matrix defined on the basis of

And reference codebook

Is the product of

Can be stored in memory ahead of time, changing the previous preferred codeword

Adaptive new codebook by sharing only

Can produce

를 완전히(fully) 만들어 내는 케이스를 고려한다. 수신기는 이전 선호 코드워드

의 인덱스에 관한 정보를 송신기로 피드백함으로써, 송신기 및 수신기는 이전 선호 코드워드

를 공유한다. 송신기 및 수신기 각각의 메모리에는 레퍼런스 코드워드

를 기초로 정의되는 매트릭스

와 레퍼런스 코드북

사이의 곱(product)인

가 미리 저장될 수 있다. 송신기 및 수신기 각각은 이전 선호 코드워드

를 기초로

를 계산한 후, 그

과

를 기초로 동일한 새로운 코드북

를 만들어낼 수 있다. 그리고 나서, 수신기는 새로운 코드북

으로부터 새로운 선호 코드워드를 선택하고, 그 새로운 선호 코드워드에 관한 정보를 송신기로 피드백한다. 송신기 수신기로부터 피드백된 정보를 기초로 새로운 코드북

으로부터 새로운 선호 코드워드를 파악할 수 있다.

가 미리 메모리에 저장되어 있으므로, 수신기 및 송신기는 새로운 코드북

을 생성하기 위하여

와

의 내적을 계산할 필요가 없다. 따라서,

를 미리 메모리에 저장함으로써 새로운 코드북

을 생성하는 데에 필요한 계산량이 줄어들 수 있다.More specifically, for example, the transmitter and the receiver are new codebooks

Consider a case that makes it fully. Receiver prefers previous codeword

By feeding back information about the index of the transmitter to the transmitter, the transmitter and receiver determine the previous preferred codeword.

Share it. Each code in the transmitter and receiver contains a reference codeword

Matrix defined on the basis of

And reference codebook

Is the product of

Can be stored in advance. Each of the transmitter and receiver is the previous preferred codeword

Based on

After calculating

and

Same new codebook based on

Can produce Then, the receiver sends a new codebook

Selects a new preferred codeword from and feeds back information about the new preferred codeword to the transmitter. New codebook based on information fed back from transmitter receiver

From the new preferred codeword can be identified.

Is stored in memory in advance, so the receiver and transmitter

To produce

Wow

There is no need to calculate the dot product of. therefore,

Codebook by storing the code in memory in advance

The amount of computation required to generate the data can be reduced.

를 완전히(fully) 만들어 내지 않고, 새로운 선호 코드워드에 관한 정보를 송/수신하는 케이스를 고려한다. . 이 케이스에서도 마찬가지로, 수신기는 이전 선호 코드워드

의 인덱스에 관한 정보를 송신기로 피드백함으로써, 송신기 및 수신기는 이전 선호 코드워드

를 공유한다. 송신기 및 수신기 각각의 메모리에는 레퍼런스 코드워드

를 기초로 정의되는 매트릭스

와 레퍼런스 코드북

사이의 곱(product)인

가 미리 저장될 수 있다.

는 복수의 코드워드들을 포함하며, 수신기는

에 포함되는 복수의 코드워드들 중 어느 하나를 새로운 선호 코드워드에 대응하는 코드워드로 선택한다. 실질적인 새로운 선호 코드워드는

와

에 포함되는 복수의 코드워드들 선택된 코드워드의 내적으로 정의될 수 있다. 수신기는

에 포함되는 복수의 코드워드들 선택된 코드워드에 관한 정보(예를 들어, 선택된 코드워드의 인덱스에 관한 정보)를 새로운 선호 코드워드에 관한 정보로서 송신기로 피드백할 수 있고, 송신기는 수신기로부터 피드백된 정보를 기초로

에 포함되는 복수의 코드워드들 선택된 코드워드를 추출할 수 있다. 그리고, 송신기는

와 그 선택된 코드워드의 내적을 새로운 선호 코드워드로 파악할 수 있다.In another specific example, a transmitter and a receiver may use a new codebook

Consider a case of sending / receiving information about a new preferred codeword without making fully. . In this case as well, the receiver used the previous preferred codeword

By feeding back information about the index of the transmitter to the transmitter, the transmitter and receiver determine the previous preferred codeword.

Share it. Each code in the transmitter and receiver contains a reference codeword

Matrix defined on the basis of

And reference codebook

Is the product of

Can be stored in advance.

Includes a plurality of codewords, the receiver being

Any one of a plurality of codewords included in is selected as a codeword corresponding to the new preferred codeword. The actual new preferred codeword is

Wow

A plurality of codewords included in may be defined internally of the selected codeword. Receiver

A plurality of codewords included in may feed back information about the selected codeword (eg, information about the index of the selected codeword) to the transmitter as information about the new preferred codeword, the transmitter being fed back from the receiver. Based on information

A plurality of codewords included in the selected codeword may be extracted. And the transmitter

The inner product of and the selected codeword can be identified as a new preferred codeword.

를 실시간으로 계산하지 않고도 레퍼런스 코드워드 w_b에 의해 정의되는

와 레퍼런스 코드북 C의 내적을 미리 메모리에 저장함으로써, 이전 선호 코드워드

에 대응하는 새로운 코드북을 만들어내거나, 새로운 선호 코드워드를 만들어낼 수 있다.
The above discussion can be applied even when explicit feedback is used. In other words, if the receiver and transmitter use explicit feedback, the receiver and transmitter have a rotation matrix.

Is defined by the reference codeword w _b without calculating

Pre-preferred codewords by storing the dot product of C and reference codebook C in memory in advance

Can generate a new codebook corresponding to a new codebook or a new preferred codeword.

The above-described methods and codebooks may be embodied in the form of program instructions that may be executed by various computer means and may be recorded in a computer readable medium. The computer readable medium may include program instructions, data files, data structures, etc. alone or in combination. Program instructions recorded on the media may be those specially designed and constructed for the purposes of the present invention, or they may be of the kind well-known and available to those having skill in the computer software arts. Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tape, optical media such as CD-ROMs, DVDs, and magnetic disks, 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 not only machine code generated by a compiler, but also high-level language code that can be executed by a computer using an interpreter or the like. The hardware device described above may be configured to operate as one or more software modules to perform the operations of the present invention, and vice versa.

7 is a block diagram illustrating a base station and a terminal according to an embodiment of the present invention.

Referring to FIG. 7, the base station 710 includes a recognizer 711, a calculator 712, a generator 713, and a precoder 714, and the terminal 720 includes a selector 721 and a calculator. The unit 722 and the generator 723 are included.

The selector 721 of the terminal 720 selects a previous preferred codeword using a basic codebook and feeds back information on the selected previous preferred codeword to the base station 710. The calculator 722 calculates a rotation matrix based on any codeword among the previous preferred codeword and the codewords included in the DFT codebook. In addition, the generation unit 723 generates a new codebook using the rotation matrix.

Also, the recognizer 711 of the base station 711 recognizes the previous preferred codeword based on the information about the previous preferred codeword previously fed back from the terminal 720. The calculator 712 calculates a rotation matrix based on any codeword among the previous preferred codeword and the codewords included in the DFT codebook. In addition, the generation unit 713 generates a new codebook using the rotation matrix.

When the selector 721 of the terminal 720 selects a new preferred codeword and feeds back information about the new preferred codeword, the base station 710 recognizes the new preferred codeword using the new codebook, Generate a new precoding matrix based on the preference codeword. At this time, the precoder 714 precodes at least one data stream using the new precoding matrix.

8 is a block diagram illustrating a transmitter and a receiver according to another embodiment of the present invention.

Referring to FIG. 8, a transmitter 810 according to another embodiment of the present invention includes a memory 811, a recognizer 812, a calculator 813, and a generator 814. In addition, the receiver 820 according to another embodiment of the present invention includes a memory 821, a vectorizer 822, a selector 823, a calculator 824, and a generator 825.

The basic codebook and the reference codebook are stored in the memory 811. In addition, new codebooks generated later are also stored in the memory 811.

In addition, the recognizer 812 recognizes the previous preferred codeword selected by the receiver 820 based on a previous explicit channel matrix between the transmitter 810 and the receiver 820.

In addition, the calculator 813 calculates a rotation matrix based on the previous preferred codeword.

In addition, the generation unit 814 rotates the reference codebook using the rotation matrix to generate a new codebook.

When a new codebook is generated, the recognition unit 812 recognizes a new preferred codeword, and the precoder of the transmitter 810 (not shown) performs precoding using a precoding matrix generated based on the new preferred codeword. do.

In addition, the basic codebook and the reference codebook are also stored in the memory 821 of the receiver 820. In addition, new codebooks generated later are also stored in the memory 821.

In addition, vectorizer 822 vectorizes the information associated with the previous explicit channel matrix between the transmitter and receiver to obtain vectorized channel information.

In addition, the selector 823 selects a previous preferred codeword based on the vectorized channel information.

In addition, the calculator 824 calculates a rotation matrix based on the previous preferred codeword.

In addition, the generation unit 825 rotates the reference codebook using the rotation matrix to generate a new codebook.

When a new codebook is generated, the receiver 820 calculates the next explicit channel matrix and selects a new preferred codeword from the new codebook that corresponds to the next explicit channel matrix. Information about this new preferred codeword is fed back to the transmitter 810.

The descriptions of the embodiments related to FIGS. 1 to 6 may be applied to each of the units shown in FIGS. 7 and 8 as it is. In particular, the receiver and transmitter of FIGS. 7 and 8 may not only generate a new codebook using the rotation matrix but also generate a product between the reference codebook and a matrix defined based on a reference codeword previously stored in memory. Can be used to generate a new codebook.

Detailed description of each of the units shown in FIGS. 7 and 8 will be omitted below.

, 전송 안테나들의 개수에 따라 새로운 코드북의 실제 수치들을 나타낸다. 아래의 codebook(:,:,n)은 새로운 코드북에서 n 번째 코드워드를 나타낸다. 다만, 표 1 및 표 2에 기재된 코드북들에는

를 기초로 정의되는 유니터리 매트릭스

가 미리 곱해질 수 있고, 그 곱이 수신기 및 송신기 각각의 메모리에 미리 저장될 수 있다.
Tables 1 and 2 below show the system using inherent feedback.

