KR101516665B1 - Codebook construction - Google Patents

Abstract

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

Description

Codebook Configuration {CODEBOOK CONSTRUCTION}

This application claims priority to US Provisional Application No. 61 / 774,275 entitled " Observations on Codebook Construction, " filed on Mar. 7, 2013, entitled " Observations on Codebook Construction Provisional Application No. 61 / 775,058, filed April 5, 2013, entitled " Enhancements to a Structured Codebook, " U.S. Provisional Application No. 61 / 808,934, 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, 61 / 817,247, entitled " Improvements to the 4 Transmit Antenna Precoding Codebook, "filed on May 10, 2013, , The contents of which are incorporated herein by reference in their entirety. .

The present invention relates to precoding matrix design and, more particularly, to 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 closed loop transmission techniques, especially beamforming and precoding, have been extensively considered to improve spectral efficiency. In MIMO precoding schemes, the data to be transmitted is divided into one or more streams, which are mapped to one or more transport layers, and the data in the transport layers are pre-coded or pre-coded Lt; / RTI > The number of transport layers is referred to as the transmission rank. This transmission rank can be optimally selected for a given channel implementation, for example, by taking into account the transmission power and overall channel statistics.

In codebook-based precoding strategies, a predetermined codebook is made available to the transmitter, i. E. The base station (BS), and all receivers, i. E., Mobile stations (MS) or user equipment (UE). Then, the receiver selects, from the codebook, a precoder that maximizes its performance (e.g., data rate) and feeds back the precoder index. In addition, the selection of the precoder rank may be included in the precoder selection algorithm. The feedback rate may vary from short-term feedback once every consecutive time interval to long-term feedback once every several consecutive time intervals.

In many systems, the optimal precoders from the codebook for two adjacent transmission blocks are close to the appropriate distance measurement in all possible sets of precoders. Here, the neighboring blocks can be used for a set of tones in, for example, orthogonal frequency-division multiplexing (OFDM) systems, since in real systems the channel does not change abruptly from one transmission block to the adjacent block. Time or frequency. Thus, the precoder used in these blocks may be the same if the channel is fairly stable and the codebook resolution is not too high. By increasing the codebook resolution or by providing a more dynamic channel, the precoders of adjacent blocks are no longer identical, but can be close together. The proximity between two precocoders can be measured based on the appropriate distance metric in the space of all these precoders. Some examples of differential, dual and multi-resolution codebooks are described in references [5] and [6].

In order to obtain an effective codebook for both a uniform linear array (ULA) and a cross-pole configuration, it is advantageous to use four transmit antennas TX) MIMO downlink channel and provides a detailed description of a suitable codebook structure for both uniform linear array (ULA) and cross-pole antenna configurations. Some documents have proposed codebook designs for specific antenna configurations [7]. The basic properties of the spatial correlation matrices used by the present invention are not used in the prior art. In the present specification, the codebook structure is derived using basic properties of spatial correlation matrices under ULA and cross-pole antenna configurations. Each precoded codeword is derived as a product of two matrices, which makes the matrices efficient and also achieves a 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," 3 GPP 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," 3 GPP TSG RAN WG1 R1 -130364 .

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

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

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

One aspect of the invention includes a method implemented in a base station for use in a wireless communication system. The method comprises the steps of: 1-layer, 2-layer, 3-layer, and 4-layer codebooks for transmitting 4TX (4 transmit) antennas, wherein each codebook comprises a plurality of precoding matrices Precoding data to one of the plurality of precoding matrices; and transmitting the precoded data to a user equipment, wherein each of the one-layer and two-layer codebooks comprises 1 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 user equipment for use in a wireless communication system. The method includes receiving precoded data from a base station, wherein each of the 1-layer, 2-layer, 3-layer, and 4-layer codebooks for transmitting 4TX (4 transmit) Coding matrices and each of the one-layer and two-layer codebooks includes a first codebook and a second codebook, wherein each precoding matrix in the first codebook includes a first index and a second index do.

Another aspect of the present invention includes a base station used in a wireless communication system. The base station includes a transmitter for transmitting precoded data to the user equipment, and each of the 1-layer, 2-layer, 3-layer, and 4-layer codebooks for transmitting 4TX (4 transmit) Each of the 1-layer, 2-layer, 3-layer, and 4-layer codebooks for 4TX (4 transmit) antenna transmission comprising a plurality of precoding matrices, Each of 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.

Another aspect of the invention includes user equipment used in a wireless communication system. Wherein the user equipment comprises a receiver for receiving precoded data from a base station and wherein each of the 1-layer, 2-layer, 3-layer, and 4-layer codebooks for transmitting 4TX (4 transmit) Wherein each of the first-layer and the 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 second codebook, 2 index.

Another aspect of the present invention includes a wireless communication system, wherein the wireless communication system is configured as a one-tier, two-tier, three-tier, and four-tier codebook for transmitting 4TX (4 transmit) A base station having the codebooks comprising a plurality of precoding matrices and precoding data to one of the plurality of precoding matrices and user equipment for receiving the precoded data from the base station, Layer and the 2-layer codebooks each include a first codebook and a second codebook, and each precoding matrix in the first codebook includes a first index and a second index.

