KR20160116046A  Codebook construction  Google Patents
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 KR20160116046A KR20160116046A KR1020167026694A KR20167026694A KR20160116046A KR 20160116046 A KR20160116046 A KR 20160116046A KR 1020167026694 A KR1020167026694 A KR 1020167026694A KR 20167026694 A KR20167026694 A KR 20167026694A KR 20160116046 A KR20160116046 A KR 20160116046A
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 H04B7/02—Diversity systems; Multiantenna system, i.e. transmission or reception using multiple antennas
 H04B7/04—Diversity systems; Multiantenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
 H04B7/0413—MIMO systems
 H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
 H04B7/046—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting taking physical layer constraints into account
 H04B7/0469—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting taking physical layer constraints into account taking special antenna structures, e.g. cross polarized antennas into account

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 H04B7/0413—MIMO systems
 H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
 H04B7/0478—Special codebook structures directed to feedback optimization

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 H04B7/0615—Diversity systems; Multiantenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
 H04B7/0617—Diversity systems; Multiantenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming

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 H04B7/0619—Diversity systems; Multiantenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal using feedback from receiving side
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 H04B7/0615—Diversity systems; Multiantenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
 H04B7/0619—Diversity systems; Multiantenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal using feedback from receiving side
 H04B7/0636—Feedback format
 H04B7/0639—Using selective indices, e.g. of a codebook, e.g. predistortion matrix index [PMI] or for beam selection

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 H04B7/06—Diversity systems; Multiantenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
 H04B7/0613—Diversity systems; Multiantenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
 H04B7/0615—Diversity systems; Multiantenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
 H04B7/0619—Diversity systems; Multiantenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal using feedback from receiving side
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 H04B7/04—Diversity systems; Multiantenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
 H04B7/06—Diversity systems; Multiantenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
 H04B7/0613—Diversity systems; Multiantenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
 H04B7/0615—Diversity systems; Multiantenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
 H04B7/0619—Diversity systems; Multiantenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal using feedback from receiving side
 H04B7/0636—Feedback format
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 H04L1/0001—Systems modifying transmission characteristics according to link quality, e.g. power backoff
 H04L1/0023—Systems modifying transmission characteristics according to link quality, e.g. power backoff characterised by the signalling
 H04L1/0026—Transmission of channel quality indication

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 H04L1/0001—Systems modifying transmission characteristics according to link quality, e.g. power backoff
 H04L1/0023—Systems modifying transmission characteristics according to link quality, e.g. power backoff characterised by the signalling
 H04L1/0027—Scheduling of signalling, e.g. occurrence thereof

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 H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks ; Receiver end arrangements for processing baseband signals
 H04L25/03891—Spatial equalizers
 H04L25/03898—Spatial equalizers codebookbased design
 H04L25/0391—Spatial equalizers codebookbased design construction details of matrices