The actual values of the new codebook are represented according to the number of transmit antennas. Codebook (:,:, n) below represents the nth codeword in the new codebook. However, the codebooks listed in Tables 1 and 2

Unitary matrix defined based on

Can be multiplied in advance, and the product can be stored in advance in the memory of each of the receiver and transmitter.

가

이고, 기지국의 전송 안테나들의 개수가 4인 경우
(One)

end

When the number of transmit antennas of the base station is 4

If the reference codebook includes codewords of three DFT codebooks and codewords of 13 polar cap codebooks, If the reference codebook includes codewords of 5 DFT codebooks and codewords of 11 polar cap codebooks, codebook (:,:, 1) =

0.5000
0.4619-0.1913i
0.3536-0.3536i
0.1913-0.4619i
codebook (:,:, 1) =

0.5000
0.4619-0.1913i
0.3536-0.3536i
0.1913-0.4619i
codebook (:,:, 2) =

0.5000
0.5000
0.5000
0.5000
codebook (:,:, 2) =

0.5000
0.4904-0.0975i
0.4619-0.1913i
0.4157-0.2778i
codebook (:,:, 3) =

0.5000
0.4619 + 0.1913i
0.3536 + 0.3536i
0.1913 + 0.4619i
codebook (:,:, 3) =

0.5000
0.5000
0.5000
0.5000
codebook (:,:, 4) =

0.4018-0.1885i
0.6033 + 0.0472i
0.3626 + 0.2002i
0.5117-0.0588i
codebook (:,:, 4) =

0.5000
0.4904 + 0.0975i
0.4619 + 0.1913i
0.4157 + 0.2778i
codebook (:,:, 5) =

0.4687-0.1197i
0.5114-0.0280i
0.5656-0.1015i
0.3337 + 0.2492i
codebook (:,:, 5) =

0.5000
0.4619 + 0.1913i
0.3536 + 0.3536i
0.1913 + 0.4619i
codebook (:,:, 6) =

0.5132-0.0781i
0.4948 + 0.1131i
0.6244 + 0.0860i
0.2471-0.1211i
codebook (:,:, 6) =

0.5182 + 0.2035i
0.4946 + 0.0989i
0.3682-0.2059i
0.4984-0.0965i
codebook (:,:, 7) =

0.5607 + 0.0421i
0.3387 + 0.0700i
0.3081 + 0.0200i
0.6719-0.1321i
codebook (:,:, 7) =

0.4456-0.0396i
0.6368-0.0764i
0.2196 + 0.0481i
0.5773 + 0.0679i
codebook (:,:, 8) =

0.6936-0.0398i
0.5285 + 0.1146i
0.3048-0.0870i
0.3524 + 0.0121i
codebook (:,:, 8) =

0.5794-0.1936i
0.4956 + 0.2377i
0.3949-0.0149i
0.4096-0.0293i
codebook (:,:, 9) =

0.4336 + 0.1953i
0.5633 + 0.0399i
0.5476-0.2049i
0.3349-0.0302i
codebook (:,:, 9) =

0.6751 + 0.0001i
0.2514-0.0694i
0.3800 + 0.0105i
0.5729 + 0.0588i
codebook (:,:, 10) =

0.3759 + 0.0879i
0.6483-0.0644i
0.2663-0.0770i
0.5889 + 0.0535i
codebook (:,:, 10) =

0.6323 + 0.0705i
0.5466-0.0828i
0.4230 + 0.1359i
0.2776-0.1235i
codebook (:,:, 11) =

0.3737-0.1219i
0.4570 + 0.2606i
0.5131-0.1364i
0.5355-0.0023i
codebook (:,:, 11) =

0.3491 + 0.1889i
0.4217-0.1870i
0.5240 + 0.0806i
0.5846-0.0825i
codebook (:,:, 12) =

0.3004 + 0.1162i
0.4171-0.0147i
0.6176 + 0.0892i
0.5442-0.1908i
codebook (:,:, 12) =

0.4088-0.2058i
0.4407-0.0781i
0.5694 + 0.2246i
0.4605 + 0.0593i
codebook (:,:, 13) =

0.4130 + 0.0778i
0.6208-0.2176i
0.5169 + 0.1228i
0.3287 + 0.0170i
codebook (:,:, 13) =

0.2649 + 0.0123i
0.6814 + 0.0732 i
0.5641-0.0113i
0.3690-0.0742i
codebook (:,:, 14) =

0.6622-0.0806i
0.3315-0.1259i
0.4559 + 0.1909i
0.4298 + 0.0157i
codebook (:,:, 14) =

0.5078 + 0.0366i
0.2973 + 0.0731i
0.7158-0.0466i
0.3584-0.0631i
codebook (:,:, 15) =

0.3416-0.0854i
0.3779-0.1321i
0.4893 + 0.0703i
0.6706 + 0.1473i
codebook (:,:, 15) =

0.3211-0.0820i
0.3909 + 0.0864i
0.5110-0.1399i
0.6564 + 0.1355i
codebook (:,:, 16) =

0.5390 + 0.0730i
0.2130 + 0.0017i
0.6269-0.1164i
0.5006 + 0.0416i
codebook (:,:, 16) =

0.4993 + 0.0648i
0.5261-0.1446i
0.5116-0.1426i
0.3424 + 0.2225i

가

이고, 기지국의 전송 안테나들의 개수가 8인 경우
(2)

end

When the number of transmit antennas of the base station is 8

If the reference codebook contains codewords of three DFT codebooks and codewords of 13 polar cap codebooks, If the reference codebook includes codewords of 5 DFT codebooks and codewords of 11 polar cap codebooks, codebook (:,:, 1) =

0.3536
0.3481-0.0620i
0.3318-0.1221i
0.3053-0.1783i
0.2693-0.2291i
0.2249-0.2728i
0.1736-0.3080i
0.1169-0.3337i
codebook (:,:, 1) =

0.3536
0.3466-0.0697i
0.3260-0.1367i
0.2927-0.1984i
0.2478-0.2522i
0.1932-0.2961i
0.1310-0.3284i
0.0636-0.3478i
codebook (:,:, 2) =

0.3536
0.3536
0.3536
0.3536
0.3536
0.3536
0.3536
0.3536
codebook (:,:, 2) =

0.3536
0.3489-0.0574i
0.3349-0.1133i
0.3121-0.1661i
0.2810-0.2146i
0.2424-0.2573i
0.1974-0.2933i
0.1472-0.3214i
codebook (:,:, 3) =

0.3536
0.3481 + 0.0620i
0.3318 + 0.1221i
0.3053 + 0.1783i
0.2693 + 0.2291i
0.2249 + 0.2728i
0.1736 + 0.3080i
0.1169 + 0.3337i
codebook (:,:, 3) =

0.3536
0.3536
0.3536
0.3536
0.3536
0.3536
0.3536
0.3536
codebook (:,:, 4) =

0.2906-0.0200i
0.4444 + 0.0108i
0.4342 + 0.0303i
0.1793-0.0863i
0.2521-0.1518i
0.3282 + 0.0218i
0.3004 + 0.1157i
0.4287 + 0.0795i
codebook (:,:, 4) =

0.3536
0.3489 + 0.0574i
0.3349 + 0.1133i
0.3121 + 0.1661i
0.2810 + 0.2146i
0.2424 + 0.2573i
0.1974 + 0.2933i
0.1472 + 0.3214i
codebook (:,:, 5) =

0.3311-0.1474i
0.3272 + 0.1143i
0.3873 + 0.0384i
0.3626-0.0583i
0.3737 + 0.0192i
0.1792 + 0.0889 i
0.4404 + 0.0747i
0.2563-0.1298i
codebook (:,:, 5) =

0.3536
0.3466 + 0.0697i
0.3260 + 0.1367i
0.2927 + 0.1984i
0.2478 + 0.2522i
0.1932 + 0.2961i
0.1310 + 0.3284i
0.0636 + 0.3478i
codebook (:,:, 6) =

0.2673-0.0837i
0.2992 + 0.1142i
0.4013-0.1815i
0.3279 + 0.0871i
0.4244-0.0023i
0.3868 + 0.0546i
0.1992-0.0770i
0.3517 + 0.0886i
codebook (:,:, 6) =

0.4087-0.1423 i
0.3424 + 0.0171i
0.4275 + 0.0098i
0.2875 + 0.0866i
0.2881 + 0.0528i
0.1225 + 0.0462 i
0.4079-0.1094i
0.3733 + 0.0392i
codebook (:,:, 7) =

0.3565 + 0.0150i
0.3273 + 0.2208i
0.2443 + 0.0437i
0.3531-0.0023i
0.1877-0.0503i
0.3968-0.0686i
0.3967-0.1257i
0.3954-0.0325i
codebook (:,:, 7) =

0.3188 + 0.0333i
0.2778 + 0.0529i
0.2487 + 0.0578i
0.2626-0.1090i
0.2024-0.1105i
0.4407 + 0.0651i
0.5149-0.0148i
0.3919 + 0.0252i
codebook (:,:, 8) =

0.2692 + 0.0564i
0.1377-0.0422i
0.3737 + 0.0732 i
0.4682 + 0.0232i
0.3543-0.1060i
0.3830-0.1081i
0.3267 + 0.1309i
0.3452-0.0274i
codebook (:,:, 8) =

0.3249 + 0.1225i
0.1663-0.1050i
0.4730-0.0628i
0.4463-0.0522i
0.3211-0.0360i
0.2917 + 0.0030i
0.2622 + 0.0116i
0.3723 + 0.1189i
codebook (:,:, 9) =

0.5558-0.0265i
0.2917-0.1080i
0.2468-0.0112i
0.2349 + 0.0975i
0.3841-0.0851i
0.3777 + 0.0857i
0.2959 + 0.0462i
0.2710 + 0.0014i
codebook (:,:, 9) =

0.3023 + 0.1017i
0.4171-0.1082i
0.3013-0.0774i
0.2540-0.0943i
0.4626 + 0.0800i
0.2419 + 0.0756i
0.4456 + 0.0591i
0.2329-0.0365i
codebook (:,:, 10) =