Yet another aspect of the invention includes a method implemented in a wireless communication system. The method includes precoding data; And transmitting the precoded data from a base station to a user equipment, wherein each of the 1-layer, 2-layer, 3-layer, and 4-layer codebooks for transmitting 4TX (4 transmit) And wherein each of the one-layer and 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 .

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

The second codebook may include a legacy codebook or a house-holder codebook.

Each of the 3-layer and 4-layer codebooks may include a legacy codebook or a house-holder 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⁾

And the second matrix W ⁽²⁾ may be selected from the outer 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 for use in a wireless communication system. The method comprising: providing a codebook comprising a plurality of precoding matrices; precoding data to 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⁾

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 user equipment for use in a wireless communication system. The method includes receiving precoded data from a base station into one of a plurality of precoding matrices, wherein the codebook comprises the plurality of precoding matrices and each precoding matrix W further comprises: W = W ^{(1 )} W ⁽²⁾ , and the first matrix W ⁽¹⁾ satisfies 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 present invention includes a base station used in a wireless communication system. The base station to the user equipment, comprising: a transmitter for transmitting the pre-coded data into one of a plurality of precoding matrices, the codebook comprises the plurality of precoding matrices, and each precoding matrix W is W = W ^{( 1)} W ⁽²⁾ , and the first matrix W ⁽¹⁾

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 for receiving data to be pre-coding one of a plurality of precoding matrix from the base station, and the codebook comprises the plurality of precoding matrices, and each precoding matrix W is W = W ^{( 1)} W ⁽²⁾ , and the first matrix W ⁽¹⁾

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 present invention is directed to a wireless communication system including a base station having a codebook including a plurality of precoding matrices and precoding data to one of the plurality of precoding matrices, Wherein each precoding matrix W satisfies W = W ⁽¹⁾ W ⁽²⁾ , and wherein the first matrix W ⁽¹⁾

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.Yet another aspect of the invention includes a method implemented in a wireless communication system. The method includes precoding data to one of a plurality of precoding matrices, and transmitting the precoded data from a base station to a user equipment, wherein the codebook comprises the plurality of precoding matrices, Also, each precoding matrix W satisfies W = W ⁽¹⁾ W ⁽²⁾ , and the first matrix W ⁽¹⁾

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

를 참조하는 이득 벡터들의 비트 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.FIG. 1 illustrates an exemplary embodiment of a receiver having N _T transmit-antennas at the transmitter and N _R / RTI > is a diagram of a downlink multiuser MIMO system with receive antennas.
Figure 2 shows the

≪ / RTI > is a diagram of a bit-codebook of gain vectors referencing <
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 diagram 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 for common-phase terms in the 16-PSK alphabet for rank-2.

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

In systems using beamforming such as MIMO systems, a beamforming matrix (also referred to as a precoding matrix, precoder, code word, or precoded codeword) generated corresponding to received channel conditions is first transmitted to a receiver (E.g., via feedback) after being computed and quantized in the source transmitter. A conventional approach to reducing the overhead associated with this feedback is to provide matrix codebook (s) in each of the transmitter and the receiver, where each codebook (s) can be used according to channel conditions recognized at the receiver A plurality of potential beamforming matrices or a set of beamforming matrices. If the receiver has identified the proper matrix codebook (s), the receiver will feed back one or more indexes (instead of the actual matrix entries) indicating the appropriate codeword in the codebook (s) stored in the transmitter.

I. Example 1

1 uniform linear array ( Uniform Linear Array )

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

인 것으로 규정하도록 하며, 여기서The inventors have made the following observations on the construction of a uniform linear array (ULA) transmission antenna. Consider a system with N common-polarized transmit antennas, where C is set to indicate a transmit spatial correlation matrix. J is a matrix with zeros everywhere except for cross diagonal elements, i. E.

, Where < RTI ID = 0.0 >

In the following equations, the vector becomes a 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

Lt; / RTI > The present inventors propose a set of properties as follows. The first observation relates to the spatial correlation matrix of the ULA transmit antenna configuration, which is effective with wide versatility (see [2]).

Observation 1 procession C Hermitage Teplitz  Matrix, C ≪ / RTI > satisfies <

는 C의 켤레를 나타낸다.here,

Represents the pair of C.

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 a Hermitian vector. In other words,

And the eigen vector x of the Hermitian trellis matrix A satisfy the following equations

Y. & Lt ; / RTI >

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

를 만족시키는 고유벡터라면,

인 경우에 대하여 다음과 같이 된다. Lemma 2

The algebraic multiplicity (algebraic Let's assume that the eigenvalues of the Hermitian matrix A Te pleats having a multiplicity) value. Then, x

If the eigenvector satisfies < RTI ID = 0.0 &

The following is obtained.

이다.here

to be.

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

이다.
here,

to be.

2.1 4 TX ULA

In this section, consider the case of N = 4 common-polarized transmit antennas. First, if there is no loss of generality, the following structure can be applied to 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 must be an Hermitian trellis matrix, we can deduce that if we call the lemmas 1 and 2,

Then, any two eigen-vectors of the form (8) given by the following are considered.

