KR102115853B1 - Codebook construction - Google Patents

Abstract

A method implemented in a base station used in a wireless communication system is disclosed. The method comprises providing a 1-layer, 2-layer, 3-layer, and 4-layer codebook for 4 transmit (4 transmit) antenna transmission, wherein each codebook comprises a plurality of precoding matrices. And precoding data into one of the plurality of precoding matrices, and transmitting the precoded data to user equipment, wherein the 1-layer and 2-layer codebooks are the first codebook and the first codebook. 2 codebooks, and each precoding matrix in the first codebook includes a first index and a second index. Other apparatus, systems, and methods are also disclosed.

Description

Codebook Configuration {CODEBOOK CONSTRUCTION}

U.S. Provisional Application No. 61 / 774,275, entitled "Observations on Codebook Construction," filed on March 7, 2013, entitled "Observations on Codebook," filed on March 8, 2013 US Provisional Application No. 61 / 775,058, Construction, "US Provisional Application No. 61 / 808,934, entitled" Enhancements to a Structured Codebook, "filed on April 5, 2013, April 29, 2013 United States Provisional Application No. 61 / 817,150, entitled "Enhancement to the 4 Transmit Antenna Precoding Codebook," filed on April 29, 2013, entitled "Enhancement to the 4 Transmit Antenna Precoding Codebook," Claims priority to U.S. Provisional Application No. 61 / 817,247, filed May 10, 2013, U.S. Provisional Application No. 61 / 821,989 entitled "Improvements to the 4 Transmit Antenna Precoding Codebook," The contents of all of these documents are incorporated herein by reference.

The present invention relates to precoding matrix design, and more particularly, to a precoding matrix design that derives a precoding matrix as a product of two matrices.

Wireless communication systems require even higher spectral efficiencies to accommodate higher throughput requirements within limited frequency bands. Multiple antenna or multiple-input and multiple-output (MIMO) systems and in particular closed loop transmission techniques such as beamforming and precoding have been extensively considered to improve spectral efficiency. In MIMO precoding schemes, data to be transmitted is divided into one or more streams, and the streams are mapped to one or more transport layers, and data in the transport layers is pre-coded into a precoder or precoding matrix before being transmitted. Is coded. The number of transport layers is called a transmission rank. This transmission rank can be optimally selected for a given channel implementation, for example by considering transmission power and overall channel statistics.

In codebook-based precoding strategies, a predetermined codebook is created that can be used for a transmitter, ie a base station (BS), and all receivers, ie, mobile stations (MSs) or user equipments (UEs). The receiver then selects a precoder that maximizes its performance (eg, data rate) from the codebook, and feeds back the precoder index. Also, the selection of the precoder rank may be included in the precoder selection algorithm. The feedback rate may vary from short-term feedback once for every successive time interval to long-term feedback once for every several successive time intervals.

delete

In many systems, optimal precoders from the codebook for two adjacent transmission blocks are close for proper distance measurement in a set of all possible precoders. Here, adjacent blocks are for a set of tones in, for example, orthogonal frequency-division multiplexing (OFDM) systems, because in actual systems the channel does not change abruptly from one transmit block to the adjacent block. It can be considered in time or frequency. Thus, the precoder used in these blocks can be the same if the channel is fairly stable and the codebook resolution is not too high. By increasing the codebook resolution or by having a more dynamic channel, the precoders of adjacent blocks are no longer identical, but can be brought closer. Proximity between two precoders can be measured based on an appropriate distance metric in the space of all these precoders. Several examples of differential, dual and multi-resolution codebooks are disclosed in references [5] and [6].

In order to obtain an efficient codebook, that is, easy to store and search with low feedback overhead, and also to obtain a codebook valid for both uniform linear array (ULA) and cross-pole configurations, 4 transmit antennas ( TX) Consider the design of the precoding codebook for the MIMO downlink channel, and describe the appropriate codebook structure in detail for both uniform linear array (ULA) and cross-pole antenna configurations. Some documents have proposed codebook designs for specific antenna configurations [7]. The basic characteristics of the spatial correlation matrices used by the present invention are not used in the prior art. In this specification, the codebook structure is derived using the basic characteristics of spatial correlation matrices under ULA and cross-pole antenna configurations. Each precoding codeword is derived as a product of two matrices, which makes them efficient and also achieves lower feedback overhead for a given performance level and better performance for a given feedback overhead.

References

[1] Ericsson, ST-Ericsson, "Design and Evaluation of 4 TX Precoder Codebooks for CSI Feedback," 3GPP TSG RAN WG1 R1-104847 62, Madrid, August 2010.

[2] A. Forenza, D. Love and R. Heath, "Simplified Spatial Correlation Models for Clustered MIMO Channels With Different Array Configurations," IEEE Trans. Veh . Tech. , July 2007.

[3] S. Loyka, "Channel capacity of MIMO architecture using the exponential correlation model," IEEE Commun . Letters , 2001.

[4] D. Love, R. Heath and T. Strohmer, "Grassmannian beamforming for multiple-input multiple-output wireless systems," IEEE Trans. Inf . Theory , Oct. 2003.

[5] MA Khojastepour et al ., "STATIC AND DIFFERENTIAL PRECODING CODEBOOK FOR MIMO SYSTEMS," US Patent Application Publication US 2008/0232501 A1.

[6] MA Khojastepour et al ., "MULTI-RESOLUTION PRECODING CODEBOOK," US Patent Application Publication US 2009/0274225 A1.

[7] 3GPP TS 36.213 V10.8.0 (2012-12), 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical layer procedures (Release 10), http://www.3gpp.org/ .

[8] NEC Group, "DL MU-MIMO Enhancement Schemes," 3GPP TSG RAN WG1 R1- 130364.

[9] NEC Group, MU-MIMO: "CQI Computation and PMI Selection," 3GPP TSG RAN WG1 R1-103832.

[10] NEC Group, "DL MU-MIMO enhancement via Residual Error Norm feedback," 3GPP TSG RAN WG1 R1-113874 .

It is an object of the present invention to provide a codebook with efficient precoding codewords that require lower feedback overhead for a given performance level and also achieve better performance for a given feedback overhead.

One aspect of the present invention includes a method implemented in a base station used in a wireless communication system. The method comprises providing 1-layer, 2-layer, 3-layer, and 4-layer codebooks for 4 transmit (4TX) antenna transmission, wherein each codebook comprises a plurality of precoding matrices. And precoding data into one of the plurality of precoding matrices, and transmitting the precoded data to user equipment, each of the 1-layer and the 2-layer codebooks comprising It includes one codebook and a second codebook, and each precoding matrix in the first codebook includes a first index and a second index.

Another aspect of the invention includes a method implemented in user equipment used in a wireless communication system. The method includes receiving precoded data from a base station, and each of the 1-layer, 2-layer, 3-layer, and 4-layer codebooks for transmitting 4 transmit (4TX) antennas comprises a plurality of frees. Coding matrices, and each of the 1-layer and the 2-layer codebooks includes a first codebook and a second codebook, and each precoding matrix in the first codebook includes a first index and a second index do.

Another aspect of the invention includes a base station used in a wireless communication system. The base station includes a transmitter that transmits pre-coded data to user equipment, and each of the 1-layer, 2-layer, 3-layer, and 4-layer codebooks for 4TX (4 transmit) antenna transmission is a plurality of Precoding matrices, each of the 1-layer and the 2-layer codebooks including a first codebook and a second codebook, and each precoding matrix in the first codebook has a first index and a second index. Includes.

Another aspect of the invention includes user equipment used in a wireless communication system. The user equipment includes a receiver that receives pre-coded data from a base station, and each of the 1-layer, 2-layer, 3-layer, and 4-layer codebooks for 4TX (4 transmit) antenna transmission is a plurality of Precoding matrices of, wherein each of the first-layer and second-layer codebooks includes a first codebook and a second codebook, and each precoding matrix in the first codebook includes a first index and a first 2 Includes index.

Another aspect of the present invention includes a wireless communication system, wherein each codebook comprises 1-layer, 2-layer, 3-layer, and 4-layer codebooks for 4 transmit (4TX) antenna transmission. The base station having the codebooks comprising a plurality of precoding matrices, precoding data into one of the plurality of precoding matrices, and user equipment receiving the precoded data from the base station, wherein the 1- Each of the layer and the two-layer codebooks includes a first codebook and a second codebook, and each precoding matrix in the first codebook includes a first index and a second index.

Another aspect of the invention includes a method implemented in a wireless communication system. The method comprises precoding data; And transmitting, from the base station to the user equipment, the precoded data, each of the 1-layer, 2-layer, 3-layer, and 4-layer codebooks for transmitting a 4TX (4 transmit) antenna. Precoding matrices of, wherein each of the 1-layer and the 2-layer codebooks includes a first codebook and a second codebook, and each precoding matrix in the first codebook includes a first index and a second index. It includes.

The first index may be for a plurality of subbands, and the second index may be for each subband.

The second codebook may include a legacy codebook or a householder codebook.

Each of the three-layer and four-layer codebooks may include a legacy codebook or a householder codebook.

으로부터 선택되고, 또한 제 2 행렬 W ⁽²⁾는 외부 코드북으로부터 선택될 수 있다.Each precoding matrix W in the first codebook satisfies W = W ⁽¹⁾ W ⁽²⁾ , and the first matrix W ⁽¹⁾ is an internal codebook.

, And also the second matrix W ⁽²⁾ can be selected from an external codebook.

으로부터 선택되고, 또한 제 2 행렬 W ⁽²⁾는 제 2 코드북으로부터 선택된다.Another aspect of the invention includes a method implemented in a base station used in a wireless communication system. The method includes providing a codebook comprising a plurality of precoding matrices, precoding data into one of the plurality of precoding matrices, and transmitting the precoded data to a user equipment. And each precoding matrix W satisfies W = W ⁽¹⁾ W ⁽²⁾ , and the first matrix W ⁽¹⁾ is the first codebook

And the second matrix W ⁽²⁾ is selected from the second codebook.