0.3512-0.0135i
0.3684-0.0787i
0.3290-0.1587i
0.4496 + 0.0104i
0.1138 + 0.0889i
0.3743 + 0.0376i
0.3744 + 0.0846i
0.2972 + 0.0294i
codebook (:,:, 10) =

0.4777 + 0.0271i
0.3758 + 0.0304i
0.3884-0.0726i
0.1430 + 0.0150i
0.2631 + 0.0491i
0.4234-0.1415i
0.2543 + 0.0771i
0.3321 + 0.0155i
codebook (:,:, 11) =

0.3019-0.0112i
0.3290-0.0413i
0.2526 + 0.0865i
0.3723-0.1501i
0.3556 + 0.0874i
0.4419 + 0.1317i
0.1810-0.0185i
0.4235-0.0845i
codebook (:,:, 11) =

0.3258 + 0.0077 i
0.4535 + 0.1335i
0.2207-0.1357i
0.4762-0.0651i
0.2862 + 0.0479i
0.3398 + 0.0154i
0.2637-0.0952i
0.2919 + 0.0916i
codebook (:,:, 12) =

0.4414 + 0.1170i
0.2544-0.0440i
0.5248 + 0.0495i
0.2776-0.0560i
0.2809 + 0.0889 i
0.2543-0.0280i
0.3243-0.1383i
0.3002 + 0.0109i
codebook (:,:, 12) =

0.3206-0.1515i
0.2309 + 0.0076i
0.3581-0.0484i
0.2996 + 0.0536i
0.4396-0.0205i
0.4923 + 0.1656i
0.2596 + 0.0153i
0.2573-0.0217i
codebook (:,:, 13) =

0.3326 + 0.0290i
0.3162-0.0246i
0.2439-0.0715i
0.2435 + 0.0394i
0.4144 + 0.1580i
0.2499-0.1466i
0.3653 + 0.0636i
0.4921-0.0474i
codebook (:,:, 13) =

0.3051-0.0012i
0.2855 + 0.0357i
0.3594 + 0.0434i
0.4562 + 0.0575i
0.2306 + 0.1272i
0.3672-0.0690i
0.3967 + 0.0267i
0.2572-0.2202i
codebook (:,:, 14) =

0.2175 + 0.0841i
0.3069-0.0547i
0.2585-0.0121i
0.3180-0.0758i
0.4315-0.0575i
0.3420 + 0.0932i
0.5086-0.1004i
0.2749 + 0.1231i
codebook (:,:, 14) =

0.3081-0.0503i
0.3402-0.0946i
0.2667 + 0.2106i
0.3316-0.0211i
0.4165 + 0.0586i
0.3835-0.1392i
0.3140-0.0845i
0.2972 + 0.1204i
codebook (:,:, 15) =

0.2964 + 0.1588i
0.5326 + 0.0223i
0.3281-0.0056i
0.3657 + 0.0395i
0.3868-0.0507i
0.3071-0.0468i
0.2536-0.0103i
0.1876-0.1073i
codebook (:,:, 15) =

0.2917 + 0.1081i
0.4485-0.0486i
0.3132 + 0.0894i
0.3024 + 0.0441i
0.3313-0.0770i
0.3187 + 0.0794i
0.1801-0.0633i
0.4720-0.1320i
codebook (:,:, 16) =

0.3207-0.1592i
0.4222-0.0774i
0.3093 + 0.1507i
0.4130 + 0.0336i
0.3435 + 0.0559i
0.2832-0.1124i
0.2810-0.0390i
0.2851 + 0.1478i
codebook (:,:, 16) =

0.3444-0.0422i
0.3012 + 0.0864i
0.2281-0.0137i
0.3942 + 0.0675i
0.4403-0.1554i
0.2275-0.1057i
0.3523 + 0.1654 i
0.3700-0.0024i

가 이미 곱해진 결과를 나타낸다.
In addition, the following tables show actual numbers of the new codebook according to the number of feedback bits (size of the new codebook). Codebook (:,:, n) below represents the nth codeword in the new codebook. Codebook (:,:, n) is a unitary matrix created by w_b.

Represents the result of multiplication.

[Table 3]