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

And a sufficient condition to enhance the orthogonality between these two eigenvectors is to ensure the following equation.

This can be simplified to the next.

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

Lt; / RTI >

2 Polarization setting ( 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. The correlation matrix for each of these two common-polarization sets is then denoted by C , which is Hermitian and Toeplitz. The entire 2N x 2N correlation matrix

Can be expressed as:

는 크로네커 프로덕트(kronecker product)를 나타내며,

이다.

의 임의의 고유벡터

는 다음의 형태를 갖는 것으로 나타낼 수 있다.here,

Represents a kronecker product,

to be.

≪ / RTI >

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

And x is an eigenvector of C. Also,

The two eigenvectors of

And

, Where

Represents a transpose operation, and if there is no loss of optimality

Can be ignored. The two eigenvalues are

to be. Also,

Is a model of the correlation matrix of two transmitted ULA.

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.We now proceed to assign codebooks using the observations generated in section 1 and section 2. In particular, it allows to specify a subset of codebooks that are well suited to other configurations as well as to closely spaced 4TX ULA and cross-pole antenna configurations. First, consider a rank-1 codebook that includes a set of 4x1 vectors. If there is no loss of generality,

Is considered first, where

to be. Thereby defining three component codebooks configured to form a rank-1 codebook. The first component codebook is referred to as a gain vector codebook

Lt; RTI ID = 0.0 >

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

Lt; RTI ID = 0.0 > codebooks, < / RTI &

And

Respectively. Gain vector codebook

. To cover the closely spaced 4TX ULA, sufficient vectors are needed in the rank-1 codebook with the (8) -shaped structure.

2 as a gain vector, and in Figure 2 provides a 3-bit codebook for gain vectors, where a settable scalar

, ≪ / RTI >

to be. Note that the gain vectors corresponding to indices 0, 1, and 2 are suitable for the ULA case spaced at 4 TX spacing by following the constraints in (8). The gain vector corresponding to index 0 is suitable for a 4 TX cross-pole case and the gain vectors corresponding to indices 3, 4 are referred to herein as a power imbalance case (see Appendix 8) . Index 7 represents re-use of the existing default codebook, and indices 5, 6 are 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

.

(8), so that 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 selects a codebook

Using

. A simple scheme for constructing these two codebooks is through uniform quantization of [0, 2 [pi]) using a predetermined number of bits for each codebook. By choosing a gain vector corresponding to index 0 in the gain vector codebook of FIG. 2 with the choice of adopting these phases, it can be seen that the result vector follows the general eigenvector structure of the 4TX cross-poll correlation matrix. Similarly, when adopting a gain vector corresponding to any of indices 0, 1, 2 in the gain vector codebook, it can be seen that the result vector follows the general eigenvector structure of the 4TX ULA correlation matrix.

Now consider a rank-2 codebook consisting of a set of semi-unitary 4x2 matrices. From the observations made in section 1, we can define 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 configuration with the exponential correlation model (discussed in Section 6)

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

This does not satisfy 4TX ULA.

4 Product form codebook configuration

In the following, two codebook configurations are discussed, in which each code word is derived as a matrix product, based on the principles outlined in section 1 and section 2. In each case, we use the codebook designed in [1] as a base, and extend it by following the principles outlined in section 1 and section 2.

인 경우에 대하여,

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

, ≪ / RTI >

. This codebook is referred to as a first embodiment, and its inner (wideband) codebook is defined as follows.

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

Represents a Hadamard product, and

랭크-1 외부 코드북은 다음과 같이 규정된다.here,

The rank-1 outer codebook is defined as follows.

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

인 경우에 대하여,

,

임에 유의한다.Scalar a _q , b _q Lt; RTI ID = 0.0 > scalable < / RTI &

, ≪ / RTI >

,

.

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.In each feedback interval for selecting rank-2 code words, one for each subband, an inner (broadband) codebook

One common matrix, i. E.

. Then, on each subband n, an outer (subband) rank-2 codebook

≪ / RTI >

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

. for your convenience,

(Final) codebook corresponding to rank-2, which corresponds to the

Lt; RTI ID = 0.0 > precoder < / RTI > Other ranks and internal precoder

Similar procedures and notations are adopted for other choices on the.

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.

Lt; RTI ID = 0.0 > scalar < / RTI &

, ≪ / RTI >

In order to ensure that there is no problem. Under this choice, the triple set

Will be described below. From the discussion in Appendix 7 using the exponential correlation model, the (non-quantized)

Is assumed to be uniformly distributed at [0, 1) so that it is a desirable choice

. Therefore,

Is through uniform quantization of [0, 1) using a predetermined number of bits. For example,

.

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.