으로부터 선택되고, 또한 제 2 행렬 W ⁽²⁾는 제 2 코드북으로부터 선택된다.Another aspect of the invention includes a method implemented in user equipment used in a wireless communication system. The method includes receiving, from a base station, precoded data as one of a plurality of precoding matrices, the codebook comprising the plurality of precoding matrices, and each precoding matrix W is W = W ^{(1 )} W ⁽²⁾ , and the first matrix W ⁽¹⁾ is the first codebook.

And the second matrix W ⁽²⁾ is selected from the second codebook.

으로부터 선택되고, 또한 제 2 행렬 W ⁽²⁾는 제 2 코드북으로부터 선택된다.Another aspect of the invention includes a base station used in a wireless communication system. The base station includes a transmitter that transmits precoded data to one of a plurality of precoding matrices to user equipment, the codebook includes the plurality of precoding matrices, and each precoding matrix W is W = W ^{( 1)} W ⁽²⁾ is satisfied, and the first matrix W ⁽¹⁾ is the first codebook

And the second matrix W ⁽²⁾ is selected from the second codebook.

으로부터 선택되고, 또한 제 2 행렬 W ⁽²⁾는 제 2 코드북으로부터 선택된다.Another aspect of the invention includes user equipment used in a wireless communication system. The user equipment includes a receiver that receives data precoded from one of a plurality of precoding matrices from a base station, the codebook includes the plurality of precoding matrices, and each precoding matrix W is W = W ^{( 1)} W ⁽²⁾ is satisfied, and the first matrix W ⁽¹⁾ is the first codebook

And the second matrix W ⁽²⁾ is selected from the second codebook.

으로부터 선택되고, 또한 제 2 행렬 W ⁽²⁾는 제 2 코드북으로부터 선택된다.Another aspect of the invention includes a wireless communication system, the wireless communication system having a codebook including a plurality of precoding matrices, a base station precoding data into one of the plurality of precoding matrices, and And user equipment for receiving the precoded data from the base station, each precoding matrix W satisfies W = W ⁽¹⁾ W ⁽²⁾ , and the first matrix W ⁽¹⁾ is the first codebook

And the second matrix W ⁽²⁾ is selected from the second codebook.

으로부터 선택되고, 또한 제 2 행렬 W ⁽²⁾는 제 2 코드북으로부터 선택된다.Another aspect of the invention includes a method implemented in a wireless communication system. The method includes precoding data into one of a plurality of precoding matrices, and transmitting the precoded data from a base station to user equipment, the codebook comprising the plurality of precoding matrices, Also, each precoding matrix W satisfies W = W ⁽¹⁾ W ⁽²⁾ , and the first matrix W ⁽¹⁾ is the first codebook.

And the second matrix W ⁽²⁾ is selected from the second codebook.

를 참조하는 이득 벡터들의 3비트 코드북의 도면.
도 3은 랭크-1에 대한 8-PSK 알파벳에서의 공통-위상 항들의 도면.
도 4a는 랭크-2에 대한 16-PSK 알파벳에서의 공통-위상 항들의 도면.
도 4b는 랭크-2에 대한 16-PSK 알파벳에서의 다른 공통-위상 항들의 도면.
도 5는 랭크-2에 대한 8-PSK 알파벳에서의 공통-위상 항들의 도면.
도 6a는 랭크-1에 대한 8-PSK 알파벳에서의 공통-위상 항들의 도면.
도 6b는 랭크-1에 대한 8-PSK 알파벳에서의 다른 공통-위상 항들의 도면.
도 7은 랭크-2에 대한 24-PSK 알파벳에서의 공통-위상 항들의 도면.
도 8a는 랭크-2에 대한 24-PSK 알파벳에서의 공통-위상 항들의 도면.
도 8b는 랭크-2에 대한 12-PSK 알파벳에서의 공통-위상 항들의 도면.
도 9는 랭크-2에 대한 16-PSK 알파벳에서의 공통-위상 항들의 도면.
도 10은 랭크-2에 대한 16-PSK 알파벳에서의 공통-위상 항들에 대한 도면.1 has N _T transmit-antennas at the transmitter and also N _R at the receiver. Drawing of a downlink multiuser MIMO system with receive antennas.
2 is a gain vector

A diagram of a 3-bit codebook of gain vectors referring to.
3 is a diagram of common-phase terms in the 8-PSK alphabet for rank-1.
4A is a diagram of common-phase terms in the 16-PSK alphabet for rank-2.
4B is a diagram of other common-phase terms in the 16-PSK alphabet for rank-2.
5 is a diagram of common-phase terms in the 8-PSK alphabet for rank-2.
6A is a diagram of common-phase terms in the 8-PSK alphabet for rank-1.
6B is a diagram of other common-phase terms in the 8-PSK alphabet for rank-1.
7 is a diagram of common-phase terms in the 24-PSK alphabet for rank-2.
8A is a plot of common-phase terms in the 24-PSK alphabet for rank-2.
8B is a diagram of common-phase terms in the 12-PSK alphabet for rank-2.
9 is a diagram of common-phase terms in the 16-PSK alphabet for rank-2.
10 is a diagram of common-phase terms in the 16-PSK alphabet for rank-2.

1 shows a downlink multiuser MIMO system with N _T transmit-antennas in the BS and N _R receive antennas in the UE. A multi-antenna communication system 100 with a multi-level precoding codebook is schematically illustrated in FIG. 1. The transmitter 110 transmits from t transmit antennas 111.1-111.t to r receive antennas 121.1-121.r coupled to the receiver 120 through the fading channels 130 to r. Send. Channel estimator 125 provides an estimate of channel 130 to receiver 120. In addition, the channel estimation is quantized and provided to the transmitter 110 through the quantization rate control feedback channel 135.

In systems using beamforming, such as MIMO systems, the beamforming matrix (also referred to as a precoding matrix, precoder, codeword, or precoding codeword) generated in response to received channel conditions is first a receiver. After being calculated and quantized at, it is provided to the source transmitter (eg, via feedback). A conventional approach to reducing the overhead associated with this feedback is to provide matrix codebook (s) at each of the transmitter and receiver, where each codebook (s) can be used depending on the channel conditions recognized by the receiver. It includes a plurality of potential beamforming matrices or a set of beamforming matrices. If the receiver has identified the appropriate matrix codebook (s), the receiver will feed back one or more indices pointing to the appropriate codeword from the codebook (s) stored in the transmitter (instead of the actual matrix entries).

I. Example 1

1 Uniform Linear Array

Unless otherwise stated below, it is assumed that the co-polarized antennas are closely spaced.

인 것으로 규정하도록 하며, 여기서The present inventors made the following observations regarding the configuration of a uniform linear array (ULA) transmit antenna. Consider a system with N common-polarized transmit antennas, where C is set to represent the transmit spatial correlation matrix. J is a matrix with zeros everywhere except cross diagonal elements, i.e.

To be defined as

In the case of the following equation, the vector becomes Hermitian.

는

의 켤레를 나타낸다. 본 발명자들은 다음과 같은 특성들의 세트를 제안한다. 제 1 관찰은 ULA 송신 안테나 구성의 공간 상관 행렬에 관한 것으로서, 넓은 범용성을 가지고서 유효하다([2] 참조).here,

The

Represents a pair of The inventors propose the following set of properties. The first observation relates to the spatial correlation matrix of the ULA transmit antenna configuration, and is effective with wide versatility (see [2]).

observe One procession C The Hermit Teplits  Matrix, i.e. C Satisfies the following,

는 C의 켤레를 나타낸다.here,

Denotes a pair of C 's.

를 만족시키는 에르미트 테플리츠 행렬 A 및 그것의 고유벡터인 x 를 고려하는 경우, 다음의 등식과

를 만족시키는 y 가 존재한다. Lemma 1, any Hermitian eigenspace of Te pleated matrix (eigenspace) can be fully described by the LE is committed vector. In other words,

Considering the Hermitt-Teplits matrix A and x , its eigenvector , satisfying the equation

Y satisfying exists.

는 대수적 다중도(algebraic multiplicity) 값을 갖는 에르미트 테플리츠 행렬 A의 고유값인 것으로 가정하자. 그러면, x가

를 만족시키는 고유벡터라면,

인 경우에 대하여 다음과 같이 된다. Assistant Theorem 2

Let's assume that the eigenvalues of matrix A pleated Te Er US agent also has a multi-algebraic values (algebraic multiplicity). Then, x

If the eigenvector satisfies

In the case of, it becomes as follows.

이다.here

to be.

The simplified model for the correlation matrix is the exponential correlation model [3], which is further described in the appendix and is given as follows.

이다.here,

to be.

2.1 4  TX ULA

In this section, consider the case where N = 4 common-polarized transmit antennas. First, if there is no loss of generality, the following structure can be imposed on each eigenvector x of the spatial correlation matrix C.

행렬 C가 에르미트 테플리츠 행렬이어야 함을 고려하여, 보조정리들 1 및 2를 불러들이면, 다음과 같이 됨을 추론할 수 있다.here,

Considering that the matrix C should be the Hermitt-Teplits matrix, it can be inferred that if the auxiliary theorems 1 and 2 are called, then

Next, consider any two eigen-vectors of the form (8) given by

그리고, 이들 2개의 고유벡터 간의 직교성을 강화하는 충분조건은 다음의 등식을 보장하기 위한 것이다.here,

In addition, the sufficient condition for enhancing orthogonality between these two eigenvectors is to ensure the following equation.

This can be simplified to the following:

에 대해서 유효하다.(11) is not required, but scalars of all possible values

It is valid for

2 polarization  Polarized Setup

는 다음과 같이 표기될 수 있다.The transmitter is assumed to have 2N cross-polarized antennas, each of which includes a pair of N common-polarized antennas. Then, the correlation matrix for each of these two common-polarization sets is denoted by C , Hermitian and Toeplitz. Full 2N × 2N correlation matrix

Can be written as

는 크로네커 프로덕트(kronecker product)를 나타내며,

이다.