4 bits

codebook (:,:, 1) =

  -0.9248

  -0.1939-0.0898i

  -0.0514-0.0371i

  -0.0312 + 0.0349i

  -0.1155-0.0762i

  -0.0404-0.0724i

  -0.0310-0.0588i

  -0.0006 + 0.1318i

  -0.0090 + 0.0654i

   0.0621 + 0.0212i

   0.0483 + 0.0347i

  -0.1079-0.0077i

  -0.0890 + 0.0549i

  -0.0122 + 0.0395i

  -0.0033-0.0353i

-0.0835 + 0.0195i

codebook (:,:, 2) =

  -0.9551 + 0.0000i

   0.0064-0.0429i

   0.0953 + 0.0400i

  -0.0871-0.0228i

  -0.0324 + 0.0215i

   0.0076 + 0.0261i

   0.0100 + 0.0138i

   0.0720 + 0.0218i

   0.0560-0.1152i

   0.0172 + 0.0461i

  -0.0094 + 0.0325i

  -0.0708-0.0204i

   0.0645 + 0.0761i

  -0.0635 + 0.0691i

  -0.0466 + 0.0667i

-0.0233-0.0875i

codebook (:,:, 3) =

  -0.9305-0.0000i

   0.1122-0.0896i

   0.0058-0.0430i

  -0.0635-0.0212i

  -0.0797 + 0.0738i

   0.0121 + 0.0048i

  -0.0603-0.0627i

  -0.0182 + 0.0744i

   0.0378 + 0.1520i

   0.0694 + 0.0440i

   0.0019-0.0240i

  -0.0746 + 0.0549i

   0.1238 + 0.0747i

  -0.0800 + 0.1079i

   0.0235 + 0.0362i

-0.0188-0.0148i

codebook (:,:, 4) =

  -0.9356-0.0000i

  -0.0371 + 0.0431i

  -0.1056 + 0.0140i

   0.0467-0.0303i

   0.0747-0.0909i

   0.0106-0.0378i

   0.0023-0.0637i

   0.0457-0.0124i

  -0.0963 + 0.1173i

  -0.0005-0.0863i

   0.0024 + 0.1033i

   0.0350 + 0.0638i

  -0.0938-0.0965i

   0.0328-0.0362i

  -0.0233-0.0913i

0.0020 + 0.0969i

codebook (:,:, 5) =

  -0.9425-0.0000i

  -0.1154 + 0.0301i

   0.0286-0.0049i

   0.0230 + 0.0002i

   0.0250-0.1479i

   0.0060-0.0410i

   0.0116 + 0.0162i

   0.0101 + 0.0322i

   0.0428-0.1128i

  -0.0371-0.0486i

  -0.0410 + 0.1445i

  -0.0535 + 0.0380i

  -0.0879 + 0.0073i

  -0.0182-0.0162i

  -0.0528 + 0.0282i

-0.0575 + 0.1001i

codebook (:,:, 6) =

  -0.9316-0.0000i

   0.0668 + 0.0186i

   0.0882-0.0645i

  -0.1531-0.1028i

   0.1533 + 0.1260i

  -0.0329 + 0.0220i

  -0.0149-0.0419i

  -0.0428 + 0.0518i

   0.0249 + 0.0691i

   0.0114 + 0.0120i

   0.0633-0.0106i

  -0.0465 + 0.0556i

   0.0596 + 0.0137i

  -0.0745 + 0.0452i

  -0.0093 + 0.0308i

0.0743 + 0.0318i

codebook (:,:, 7) =

  -0.9447-0.0000i

   0.0828-0.0350i

   0.0146 + 0.0825i

  -0.0086-0.0572i

   0.1469-0.0417i

   0.0076 + 0.0230i

  -0.0280-0.0008i

   0.0455-0.0611i

  -0.0681-0.0221i

  -0.0509-0.0039i

  -0.0656 + 0.0744i

   0.0149 + 0.0840i

   0.1008 + 0.0520i

   0.0093-0.0018i

  -0.0941 + 0.0041i

0.0407 + 0.1012i

codebook (:,:, 8) =

  -0.9378-0.0000i

  -0.1491-0.0143i

  -0.1318 + 0.0674i

  -0.0880-0.0211i

  -0.0760-0.0766i

  -0.0114-0.0344i

  -0.0407-0.0132i

   0.0475-0.0577i

  -0.1121-0.0748i

  -0.0588-0.0346i

  -0.0964 + 0.0389i

   0.0212-0.0223i

  -0.0355-0.0301i

  -0.0001-0.0053i

  -0.0794-0.0478i

-0.0394-0.0256i

codebook (:,:, 9) =

  -0.9480 + 0.0000i

  -0.0999 + 0.0359i

  -0.0118-0.0955i

  -0.1305-0.0252i

  -0.1072 + 0.0635i

   0.0163 + 0.0485i

  -0.0096-0.0531i

  -0.0044 + 0.0751i

   0.0432 + 0.0286i

   0.0469 + 0.0134i

   0.0617-0.0093i

  -0.0147-0.0970i

  -0.0681-0.0418i

  -0.0345 + 0.0359i

   0.0352-0.0292i

-0.0489-0.0668i

codebook (:,:, 10) =

  -0.9565-0.0000i

   0.0339 + 0.0222i

   0.0400-0.1210i

   0.0599-0.0010i

   0.0476 + 0.0177i

   0.0646 + 0.0713i

   0.0104-0.0667i

  -0.0220 + 0.0508i

   0.1152 + 0.0787i

   0.0241 + 0.0319i

   0.0410 + 0.1009i

  -0.0156 + 0.0185i

  -0.0144 + 0.0410i

   0.0058-0.0004i

   0.0346 + 0.0451i

-0.0110 + 0.0730i

codebook (:,:, 11) =

  -0.9146-0.0000i

  -0.0456-0.0408i

  -0.0528-0.0113i

  -0.1082-0.0432i

   0.0075-0.0208i

  -0.0808-0.1170i

  -0.1209-0.1316i

  -0.0552 + 0.0773i

  -0.0764 + 0.0674i

  -0.0176 + 0.0106i

  -0.0348 + 0.0055i

  -0.0706 + 0.1355i

   0.0296-0.0593i

  -0.1045 + 0.0597i

  -0.1278-0.0382i

-0.0041 + 0.0970i

codebook (:,:, 12) =

   0.8211

  -0.2039-0.0406i

  -0.0530-0.0219i

  -0.0000 + 0.0000i

   0.1362 + 0.1362i

  -0.0478-0.0716i

  -0.0124-0.0300i

   0.0000 + 0.0000i

  -0.0000 + 0.1633i

   0.0168-0.0844i

   0.0147-0.0354i

   0.0000 + 0.0000i

  -0.2039 + 0.2039i

   0.1728-0.1155i

   0.1509-0.0625i

0.2085-0.0415i

codebook (:,:, 13) =

   0.9527

  -0.1177-0.0234i

  -0.0435-0.0180i

  -0.0155-0.0104i

   0.0854 + 0.0854i

  -0.0219-0.0328i

  -0.0089-0.0214i

  -0.0023-0.0117i

  -0.0000 + 0.0938i

   0.0071-0.0357i

   0.0096-0.0233i

   0.0085-0.0127i

  -0.1041 + 0.1041i

   0.0614-0.0411i

   0.0707-0.0293i

0.1185-0.0236i

codebook (:,:, 14) =

   1.0000

   0.0000 + 0.0000i

  -0.0000 + 0.0000i

   0.0000-0.0000i

   0.0000 + 0.0000i

   0.0000 + 0.0000i

   0.0000-0.0000i

  -0.0000 + 0.0000i

  -0.0000-0.0000i

  -0.0000-0.0000i

   0.0000-0.0000i

   0.0000-0.0000i

  -0.0000-0.0000i

   0.0000 + 0.0000i

   0.0000-0.0000i

-0.0000 + 0.0000i

codebook (:,:, 15) =

   0.9527

   0.1185 + 0.0236i

   0.0707 + 0.0293i

   0.0614 + 0.0411i

  -0.1041-0.1041i

   0.0085 + 0.0127i

   0.0096 + 0.0233i

   0.0071 + 0.0357i

   0.0000-0.0938i

  -0.0023 + 0.0117i

  -0.0089 + 0.0214i

  -0.0219 + 0.0328i

   0.0854-0.0854i

  -0.0155 + 0.0104i

  -0.0435 + 0.0180i

-0.1177 + 0.0234i

codebook (:,:, 16) =

   0.8211

   0.2085 + 0.0415i

   0.1509 + 0.0625i

   0.1728 + 0.1155i

  -0.2039-0.2039i

   0.0000 + 0.0000i

   0.0147 + 0.0354i

   0.0168 + 0.0844i

   0.0000-0.1633i

  -0.0000 + 0.0000i

  -0.0124 + 0.0300i

  -0.0478 + 0.0716i

   0.1362-0.1362i

  -0.0000 + 0.0000i

  -0.0530 + 0.0219i

-0.2039 + 0.0406i

6 bits

codebook (:,:, 1) =

  -0.9235-0.0000i

  -0.1099-0.0503i

   0.0387 + 0.0387i

  -0.2053-0.0732i

   0.0558 + 0.0807i

  -0.0723 + 0.0277i

   0.0353 + 0.0464i

   0.0504 + 0.0121i

  -0.0250-0.0474i

  -0.0003-0.0385i

   0.0640-0.0294i

  -0.1012-0.0833i

   0.0100 + 0.0719i

  -0.0948 + 0.0678i

   0.0391 + 0.0475i

0.0430-0.0964i

codebook (:,:, 2) =

  -0.9020-0.0000i

  -0.0748-0.1176i

  -0.0747-0.0740i

   0.0035 + 0.0369i

  -0.1370-0.0091i

   0.0307-0.0657i

  -0.0898-0.1464i

  -0.0132 + 0.1441i

  -0.0111 + 0.2122i

   0.0696 + 0.0657i

   0.0022 + 0.0215i

  -0.0570 + 0.0452i

  -0.0110 + 0.1031i

   0.0494 + 0.0220i

   0.0430-0.0186i

-0.0620 + 0.0156i

codebook (:,:, 3) =

  -0.8795 + 0.0000i

  -0.1335-0.0662i

  -0.1131-0.0594i

  -0.2664-0.0680i

  -0.1604 + 0.0144i

  -0.0973-0.0400i

  -0.1067-0.0488i

  -0.0785 + 0.1053i

  -0.0611 + 0.0870i

   0.0432 + 0.0184i

   0.0060-0.0576i

  -0.1187 + 0.0120i

  -0.0201-0.0232i

  -0.0360 + 0.0408i

  -0.0225-0.0671i

-0.0656 + 0.0045i

codebook (:,:, 4) =

  -0.9387 + 0.0000i

  -0.0045-0.0014i

  -0.1235-0.0567i

  -0.0089-0.0039i

  -0.1095 + 0.0361i

   0.0785 + 0.0835i

  -0.0161-0.0613i

   0.0296-0.0043i

  -0.0362 + 0.1677i

   0.0628-0.0274i

   0.0145 + 0.0352i

   0.0598-0.0704i

  -0.0305-0.0004i

   0.0830-0.0087i

   0.0780-0.0780i

-0.0253-0.0648i

codebook (:,:, 5) =

  -0.9271-0.0000i

   0.1474-0.0671i

   0.0438 + 0.1092i

  -0.0783-0.0643i

   0.0794 + 0.0701i

  -0.0116 + 0.0344i

  -0.0123-0.0055i

   0.0887-0.0546i

  -0.0614-0.0017i

   0.0163 + 0.0131i

  -0.0157-0.0004i

  -0.0189 + 0.0441i