, One possibility is to consider them as variables < RTI ID = 0.0 >

. Accordingly, the correlation magnitude parameter

A finite set of values for < RTI ID = 0.0 >

Can be obtained. For example, the correlation size parameter

Set for

. Then, by applying the equations in Appendix 7,

end

As shown in Fig. Then, triple set

(Cartesian product)

, Which is used herein to denote a Cartesian product

Were used. For example, the specific instances provided above

And

Lt; RTI ID = 0.0 >

Lt; RTI ID = 0.0 > 16, < / RTI > Another example is

And three values for the correlation magnitude parameter

A set that uses only

To obtain a cartesian product having a size of 15 by using < RTI ID = 0.0 > Another example is that the Cartesian product has size 16,

And two values for the correlation size parameter

A set that uses only

.

Now, let us consider another alternate codebook, hereinafter referred to as a second embodiment, whose codewords are also derived in product form. Now, the inner broadband codebook is defined as follows.

here,

or,

The rank-1 outer codebook is defined as follows.

The rank-2 outer codebook is defined as follows.

In either case, rank-3 and rank-4 codebooks are fixed to legacy (house holder) rank-3 and rank-4 codebooks. In addition, 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 is expressed by the following equation

In this case,

In each selection of the codebook, the codebook corresponding to the rank

And that the expected value of the standard square of each row for the selected precoder matrix (i.e., the sum of the magnitude squared of the elements of the row) is the same. This characteristic is beneficial in operating the power amplifiers (i.e., controlling the backoff of the power amplifiers) and utilizing available transmit power.

4.1 For larger codebooks Embedding

Note that the channel matrix implementation is determined by a spatial correlation matrix and short-term (so-called fast) fading. In some scenarios, there may be significant deviations in the observed channel matrix due to fast-fading, such as when the common-polarized antennas are widely spaced. Thus, the preferred codebook needs to accommodate significant deviations in the observed channel matrix due to this fast-fading, and therefore needs to include codewords designed using other criteria such as the minimum chordal distance . A useful way of solving these cases is to embed a codebook obtained using the principles described above as a subset within a larger codebook.

5 Conclusion

The anomaly codebook structure has been described in detail and two embodiments according to the matrix product form have been presented. This structure is derived by the basic properties of the spatial correlation matrix and makes it possible to realize the codebook optimization.

6 Appendix: 4 with Exponential Correlation Model TX ULA

Next, consider a case where 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

. Note that the matrix C is Hermite Teflitz, and may be fully characterized by a single complex scalar. Thus, its eigenvectors can be expected to have more structure than being processed by the eigenvectors of a normal Hermite teplitz matrix. In the following, 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,

Is considered. In this case, the eigen-vectors for any matrix of the form in (24) will have the following properties. Considering any 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 set to indicate its intrinsic decomposition, where

Represents a conjugate transpose operation,

In this case,

And they represent eigenvalues that are four real values. Then, the following equation is obtained,

는 하다마드 프로덕트를 나타내고,

는,

인 경우에 대하여, 다음의 형태의 대각 행렬이 된다.here,

Represents a Hadamard product,

Quot;

, A diagonal matrix of the following form is obtained.

가

및

를 만족하는 경우에 대하여, 다음의 구조를 갖는다.The matrix S is a positive real number scalar

end

And

, The following structure is obtained.

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

Each row of the table must satisfy the following conditions.

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

An important example is H :

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

, The following scalar < RTI ID = 0.0 >

Can be derived. first,

. (26), the following equation is calculated 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,

, The correlation matrix C reduces the identity matrix,

(The application of each standard constraint). Also,

Quot;

With a relationship of

, Where < RTI ID = 0.0 >

to be.

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

, Then matrix C is a rank-1 matrix given by

Then, the eigenvector 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,

.

May be arbitrary, since the corresponding eigenvalue is zero (application of standard constraints).

7 Appendix: Acceptance of Power Imbalance

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

Can be expressed as:

이고,

이며 이것은

을 만족시킨다.

의 임의의 고유벡터

는 다음의 형태를 가질 수 있다.here,

ego,

And

Lt; / RTI >

≪ / RTI >

Can 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

And x is an eigenvector of C. procession

Quot; may represent any 2 x 2 positive semi-definite matrix up to a scaling factor. Thus, a 2x2 unitary matrix formed by two eigenvectors may be any 2x2 unitary matrix. And, in order to design codebooks suitable for such scenarios, considering the first embodiment presented in section 4,

To be expanded as follows.

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

는

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

The

Are pre-determined scalars. Now, the outer rank-2 codebook is defined as follows.

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

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

는 다음과 같이 표기될 수 있다.It is noted that the above-defined codebooks are also suitable when the transmitter has geographically separated 4 common-polarized antennas comprising a pair of 2 common-polarized antennas at each location. And, the correlation matrix for each of these two common-polarization sets is given by Hermit and Teplitz, C. The entire 4x4 correlation matrix

Can be expressed as:

는 크로네커 프로덕트를 나타내고,

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

Represents a Kronecker product,

Is a normalized gain term that reflects different average propagation gain from the two positions.

II . Example 2

Product-oriented codebook configuration

Now, based on the principles derived above, let us discuss the structured codebook configuration where each codeword is derived as a matrix product.

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,

. The inner (broadband) codebook is defined as follows. First, the positive integers K, J, and L are defined by the following equations.