의 임의의 고유벡터

는 다음의 형태를 갖는 것으로 나타낼 수 있다.here,

Denotes a kronecker product,

to be.

Random eigenvectors of

Can be represented as having the following form.

는 행렬

의 고유벡터이며, x는 C의 고유벡터이다. 또한, 행렬

의 2개의 고유벡터는

및

이며, 여기서

은 전치 연산(transpose operation)을 나타내고, 최적성의 손실이 없는 경우

는 무시할 수 있다. 2개의 고유-값들은

이다. 또한, 행렬

는 2개의 송신 ULA의 상관 행렬을 모델링한 것임에 유의한다.here,

The matrix

Is the eigenvector of, and x is the eigenvector of C. Also, the matrix

The two eigenvectors of

And

Where

Denotes a transpose operation and there is no loss of optimality

Can be ignored. The two eigen-values

to be. Also, the matrix

Note that is a model of the correlation matrix of two transmitting ULAs.

3 Codebook  Configuration

를 먼저 고려하도록 하며, 여기서

이다. 랭크-1 코드북을 형성하도록 구성되는 3개의 컴포넌트 코드북들을 규정하도록 한다. 첫 번째 컴포넌트 코드북은, 이득 벡터 코드북으로 지칭되고

으로 표기되며, 이것은 이득들

이 도출되는 코드북이다. 다른 2개의 컴포넌트 코드북은 위상 항(phase term)들

을 양자화하기 위한 코드북들이며,

및

로 표기된다. 이득 벡터 코드북

에 대하여 고려해 보도록 한다. 근접 이격된 4TX ULA를 커버하기 위해서는, (8) 형태의 구조를 가진 랭크-1 코드북에서의 충분한 벡터들이 필요하다.

를 이득 벡터로 지칭하도록 하며, 도 2에서는 이득 벡터들에 대한 3 비트 코드북을 제공하고 있으며, 여기서 설정가능한 스칼라

인 경우에 대하여,

이다. 인덱스들 0,1,2에 대응하는 이득 벡터들은 (8)에서의 제약조건을 따름으로써, 4 TX 근접 이격된 ULA 케이스에 적합함에 유의한다. 인덱스 0에 대응하는 이득 벡터는 4 TX 크로스-폴 케이스에 적합하며, 인덱스들 3,4에 대응하는 이득 벡터들은 본 명세서에서 전력 불균형(power imbalance) 케이스(부록 8 참조)로 지칭되는 시나리오를 처리하는데 적합하다. 인덱스 7은 기존의 디폴트 코드북의 재-사용을 나타내며, 인덱스들 5,6은 단순히 더 많은 선택들을 제공하기 위해 포함된 것이다.Now, proceed to specifying the codebook using the observations generated in sections 1 and 2. In particular, a subset of codebooks suitable for proximity-spaced 4TX ULA and cross-pole antenna configurations, as well as other configurations, should be specified. First, consider a rank-1 codebook that includes a set of 4x1 vectors. If there is no loss of generality, the general structure

Let's consider first, where

to be. Three component codebooks configured to form a rank-1 codebook are defined. The first component codebook is called a gain vector codebook

Is denoted by, and these are the benefits

This is the derived codebook. The other two component codebooks are phase terms.

Codebooks for quantizing

And

Is denoted as. Gain vector codebook

Let's consider. To cover the closely spaced 4TX ULA, sufficient vectors in the rank-1 codebook having the structure (8) are needed.

Is referred to as a gain vector, and FIG. 2 provides a 3-bit codebook for gain vectors, which can be set here.

In the case of,

to be. Note that the gain vectors corresponding to the indices 0,1,2 are suitable for the 4 TX proximity spaced ULA case by following the constraint in (8). The gain vector corresponding to index 0 is suitable for a 4 TX cross-pole case, and the gain vectors corresponding to indexes 3 and 4 deal with a scenario referred to herein as a power imbalance case (see Appendix 8). It is suitable for. Index 7 represents the re-use of the existing default codebook, and indexes 5 and 6 are simply included to provide more choices.

및

을 도입하도록 한다.

인 (8)에서의 제약조건을 적용하도록 하며, 이에 따라 벡터 x는 다음과 같이 확장될 수 있다. Next, to quantize the phases, two phase codebooks,

And

To introduce.

The constraint in phosphorus (8) is applied, and the vector x can be expanded as follows.

을 사용하여

를 선택하고, 또한 코드북

을 사용하여

을 선택하도록 한다. 이들 2개의 코드북을 구성하기 위한 단순 방식은, 각 코드북에 대한 소정 수의 비트들을 사용하는 [0,2π)의 균일 양자화(uniform quantization)를 통한 것이다. 이러한 위상들을 채택하는 선택으로, 도 2의 이득 벡터 코드북에서 인덱스 0에 대응하는 이득 벡터를 선택하면, 결과 벡터는 4TX 크로스-폴의 상관 행렬의 일반 고유-벡터 구조를 따르게 됨을 알 수 있다. 마찬가지로, 이득 벡터 코드북에서 인덱스들 0,1,2 중의 어느 것에 대응하는 이득 벡터를 채택할 시에는, 결과 벡터가 4TX ULA의 상관 행렬의 일반 고유-벡터 구조를 따르게 됨을 알 수 있다.Codebook

Using

And also the codebook

Using

Choose to. A simple way to construct these two codebooks is through uniform quantization of [0,2π) using a predetermined number of bits for each codebook. As a selection that adopts these phases, it can be seen that when a gain vector corresponding to index 0 is selected in the gain vector codebook of FIG. 2, the resulting vector follows the general eigen-vector structure of the 4TX cross-pole correlation matrix. Similarly, when adopting a gain vector corresponding to any of the indexes 0, 1, 2 in the gain vector codebook, it can be seen that the result vector follows the general eigen-vector structure of the correlation matrix of 4TX ULA.

Now, consider a rank-2 codebook consisting of a set of semi-unitary 4x2 matrices. From the observations made in section 1, it is possible to specify a subset of matrices with the following structure.

인 경우에는, 이 구조가 4TX 크로스-폴 구성(섹션 2에서 논의됨)에 적합할 수도 있음에 유의한다. 또한, 다음의 구조를 가진 행렬들을 포함하도록 할 수 있으며,This structure does not satisfy the 4TX ULA (see Section 1), and also does not satisfy the structure of the first two major eigenvectors of the 4TX ULA construct with exponential correlation model (discussed in Section 6),

Note that in the case, this structure may be suitable for a 4TX cross-pole configuration (discussed in Section 2). Also, it is possible to include matrices having the following structure,

This does not satisfy 4TX ULA.

4 Products  Form of codebook

Next, based on the principles outlined in Sections 1 and 2, two codebook configurations will be discussed in which each codeword is derived as a matrix product. In each case, using the codebook designed in [1] as a base, we will extend this by following the principles outlined in Sections 1 and 2.

인 경우에 대하여,

인 것으로 놓도록 한다. 이러한 코드북을 제 1 실시예로 지칭하도록 하며, 그것의 내부 (광대역) 코드북을 다음과 같이 규정하도록 한다.

In the case of,

Put it on. This codebook is referred to as the first embodiment, and its internal (broadband) codebook is defined as follows.

은 하다마드 프로덕트(Hadamard product)를 나타내며, 또한here,

Represents the Hadamard product, and

랭크-1 외부 코드북은 다음과 같이 규정된다.here,

The rank-1 external codebook is defined as follows.

Here, e _i represents a 4 × 1 column selection vector. The external rank-2 codebook is defined as follows.

인 경우에 대하여,

,

임에 유의한다.Scalars a _q , b _q One of the choices is configurable scalars

In the case of,

,

Note that it is.

로부터 하나의 공통 행렬, 즉

를 먼저 선택하도록 한다. 그러면, 각각의 서브대역 n 상에, 외부 (서브대역) 랭크-2 코드북

로부터의 행렬, 즉

가 선택되며, 해당 서브대역에 대한 최종 프리코더 선택은

로서 획득된다. 편의를 위해,

가 랭크-2에 대응하는 (최종) 코드북을 나타내며, 이것은 내부 프리코더

의 선택에 주어진 모든 가능한 최종 프리코더 선택들을 포함하는 것으로 놓도록 한다. 그 밖의 랭크들 및 내부 프리코더

에 대한 다른 선택들을 위하여 유사한 절차 및 표기법이 채택된다.Internal (wideband) codebook, one for each subband, at each feedback interval to select rank-2 codewords

From one common matrix, i.e.

Choose first. Then, on each subband n, the external (subband) rank-2 codebook

Matrices from

Is selected, and the final precoder selection for that subband is

Is obtained as. for your convenience,

Indicates a (final) codebook corresponding to rank-2, which is an internal precoder

Be sure to include all possible final precoder choices given in the choice of. Other ranks and internal precoder

Similar procedures and notations are adopted for other options for.

중의 하나의 선택은, 설정가능한 스칼라들이

인 경우에 대하여,

가 되도록 하기 위한 것임에 유의한다. 이러한 선택 하에서, 3중항 세트

를 결정하는 방식을 이하 기술하도록 한다. 지수 상관(exponential correlation) 모델을 사용하는 부록 7에서의 논의로부터, (비-양자화된)

가 [0,1)에서 균일하게 분포되는 것으로 가정하는 것이 바람직한 선택이 되도록

를 관련시키도록 한다. 따라서, 유한 집합

을 획득하기 위한 바람직한 전략은, 소정 수의 비트들을 사용하는 [0,1)의 균일 양자화를 통한 것이다. 일 예로는 2 비트에 관한

가 될 수 있다.

One of the choices is that the configurable scalars

In the case of,

Note that it is intended to be. Under these choices, triplet sets

The method of determining is described below. From the discussion in Appendix 7 using the exponential correlation model, (non-quantized)

To be assumed to be uniformly distributed at [0,1), it is a desirable choice.