   0.1683 + 0.0499i

  -0.0741 + 0.0926i

  -0.0835 + 0.0113i

0.0604-0.0646i

codebook (:,:, 6) =

  -0.9353 + 0.0000i

  -0.1427-0.0816i

  -0.0418-0.0404i

  -0.0910 + 0.0180i

  -0.1575 + 0.0123i

  -0.0175 + 0.0124i

   0.0009 + 0.0078i

   0.0059 + 0.0801i

   0.0191 + 0.0419i

   0.0710 + 0.0252i

   0.0539-0.0252i

  -0.0830-0.0941i

  -0.0433 + 0.0836i

  -0.0045 + 0.0481i

   0.0640-0.0072i

-0.0678-0.0849i

codebook (:,:, 7) =

  -0.9458-0.0000i

  -0.0568 + 0.0110i

  -0.0071-0.1340i

   0.0689 + 0.0183i

   0.0265 + 0.0192i

   0.0545 + 0.0730i

   0.0405-0.0582i

  -0.0139 + 0.0577i

   0.0901 + 0.1176i

   0.0505 + 0.0173i

   0.0912 + 0.0903i

  -0.0120-0.0388i

  -0.0808 + 0.0518i

   0.0385-0.0118i

   0.0765 + 0.0097i

-0.0139 + 0.0352i

codebook (:,:, 8) =

  -0.8995-0.0000i

   0.0911 + 0.0821i

   0.0579-0.0025i

  -0.2205-0.1560i

   0.1364 + 0.0860i

  -0.0331-0.1070i

  -0.0292-0.0469i

  -0.0098 + 0.0534i

  -0.0605 + 0.0859i

   0.0049-0.0417i

  -0.0040-0.0186i

  -0.0126 + 0.1502i

   0.0166-0.0946i

  -0.0518 + 0.0134i

  -0.0420-0.0194i

0.0690 + 0.0068i

codebook (:,:, 9) =

  -0.8961-0.0000i

  -0.2279 + 0.0200i

  -0.1278 + 0.0001i

  -0.0958-0.0031i

  -0.0987-0.0957i

  -0.0654-0.0383i

  -0.0532-0.0590i

  -0.0003 + 0.0109i

  -0.0615-0.0764i

  -0.0575-0.0540i

  -0.0271 + 0.0256i

  -0.0363-0.0514i

  -0.1022-0.1384i

  -0.1282 + 0.0455i

  -0.0828-0.0557i

-0.0763 + 0.0554i

codebook (:,:, 10) =

  -0.9168-0.0000i

  -0.1296-0.1196i

  -0.1409 + 0.0747i

  -0.0936-0.0129i

  -0.1219-0.0879i

  -0.0059-0.0497i

  -0.0630 + 0.0192i

   0.0319-0.0032i

  -0.1386 + 0.0422i

   0.0051-0.0384i

  -0.0952 + 0.0352i

  -0.0294 + 0.0015i

   0.0033 + 0.1225i

   0.0923-0.0118i

  -0.0056-0.0541i

-0.0465-0.0337i

codebook (:,:, 11) =

  -0.9292 + 0.0000i

   0.0877 + 0.0279i

   0.1202-0.0339i

  -0.1621-0.0597i

  -0.0711 + 0.1258i

   0.0356 + 0.0161i

  -0.0180-0.0533i

   0.0400 + 0.0808i

   0.0827-0.0158i

   0.0510 + 0.0694i

   0.0184-0.0401i

  -0.0313-0.0082i

   0.0609-0.0170i

  -0.0715 + 0.0700i

  -0.0020 + 0.0464i

-0.0174-0.1228i

codebook (:,:, 12) =

  -0.8802-0.0000i

   0.0901-0.1238i

   0.0217-0.0094i

  -0.1196-0.0402i

  -0.0292 + 0.0680i

  -0.0811-0.0633i

  -0.0865-0.0749i

  -0.0421 + 0.1065i

  -0.0060 + 0.1416i

   0.0711 + 0.0372i

   0.0286-0.0546i

  -0.1459 + 0.1135i

   0.1450 + 0.0487i

  -0.1655 + 0.1570i

  -0.0477 + 0.0213i

0.0041 + 0.0190i

codebook (:,:, 13) =

  -0.9387-0.0000i

   0.0974-0.0397i

  -0.0405 + 0.0127i

   0.1109-0.0019 i

   0.0132-0.1080i

   0.0791 + 0.0898i

  -0.0003-0.0123i

   0.0678-0.0139i

   0.0153 + 0.1005i

   0.0131 + 0.0032i

  -0.0299 + 0.1198i

   0.0021 + 0.0368i

   0.0287 + 0.0424i

   0.0706-0.0275i

   0.0292-0.0019i

-0.0552 + 0.1521i

codebook (:,:, 14) =

  -0.9370-0.0000i

  -0.1211-0.0460i

   0.0903-0.0443i

   0.0433 + 0.0100i

   0.1167-0.0468i

   0.0142 + 0.0009i

   0.0650 + 0.0379i

   0.0053 + 0.0618i

   0.0750-0.0267i

   0.0148 + 0.0058i

   0.0601 + 0.1085i

  -0.0649-0.0100i

  -0.0424 + 0.1741i

  -0.0107 + 0.0281i

   0.0106 + 0.0643i

-0.0050 + 0.0641i

codebook (:,:, 15) =

  -0.9297-0.0000i

   0.1507 + 0.0117i

  -0.0532-0.0418i

  -0.0309-0.0807i

   0.1175 + 0.0910i

   0.0182 + 0.0761i

   0.0157-0.0177i

  -0.0074-0.0474i

  -0.0169 + 0.2046i

   0.0226-0.0677i

   0.0312 + 0.0267i

   0.0030 + 0.0489i

   0.0611-0.0027i

  -0.0180 + 0.0184i

   0.0840 + 0.0071i

0.0774 + 0.0306i

codebook (:,:, 16) =

  -0.8752-0.0000i

   0.0597 + 0.0105i

  -0.0873 + 0.0631i

  -0.0374-0.0610i

   0.0666-0.0906i

  -0.0772-0.0798i

  -0.0960-0.1060i

   0.0028 + 0.0010i

  -0.1313 + 0.0759i

  -0.0247-0.0599i

  -0.0404 + 0.0428i

  -0.0262 + 0.1602i

   0.0296-0.1818i

  -0.1083 + 0.0446i

  -0.1569-0.0995i

0.0018 + 0.1704i

codebook (:,:, 17) =

  -0.9170-0.0000i

  -0.0557-0.0250i

   0.0330 + 0.0302i

  -0.0872-0.0270i

  -0.0686-0.0939i

  -0.0780-0.1029i

  -0.0247-0.0647i

   0.0570 + 0.1450i

  -0.0072 + 0.0142i

   0.0848-0.0017i

   0.0600 + 0.0497i

  -0.1522 + 0.0827i

  -0.0679-0.0934i

  -0.0871 + 0.0658i

  -0.0836-0.0530i

-0.0798 + 0.0311i

codebook (:,:, 18) =

  -0.9312 + 0.0000i

  -0.0620 + 0.0453i

  -0.0797 + 0.0290i

  -0.1499-0.0480i

  -0.1528 + 0.0256i

   0.0504 + 0.0352i

   0.0032-0.0047i

   0.0923-0.0512i

  -0.0326-0.0686i

  -0.0072 + 0.0042i

  -0.0579-0.0099i

   0.0568-0.0947i

  -0.0179-0.0791i

  -0.0360 + 0.0379i

  -0.0294-0.0315i

-0.0642-0.1390i

codebook (:,:, 19) =

  -0.9369 + 0.0000i

  -0.1630 + 0.1047i

   0.0765-0.0753i

  -0.0818-0.0256i

   0.0501 + 0.0405i

   0.0245 + 0.0111i

   0.0453-0.0250i

   0.0118 + 0.0474i

   0.0611-0.0939i

  -0.0227-0.0458i

   0.0594 + 0.0466i

   0.0181-0.1002i

  -0.1166-0.0386i

  -0.0802 + 0.0258i

   0.0122 + 0.0208i

0.0024-0.0436i

codebook (:,:, 20) =

  -0.9332 + 0.0000i

   0.0864 + 0.1046i

   0.0401 + 0.0549i

  -0.0863-0.0864i

   0.1040 + 0.0828i

   0.0495-0.0397i

   0.0133-0.0403i

   0.0782-0.0718i

  -0.0453-0.0494i

  -0.0547-0.0297i

  -0.0638 + 0.0085i

   0.0986 + 0.0472i

   0.0410-0.0923i

  -0.0639 + 0.0220i

  -0.0678 + 0.0154i

0.0678-0.0881i

codebook (:,:, 21) =

  -0.9236 + 0.0000i

  -0.0597 + 0.0365i

   0.0135-0.0829i

  -0.0664 + 0.0102i

  -0.1997-0.0173i

   0.0586 + 0.0651i

  -0.0394-0.0909i

   0.0378 + 0.1229i

   0.0765 + 0.0106i

   0.0719 + 0.0462i

   0.0424 + 0.0344i

  -0.0192-0.0895i

  -0.0825-0.0774i

   0.0137 + 0.0102i

   0.0197-0.0510i

-0.1229-0.0230i

codebook (:,:, 22) =

  -0.9357-0.0000i

  -0.1435-0.0328i

  -0.0015 + 0.0431i

  -0.0441 + 0.0143i

  -0.1158-0.1278i

  -0.0041-0.0011i

   0.0140 + 0.0587i

   0.0579 + 0.0178i

   0.0315-0.1571i

  -0.0081-0.0138i

  -0.0455 + 0.0857i

  -0.0828-0.0492i

  -0.0579 + 0.0449i

  -0.0104 + 0.0098i

  -0.0296 + 0.0278i

-0.0982-0.0164i

codebook (:,:, 23) =

  -0.9300-0.0000i

   0.0917-0.0387i

  -0.0640 + 0.0238i

  -0.1552-0.0769i

  -0.0746 + 0.1086i

   0.0125 + 0.0315i

   0.0045 + 0.0262i

   0.0435-0.0331i

  -0.0490 + 0.1223i

   0.0668-0.0392i

  -0.0076-0.0413i

  -0.0178-0.0120i

   0.0853 + 0.0332i

  -0.0312 + 0.0761i

   0.0583-0.0097i

0.0200-0.1539i

codebook (:,:, 24) =

  -0.9204-0.0000i

  -0.1135 + 0.0136i

   0.0000 + 0.0363i

   0.0347-0.0294i

   0.1404-0.1551i

   0.0094-0.0884i

   0.0256 + 0.0411i

   0.0183 + 0.0037 i

  -0.0494-0.0355i

  -0.0545-0.0707i

  -0.0537 + 0.1370i

  -0.0029 + 0.0863i

  -0.0888 + 0.0601i

   0.0654-0.0665i

  -0.0359 + 0.0002i

-0.0046 + 0.1406i

codebook (:,:, 25) =

  -0.9165 + 0.0000i

  -0.0156 + 0.0247i

   0.0369-0.1581i

  -0.1828-0.0836i

   0.0503 + 0.1611i

  -0.0159 + 0.0702i

  -0.0134-0.0475i

  -0.0898 + 0.0829i

   0.0636 + 0.1132i

   0.0461 + 0.0349i

   0.1024-0.0325i

  -0.0395-0.0277i

   0.0016 + 0.0257i

  -0.0366 + 0.0343i

   0.0515 + 0.0083 i

0.0359-0.0080i

codebook (:,:, 26) =

  -0.9089-0.0000i

  -0.0124 + 0.0003i

   0.0395-0.0525i

  -0.1054-0.0368i

   0.0123 + 0.0583i