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Abstract
Description
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 multipleinput and multipleoutput (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 precoded or precoded 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 codebookbased 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 shortterm feedback once every consecutive time interval to longterm 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 frequencydivision 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 multiresolution codebooks are described in references [5] and [6].
In order to obtain an effective codebook for both a uniform linear array (ULA) and a crosspole 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 crosspole 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 crosspole 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, STEricsson, "Design and Evaluation of 4 TX Precoder Codebooks for CSI Feedback," 3GPP TSG RAN WG1 R1104847 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 multipleinput multipleoutput 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 ., "MULTIRESOLUTION PRECODING CODEBOOK," US Patent Application Publication US 2009/0274225 A1.
[7] 3GPP TS 36.213 V10.8.0 (201212), 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (EUTRA); Physical layer procedures (Release 10), http://www.3gpp.org/ .
[8] NEC Group, "DL MUMIMO Enhancement Schemes," 3GPP TSG RAN WG1 R1 130364.
[9] NEC Group, MUMIMO: "CQI Computation and PMI Selection," 3GPP TSG RAN WG1 R1103832.
[10] NEC Group, "DL MUMIMO enhancement via Residual Error Norm feedback," 3GPP TSG RAN WG1 R1113874 .
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: 1layer, 2layer, 3layer, and 4layer 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 onelayer and twolayer 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 1layer, 2layer, 3layer, and 4layer codebooks for transmitting 4TX (4 transmit) Coding matrices and each of the onelayer and twolayer 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 1layer, 2layer, 3layer, and 4layer codebooks for transmitting 4TX (4 transmit) Wherein each of the onelayer and twolayer 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 1layer, 2layer, 3layer, and 4layer codebooks for transmitting 4TX (4 transmit) Wherein each of the firstlayer and the secondlayer 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 onetier, twotier, threetier, and fourtier 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 2layer 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 1layer, 2layer, 3layer, and 4layer codebooks for transmitting 4TX (4 transmit) And wherein each of the onelayer and twolayer 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 householder codebook.
Each of the 3layer and 4layer codebooks may include a legacy codebook or a householder codebook.
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.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.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.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 precoded 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.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 precoding 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.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.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.FIG. 1 illustrates an exemplary embodiment of a receiver having N _{T} transmitantennas at the transmitter and N _{R} _{ } / RTI > is a diagram of a downlink multiuser MIMO system with receive antennas.
Figure 2 shows the
3 is a diagram of commonphase terms in the 8PSK alphabet for rank1.
4A is a diagram of commonphase terms in the 16PSK alphabet for rank2.
4B is a diagram of other commonphase terms in the 16PSK alphabet for rank2.
5 is a diagram of commonphase terms in the 8PSK alphabet for rank2.
6A is a diagram of commonphase terms in the 8PSK alphabet for rank1.
6B is a diagram of other commonphase terms in the 8PSK alphabet for rank1.
7 is a diagram of commonphase terms in the 24PSK alphabet for rank2.
8A is a diagram of commonphase terms in the 24PSK alphabet for rank2.
8B is a diagram of commonphase terms in the 12PSK alphabet for rank2.
9 is a diagram of commonphase terms in the 16PSK alphabet for rank2.
10 is a diagram for commonphase terms in the 16PSK alphabet for rank2.
1 shows a downlink multiuser MIMO system with N _{T} transmitantennas at the BS and with N _{R} receive antennas at the UE. A multiantenna communication system 100 with a multilevel precoding codebook is schematically illustrated in FIG. Transmitter 110 transmits to r receive antennas 121.1121.r coupled to receiver 120 through fading channels 130 through r from t transmit antennas 111.1111.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
Unless otherwise stated below, it is assumed that copolarized antennas are closely spaced.
The inventors have made the following observations on the construction of a uniform linear array (ULA) transmission antenna. Consider a system with N commonpolarized 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
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]).observe One procession C Hermitage Teplitz Matrix, C ≪ / RTI > satisfies <
here,
Represents the pair of C.Lemma 1, any Hermitian eigenspace of Te pleated matrix (eigenspace) can be fully described by the LE is committed vector. In other words,
And the eigen vector x of the Hermitian trellis matrix A satisfy the following equations Y. & Lt ; / RTI >
Lemma 2
Is an eigenvalue of the Hermitian Teplitz matrix A with an algebraic multiplicity value . Then, x If the eigenvector satisfies < RTI ID = 0.0 & The following is obtained.
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.
here,
to be.
2.1 4 TX ULA
In this section, consider the case of N = 4 commonpolarized 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 :
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 eigenvectors of the form (8) given by the following are considered.
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.
(11) is not required, but the scalar of all possible values
Lt; / RTI >
2 polarized waves Setting (Polarized Setup)
The transmitter is assumed to have 2N crosspolarized antennas, each of which includes a pair of N commonpolarized antennas. The correlation matrix for each of these two commonpolarization sets is then denoted by C , which is Hermitian and Toeplitz. The entire 2N x 2N correlation matrix
Can be expressed as:
here,
Represents a kronecker product, to be. ≪ / RTI > Can be represented as having the following form.
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 codebooks Configuration