To be related. Thus, a finite set

The preferred strategy for acquiring is through uniform quantization of [0,1) using a certain number of bits. One example is about 2 bits

Can be

의 선택을 고려하면, 하나의 가능성은 그것들을 부록 7에서 논의되어 있는 변수들

과 관련시키는 것이다. 이에 따라, 상관 크기 파라미터

에 대한 값들의 유한 집합이 선택될 수 있으며, 이로부터 벡터들의 집합

가 획득될 수 있다. 예를 들어, 상관 크기 파라미터

에 대한 집합

을 가정할 수 있다. 그러면, 부록 7의 공식들을 적용하여 벡터들의 집합

가

이 되는 것을 확인할 수 있다. 그러면, 3중항 세트

는 카티션 프로덕트(Cartesian product)

로서 규정될 수 있으며, 여기서는 카티션 프로덕트를 나타내기 위해

를 사용하였다. 예를 들어, 위에서 제공된 특정 인스턴스들

및

을 사용하면, 카티션 프로덕트

는 사이즈 16 또는 동등하게는 4 비트를 갖는다는 것을 알 수 있다. 다른 예는

및 상관 크기(correlation magnitude) 파라미터에 대한 3개의 값

만을 사용하는 집합

를 사용함으로써 사이즈 15를 가진 카티션 프로덕트를 획득하는 것일 수 있다. 다른 예는 카티션 프로덕트가 사이즈 16을 가지며,

및 상관 크기 파라미터에 대한 2개의 값

만을 사용하는 집합

를 사용함으로써 획득되는 것이다.

Given the choice of, one possibility is that they are the variables discussed in Appendix 7.

It is related to. Accordingly, the correlation size parameter

A finite set of values for can be selected, from which a set of vectors

Can be obtained. For example, correlation size parameter

Set for

Can assume Then, apply the formulas in Appendix 7 to set the vectors

end

This can be confirmed. Then, triplet set

Is a Cartesian product

It can be defined as, here to represent a Cartesian product

Was used. For example, the specific instances provided above

And

If you use a Cartesian product

It can be seen that has size 16 or equivalently 4 bits. Another example

And three values for the correlation magnitude parameter

A set using only

It may be to obtain a Cartesian product having a size of 15 by using. In another example, the Cartesian product has a size of 16,

And two values for the correlation size parameter

A set using only

It is obtained by using.

Now, hereinafter referred to as the second embodiment, let us consider another alternative codebook whose codewords are also derived in product form. Now, define the internal broadband codebook as follows.

here,

or,

The rank-1 external codebook is defined as follows.

And, the rank-2 external codebook is defined as follows.

In either case, the rank-3 and rank-4 codebooks are fixed to legacy (householder) rank-3 and rank-4 codebooks. Also, the entire legacy codebook can be included as a subset.

의 경우, 내부 프리코더

의 각각의 선택에 있어서, 해당 랭크에 대응하는 코드북

내의 각 프리코더 행렬이 확률이 같게 선택될 수 있으며, 그 선택된 프리코더 행렬에 대한 각 행의 표준 제곱의 기대값(즉, 해당 행의 원소들의 크기 제곱들의 합)이 동일한 것으로 가정하는 것이다. 이러한 특성은 전력 증폭기들을 작동시키고(즉, 전력 증폭기들의 백오프(backoff)를 제어하고) 사용가능한 전송 전력을 활용함에 있어서 유익하다.Note that the first embodiment has desirable characteristics that are overlooked in the second embodiment. This characteristic, each rank

In the case of an internal precoder

For each selection of, the codebook corresponding to the rank

Each precoder matrix within may be selected with equal probability, and it is assumed that the expected value of the standard square of each row for the selected precoder matrix (that is, the sum of squares of the magnitudes of the elements of the row) is the same. This property is beneficial in operating power amplifiers (ie, controlling the backoff of power amplifiers) and utilizing available transmit power.

4.1 more  To a large codebook Embedding

Note that the channel matrix implementation is determined according to the spatial correlation matrix and short-term (so-called fast) fading. In some scenarios, there may be significant variations in the observed channel matrix due to fast-fading, such as when common-polarized antennas are widely spaced apart. Therefore, the preferred codebook needs to accommodate significant deviations in the observed channel matrix due to such fast-fading, thereby including codewords designed using other criteria such as minimum chordal distance. There is [4]. A useful way to solve these cases is to embed a codebook obtained using the principles described above as a subset within a larger codebook.

5 Conclusion

The codebook structure has been described in detail above, and two examples according to the matrix product form are presented. This structure is derived by the basic characteristics of the spatial correlation matrix, and makes codebook optimization feasible.

6 Appendix : 4 TX with exponential correlation model ULA

Next, consider a case in which the correlation matrix is further specialized as follows.

이고,

및

를 만족시킨다. 행렬 C는 에르미트 테플리츠이며, 하나의 복소 스칼라(complex scalar)에 의해서 완전히 특징지어질 수도 있음에 유의한다. 따라서, 그것의 고유벡터들은 일반적인 에르미트 테플리츠 행렬의 고유벡터에 의해 처리되는 것 이외에, 더 많은 구조를 가질 것으로 예상될 수 있다. 또한, 이하에서는 이 추가 구조를 활용할 것이다. 이 케이스에 대한 행렬 J는 다음과 같이 표기될 수 있다.here,

ego,

And

Satisfy. Note that the matrix C is Hermit Teplits, and may be fully characterized by one complex scalar. Thus, its eigenvectors can be expected to have more structures besides being processed by the eigenvectors of a typical Hermitt-Teplits matrix. In addition, hereinafter, this additional structure will be utilized. The matrix J for this case can be written as

인 경우를 고려하도록 한다. 이 경우에, (24)에서의 형태의 임의의 행렬에 대한 고유-벡터들은 다음의 특성들을 가지게 된다. (24)에서의 형태의 임의의 행렬 C를 고려하여,first,

Consider the case. In this case, the eigen-vectors for any matrix of the form in (24) have the following properties. Taking into account the arbitrary matrix C of the form in (24),

는 켤레 전치 연산을 나타내고,

이며, 이 경우

이며 이들은 4개의 실수값인 고유값들을 나타낸다. 그러면, 다음의 등식이 되며,Let (25) be put to indicate its eigen-decomposition, where

Denotes a conjugate transposition,

And in this case

And these represent the eigenvalues, which are four real values. Then, it becomes the following equation,

는 하다마드 프로덕트를 나타내고,

는,

인 경우에 대하여, 다음의 형태의 대각 행렬이 된다.here,

Represents the Hadamard product,

Is,

In the case of, it becomes a diagonal matrix of the following form.

가

및

를 만족하는 경우에 대하여, 다음의 구조를 갖는다.Matrix S is positive real scalars

end

And

In the case of satisfying, it has the following structure.

의 각 열은 다음의 조건들을 만족해야만 한다.The matrix H is a 4x4 real-valued Hadamard matrix, that is, the columns of H are mutually orthogonal, and all of its elements belong to the set {± 1}. Then, because each column of E must satisfy the conditions in (5),

Each column of must satisfy the following conditions.

In addition, since E must be a unitary matrix, H must also satisfy the following additional conditions.

An important example H is as follows:

임을 고려하면, 다음과 같은 스칼라들

를 산출하는 공식들을 유도해 낼 수 있다. 먼저,

로 놓도록 한다. (26)에서 이것으로 대체하면, 일부 처리 이후에 다음의 등식을 산출하게 된다.Using the H given above

Considering that, the following scalars

We can derive the formulas that yield. first,

Put it on. Substituting this in (26) yields the following equation after some processing.

이고,

이다. 특별한 경우에,

이면, 상관 행렬 C는 항등 행렬을 감소시킴으로써,

를 임의적으로 선택할 수 있도록 한다(각각의 표준 제약사항들의 적용). 또한,

인 경우,

의 관계를 가진

인 것으로 결정할 수 있으며, 여기서,

이다.here,

ego,

to be. In special cases,

Is, the correlation matrix C decreases the identity matrix,

Can be arbitrarily selected (the application of each standard constraint). In addition,

If it is,

With

Can be determined, where:

to be.

이면, 행렬 C는 다음에 의해 주어지는 랭크-1 행렬이 됨에 유의한다.Meanwhile,

Note that if it is, matrix C is a rank-1 matrix given by

Then, the eigen-vector of C corresponding to one non-zero eigenvalue can be represented as having the following form.

이며, 이에 따라

이 된다.

의 선택은 해당 고유-값이 0이기 때문에, 임의적일 수 있다(표준 제약사항의 적용).here,

And accordingly

It becomes.

The choice of can be arbitrary, since its eigen-value is 0 (application of standard constraints).

7 Appendix : Acceptance of power imbalance

는 다음과 같이 표기될 수 있다.A more general model for spatial correlation of the cross-pole antenna configuration is as follows. Consider a transmitter with 2N cross-polarized antennas each comprising a pair of N common-polarized antennas. Then, the correlation matrix for each of these two common-polarization sets is denoted by Hermit and Teplits C. Full 2N × 2N correlation matrix

Can be written as

이고,

이며 이것은

을 만족시킨다.

의 임의의 고유벡터

는 다음의 형태를 가질 수 있다.here,

ego,

And this is

Satisfies

Random eigenvectors of

May have the following form.

는 행렬

의 고유벡터이고, x는 C의 고유벡터이다. 행렬

는 스케일링 팩터(scaling factor)까지의 임의의 2×2 양의 준-한정(positive semi-definite) 행렬을 나타낼 수 있음에 유의한다. 따라서, 2개의 고유벡터들에 의해 형성되는 2×2 유니터리 행렬은, 임의의 2×2 유니터리 행렬일 수 있다. 그리고, 이러한 시나리오들에 적합한 코드북들을 설계하기 위해, 섹션 4에서 제시된 제 1 실시예를 고려하여 그것의 외부 코드북

을 다음과 같이 확장시키도록 한다.here,

The matrix

Is the eigenvector of, and x is the eigenvector of C. procession

Note that can represent an arbitrary 2x2 positive semi-definite matrix up to a scaling factor. Accordingly, a 2x2 unitary matrix formed by two eigenvectors may be any 2x2 unitary matrix. And, in order to design codebooks suitable for these scenarios, taking into account the first embodiment presented in section 4, its external codebook

Let's expand it as follows.