   0.0035-0.1208i

  -0.1482-0.2161i

  -0.0420 + 0.1115i

  -0.0253 + 0.0317i

  -0.0333 + 0.0851i

  -0.0684 + 0.0205i

  -0.0030 + 0.1411i

   0.0425-0.0189i

  -0.0247 + 0.0086i

  -0.1317 + 0.0029i

0.0207 + 0.0152i

codebook (:,:, 27) =

  -0.9249 + 0.0000i

   0.0184-0.0016i

   0.1353-0.0838i

   0.0114 + 0.0206i

  -0.0521 + 0.0005i

   0.0492 + 0.0585i

  -0.0259-0.1076i

   0.0273 + 0.1137i

   0.1677-0.0736i

   0.0365 + 0.1184i

   0.0302 + 0.0998i

  -0.0778 + 0.0082i

   0.0130 + 0.0256i

  -0.0443 + 0.0391i

  -0.0608 + 0.0692i

-0.0699 + 0.0170i

codebook (:,:, 28) =

  -0.9295-0.0000i

   0.0713 + 0.1154i

   0.1264-0.1002i

  -0.0122-0.0462i

   0.1108 + 0.0236i

   0.0636 + 0.0066i

  -0.0234-0.0598i

  -0.0569 + 0.0295i

   0.1227-0.0714i

  -0.0560-0.0083i

  -0.0508 + 0.1122i

   0.0155 + 0.0855i

   0.0110-0.0208i

  -0.0478-0.0106i

  -0.0459 + 0.0854i

0.0241 + 0.0724i

codebook (:,:, 29) =

  -0.9111-0.0000i

  -0.0824 + 0.0070i

  -0.1296 + 0.0230i

   0.0323 + 0.0154i

  -0.1138-0.1559i

   0.0192 + 0.0062i

  -0.0589-0.0851i

   0.0600 + 0.0297i

  -0.0856 + 0.0519i

   0.0188-0.0298i

  -0.0219 + 0.0891i

   0.0204-0.0045i

  -0.0973-0.1213i

   0.0592-0.0359i

  -0.0565-0.1357i

-0.1013 + 0.1030i

codebook (:,:, 30) =

  -0.9022 + 0.0000i

   0.2135 + 0.0694i

   0.0011-0.0367i

  -0.0470-0.0590i

  -0.0449 + 0.0717i

   0.0690-0.0508i

  -0.0714-0.1024i

  -0.0136 + 0.0182i

   0.0166 + 0.1340i

   0.0171-0.0493i

  -0.0793 + 0.0033i

   0.0417 + 0.1211i

   0.1054-0.1114i

  -0.1395 + 0.1039i

  -0.0208 + 0.0110i

0.0038-0.0094i

codebook (:,:, 31) =

  -0.9548-0.0000i

  -0.0264-0.1146i

  -0.0342 + 0.0286i

   0.0087 + 0.0023i

   0.0166 + 0.0127i

   0.0247 + 0.0488i

   0.0325 + 0.0459i

   0.0493-0.0158i

  -0.0281 + 0.0937i

   0.0297-0.0187i

   0.0173 + 0.0220i

  -0.0298-0.0502i

   0.0471 + 0.1830 i

   0.0327 + 0.0321i

   0.0903 + 0.0315i

0.0153-0.0310i

codebook (:,:, 32) =

  -0.8838-0.0000i

  -0.1506-0.0443i

  -0.0411 + 0.0313i

  -0.0841-0.0280i

  -0.0099-0.1372i

  -0.0662-0.2336i

  -0.0835-0.0379i

  -0.0466 + 0.0984i

  -0.0889 + 0.0120i

  -0.0317-0.0666i

  -0.0968 + 0.0595i

  -0.0921 + 0.1660i

  -0.0524 + 0.0238i

  -0.0468 + 0.0192i

  -0.0857-0.0097i

-0.0355 + 0.0930i

codebook (:,:, 33) =

  -0.9170-0.0000i

   0.1247-0.0278i

   0.0056-0.1252i

  -0.0101-0.0021i

  -0.1051 + 0.0864i

   0.0752 + 0.0469i

  -0.0668-0.1131i

  -0.0422 + 0.0928i

   0.0974 + 0.1879i

   0.0668 + 0.0469i

   0.0028 + 0.0121i

  -0.0287 + 0.0341i

   0.0735 + 0.0424i

  -0.0237 + 0.0549i

   0.0769 + 0.0404i

-0.0314-0.0002i

codebook (:,:, 34) =

  -0.9254 + 0.0000i

  -0.0777-0.0081i

  -0.1148 + 0.0183i

   0.0622-0.0251i

   0.1201-0.0605i

   0.0199-0.0378i

   0.0377-0.0461i

   0.0669-0.0174i

  -0.1110 + 0.1708i

   0.0056-0.0709i

   0.0268 + 0.0965i

   0.0326 + 0.0428i

  -0.0990 + 0.0099i

   0.0897-0.0572i

   0.0401-0.0639i

0.0336 + 0.0622i

codebook (:,:, 35) =

  -0.9209-0.0000i

  -0.0838-0.1079i

  -0.0089 + 0.0172i

   0.0745 + 0.0396i

  -0.0863-0.1657i

   0.0338-0.0407i

   0.0086 + 0.0039 i

   0.0679 + 0.0968i

   0.0295 + 0.0418i

   0.0595 + 0.0499i

  -0.0066 + 0.1083i

  -0.0882 + 0.0381i

  -0.0445 + 0.1247i

   0.0590 + 0.0073 i

  -0.0020 + 0.0046i

-0.1211 + 0.0931i

codebook (:,:, 36) =

  -0.9583-0.0000i

   0.0012-0.0319i

  -0.0531 + 0.1083i

  -0.0098-0.0281i

   0.0345-0.0335i

   0.0385 + 0.0393i

   0.0231 + 0.0518i

   0.0991-0.1040i

  -0.0933-0.0353i

  -0.0300-0.0429i

  -0.0655 + 0.0519i

   0.0518-0.0280i

   0.0375 + 0.0650i

   0.0622-0.0186i

  -0.0132-0.0148i

0.0205-0.0466i

codebook (:,:, 37) =

  -0.9068-0.0000i

  -0.1121 + 0.0026i

  -0.1273 + 0.1015i

  -0.0711-0.0462i

   0.0655-0.0154i

  -0.0128-0.0877i

  -0.0481-0.0888i

   0.0749-0.0899i

  -0.1896-0.0296i

  -0.0867-0.0280i

  -0.0971 + 0.0360i

   0.0835 + 0.0441i

  -0.0109-0.0506i

   0.0100-0.0198i

  -0.1338-0.0663i

0.0518-0.0469i

codebook (:,:, 38) =

  -0.9364-0.0000i

  -0.0212-0.0750i

  -0.0474-0.0116i

  -0.0697-0.0353i

   0.0276-0.0321i

  -0.0497 + 0.0618i

  -0.1025-0.1138i

  -0.0073 + 0.0595i

  -0.0743 + 0.0773i

   0.0215 + 0.0721i

   0.0401 + 0.0321i

  -0.0400 + 0.0323i

   0.0417-0.0162i

   0.0107 + 0.0146i

  -0.1180-0.1012i

-0.0252 + 0.1549i

codebook (:,:, 39) =

  -0.8904-0.0000i

   0.1091 + 0.0128i

  -0.0099-0.0959i

  -0.0871-0.0938i

   0.1224 + 0.0005 i

  -0.0429 + 0.0027i

  -0.0941-0.0645i

  -0.1317 + 0.0281i

   0.0313 + 0.0917i

  -0.0472-0.0012i

  -0.0488 + 0.0610i

  -0.0723 + 0.1791i

   0.0804-0.0271i

  -0.0691 + 0.0067i

  -0.0627 + 0.0380i

0.0258 + 0.2199i

codebook (:,:, 40) =

  -0.9030-0.0000i

   0.1471-0.0259i

   0.0141 + 0.0353i

   0.0164-0.0212i

   0.0169-0.0043i

   0.0367 + 0.0004 i

  -0.0829-0.1109i

   0.0362-0.0355i

   0.0147-0.0371i

  -0.0539 + 0.0899i

  -0.1094 + 0.0449i

   0.0180 + 0.1159i

   0.1691-0.0311i

  -0.1356 + 0.0960i

  -0.1742 + 0.0460i

-0.0182 + 0.0801i

codebook (:,:, 41) =

  -0.9301-0.0000i

   0.0141-0.0650i

   0.0753 + 0.0749i

  -0.0181-0.0339i

   0.1175-0.0633i

   0.0100 + 0.0212i

  -0.0203 + 0.0310i

   0.0392-0.0342i

  -0.0133-0.1301i

  -0.0505 + 0.0298i

  -0.0757 + 0.1064i

  -0.0257 + 0.0599i

   0.1015 + 0.1438i

   0.0090 + 0.0119i

  -0.1223 + 0.0481i

0.0142 + 0.0697i

codebook (:,:, 42) =

  -0.9088 + 0.0000i

  -0.0671 + 0.1449i

  -0.0466 + 0.0066i

   0.0045-0.0487i

   0.1063-0.0597i

   0.0224-0.1374i

   0.0151-0.0558i

   0.0199-0.0245i

  -0.0743 + 0.0082i

  -0.0595-0.1326i

  -0.0508 + 0.0838i

   0.0858 + 0.0857i

  -0.1160-0.1633i

  -0.0736-0.0008i

  -0.0642-0.0473i

0.0258 + 0.0429i

codebook (:,:, 43) =

  -0.9255 + 0.0000i

  -0.1152 + 0.0436i

  -0.0608-0.1027i

  -0.0262-0.0170i

   0.0649 + 0.0497i

  -0.0250-0.0818i

  -0.0266-0.1383i

  -0.0559 + 0.0530i

  -0.0202 + 0.1152i

  -0.0073-0.0335i

   0.0508 + 0.0176i

   0.0112 + 0.0366i

  -0.0573-0.0858i

  -0.1652 + 0.0971i

  -0.0558-0.0311i

0.0252 + 0.0451i

codebook (:,:, 44) =

  -0.9133-0.0000i

  -0.0177-0.0037i

  -0.0908 + 0.0713i

  -0.0350-0.0318i

  -0.0566-0.1628i

   0.0070 + 0.0103i

  -0.0711 + 0.0004i

   0.0314-0.0656i

  -0.0550-0.1195i

  -0.0809 + 0.0015i

  -0.1518 + 0.0985i

   0.0040 + 0.0611i

   0.0258-0.0560i

   0.0065-0.0262i

  -0.1415-0.0265i

-0.0840 + 0.1305i

codebook (:,:, 45) =

  -0.8997 + 0.0000i

  -0.1586-0.0972i

   0.0706-0.0957i

  -0.0545 + 0.0226i

   0.0146 + 0.0398i

  -0.0702 + 0.0010i

  -0.0150-0.0795i

  -0.0398 + 0.1517i

   0.0731 + 0.0269i

   0.0657 + 0.0774i

   0.1400 + 0.0144i

  -0.1406-0.0353i

  -0.0131 + 0.1033i

  -0.1241 + 0.1171i

  -0.0403 + 0.0215i

-0.0211 + 0.0283i

codebook (:,:, 46) =

  -0.9103-0.0000i

   0.0390-0.0044i

   0.1701-0.0280i

  -0.1450-0.0892i

   0.1991 + 0.0939i

  -0.0435 + 0.0252i

  -0.0327-0.0458i

  -0.0269 + 0.0680i

   0.0320-0.0481i

  -0.0123 + 0.0460i

   0.0542 + 0.0220i

  -0.0624 + 0.0563i

   0.0835 + 0.0624i

  -0.0688 + 0.0413i