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 crosspole antenna configurations. First, consider a rank1 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 rank1 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 rank1 codebook with the (8) shaped structure. 2 as a gain vector, and in Figure 2 provides a 3bit 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 crosspole 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 reuse of the existing default codebook, and indices 5, 6 are included to provide more choices.Next, to quantize the phases, two phase codebooks,
And . (8), so that the vector x can be expanded as follows.
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 crosspoll 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 rank2 codebook consisting of a set of semiunitary 4x2 matrices. From the observations made in section 1, we can define a subset of matrices with the following structure.
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 crosspole configuration (discussed in Section 2). It is also possible to include matrices having the following structure,
This does not satisfy 4TX ULA.
4 products Configuration of a codebook
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.
, ≪ / RTI > . This codebook is referred to as a first embodiment, and its inner (wideband) codebook is defined as follows.
here,
Represents a Hadamard product, and
here,
The rank1 outer codebook is defined as follows.
Here, e _{i} represents a 4 × 1 column selection vector. The outer rank2 codebook is defined as follows.
Scalar a _{q} , b _{q} _{ } Lt; RTI ID = 0.0 > scalable < / RTI &
, ≪ / RTI > , .In each feedback interval for selecting rank2 code words, one for each subband, an inner (broadband) codebook
One common matrix, i. E. . Then, on each subband n, an outer (subband) rank2 codebook ≪ / RTI > Is selected, and the final precoder selection for that subband is . for your convenience, (Final) codebook corresponding to rank2, 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.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 (nonquantized) 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, .
, 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 rank1 outer codebook is defined as follows.
The rank2 outer codebook is defined as follows.
In either case, rank3 and rank4 codebooks are fixed to legacy (house holder) rank3 and rank4 codebooks. In addition, the entire legacy codebook can be included as a subset.
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 More Large codebook Embedding
Note that the channel matrix implementation is determined by a spatial correlation matrix and shortterm (socalled fast) fading. In some scenarios, there may be significant deviations in the observed channel matrix due to fastfading, such as when the commonpolarized antennas are widely spaced. Thus, the preferred codebook needs to accommodate significant deviations in the observed channel matrix due to this fastfading, 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 TX with exponential correlation model ULA
Next, consider a case where the correlation matrix is further specialized as follows.
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:
first,
Is considered. In this case, the eigenvectors for any matrix of the form in (24) will have the following properties. Considering any matrix C of the form in (24)
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,
here,
Represents a Hadamard product, Quot; , A diagonal matrix of the following form is obtained.
The matrix S is a positive real number scalar
end And , The following structure is obtained.
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 :
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.
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.Meanwhile,
, Then matrix C is a rank1 matrix given by
Then, the eigenvector of C corresponding to one nonzero eigenvalue can be represented as having the following form.
here,
And accordingly, . May be arbitrary, since the corresponding eigenvalue is zero (application of standard constraints).
7 Appendix : Acceptance of power imbalance
A more general model for the spatial dependence of the crosspole antenna configuration is as follows. Consider a transmitter with 2N crosspolarized antennas each including a pair of N commonpolarized antennas. Then, the correlation matrix for each of these two commonpolarization sets is denoted by Hermit and the triplet C. The entire 2N x 2N correlation matrix
Can be expressed as:
here,
ego, And Lt; / RTI > ≪ / RTI > Can have the following form.
here,
The matrix And x is an eigenvector of C. procession Quot; may represent any 2 x 2 positive semidefinite 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 rank1 outer codebook is defined as follows.
here,
The Are predetermined scalars. Now, the outer rank2 codebook is defined as follows.
Likewise, in the case of the second embodiment, the rank1 outer codebook is defined as follows.
In addition, the rank2 outer codebook is defined as follows.
It is noted that the abovedefined codebooks are also suitable when the transmitter has geographically separated 4 commonpolarized antennas comprising a pair of 2 commonpolarized antennas at each location. And, the two commoncorrelation matrix about each set of polarization is given by the Hermitian and Te of the pleated C. The entire 4x4 correlation matrix
Can be expressed as:
here,
Represents a Kronecker product, Is a normalized gain term that reflects different average propagation gain from the two positions.
II. Example 2
Productoriented 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.
about, . The inner (broadband) codebook is defined as follows. First, the positive integers K, J, and L are defined by the following equations.
Here, K is referred to as a step , J is referred to as a width, and L is referred to as an extent . These parameters are generally
And . Now let the internal (wideband) codebook be described in detail as follows.
here,
Represents a Hadamard product, Lt; Its main diagonal is the vector , Where < RTI ID = 0.0 > And is as follows,
here,
to be.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 >Rank1 outer codebooks are defined as follows.
Here, for given r, s
May be any of the four display vectors, Denotes a J × 1 column selection vector that selects the ith column of the J × J identity matrix. To limit the size, it is noted that only certain combinations of (r, s) referred to herein as feasible combinations may be allowed, where r = s may be a feasible combination . For any subband, the rank1 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.Next, in order to extend the selectivity in each subband,
To an external codebook. That is, With the outer subband rank1 codebook of the following equation (25) 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 (25) in (24) 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 rank2 case. The first possibility is to keep the inner codebook defined in (22) with the next outer subband rank2 codebook invariant to the choice of inner code word.