Now, the rank-1 external codebook is defined as follows.

는

에 대한, 사전 결정된 스칼라들이다. 이제, 외부 랭크-2 코드북이 다음과 같이 규정된다.here,

The

For, these are pre-determined scalars. Now, the external rank-2 codebook is defined as follows.

Similarly, in the case of the second embodiment, the rank-1 external codebook is defined as follows.

In addition, the rank-2 external codebook is defined as follows.

는 다음과 같이 표기될 수 있다.Note that the codebooks defined above are also suitable when the transmitter has geographically separated 4 common-polarization antennas comprising 2 pairs of common-polarization antennas at each location. And, the correlation matrix for each of these two common-polarization sets is given by Hermit and Teplits C. Full 4 × 4 correlation matrix

Can be written as

는 크로네커 프로덕트를 나타내고,

는 상기 2개의 위치들로부터의 상이한 평균 전파로 이득들을 반영한 정규화된 이득 항이다.here,

Denotes a Kronecker product,

Is a normalized gain term reflecting the different average propagation gains from the two locations.

II. Example 2

Product type codebook composition

Now, based on the principles derived above, a structured codebook construction in which each codeword is derived as a matrix product is discussed.

에 대하여,

인 것으로 놓도록 한다. 내부 (광대역) 코드북을 다음과 같이 규정하도록 한다. 먼저, 양의 정수 K, J, L에 대하여 다음의 등식과 같이 규정한다.

about,

Put it on. The internal (broadband) codebook should be defined as follows. First, the positive integers K, J, and L are defined as in the following equation.

및

를 만족하도록 선택된다. 이제, 내부 (광대역) 코드북을 다음과 같이 상세히 나타내도록 한다.Here, K is referred to as a step , J is referred to as width, and L is referred to as extent . These parameters are usually

And

It is chosen to satisfy. Now, the internal (broadband) codebook is described in detail as follows.

는 하다마드 프로덕트를 나타내고,

이며,

는 그것의 주대각선(main diagonal)이 벡터

를 포함하는 대각 행렬이며, 여기서

이고 또한 다음과 같으며,here,

Represents the Hadamard product,

And

Is its main diagonal vector

Is a diagonal matrix containing, where

And also:

이다.here,

to be.

에 대하여,

인 경우, 연속적인 k의 선택을 위하여

간의 중첩(overlap)을 도입할 수 있다. 특히,

인 것을 보장하는 것에 의해,

의 일부 열들이

의 것과 동일하게 되는 것을 확인할 수 있다. 이것은 내부 광대역 코드북에서 가지는 유용한 특징이 되며, 그 이유는 시간 또는 주파수에서의 상관관계는 점진적으로 변화하기 때문이다. 그러나, 이것은

인 m인 경우에는, 유지될 필요가 없다. 이러한 경우에 있어서, 상이한 내부 코드북들 간의 중첩을 도입하기 위해서는, 먼저

을 보장한 후에,

인

을 적절히 선택함으로써(

을 선택하면

도 고정된다는 것을 고려),

및

의 열들이 중첩을 갖는 것을 보장할 수 있다.given

about,

In case of, to select consecutive k

An overlap of the liver can be introduced. Especially,

By ensuring that it is,

Some columns of

It can be confirmed that it becomes the same as that of. This is a useful feature of internal broadband codebooks because the correlation in time or frequency gradually changes. However, this

In the case of m, it need not be maintained. In this case, to introduce overlap between different inner codebooks, first

After guaranteeing,

sign

By properly selecting (

If you select

Considering that it is also fixed),

And

Can ensure that the columns have overlap.

The rank-1 external codebook is defined as follows.

는 4개의 표시 벡터들 중의 어느 하나일 수 있고,

는 J ×J 항등 행렬의 i번째 열을 선택한 J× 1 열 선택 벡터를 나타낸다. 사이즈를 제한하기 위해, 본 명세서에서는 실현가능한 (feasible) 조합들로 지칭되는 (r,s)의 소정 조합들만이 허용될 수 있으며, 여기서는 r = s인 것이 실현가능한 조합이 될 수 있음에 유의한다. 임의의 서브대역에 있어서, 랭크-1 최종 코드워드는,

로부터

를 선택하고 또한

로부터 외부 코드워드

를 선택하여

로서 해당 서브대역에 대한 최종 코드워드를 획득하는 것에 의해 형성된다. 내부 코드워드의 선택은 모든 서브대역들에 걸쳐 공통된 것일 수 있음에 유의한다.Where, for a given r, s

May be any one of four display vectors,

Denotes a J × 1 column selection vector selecting the i-th column of the J × J identity matrix. Note that to limit the size, only certain combinations of (r, s), referred to herein as feasible combinations, may be allowed, where r = s can be a feasible combination. . For any subband, the rank-1 final codeword,

from

And also

From external codeword

By selecting

Is formed by obtaining the final codeword for the subband. Note that the choice of internal codeword may be common across all subbands.

을 외부 코드북으로 바꿀 수 있다. 즉, 실현가능한 조합들

에 대하여 하기의 등식 (2-5)의 외부 서브대역 랭크-1 코드북을 가지는

으로서 내부 광대역 코드북을 규정할 수 있다.Next, in order to expand the selection possibilities in each subband,

Can be replaced with an external codebook. In other words, feasible combinations

With the external subband rank-1 codebook of the following equation (2-5)

As an example, an internal broadband codebook can be defined.

In all cases described above, the external codebook can be determined according to the selection of the internal codeword . That is, each of (r, s) in (2-4) or (r, s, q2) in (2-5) may itself be functions of selection of an internal codeword. Stated differently, two different inner codewords can have different feasible combinations for selecting codewords from an outer codebook. In each case, a set of feasible combinations for the selection of each internal codeword is predetermined and known to all users and base stations.

Now, consider the rank-2 case. The first possibility is to maintain the inner codebook specified in (2-2) along with the next outer subband rank-2 codebook that is invariant to the selection of the inner codeword.

의 열들은 내부 코드워드의 각 선택에 대하여 상호 직교해야 한다. r = s는 내부 코드워드

의 각 선택에 대한 직교성을 보장하는 하나의 선택임에 유의한다.To limit the size, only certain combinations of (r, s) may be allowed. Since the set of allowed combinations is common across all choices of the inner codeword, for each allowed (r, s)

The columns of must be orthogonal to each choice of inner codeword. r = s is an internal codeword

Note that it is one choice that guarantees orthogonality to each choice of.

인 아래의 (2-7) 형태를 갖는

에 의해 표시되는 코드워드들을 포함하는 (인덱스들 q1, q2, k에 의해 식별되는) 내부 코드워드

의 선택에 따라 결정되는 외부 서브대역 코드북을 규정할 수 있다.To expand the final rank-2 codewords that can be set to not have excessive overhead, allowable combinations can be made to be determined according to the choice of the inner codeword. Especially,

Having the form (2-7) below phosphorus

An inner codeword (identified by indexes q1, q2, k) that includes the codewords denoted by

It is possible to define an external subband codebook determined by the selection of.

은, 상기 허용된 조합들 (r,s)와 함께, 결과물인 최종 코드워드

의 2개의 열들이 직교하는 것을 보장해야 한다. 내부 코드북의 구조로 인하여, 이러한 위상 항은

만의 함수가 되기에 충분하며, 이에 따라 그 위상 항을

로 표기할 수 있음에 유의한다. 외부 코드북에서의 더 많은 선택들을 가능하게 하기 위해, 랭크-1 케이스에서 행해진 바와 같이,

을 외부 코드북으로 바꿀 수 있다. 즉, 실현가능한 조합들 (r,s,q2)에 대하여

인 아래의 형태의 코드워드들을 구비하는 외부 서브대역 랭크-2 코드북을 가진

으로서 내부 광대역 코드북을 규정할 수 있다.Phase

Is the resulting final codeword, with the allowed combinations (r, s)

The two columns of must be guaranteed to be orthogonal. Due to the structure of the internal codebook, this phase term

Is enough to be a function of the

Note that can be written as. To enable more choices in external codebooks, as done in the Rank-1 case,

Can be replaced with an external codebook. That is, for possible combinations (r, s, q2)

Has an external subband rank-2 codebook with codewords of the form below

As an example, an internal broadband codebook can be defined.

으로 규정되며,

는 주어진 단계들이 간단한 변경들 이후에 적용될 수 있기 때문에 외부 코드북으로 바뀌는 케이스에 대하여는 생략하도록 한다). 그리고, 랭크-2 외부 코드북은 내부 코드워드의 선택에 따라 결정되고, (2-7)에서의 형태를 가진 코드워드들을 포함하는 것으로 가정하도록 한다. 또한, 내부 코드워드

의 선택을 위하여,

이며,

가

을 만족시키는

의 의사-역(pseudo-inverse)인 아래의 (2-8) 형태의 코드워드들을 구비할 수도 있다.In order to further expand the set of rank-2 codewords, it is possible to guarantee orthogonality between the columns of the resulting final codeword in different ways. The internal codebook is assumed to be defined as in (2-2) (the internal codebook

Is defined as,

Is omitted for cases that change to an external codebook because the given steps can be applied after simple changes). In addition, it is assumed that the rank-2 external codebook is determined according to the selection of the internal codeword, and includes codewords having the form in (2-7). Also, internal codeword

For your choice,

And

end

Satisfying

Codewords of the form (2-8) below that are pseudo-inverse of may be provided.