  -0.0842 + 0.0451i

0.0772 + 0.0559i

codebook (:,:, 47) =

  -0.9200 + 0.0000i

  -0.0203-0.1267i

   0.0708 + 0.0614i

  -0.0922-0.0045i

  -0.1002-0.0214i

  -0.0276-0.0249i

  -0.0045 + 0.0291i

   0.0683 + 0.0686i

   0.0370-0.0691i

   0.0677 + 0.0521i

  -0.0018 + 0.0258i

  -0.1430 + 0.0096i

   0.0817 + 0.1350i

  -0.0835 + 0.1184i

  -0.0564 + 0.0534i

-0.0600-0.0869i

codebook (:,:, 48) =

  -0.9445 + 0.0000i

   0.0701 + 0.1507i

   0.0121-0.1009i

  -0.0337-0.0520i

   0.0041 + 0.0776 i

   0.1020 + 0.0531i

   0.0176-0.0564i

   0.0015-0.0002i

   0.0535 + 0.0673i

   0.0189-0.0595i

   0.0098 + 0.0503i

   0.0989-0.0240i

  -0.0460-0.1119i

  -0.0210 + 0.0075i

   0.0420-0.0229i

0.0072-0.0412i

codebook (:,:, 49) =

  -0.9400-0.0000i

   0.1034-0.0677i

  -0.0039 + 0.0433i

   0.0065 + 0.0065i

  -0.1735-0.0510i

   0.0971 + 0.0512i

  -0.0193 + 0.0046i

   0.0989 + 0.0154i

   0.0366 + 0.0220i

   0.0582 + 0.0611i

  -0.0681 + 0.0384i

  -0.0039-0.0075i

   0.0904 + 0.0645i

   0.0119 + 0.0594i

  -0.0051 + 0.0107i

-0.1099-0.0251i

codebook (:,:, 50) =

  -0.9608 + 0.0000i

  -0.1325 + 0.0504i

  -0.0679-0.0073i

   0.0404 + 0.0175i

  -0.0193-0.0541i

   0.0459 + 0.0154i

   0.0439-0.0069i

   0.0544-0.0284i

  -0.0245-0.0182i

  -0.0121-0.0479i

   0.0064 + 0.0670i

   0.0615-0.0786i

  -0.1176-0.0367i

   0.0366-0.0306i

   0.0161-0.0438i

-0.0291-0.0207i

codebook (:,:, 51) =

  -0.9209 + 0.0000i

  -0.0762 + 0.0821i

   0.0532 + 0.0439i

  -0.0729-0.0371i

   0.0487-0.0296i

   0.0281-0.0631i

  -0.0268-0.0385i

   0.0418-0.0418i

   0.0032-0.2144i

  -0.1257-0.0385i

  -0.1296 + 0.0849i

   0.0292 + 0.0292i

  -0.0111-0.0415i

  -0.0773-0.0036i

  -0.1029 + 0.0754i

0.0127-0.0308i

codebook (:,:, 52) =

  -0.9183-0.0000i

   0.0593-0.0607i

  -0.0107 + 0.1121i

  -0.0448-0.0876i

   0.2139-0.0257i

  -0.0290-0.0087i

  -0.0117-0.0006i

   0.0698-0.0406i

  -0.1453 + 0.0861i

  -0.0253-0.0519i

  -0.0113 + 0.0521i

  -0.0064 + 0.0934i

   0.0692 + 0.0609i

   0.0377-0.0160i

  -0.0369-0.0318i

0.0836 + 0.1005i

codebook (:,:, 53) =

  -0.9021 + 0.0000i

  -0.2871-0.0566i

  -0.1142-0.0544i

   0.0147 + 0.0456i

  -0.0343-0.0601i

  -0.0414-0.0991i

  -0.0029-0.0839i

  -0.0090 + 0.0873i

  -0.0592 + 0.0930i

   0.0246-0.0110i

   0.0656 + 0.0399i

  -0.0422-0.0288i

  -0.1522 + 0.0327i

  -0.0105 + 0.0200i

  -0.0027-0.0590i

-0.0365 + 0.0167i

codebook (:,:, 54) =

  -0.9395-0.0000i

   0.1234-0.0621i

   0.0632-0.0522i

   0.0485-0.0089i

   0.0756 + 0.0478i

   0.0447 + 0.0815i

  -0.0011-0.0280i

  -0.0061 + 0.0151i

   0.0921 + 0.0750i

   0.0165 + 0.0695i

   0.0160 + 0.0458i

  -0.0350 + 0.0406i

   0.1194 + 0.1218i

  -0.0416 + 0.0573i

   0.0106 + 0.0839 i

0.0130 + 0.0744i

codebook (:,:, 55) =

  -0.9392-0.0000i

   0.1277 + 0.0828i

   0.0006 + 0.0042i

   0.0686-0.0462i

   0.1299-0.0582i

   0.0475 + 0.0340i

   0.0036-0.0178i

   0.0162-0.0606i

   0.0041 + 0.0189i

  -0.0473-0.0584i

  -0.0504 + 0.1087i

   0.0497 + 0.0915i

   0.0135-0.0820i

  -0.0020-0.0343i

  -0.0359 + 0.0013i

0.0212 + 0.1372i

codebook (:,:, 56) =

  -0.9259-0.0000i

  -0.0650 + 0.1012i

   0.0265-0.0698i

   0.0816 + 0.0131i

   0.0142-0.1291i

   0.0383 + 0.0006i

   0.0165-0.0456i

   0.0027 + 0.0454 i

   0.0930-0.0608i

  -0.0151-0.0644i

  -0.0018 + 0.1734i

  -0.0264 + 0.0293i

  -0.1280-0.0931i

  -0.0359-0.0194i

  -0.0317 + 0.0077i

-0.0631 + 0.1139i

codebook (:,:, 57) =

  -0.9025-0.0000i

  -0.0927-0.1592i

  -0.0831-0.0494i

  -0.0662-0.0140i

   0.0408 + 0.0739i

  -0.0525-0.0014i

  -0.0212-0.0250i

  -0.0478 + 0.0376i

  -0.0295 + 0.1932i

   0.0132-0.0122i

   0.0455-0.0257i

  -0.1069-0.0066i

   0.0632 + 0.1892i

  -0.0812 + 0.0914i

   0.0965 + 0.0625i

0.0432 + 0.0213i

codebook (:,:, 58) =

  -0.9295-0.0000i

  -0.2288-0.0367i

  -0.0244 + 0.0503i

  -0.0671-0.0195i

   0.0977-0.0286i

  -0.0268-0.1093i

   0.0222 + 0.0214i

   0.0291-0.0061i

  -0.0878-0.0464i

  -0.0722-0.0873i

  -0.0334 + 0.0395i

  -0.0170-0.0180i

  -0.0655 + 0.1138i

  -0.0310 + 0.0091i

   0.0145 + 0.0414 i

0.0463-0.0328i

codebook (:,:, 59) =

  -0.9338 + 0.0000i

   0.1266 + 0.0201i

  -0.1067 + 0.0745i

   0.0235-0.0305i

  -0.0407-0.0316i

   0.0728 + 0.0690i

  -0.0302-0.0393i

   0.0951-0.0970i

  -0.0963 + 0.0668i

   0.0045-0.0496i

  -0.0696 + 0.0501i

   0.1024 + 0.0027 i

   0.0681-0.0921i

  -0.0042 + 0.0329i

  -0.0552-0.0889i

-0.0186 + 0.0069i

codebook (:,:, 60) =

   0.8211

  -0.2039-0.0406i

  -0.0530-0.0219i

  -0.0000 + 0.0000i

   0.1362 + 0.1362i

  -0.0478-0.0716i

  -0.0124-0.0300i

   0.0000 + 0.0000i

  -0.0000 + 0.1633i

   0.0168-0.0844i

   0.0147-0.0354i

   0.0000 + 0.0000i

  -0.2039 + 0.2039i

   0.1728-0.1155i

   0.1509-0.0625i

0.2085-0.0415i

codebook (:,:, 61) =

   0.9527

  -0.1177-0.0234i

  -0.0435-0.0180i

  -0.0155-0.0104i

   0.0854 + 0.0854i

  -0.0219-0.0328i

  -0.0089-0.0214i

  -0.0023-0.0117i

  -0.0000 + 0.0938i

   0.0071-0.0357i

   0.0096-0.0233i

   0.0085-0.0127i

  -0.1041 + 0.1041i

   0.0614-0.0411i

   0.0707-0.0293i

0.1185-0.0236i

codebook (:,:, 62) =

   1.0000

   0.0000 + 0.0000i

  -0.0000 + 0.0000i

   0.0000-0.0000i

   0.0000 + 0.0000i

   0.0000 + 0.0000i

   0.0000-0.0000i

  -0.0000 + 0.0000i

  -0.0000-0.0000i

  -0.0000-0.0000i

   0.0000-0.0000i

   0.0000-0.0000i

  -0.0000-0.0000i

   0.0000 + 0.0000i

   0.0000-0.0000i

-0.0000 + 0.0000i

codebook (:,:, 63) =

   0.9527

   0.1185 + 0.0236i

   0.0707 + 0.0293i

   0.0614 + 0.0411i

  -0.1041-0.1041i

   0.0085 + 0.0127i

   0.0096 + 0.0233i

   0.0071 + 0.0357i

   0.0000-0.0938i

  -0.0023 + 0.0117i

  -0.0089 + 0.0214i

  -0.0219 + 0.0328i

   0.0854-0.0854i

  -0.0155 + 0.0104i

  -0.0435 + 0.0180i

-0.1177 + 0.0234i

codebook (:,:, 64) =

   0.8211

   0.2085 + 0.0415i

   0.1509 + 0.0625i

   0.1728 + 0.1155i

  -0.2039-0.2039i

   0.0000 + 0.0000i

   0.0147 + 0.0354i

   0.0168 + 0.0844i

   0.0000-0.1633i

  -0.0000 + 0.0000i

  -0.0124 + 0.0300i

  -0.0478 + 0.0716i

   0.1362-0.1362i

  -0.0000 + 0.0000i

  -0.0530 + 0.0219i

-0.2039 + 0.0406i

Embodiments of the present invention can be applied to various types of communication devices operating as receivers and transmitters. In particular, the terminal operates as a receiver in the downlink, while operating as a transmitter in the uplink, and vice versa, while the base station operates as a transmitter in the downlink, while operating as a receiver in the uplink.

As described above, the present invention has been described by way of limited embodiments and drawings, but the present invention is not limited to the above embodiments, and those skilled in the art to which the present invention pertains various modifications and variations from such descriptions. This is possible.

Therefore, the scope of the present invention should not be limited to the described embodiments, but should be determined not only by the claims below but also by the equivalents of the claims.