및

를 만족하도록 선택된다. 이제, 내부 (광대역) 코드북을 다음과 같이 상세히 나타내도록 한다.Here, K is referred to as a step (step), J is referred to in the lateral (width), L also is referred to as a range (extent). These parameters are generally

And

. Now let the internal (wideband) codebook be 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 a Hadamard product,

Lt;

Its main diagonal is the vector

, Where < RTI ID = 0.0 >

And is as follows,

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,

, Then for continuous k selection

Can be introduced. Especially,

By ensuring that,

Some rows of

As shown in Fig. This is a useful feature of the inner broadband codebook because the correlation in time or frequency changes gradually. However,

In case of m, it does not need to be maintained. In this case, in order to introduce overlap between different inner codebooks,

Lt; RTI ID = 0.0 >

sign

By appropriately selecting (

If you select

Quot; is also fixed)

And

Lt; RTI ID = 0.0 > overlap. ≪ / RTI >

Rank-1 outer codebooks are 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.Here, for given r, s

May be any of the four display vectors,

Denotes a J × 1 column selection vector that selects the i-th column of the J × J identity matrix. It should be noted that, in the present specification, the realizable (feasible) (r, s) and the subject to allow only certain combinations are referred to as a combination, in which can be a feasible combination that the r = s to limit the size . For any subband, the rank-1 final code word may be < RTI ID =

from

And

Lt; RTI ID = 0.0 >

By selecting

To obtain the final codeword for that subband. Note that the selection of the inner 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 extend the selectivity in each subband,

To an external codebook. That is,

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

And may define an internal wideband codebook.

In all of the above cases, the outer codebook may be determined according to the selection of the inner code word . That is, each of (r, s, q2) in (r, s) or (2-5) in (2-4) may itself be a function of selection of the inner codeword. In other words, the two different inner codewords may have different feasible combinations for selecting codewords from the outer codebook. In each case, a set of feasible combinations for 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 keep the inner codebook defined in (2-2) with the next outer subband rank-2 codebook invariant to the choice of inner code word.

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)

Lt; / RTI > must be mutually orthogonal for each selection of the inner codeword. r = s is the internal codeword

Is an option that ensures orthogonality for each selection of < RTI ID = 0.0 >

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.In order to extend the last rank-2 code words that can be set not to have excessive overhead, the allowable combinations may be determined according to the selection of the inner code word. Especially,

Having the form (2-7) below

(Identified by indices q1, q2, k) containing the codewords represented by < RTI ID = 0.0 >

Lt; RTI ID = 0.0 > sub-band codebook determined < / RTI >

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

With the permissible combinations (r, s), the resulting final codeword

Lt; RTI ID = 0.0 > orthogonal < / RTI > Due to the structure of the inner codebook,

Is sufficient to be a function of the < RTI ID = 0.0 >

It should be noted that To enable more choices in the outer codebook, as done in the rank-1 case,

To an external codebook. That is, for possible combinations (r, s, q2)

Having an outer subband rank-2 codebook having codewords of the form

And may define an internal wideband codebook.

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.To further extend the set of rank-2 code words, it is possible to ensure orthogonality between the columns of the final codeword resulting in other schemes. The inner codebook is assumed to be defined as in (2-2)

And,

Omit for cases where the given steps change to external codebooks since they can be applied after simple changes). Then, the rank-2 outer codebook is determined according to the selection of the inner code word, and assumes that it contains code words having the form in (2-7). In addition,

For the selection of <

Lt;

end

Satisfying

(2-8) below, which are pseudo-inverse of the codeword of the codeword.

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 an arbitrary unit-norm vector x ,

Part-space

Lt; / RTI > is a predefined operator that satisfies the fact that it is a unit norm vector in < / RTI > Preferably, such an operator, if the vector x has a constant magnitude property such that all of its elements have a constant magnitude,

Can also have characteristics that have such characteristics. One example of such an operator,

And for any unit nominal vector x whose first element is a real number value and exactly less than one,

Lt; th > column of the 4x4 unitary matrix obtained through the < RTI ID = 0.0 >

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

≪ / RTI > satisfies the two conditions required to define the house-holder transformation. Further, when the vector x has a constant size characteristic,

And so on.

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.Another example of such an operator is

, Where P is a permutation matrix, and D (x) is its diagonal entries

Lt; RTI ID = 0.0 > x < / RTI > If x has a constant size property, the non-zero entries may constitute a diagonal matrix D (x) with a unit size, and

And vector

Lt; RTI ID = 0.0 > a < / RTI > constant size characteristic.

(2-2) can define a different set of internal codewords (i.e., an internal codebook) for both of them, although both rank-1 and rank-2 and other ranks are assumed to have a general structure . Thus, rank specific internal codebooks can be defined. Recall that the function of the inner codeword may already exist for each subband outer codebook. It should also be noted that, in the above-described codebooks, de-duplication may be performed if necessary. In particular, for any rank r, if there are any two inner code words that produce rank-r code words per equivalent sub-band of the last set, then the inner codebook of that rank-r contains these two inner codes Only one of the words should be retained. Here, one of the two final codewords is the same as the other codeword until the right multiplication by a column permutation and / or a diagonal matrix, and all of its non-zero entries Note that, in the case of a unit size, the two last codewords are the same.