는 임의의 단위-놈 벡터 x에 있어서,

가 부분-공간

에서 단위 놈 벡터가 되는 것을 만족하는 사전 정의된 연산자이다. 바람직하게는, 이러한 연산자는, 벡터 x가 그것의 모든 원소들이 상수 크기를 갖게 되는 상수 크기 특성을 가지는 경우,

도 그 특성을 갖게 되는 특성을 가질 수 있다. 이러한 연산자의 일 예는,

및 첫 번째 원소가 실수값이고 정확하게는 1 미만의 값인 임의의 단위 놈 벡터 x에 대하여, 하우스홀더 변환

을 통해 획득된 4×4 유니터리 행렬의 t번째 열을 산출하는

이다. 여기서, 본 발명의 구성들에 있어서는,

가 하우스홀더 변환을 규정하기 위해 필요로 하는 2개의 조건들을 만족시킨다는 것에 유의한다. 또한, 벡터 x가 상수 크기 특성을 갖는 경우,

도 그 특성을 갖게 된다.

Is for any unit-nom vector x ,

Autumn part-space

Is a predefined operator that satisfies being a unit norm vector in. Preferably, such an operator is such that if the vector x has a constant size characteristic where all its elements have a constant size,

It can also have properties that will have that property. An example of such an operator is,

And for any unit norm vector x where the first element is a real value and exactly less than 1, the householder transformation

To calculate the t-th column of the 4 × 4 unitary matrix obtained through

to be. Here, in the configuration of the present invention,

Note that satisfies the two conditions required to specify the householder transformation. Also, if the vector x has a constant size characteristic,

It also has its characteristics.

로 설정하는 것이며, 여기서 P는 순열 행렬(permutation matrix)이고, D(x)는 그것의 대각 엔트리들이

을 만족시키는 x에 따라 결정되는 대각 행렬이다. x가 상수 크기 특성을 갖는 경우, 넌-제로 엔트리들이 유닛 크기를 갖는 대각 행렬 D(x)을 구성할 수 있고, 또한

및 벡터

에 대한 상수 크기 특성을 보장할 수 있음에 유의한다.Other examples of these operators

Is set to, where P is the permutation matrix and D (x) is its diagonal entries

Is a diagonal matrix determined by x satisfying. If x has a constant size characteristic, non-zero entries can construct a diagonal matrix D (x) with unit size, and also

And vectors

Note that it is possible to guarantee a constant size characteristic for.

In (2-2), rank-1 and rank-2 and all other ranks have a general structure, but different sets of internal codewords (i.e., internal codebooks) can be defined for all of them. Please note. Accordingly, rank specific internal codebooks can be defined. Recall that the function of the internal codeword may already exist for each subband external codebook. Note also that in the above-mentioned codebooks, de-duplication can be performed if necessary. In particular, for any rank r, if there are any two inner codewords that generate rank-r codewords for each final subband of an equal set, these two inner codes are in the inner codebook of that rank-r Only one of the words should be retained. Here, one codeword of the two final codewords is the same as the other codeword up to right multiplication by a column permutation and / or a diagonal matrix, and all its non-zero entries are Note that when having a unit size, the two final codewords are the same.

Note that having a rank-2 internal codebook larger than the rank-1 codebook may be useful for MU-MIMO. A larger internal codebook may enable better quantization resolution without excessively increasing feedback, because only one internal codeword needs to be reported for all subbands. to be. Better resolution for higher rank-2 may be useful not only in SU-MIMO but also in MU-MIMO, because typically users under MU-MIMO transmission will be served using a rank lower than that reported. Because. In this case, better resolution will ensure that the thermal subsets extracted from the user's reported precoders are also efficient, i.e. have sufficient precision, thus enabling MU-MIMO gains.

III. Example 3

In a Release 11 (Rel-11) LTE cellular network, it is possible for the network to semi-statically set up multiple CSI processes for the same user. Each Rel-12 and Beyond user needs to support both the legacy 4 TX codebook and the enhanced 4 TX codebook. As described above, these two codebooks can be observed as two subsets (components) of a larger codebook. Also, individual codebook subset constraints can be applied for each CSI process. A useful corollary from these two observations can be set individually for each CSI process (for the user of interest) in a semi-static manner, ie for each CSI process for a given user. The network will be able to set up codebooks for components (ie, legacy or enhanced) available to the user. In addition, other codebook subset constraints may be applied to each CSI process base in consideration of selection of component codebooks for these processes. In order to reduce the signaling overhead, it is proposed to apply only one of the latter codebook subset constraints per CSI-process. As a result, even if the CSI process (or, equivalently, the mode defined for that CSI process) requires the user to report subband-per-precoding matrices (ie, PMIs), All such reported matrices must comply with the (common) subset constraints set for the process.

Product type codebook composition

에 대하여

는 2×1 빔 벡터를 나타내는 것으로 놓도록 하며, 내부 (광대역) 코드북을 다음과 같이 규정하도록 한다.First, a general codebook configuration in which each codeword is derived as a matrix product is presented. For convenience, the normalization factor of 1/2 should be ignored.

about

Let be set to represent the 2 × 1 beam vector, and define the internal (broadband) codebook as follows.

는 실수값의 스칼라들이며, 또한here,

Is a real-valued scalar, and

이고,

ego,

이다. 특정 내부 코드워드

내에서의 2개의 인접한 빔 벡터들에서 위상 항 간의 (각도) 분리는 2π /N이며, 이에 따라 N 및 J 모두가 각 내부 코드워드에서의 위상 항의 각도 스팬(angular span)을 결정하게 됨에 유의한다. 직관적으로, 더 큰 각도 스팬은 더 작게 상관된 페이딩 시나리오들에 대해서도 적합한 코드북을 만드는 것을 가능하게 할 것이다. 한편, 스칼라들

은

인 경우에 대해, 2개의 내부 코드워드들

및

와 관계가 있는 임의의 2개의 빔 벡터들에서, 위상 항 간의 분리를 제어하는 것에 기여한다. 직관적으로, 작은 분리는 시간 및 주파수에서 상관관계를 활용할 경우에 유용할 것이다.here,

to be. Specific internal codeword

Note that the (angle) separation between phase terms in two adjacent beam vectors within is 2π / N , so that both N and J determine the angular span of the phase term in each internal codeword. . Intuitively, a larger angular span would make it possible to create a suitable codebook for smaller correlated fading scenarios. Meanwhile, scalars

silver

For the case, two internal codewords

And

In any two beam vectors that are related to, contribute to controlling separation between phase terms. Intuitively, a small separation would be useful when utilizing correlation in time and frequency.

Then, the rank-1 external (subband) codebook is defined as follows.

delete

는 공통-위상 항이다. 따라서, 랭크-1 코드북의 (최대) 사이즈는 JS가 된다. 이러한 가능한 모든 벡터들의 서브세트만을 선택하는 것에 의해 더 작은 사이즈가 획득될 수 있다. 공통-위상 항들은, 양의 정수 M ≥ 1가 설계 파라미터인 M-PSK 알파벳으로 놓이도록 그것들을 제한한 이후에, 평균 코달 거리와 같은 적절한 메트릭(metric)을 최적화함으로써 획득될 수 있다. 이 최적화는, 공통-위상 항들 간에 최소 각도 분리가 유지되는 것을 보장하도록 제한될 수 있다. 랭크-2의 경우, 외부 (서브대역) 코드북은 다음과 같이 규정된다.Here, e _i represents a J × 1 column selection vector (ie, the i-th column of the J × J identity matrix),

Is a common-phase term. Therefore, the (maximum) size of the rank-1 codebook is JS . A smaller size can be obtained by selecting only a subset of all these possible vectors. Common-phase terms can be obtained by optimizing the appropriate metric, such as the average codall distance, after limiting them so that the positive integer M ≥ 1 lies in the design parameter M-PSK alphabet. This optimization can be limited to ensure that minimal angular separation between common-phase terms is maintained. For Rank-2, the external (subband) codebook is defined as follows.

Note that for different pairs of (m, p) and (m ', p'), it can have a different number of common-phase terms. These common-phase terms are optimized by optimizing the appropriate metric, such as the average codall distance, after limiting them to be placed in the M'-PSK alphabet, where the positive integer M ' ≥ 1 is a design parameter and can be different from M. Can be obtained. This optimization can be limited to ensure that minimal angular separation between common-phase terms is maintained.

및

을 사용하며, 이에 따라 내부 코드워드가 4×4 행렬이 되도록

을 구성하도록 한다. 이에 대응하는 서브-대역 코드북은 랭크 1 및 랭크 2 모두의 경우 3-비트의 사이즈를 갖는다. 랭크-1 코드북에서 공통-위상 항들은 8-PSK 알파벳으로 놓여 있으며, 이것이 도 3에 제공되어 있다. 도 3의 표에서 채택된 표기는 (s,i)에 대응하는 엔트리가 t인 경우, θ _s,i = 2πt /M(여기서, 8-PSK의 경우 M = 8)임에 유의한다. 랭크-2 코드북의 경우, 도 4a 또는 도 4b에서 제공된 공통-위상 항들과 함께

를 선택하도록 한다. 다르게는, 공통-위상 항들은 도 5와 같이 선택될 수 있다. 빔 조합 (1,2)에 대한 도 5에 있어서는, 더 많은 공통-위상 선택들을 사용하고 있음에 유의하도록 한다.Next, two specific embodiments are proposed. Both embodiments have a 4-bit wideband codebook. In the case of the first embodiment,

And

Use, so that the internal codeword is a 4 × 4 matrix.

To configure. The corresponding sub-band codebook has a size of 3-bit for both rank 1 and rank 2. Common-phase terms in the rank-1 codebook are laid out in the 8-PSK alphabet, which is provided in FIG. 3. Note that the notation adopted in the table of FIG. 3 is θ _{s, i} = 2 πt / M (where M = 8 for 8-PSK) when the entry corresponding to ( s, i ) is t . For a rank-2 codebook, with the common-phase terms provided in Figure 4a or Figure 4b

Choose to. Alternatively, the common-phase terms can be selected as shown in FIG. 5. Note that in FIG. 5 for the beam combination (1,2), more common-phase selections are used.