110: base station

Claims (39)

Recognizing the previous preferred codeword of the receiver;
Calculating a rotation matrix based on any codeword of a previous preferred codeword of the receiver and codewords included in a discrete Fourier transform codebook; And
Generating a new codebook by rotating a reference codebook using the rotation matrix, or recognizing a new preferred codeword of the receiver by rotating at least one codeword included in the reference codebook using the rotation matrix.
Method of operation of the transmitter comprising a. The method of claim 1,
Calculating the rotation matrix
Calculating a rotation matrix by using the following equation.
[Equation]

R is the rotation matrix,

Is the previous preferred codeword of the receiver,

Is any codeword among the codewords included in the discrete Fourier transform codebook,

Is

Is the unitary matrix associated with

Is

A unitary matrix associated with may be predefined, where H stands for Hermian. The method of claim 2,
Previous preferred codeword of the receiver

Is a codeword of any of the codewords included in the discrete Fourier transform codebook,

The operation method of the transmitter is defined by the following equation.
[Equation]

silver

Is the n th element of, where n is

Represents the nth row of m, where

Where m is the n th column and n _t is the number of transmit antennas. The method of claim 2,
Previous preferred codeword of the receiver

Does not belong to codewords of the Discrete Fourier Transform codebook,

Is a method of operating a transmitter generated by orthogonalizing a matrix of the following equation.
[Equation]

silver

Where n is the n th element, n represents the n th row of the matrix of equation, m represents the m th column of the matrix of equation, and n _t represents the number of transmit antennas. The method of claim 1,
Calculating the rotation matrix
Previous preferred codeword of the receiver using Gram-Schmidt orthogonalization

Based on

Steps to generate
Method of operation of the transmitter comprising a. The method of claim 1,
If the previous preferred codeword of the receiver is any one of the codewords included in the discrete Fourier transform codebook,
Calculating the rotation matrix
Calculating the rotation matrix in the form of a diagonal matrix. The method of claim 1,
Receiving information about the new preferred codeword from the receiver; And
Recognize the new preferred codeword using the new codebook based on the information about the new preferred codeword, or correspond to the information about the new preferred codeword among the codewords included in the rotation matrix and the reference codebook. Recognizing the new preferred codeword using a codeword
Method of operation of the transmitter further comprising. The method of claim 1,
Wherein the reference codebook comprises codewords of a polar cap codebook that surrounds any reference codeword and codewords of the discrete Fourier transform codebook. If the previous preferred codeword is one of the codewords of the Discrete Fourier Transform codebook, calculating a rotation matrix such that the codewords of the Discrete Fourier Transform codebook included in the reference codebook can be included in the new codebook; And
Generating the new codebook by rotating a reference codebook using the rotation matrix, or generating a new preferred codeword by rotating at least one codeword included in the reference codebook using the rotation matrix.
Method of operation of the receiver comprising a. 10. The method of claim 9,
Calculating the rotation matrix
Calculating the rotation matrix based on any one of the previous preferred codewords and codewords included in the discrete Fourier transform codebook. 10. The method of claim 9,
Calculating the rotation matrix
Calculating a rotation matrix by using the following equation.
[Equation]

R is the rotation matrix,

Is the previous preferred codeword,

Is any codeword among the codewords included in the discrete Fourier transform codebook,

Is

May be predefined as a unitary matrix associated with

Is

Is the unitary matrix associated with H, which represents Hermian. The method of claim 11,
The previous preferred codeword

Is a codeword of any of the codewords included in the discrete Fourier transform codebook,

The operating method of the receiver is defined by the following equation.
[Equation]

silver

Is the n th element of, where n is

Represents the nth row of m, where

Represents the m-th column, n _t denotes a number of transmit antennas of the transmitter. The method of claim 11,
The previous preferred codeword

Does not belong to codewords of the Discrete Fourier Transform codebook,

Is a method of operation of a receiver generated by orthogonalizing a matrix of the following equation.
[Equation]

silver

Where n is the n th row of the matrix of equations, m is the m th column of the matrix of equations, and n _t is the number of transmit antennas of the transmitter. 10. The method of claim 9,
Determining a new preferred codeword using the new codebook or determining the new preferred codeword using at least one codeword included in the rotation matrix and the reference codebook; And
Feeding back information about the new preferred codeword to a transmitter
Further comprising:
The information about the new preferred codeword includes information about an index of the new preferred codeword in the new codebook or information about an index of a codeword corresponding to the new preferred codeword in the reference codebook. . A computer-readable recording medium having recorded thereon a program for performing the method of claim 1. A recognition unit for recognizing a previously preferred codeword of the receiver;
A calculation unit for calculating a rotation matrix based on any codeword among previous preferred codewords of the receiver and codewords included in a discrete Fourier transform codebook; And
A generation unit for generating a new codebook by rotating a reference codebook using the rotation matrix or recognizing a new preferred codeword of the receiver by rotating at least one codeword included in the reference codebook using the rotation matrix
Transmitter comprising a. A calculation unit for calculating a rotation matrix so that codewords of the discrete Fourier transform codebook included in the reference codebook can be included in the new codebook, when the previous preferred codeword is one of the codewords of the discrete Fourier transform codebook; And
A generation unit generating the new codebook by rotating a reference codebook using the rotation matrix, or generating a new preferred codeword by rotating at least one codeword included in the reference codebook using the rotation matrix.
Receiver comprising a. Vectorizing information associated with a prior explicit channel matrix between the transmitter and receiver to obtain vectorized channel information;
Selecting a previous preferred codeword based on the vectorized channel information;
Calculating a rotation matrix based on the previous preferred codeword; And
Generating a new codebook by rotating a reference codebook using the rotation matrix, or generating a new preferred codeword by rotating at least one codeword included in the reference codebook using the rotation matrix.
Method of operation of the receiver comprising a. The method of claim 18,
The reference codebook is
And a codeword of a polar cap codebook surrounding the arbitrary reference codeword and codewords of the discrete Fourier transform codebook. The method of claim 19,
All elements included in the arbitrary reference codeword are '

', Where N _t is the number of transmit antennas of the transmitter. The method of claim 18,
Each dimension of the codewords included in the reference codebook is N _t ² x 1, where N _t is the number of transmit antennas of the transmitter. The method of claim 19,
The reference codebook
And determining coded distances between codewords of the polar cap codebook and codewords of the vectorized discrete Fourier transform codebook. The method of claim 18,
Vectorizing the information associated with the explicit channel matrix
Vectorizing the explicit channel matrix into a vector to obtain the vectorized channel information, or vectorizing the information generated by processing the explicit channel matrix into a vector. The method of claim 18,
Selecting the previous preferred codeword
Selecting the previous preferred codeword from a plurality of codewords included in a previous codebook or a basic codebook. The method of claim 18,
Feeding back information about the new preferred codeword to a transmitter
Further comprising:
The information about the new preferred codeword includes information about an index of the new preferred codeword in the new codebook or information about an index of a codeword corresponding to the new preferred codeword in the reference codebook. . The method of claim 19,
Calculating the rotation matrix
Calculating the rotation matrix based on the arbitrary reference codeword and the previous preferred codeword. Recognizing a previous preferred codeword selected by the receiver based on a previous explicit channel matrix between a transmitter and a receiver;
Calculating a rotation matrix based on the previous preferred codeword; And
Generating a new codebook by rotating a reference codebook using the rotation matrix, or generating a new preferred codeword by rotating at least one codeword included in the reference codebook using the rotation matrix.
Method of operation of the transmitter comprising a. The method of claim 27,
The reference codebook is
And a codeword of a polar cap codebook surrounding the arbitrary reference codeword or codewords of the discrete Fourier transform codebook. The method of claim 28,
Each dimension of the codewords included in the reference codebook is N _t ² x 1, where N _t is the number of transmit antennas of the transmitter. The method of claim 28,
The reference codebook is
And determining coded distances between codewords of the polar cap codebook and codewords of the vectorized discrete Fourier transform codebook. The method of claim 27,
Receiving information about the new preferred codeword from the receiver; And
Recognize the new preferred codeword using the new codebook based on the information about the new preferred codeword, or correspond to the information about the new preferred codeword among the codewords included in the rotation matrix and the reference codebook. Recognizing the new preferred codeword using a codeword
Method of operation of the transmitter further comprising. The method of claim 27,
Calculating the rotation matrix
Vectorizing the previous preferred codeword; And
Calculating the rotation matrix based on the vectorized previous preferred codeword
Method of operation of the transmitter comprising a. A vectorizer for vectorizing information associated with a prior explicit channel matrix between the transmitter and receiver to obtain vectorized channel information;
A selection unit for selecting a previous preferred codeword based on the vectorized channel information;
A calculator configured to calculate a rotation matrix based on the previous preferred codeword; And
A generation unit for generating a new codebook by rotating a reference codebook using the rotation matrix, or generating a new preferred codeword by rotating at least one codeword included in the reference codebook using the rotation matrix.
Receiver comprising a. A recognition unit for recognizing a previous preferred codeword selected by the receiver based on a previous explicit channel matrix between a transmitter and a receiver;
A calculator for calculating a rotation matrix based on the previous preferred codeword; And
A generation unit for generating a new codebook by rotating a reference codebook using the rotation matrix, or generating a new preferred codeword by rotating at least one codeword included in the reference codebook using the rotation matrix.
Transmitter comprising a. Recognizing the previous preferred codeword of the receiver;
The reference codebook includes codewords of a polar cap codebook and codewords of the discrete Fourier transform codebook surrounding a reference codeword, which is one of the codewords of the discrete Fourier transform codebook, and is defined based on the reference codeword. Accessing a memory in which a product between a matrix and the reference codebook is stored in advance; And
Generate a new codebook from the product between the reference codebook and the matrix defined based on the reference codeword using the previous preferred codeword, or between the reference codebook and the reference codeword using the previous preferred codeword. Generating a new preferred codeword from the product
Method of operation of the transmitter comprising a. 36. The method of claim 35 wherein
Receiving information about the new preferred codeword from the receiver; And
A code corresponding to the new preferred codeword from the product between the reference codebook and the reference codeword or recognizing the new preferred codeword using the new codebook based on the information about the new preferred codeword Recognizing the new preferred codeword by extracting a word
Method of operation of the transmitter further comprising. The method of claim 36,
The information about the new preferred codeword is stored in the index of the codeword corresponding to the new preferred codeword in the information about the index of the new preferred codeword in the new codebook or the product between the reference codebook and the reference codeword. A method of operation of a transmitter comprising information about. The reference codebook includes codewords of a polar cap codebook and codewords of the discrete Fourier transform codebook surrounding a reference codeword, which is one of the codewords of the discrete Fourier transform codebook, and is defined based on the reference codeword. Accessing a memory in which a product between a matrix and the reference codebook is stored in advance; And
Generate a new codebook from the product between the reference codebook and the matrix defined based on the reference codeword using the previous preferred codeword, or between the reference codebook and the reference codeword using the previous preferred codeword. Generating a new preferred codeword from the product
Method of operation of the receiver comprising a. The method of claim 38,
Determining the new preferred codeword using the new codebook or determining the new preferred codeword using at least one codeword extracted from a product between the reference codebook and the reference codeword; And
Feeding back information about the new preferred codeword to a transmitter
Further comprising:
The information about the new preferred codeword includes information about an index of the new preferred codeword in the new codebook or information about an index of a codeword corresponding to the new preferred codeword in the reference codebook. .

Images