It should be noted that having a rank-2 inner codebook that is larger than the rank-1 codebook may be useful for MU-MIMO. A larger inner codebook may allow for better quantization resolution without excessively increasing the feedback because only one inner codeword needs to be reported for all subbands to be. A better resolution for upper rank-2 may be useful in MU-MIMO as well as in SU-MIMO because a user under MU-MIMO transmission will typically be served using a lower rank than it is reported Because. In this case, better resolution will ensure that the column 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 Rel-11 LTE cellular network, it is possible for the network to set up a plurality of CSI processes for the same user on a semi-static basis. 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. In addition, a separate codebook subset constraint may be applied for each CSI process. A useful corollary from these two observations can be set for each CSI process (for the user of interest) in a quasi-static manner, i.e. for each CSI process for a given user , Which may establish a component (i. E., Legacy or enhanced) codebook available to the user. In addition, other codebook subset constraints may be applied per CSI process foundation, taking into account the selection of component codebooks for these processes. In order to reduce the signaling overhead, it is proposed to apply only the latter codebook subset constraint for each CSI-process. As a result, even if the CSI process (or, equivalently, the mode defined for that CSI process) requires that the user report subband-by-sub precoding matrices (i.e., PMIs) All such reported matrices will necessarily comply with the (common) subset constraints set for that process.

Product-oriented codebook configuration

에 대하여

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

about

Let the inner (broadband) codebook be defined as follows.

는 실수값의 스칼라들이며, 또한here,

Are real-valued scalars, 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. Certain internal codewords

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

silver

, The two inner codewords < RTI ID = 0.0 >

And

At any two beam vectors that are related to the phase vector, contributes to controlling the separation between the phase terms. Intuitively, small separations may be useful when utilizing correlations in time and frequency.

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

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. Thus, 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. The common-phase terms can be obtained by optimizing the appropriate metric, such as the average coded distance, after limiting the positive integers M > 1 to be placed in the design parameter M-PSK alphabet. This optimization can be limited to ensure that the minimum angle separation between the common-phase terms is maintained. For rank-2, the outer (subband) codebook is defined as follows.

Note that in the case of different pairs of (m, p) and (m ', p'), they may have different numbers of common-phase terms. These common-phase terms may be optimized by optimizing the appropriate metric, such as the average coded distance, after limiting them to be placed in the M'-PSK alphabet, where the positive integer M ' > 1 is a design parameter and may differ from M ≪ / RTI > This optimization can be limited to ensure that the minimum angle separation between the 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, let us propose two specific embodiments. Both embodiments have a 4 bit wideband codebook. In the case of the first embodiment,

And

So that the inner code word is a 4x4 matrix.

. The corresponding sub-band codebook has a 3-bit size for both rank 1 and rank 2. In the rank-1 codebook, the common-phase terms are placed in the 8-PSK alphabet, which is provided in FIG. Note that the notation adopted in the table of FIG. 3 is θ _{s, i} = 2 πt / M (where M = 8 for 8-PSK) if the entry corresponding to ( s, i ) is t . In the case of rank-2 codebook, with the common-phase terms provided in Fig. 4A or 4B

. Alternatively, the common-phase terms may be selected as shown in FIG. It should be noted 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

So that each inner codeword is a 4x8 matrix.

. The corresponding sub-band codebook has a 4-bit size for rank 1 and rank 2. In the rank-1 codebook, the common-phase terms are placed in the 8-PSK alphabet, which is provided in Fig. 6a or 6b. In the case of rank-2 codebook, with the common-phase terms provided in Fig. 7

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

Rank-3 and rank-4 codebooks may be fixed to legacy (house holder) rank-3 and rank-4 codebooks. Note that all codeword matrices in the above-described codebook satisfy the constant size property.