및

를 사용하며, 이에 따라 각각의 내부 코드워드가 4×8 행렬이 되도록

를 구성하도록 한다. 이에 대응하는 서브-대역 코드북은 랭크 1 및 랭크 2의 경우 4-비트 사이즈를 갖는다. 랭크-1 코드북에서 공통-위상 항들은 8-PSK 알파벳으로 놓여 있으며, 이것이 도 6a 또는 도 6b에 제공되어 있다. 랭크-2 코드북의 경우, 도 7에서 제공된 공통-위상 항들과 함께

를 선택하도록 한다. 다르게는, 도 8a 또는 도 8b에서 제공되는 공통-위상 항들을 또한 선택할 수도 있다. 다르게는, 도 9 또는 도 10에서 제공되는 공통-위상 항들을 또한 선택할 수도 있다.In the case of the second embodiment,

And

Use, so that each internal codeword is a 4x8 matrix.

To configure. The corresponding sub-band codebook has a 4-bit size for rank 1 and rank 2. Common-phase terms in the rank-1 codebook are laid out in the 8-PSK alphabet, which is provided in Figures 6A or 6B. For the rank-2 codebook, along with the common-phase terms provided in FIG. 7

Choose to. Alternatively, the common-phase terms provided in FIGS. 8A or 8B may also be selected. Alternatively, the common-phase terms provided in FIG. 9 or 10 may also be selected.

The rank-3 and rank-4 codebooks can be fixed to legacy (householder) rank-3 and rank-4 codebooks. It should be noted that all codeword matrices in the aforementioned codebook satisfy the constant size characteristic.

IV. Example 4

Other related problems are when the user configures to use a legacy 4 TX codebook as one of the CSI processes, and the process (or equivalently the mode defined for the CSI process) provides subband-per-precoding matrices to the user. Occurs when a report is requested. Here, when the user's preferred rank is 3 or 4, the size of the legacy codebook (4 bits for both rank 3 and rank 4) may be overkill for subband-per-report. That is, feedback can be reduced without a noticeable effect on performance, because the user is experiencing a good average SINR and will typically be scheduled alone on allocated resources. To achieve feedback reduction, the network defines sub-sampled versions of legacy codebooks for rank 3 and rank 4, allowing the user to view codewords from these sub-sampled codebooks when the preferred rank is 3 or 4. You can set it to report. A sub-sampled rank-3 codebook is obtained by removing one or more codewords from the rank-3 legacy codebook, and also a sub-sampled rank-4 by removing one or more codewords from the rank-4 legacy codebook. The codebook is obtained. These sub-sampled codebooks are defined by the network and delivered to all users in advance. Another approach to provide more flexibility is to leverage codebook subset constraints. Here, it is assumed that the size of the rank-3 codebook (per sub-band) is limited to M codewords. The network can then determine, from the legacy rank-3 codebook, a subset containing less than M codewords (semi-statically and possibly in a user-specific manner) and deliver this subset to the user. The user then limits the search (for rank-3 codewords) to this subset on each subband. To report the preferred codeword on each subband, the user adopts lexicographic ordering (labeling). That is, one new index is assigned to the codeword in the display subset with the smallest index (as in the original Rank-3 legacy codebook), and the second smallest (as in the original Rank-3 legacy codebook). Two new indexes are assigned to codewords in the display subset having the index. This process continues until new indexes are assigned to all codewords in the subset. Clearly, these new indices can be from 1 to M ' where M' < M . Also, it should be noted that because the subset is common across all subbands, the new set of indices also becomes common across all subbands, which must be determined by the user once. The user then reports a new index for the precoder selected on each subband. Note that the same procedure can be applied for rank-4, where the value of M can be different for rank 4 and rank 3.

Finally, to improve MU-MIMO performance, additional feedback may be included for the CSI process (or equivalently, the mode defined for that CSI process). As detailed in previous task [8], a user may also report MU-CQI (s) along with single-user (SU) CSI (channel state information) reporting. This SU-CSI (including wideband or subband-per-PMI, and subband-per-CQI) is calculated using resource elements and pilots for interference measurement established for the corresponding CSI process. Several methods for calculating these MU-CQI (s) have been described in detail in a previous work [9], one of which is a set of co-scheduled interferences (for a subband base if so configured). After the assumption, the PMI determined by the user in SU-CSI reporting to calculate the MU-CQI (s) or using SU-MIMO rules (hereinafter referred to as base-PMI (s)) Field). Here, the set of co-scheduled interfering PMIs that the user assumes for the subbands (ie, transmit precoders assigned to other users co-scheduled) is a function of the base-PMI from which it is determined. Each set of co-scheduled interfering PMIs that the user should assume may be established by the network in a semi-static (and possibly user-specific) manner. The size of the set of interfering PMIs (for each base-PMI selection) may be greater than one. To reduce overhead, the final MU-CQI (s) calculated for the subband base can be combined into one (or up to two) wideband MU-CQI (s) (for wideband residual error norm feedback Detailed in Task [10]), after which it is reported. To further improve performance, multiple sets of such interfering PMIs (for each base-PMI) can be established. Thereafter, the user reports one (or up to two) wideband MU-CQI (s) for each set of set interfering PMIs, and differential feedback is leveraged to reduce feedback overhead. Alternatively, the above-described process can be repeated for several selections for base-PMIs, and the user selects one specific base-PMI (using appropriate selection rules, such as rules to maximize the expected MU gain). By doing so, it can be reported along with the relevant MU-CQI (s).

Return to the following codebook configuration.

Product type codebook composition

에 대한

가 2×1 빔 벡터를 나타내는 것으로 놓도록 하며, 내부 (광대역) 코드북을 다음과 같이 규정하도록 한다.First, a general codebook configuration in which each codeword is derived as a matrix product is presented.

About

Let be set as representing a 2 × 1 beam vector, and define the internal (broadband) codebook as follows.

Here, {a _k } are real-valued scalars, and

이며,

And

이다. 특정 내부 코드워드

내의 임의의 2개의 인접하는 빔 벡터들의 위상 항 간의 (각도) 분리는 2π /N이며, 이에 따라 N(입도(granularity)로 지칭됨) 및 J(내부 코드워드당 빔 벡터들의 수)가 각각의 내부 코드워드 내의 위상 항의 각도 스팬을 결정하도록 함에 유의한다. 직관적으로, (주어진 J에 대한 더 작은 N(즉, 더 작은 입도 또는 더 큰 2π /N)을 갖는 것에 의해 달성될 수 있거나, 또는 주어진 N에 대한 더 큰 J를 갖는 것에 의해 달성될 수 있는) 더 큰 각도 스팬은, 더 작게 상관되는 페이딩 시나리오들에 대해서도 코드북이 적절하게 할 수 있으며, 또한 타이밍 정렬 오류(timing alignment error)들에 대한 강건성을 또한 제공하게 된다. 그러나, J의 비용 증가는 각각의 외부 서브-대역 코드북의 사이즈를 커지게 하는 반면, 더 작은 N의 선택으로 근접 이격된 크로스-폴 구성에서의 성능이 저하될 수 있으며, 그 이유는 그것이 주어진 내부 코드워드에서의 빔 벡터들의 로컬리제이션(localization)을 방해하기 때문이다. 한편, 스칼라들 {d_q}(스태거링 인자(staggering factor)들로 지칭됨)은

인 경우에 대한 2개의 내부 코드워드들

및

와 관계가 있는 임의의 2개의 빔 벡터들에서 위상 항 간의 분리를 제어하는 것을 보조한다. 직관적으로, 작은 분리가 시간 및 주파수에서 상관관계를 활용하는데 유용하게 될 것이다.here,

to be. Specific internal codeword

The (angle) separation between the phase terms of any two adjacent beam vectors within is 2π / N , whereby N (referred to as granularity) and J (number of beam vectors per inner codeword) are each Note that the angle span of the phase term in the inner codeword is determined. Intuitively, (can be achieved by having a smaller N for a given J (i.e. smaller particle size or greater 2π / N ), or by having a larger J for a given N ) A larger angular span can make the codebook appropriate for smaller correlated fading scenarios, and also provides robustness to timing alignment errors. However, the increase in cost of J increases the size of each external sub-band codebook, while the choice of smaller N can degrade performance in a closely spaced cross-pole configuration, because it is given the internal This is because the localization of beam vectors in the codeword is prevented. On the other hand, scalars {d _q } (referred to as staggering factors)

2 internal codewords for case

And

Assists in controlling separation between phase terms in any two beam vectors related to. Intuitively, a small separation would be useful to utilize correlation in time and frequency.

The extension to the internal codebook described above uses two (or more) sets of granularities, where each granularity may have its own set of staggering factors. Typically, this will increase the size of the broadband codebook, but can better meet different antenna configurations. In the following, I describe the complex inner (broadband) codebook for the selection of different particle sizes as follows.

및

는 i번째 입도 N _i 와 관련된 인덱스들의 세트이다. J는 상이한 입도들에 걸쳐 고정된 상태로 유지됨에 유의한다. (매우 낮은 상관관계를 가진) 특정 시나리오들에서, 관련 내부 코드워드들을 가진 다수 중의 하나 이상의 빔 벡터들이 상호 직교하는 것을 만족시키는 입도들 중의 적어도 하나의 입도를 선택하는 것은 유리할 수 있다.here,

And

Is a set of indices associated with the i-th particle size N _i . Note that J remains fixed across different particle sizes. In certain scenarios (with very low correlation), it may be advantageous to select a particle size of at least one of the particle sizes that satisfy one or more beam vectors of the multiples with related internal codewords being orthogonal to each other.

Then, the rank-1 external (subband) codebook is defined as follows.