IV . Example 4

Other related problems are that when the user is set to use a legacy 4 TX codebook as one of the CSI processes and when the process (or mode defined for the CSI process equally) provides the user with precoding matrices for each subband And to report it. Here, if 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 reporting every subband-by-subband. That is, feedback can be reduced without noticeable impact on performance, since the user is experiencing a good average SINR and will typically be scheduled solely on allocated resources. To achieve feedback reduction, the network defines a sub-sampled version of the legacy codebooks for rank 3 and rank 4 such that if the preferred rank is 3 or 4, the user selects the codewords from these sub-sampled codebooks Can be set to report. Rank-3 codebook is obtained by removing one or more code words from the rank-3 legacy codebook, and the sub-sampled rank-3 codebook is also obtained by removing one or more code words from the rank- A codebook is obtained. These sub-sampled codebooks are defined by the network and are delivered to all users in advance. Another approach to provide more flexibility is to leverage the codebook subset constraints. Here, it is assumed that the size (subband-per-subband) of the rank-3 codebook is limited to M codewords. The network can then determine from the legacy rank-3 codebook a subset (sub-statically and possibly user-specific) that includes less than M codewords and deliver this subset to the user. Then, the user will limit the search (for rank-3 codewords) to this subset on each subband. In order to report the preferred codeword on each subband, the user employs lexicographic ordering (labeling). That is, one new index is assigned to the codewords in the display subset with the smallest index (such as in the original rank-3 legacy codebook) and the second smallest index (such as in the original rank-3 legacy codebook) Two new indexes are assigned to codewords in a display subset with an index. This process continues until all codewords in the subset are assigned new indexes. Clearly, these new indices can range from 1 to M ' , where M' ≤ M. It should also be noted that since the subset is common across all subbands, the set of new indices will also be common across all subbands, and hence must be determined by the user. The user then reports a new index for the selected precoder on each subband. Note that the same procedure can be applied to rank-4, where the value of M may 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). The user may also report the MU-CQI (s) with a single-user (SU) CSI (channel state information) report, as described in detail in previous work [8]. This SU-CSI (including broadband or subband-by-PMI, and subband-per-CQI) is calculated using resource elements and pilots for interference measurements that are set for the corresponding CSI process. Several schemes for computing these MU-CQI (s) have been described in detail in previous work [9], one of which sets a set of co-scheduled interferences (for the subband basis if so configured) After the assumption, the PMI (s) determined by the SU-CSI report to calculate the MU-CQI (s) or determined using SU-MIMO rules (hereinafter referred to as base-PMI Quot;). ≪ / RTI > Here, the set of co-scheduled interfering PMIs (i.e., transmission precoders assigned to other users that are co-scheduled to be) that the user assumes for the subband is a function of the base-PMI for which it is determined. Each set of co-scheduled interfering PMIs that the user must assume can be set by the network in a quasi-static (and possibly user-specific) manner. The size of the set of interfering PMIs (for selection for each base-PMI) may be greater than one. In order to reduce the overhead, the final MU-CQI (s) computed for the subband basis may be combined into one (or up to two) wideband MU-CQI (s) Detailed in task [10]), after which it is reported. To further improve performance, a plurality of such sets of interfering PMIs (for each base-PMI) may be set. Thereafter, the user may report one (or at most two) wideband MU-CQI (s) for each set of interfering PMIs, and the differential feedback may be leveraged to reduce the feedback overhead. Alternatively, the above-described process may be repeated for several selections for base-PMs, and the user may select one particular base-PMI (using the appropriate selection rules, such as the rule to maximize the expected MU gain) , And report it with the associated MU-CQI (s).

Return to the next codebook configuration.

Product-oriented codebook configuration

에 대한

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

For

Is set to indicate a 2 × 1 beam vector, and the inner (wideband) codebook is defined as follows.

Where {a _k } are real scalar values, and

이며,

Lt;

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. Certain internal codewords

(Angular) separation of the phase terms of any two adjacent beam vectors in the beam vector is 2? / N and thus N (referred to as granularity) and J (the number of beam vectors per inner code word) To determine the angular span of the phase term in the inner codeword. Intuitively, (which may be accomplished by having a smaller N (i.e., smaller particle size or larger 2π / N) for a given J, or can be achieved by having a larger J for a given N) A larger angular span can also be made for the codebook to be suitable for smaller correlated fading scenarios as well as to provide robustness against timing alignment errors. However, an increase in the cost of J would increase the size of each of the outer sub-band codebooks, while a smaller N selection could degrade performance in a close-spaced cross-pole configuration, Because it hinders the localization of the beam vectors in the codeword. On the other hand, scalar {d _q } (referred to as staggering factors)

Lt; RTI ID = 0.0 > 2 < / RTI >

And

Lt; RTI ID = 0.0 > beam vectors < / RTI > Intuitively, a small separation will be useful in exploiting the correlation in time and frequency.

The extension to the inner codebook described above is to use a set of two (or more) particle sizes, where each particle may have its own set of staggering factors. Typically, this increases the size of the wideband codebook, but it can better meet the different antenna configurations. In the following, I describe a composite inner (broadband) codebook for 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 the set of indices associated with the i-th particle size N _i. Note that J remains fixed over the different particle sizes. In certain scenarios (with very low correlation), it may be advantageous to select at least one grain size of the grain sizes that satisfy the mutual orthogonality of one or more of the beam vectors of the plurality with the relevant inner codewords.

Then, the rank-1 outer (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. Thus, 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. The common-phase terms can be obtained by optimizing the appropriate metric, such as the average covariance distance, after limiting it to being placed in the M-PSK alphabet that is a design parameter with a positive integer M > This optimization can be limited to ensure that the minimum angle separation between the common-phase terms is maintained. For rank-2, the outer (subband) codebook is defined as follows.

Note that in the case of different pairs of (m, p) and (m ', p'), they may have different numbers 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 ≪ / RTI > This optimization can be limited to ensure that the minimum angle separation between the common-phase terms is maintained.

Thus, the present inventors have found that (1) the core structure that each eigenvector of the spatial correlation matrix should have in the ULA transmission antenna configuration, and the core that each eigenvector of the spatial correlation matrix has to have in the cross- (2) the inventors then performed the identified structures in at least one subset of the precoding codebooks to ensure good performance, and (3) And also provides efficient embodiments.

It is to be understood that the above description is intended to be illustrative and explanatory in all respects not restrictive and the scope of the invention as described herein is not to be determined from the foregoing detailed description, Should be determined from the claims of It is to be understood that the embodiments shown and described herein are illustrative only of the principles of the invention, and that those skilled in the art may implement various modifications that do not depart from the scope and spirit of the invention. Those skilled in the art can implement various other feature combinations that do not depart from the scope and spirit of the invention.

Claims (49)

delete delete delete delete delete delete delete delete delete delete delete delete delete delete delete delete delete delete A method implemented in a base station for use in a wireless communication system,
Comprising: providing a codebook comprising a plurality of precoding matrices;
Precoding data to one of the plurality of precoding matrices; And
And transmitting the precoded data to a user equipment,
Each precoding matrix W satisfies W = W ⁽¹⁾ W ⁽²⁾
The first matrix W ⁽¹⁾

≪ / RTI >
The second matrix W ⁽²⁾ is selected from the second codebook,

ego,
here,

Represents a Hadamard product,

ego,
J , K , and L are positive integers,

And

ego,

And

In method. delete 20. The method of claim 19,
The second codebook for rank-1 transmission,

, ≪ / RTI >
here,

, And

J × J is the identity matrix (identity matrix) i-th column, the method represents the J × 1 column selection vector for selecting the (column) in the. 22. The method of claim 21,
Wherein portions of feasible combinations ( r , s , q 2) are allowed. 20. The method of claim 19,
The second codebook for rank-

Lt; / RTI >
here,

, And

It is, how to represent the J × 1 column selection vector for selecting the i-th column from J × J identity matrix. 24. The method of claim 23,
Wherein parts of feasible combinations ( r , s ) are allowed. 24. The method of claim 23,
r = s . 20. The method of claim 19,
The second codebook for rank-

, ≪ / RTI >
here,

, And

It is, how to represent the J × 1 column selection vector for selecting the i-th column from J × J identity matrix. 27. The method of claim 26,
Wherein portions of feasible combinations ( r , s , q 2) are allowed. 20. The method of claim 19,

In method. 20. The method of claim 19,
2? (D _{q +1} -d _q ) is smaller than 2? / N. 20. The method of claim 19,
Wherein the codebook is comprised of a plurality of precoding matrices. 20. The method of claim 19,
Wherein the first matrix is common across a plurality of subbands and the second matrix is for each subband. 20. The method of claim 19,
Wherein the codebook is for 4TX (4 transmit) antenna transmission. 20. The method of claim 19,
J = 4. A method implemented in a user equipment used in a wireless communication system,
Receiving, from a base station, precoded data in one of a plurality of precoding matrices,
The codebook includes the plurality of precoding matrices,
Each precoding matrix W satisfies W = W ⁽¹⁾ W ⁽²⁾
The first matrix W ⁽¹⁾

≪ / RTI >
The second matrix W ⁽²⁾ is selected from the second codebook,

ego,
here,

Represents a Hadamard product,

ego,
J , K , and L are positive integers,

And

ego,

And

In method. 1. A base station used in a wireless communication system,
A transmitter for transmitting precoded data to one of a plurality of precoding matrices to a user equipment,
The codebook includes the plurality of precoding matrices,
Each precoding matrix W satisfies W = W ⁽¹⁾ W ⁽²⁾
The first matrix W ⁽¹⁾

≪ / RTI >
The second matrix W ⁽²⁾ is selected from the second codebook,

ego,
here,

Represents a Hadamard product,

ego,
J , K , and L are positive integers,

And

ego,

And

In base station. A user equipment for use in a wireless communication system,
Comprising: a receiver for receiving, from a base station, data precoded to one of a plurality of precoding matrices,
The codebook includes the plurality of precoding matrices,
Each precoding matrix W satisfies W = W ⁽¹⁾ W ⁽²⁾
The first matrix W ⁽¹⁾

≪ / RTI >
The second matrix W ⁽²⁾ is selected from the second codebook,

ego,
here,

Represents a Hadamard product,

ego,
J , K , and L are positive integers,

And

ego,

And

User equipment. 1. A wireless communication system,
A base station having a codebook comprising a plurality of precoding matrices, the base station precoding data to 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⁾
The first matrix W ⁽¹⁾

≪ / RTI >
The second matrix W ⁽²⁾ is selected from the second codebook,

ego,
here,

Represents a Hadamard product,

ego,
J , K , and L are positive integers,

And

ego,

And

In wireless communication system. A method implemented in a wireless communication system,
Precoding data into one of a plurality of precoding matrices; And
Transmitting the precoded data from a base station to a user equipment,
The codebook includes the plurality of precoding matrices,
Each precoding matrix W satisfies W = W ⁽¹⁾ W ⁽²⁾
The first matrix W ⁽¹⁾

≪ / RTI >
The second matrix W ⁽²⁾ is selected from the second codebook,

ego,
here,

Represents a Hadamard product,

ego,
J , K , and L are positive integers,

And

ego,

And

In method. delete delete delete delete delete delete delete delete delete delete delete

Images