은 공통-위상 항이다. 따라서, 랭크-1 코드북의 (최대) 사이즈는 JS가 된다. 이러한 모든 가능한 벡터들의 서브세트만을 선택하는 것에 의해 더 작은 사이즈가 획득될 수 있다. 공통-위상 항들은, 양의 정수 M ≥ 1인 설계 파라미터가 되는 M-PSK 알파벳에 놓이는 것으로 제한한 이후에, 평균 코달 거리와 같은 적절한 메트릭을 최적화함으로써 획득될 수 있다. 이 최적화는, 공통-위상 항들 간에 최소 각도 분리가 유지되는 것을 보장하도록 제한될 수 있다. 랭크-2의 경우, 외부 (서브대역) 코드북은 다음과 같이 규정된다.Here, e _i is the i-th J × 1 column selection vector (ie, the i-th column of the J × J identity matrix),

Is a common-phase term. Therefore, the (maximum) size of the rank-1 codebook is JS . A smaller size can be obtained by selecting only a subset of all these possible vectors. Common-phase terms can be obtained by optimizing the appropriate metric, such as the average codall distance, after limiting to being placed in the M-PSK alphabet, which becomes a design parameter with a positive integer M ≥ 1. This optimization can be limited to ensure that minimal angular separation between common-phase terms is maintained. For Rank-2, the external (subband) codebook is defined as follows.

Note that for different pairs of (m, p) and (m ', p'), it can have a different number of common-phase terms. The common-after the phase terms are, a positive integer M limit them to be placed into '≥ 1 and M is a design parameter and will be different in M' -PSK alphabet, by optimizing an appropriate metric, such as the average distance kodal Can be obtained. This optimization can be limited to ensure that minimal angular separation between common-phase terms is maintained.

As such, (1) the present inventors have a core structure that each eigenvector of the spatial correlation matrix should have under the ULA transmit antenna configuration and a core structure that each eigenvector of the spatial correlation matrix must have under the cross pole transmit antenna configuration. The structure was identified, and (2) thereafter, the inventors implemented the identified structures in at least a subset of the precoding codebooks to ensure good performance, and (3) the inventors also identified the identified structures They have been followed and presented with efficient embodiments.

The above description should be understood as illustrative and illustrative rather than limiting in all respects, and the scope of the invention described herein is not to be determined from the detailed description, but to be interpreted in accordance with the entire scope allowed by patent law. Should be determined from the claims of. It should be understood that the embodiments shown and described herein are only illustrative of the principles of the invention, and those skilled in the art can implement various modifications without departing from the scope and spirit of the invention. Those skilled in the art can implement various other combinations of features without departing from the scope and spirit of the invention.

Claims (32)

As a method implemented in a base station used in a wireless communication system,
Providing first 1-layer, 2 1-layer, 1 2-layer, 2 2-layer, 3-layer, and 4-layer codebooks for 4 transmit (4TX) antenna transmission-each codebook Contains a plurality of precoding matrices-;
Precoding data using one of the plurality of precoding matrices; And
And transmitting the precoded data to user equipment,
The first 1-layer codebook includes a plurality of precoding matrices-each precoding matrix is

Contains the element represented by-,
The first two-layer codebook includes a plurality of precoding matrices-each precoding matrix is

Contains the element represented by-,
θ ₂ and θ ₃ each take a value greater than or equal to 0 but less than 2π,

Phosphorus, how. According to claim 1,
Receiving information on channel quality including at least one of CQI and PMI from the user equipment; And
And selecting one of the plurality of precoding matrices using the information on the channel quality. According to claim 1,
The plurality of precoding matrices included in the first 1-layer codebook are

And further comprising as a factor a gain vector represented by. The method of claim 3,
The {a ₁ , a ₂ , a ₃ , a ₄ } takes at least {1/2, 1/2, 1/2, 1/2}. According to claim 1,
The plurality of precoding matrices included in the first two-layer codebook are

And further comprising as a factor a gain vector represented by. The method of claim 5,
Each of the b ₁ , b ₂ , c ₁ and c ₂ takes a settable scalar value, and satisfies the relationship of b ₁ = b ₂ = c ₁ = c ₂ . According to claim 1,
The three-layer codebook includes a precoding matrix including, as an element, a predetermined column of a 4 × 4 matrix obtained through householder transformation,
The 4-layer codebook includes a 4 × 4 matrix obtained through householder transformation as a precoding matrix. According to claim 1,
Each of the second 1-layer codebook and the second 2-layer codebook includes a precoding matrix including as elements a predetermined column of a 4x4 matrix obtained through householder transformation. A method implemented in user equipment used in a wireless communication system,
Providing first 1-layer, 2 1-layer, 1 2-layer, 2 2-layer, 3-layer, and 4-layer codebooks for 4 transmit (4TX) antenna transmission-each codebook Contains a plurality of precoding matrices-; And
And receiving, from the base station apparatus, precoded data whose data is precoded using one of the plurality of precoding matrices,
The first 1-layer codebook includes a plurality of precoding matrices-each precoding matrix is

Contains the element represented by-,
The first two-layer codebook includes a plurality of precoding matrices-each precoding matrix is

Contains the element represented by-,
θ ₂ and θ ₃ each take a value greater than or equal to 0 but less than 2π,

Phosphorus, how. The method of claim 9,
And transmitting information regarding channel quality including at least one of CQI and PMI to the base station apparatus to select one of the plurality of precoding matrices. The method of claim 9,
The plurality of precoding matrices included in the first 1-layer codebook are

And further comprising as a factor a gain vector represented by. The method of claim 11,
The {a ₁ , a ₂ , a ₃ , a ₄ } takes at least {1/2, 1/2, 1/2, 1/2}. The method of claim 9,
The plurality of precoding matrices included in the first two-layer codebook are

And further comprising as a factor a gain vector represented by. The method of claim 13,
Each of the b ₁ , b ₂ , c ₁ and c ₂ takes a settable scalar value, and satisfies the relationship of b ₁ = b ₂ = c ₁ = c ₂ . The method of claim 9,
The three-layer codebook includes a precoding matrix including, as an element, a predetermined column of a 4 × 4 matrix obtained through householder transformation,
The 4-layer codebook includes a 4 × 4 matrix obtained through householder transformation as a precoding matrix. The method of claim 9,
Each of the second 1-layer codebook and the second 2-layer codebook includes a precoding matrix including as elements a predetermined column of a 4x4 matrix obtained through householder transformation. A base station used in a wireless communication system,
And a transmitter that transmits the precoded data to user equipment,
The base station comprises first 1-layer, 2 1-layer, 1 2-layer, 2 2-layer, 3-layer, and 4-layer codebooks for 4 transmit (4 transmit) antenna transmission- Each codebook contains a plurality of precoding matrices-,
The first 1-layer codebook includes a plurality of precoding matrices-each precoding matrix is

Contains the element represented by-,
The first two-layer codebook includes a plurality of precoding matrices-each precoding matrix is

Contains the element represented by-,
θ ₂ and θ ₃ each take a value greater than or equal to 0 but less than 2π,

Phosphorus, base station. The method of claim 17,
The base station,
Receiving information regarding channel quality including at least one of CQI and PMI from the user equipment,
A base station configured to select one of the plurality of precoding matrices using the information on the channel quality. The method of claim 17,
The plurality of precoding matrices included in the first 1-layer codebook are

A base station, further comprising as a factor a gain vector represented by. The method of claim 19,
The {a ₁ , a ₂ , a ₃ , a ₄ } takes at least {1/2, 1/2, 1/2, 1/2}, a base station. The method of claim 17,
The plurality of precoding matrices included in the first two-layer codebook are

A base station, further comprising as a factor a gain vector represented by. The method of claim 21,
Each of the b ₁ , b ₂ , c ₁ and c ₂ takes a settable scalar value, and satisfies the relationship of b ₁ = b ₂ = c ₁ = c ₂ . The method of claim 17,
The three-layer codebook includes a precoding matrix including, as an element, a predetermined column of a 4 × 4 matrix obtained through householder transformation,
The 4-layer codebook includes a 4 × 4 matrix obtained through householder transformation as a precoding matrix. The method of claim 17,
Each of the second 1-layer codebook and the second 2-layer codebook includes a precoding matrix including, as an element, a predetermined column of a 4x4 matrix obtained through householder transformation. User equipment used in a wireless communication system,
And a receiver for receiving precoded data from which the data is precoded using one of a plurality of precoding matrices from the base station apparatus,
The user equipment includes first 1-layer, 2 1-layer, 1 2-layer, 2 2-layer, 3-layer, and 4-layer codebooks for 4 transmit antenna transmission. -Each codebook contains a plurality of precoding matrices-,
The first 1-layer codebook includes a plurality of precoding matrices-each precoding matrix is

Contains the element represented by-,
The first two-layer codebook includes a plurality of precoding matrices-each precoding matrix is

Contains the element represented by-,
θ ₂ and θ ₃ each take a value greater than or equal to 0 but less than 2π,

Phosphorus, user equipment. The method of claim 25,
The user equipment,
And user equipment configured to transmit information regarding channel quality including at least one of CQI and PMI to the base station apparatus to select one of the plurality of precoding matrices. The method of claim 25,
The plurality of precoding matrices included in the first 1-layer codebook are

User equipment further comprising a gain vector represented by the element. The method of claim 27,
The {a ₁ , a ₂ , a ₃ , a ₄ } takes at least {1/2, 1/2, 1/2, 1/2}, and user equipment. The method of claim 25,
The plurality of precoding matrices included in the first two-layer codebook are

User equipment further comprising a gain vector represented by the element. The method of claim 29,
Each of the b ₁ , b ₂ , c ₁ and c ₂ takes a settable scalar value, and satisfies the relationship b ₁ = b ₂ = c ₁ = c ₂ . The method of claim 25,
The three-layer codebook includes a precoding matrix including, as an element, a predetermined column of a 4 × 4 matrix obtained through householder transformation,
The 4-layer codebook comprises a 4 × 4 matrix obtained through householder transformation as a precoding matrix. The method of claim 25,
Each of the second 1-layer codebook and the second 2-layer codebook includes a precoding matrix including as elements a predetermined column of a 4x4 matrix obtained through householder transformation.

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