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 >In order to extend the last rank2 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 (27) below (Identified by indices q1, q2, k) containing the codewords represented by < RTI ID = 0.0 > Lt; RTI ID = 0.0 > subband codebook determined < / RTI >
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 rank1 case, To an external codebook. That is, for possible combinations (r, s, q2) Having an outer subband rank2 codebook having codewords of the form And may define an internal wideband codebook.
To further extend the set of rank2 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 (22)
And, Omit for cases where the given steps change to external codebooks since they can be applied after simple changes). Then, the rank2 outer codebook is determined according to the selection of the inner code word, and assumes that it contains code words having the form in (27). In addition, For the selection of < Lt; end Satisfying (28) below, which are pseudoinverse of the codeword of the codeword.
Is an arbitrary unitnorm vector x , Partspace 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 householder transformation. Further, when the vector x has a constant size characteristic, And so on.
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 nonzero 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.(22) can define a different set of internal codewords (i.e., an internal codebook) for both of them, although both rank1 and rank2 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 abovedescribed codebooks, deduplication may be performed if necessary. In particular, for any rank r, if there are any two inner code words that produce rankr code words per equivalent subband of the last set, then the inner codebook of that rankr 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 nonzero entries Note that, in the case of a unit size, the two last codewords are the same.
It should be noted that having a rank2 inner codebook that is larger than the rank1 codebook may be useful for MUMIMO. 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 rank2 may be useful in MUMIMO as well as in SUMIMO because a user under MUMIMO 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 MUMIMO gains.
III. Example 3
In a Rel11 LTE cellular network, it is possible for the network to set up a plurality of CSI processes for the same user on a semistatic basis. Each Rel12 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 quasistatic 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 CSIprocess. As a result, even if the CSI process (or, equivalently, the mode defined for that CSI process) requires that the user report subbandbysub precoding matrices (i.e., PMIs) All such reported matrices will necessarily comply with the (common) subset constraints set for that process.
Productoriented codebook configuration
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.
here,
Are realvalued scalars, andego,
here,
to be. Certain internal codewords It is noted that two (angle) of separation between the phase terms in two adjacent beam vector in the is 2π / N, thus both the N and J to determine the phase term angular span (angular span) in each of the inner code word . 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 rank1 outer (subband) codebook is defined as
Here, e _{i} represents a J × 1 column selection vector (ie, the ith column of the J × J identity matrix)
Is a commonphase term. Thus, the (maximum) size of the rank1 codebook is JS . A smaller size can be obtained by selecting only a subset of all these possible vectors. The commonphase 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 MPSK alphabet. This optimization can be limited to ensure that the minimum angle separation between the commonphase terms is maintained. For rank2, 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 commonphase terms. These commonphase 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 commonphase terms is maintained.
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 subband codebook has a 3bit size for both rank 1 and rank 2. In the rank1 codebook, the commonphase terms are placed in the 8PSK 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 8PSK) if the entry corresponding to ( s, i ) is t . In the case of rank2 codebook, with the commonphase terms provided in Fig. 4A or 4B . Alternatively, the commonphase terms may be selected as shown in FIG. It should be noted that in FIG. 5 for the beam combination (1, 2), more commonphase selections are used.In the case of the second embodiment,
And So that each inner codeword is a 4x8 matrix. . The corresponding subband codebook has a 4bit size for rank 1 and rank 2. In the rank1 codebook, the commonphase terms are placed in the 8PSK alphabet, which is provided in Fig. 6a or 6b. In the case of rank2 codebook, with the commonphase terms provided in Fig. 7 . Alternatively, the commonphase terms provided in Figure 8A or 8B may also be selected. Alternatively, the commonphase terms provided in FIG. 9 or 10 may also be selected.Rank3 and rank4 codebooks may be fixed to legacy (house holder) rank3 and rank4 codebooks. Note that all codeword matrices in the abovedescribed 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 subbandbysubband. 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 subsampled 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 subsampled codebooks Can be set to report. Rank3 codebook is obtained by removing one or more code words from the rank3 legacy codebook, and the subsampled rank3 codebook is also obtained by removing one or more code words from the rank A codebook is obtained. These subsampled 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 (subbandpersubband) of the rank3 codebook is limited to M codewords. The network can then determine from the legacy rank3 codebook a subset (substatically and possibly userspecific) that includes less than M codewords and deliver this subset to the user. Then, the user will limit the search (for rank3 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 rank3 legacy codebook) and the second smallest index (such as in the original rank3 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 rank4, where the value of M may be different for rank 4 and rank 3. [
Finally, to improve MUMIMO 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 MUCQI (s) with a singleuser (SU) CSI (channel state information) report, as described in detail in previous work [8]. This SUCSI (including broadband or subbandbyPMI, and subbandperCQI) is calculated using resource elements and pilots for interference measurements that are set for the corresponding CSI process. Several schemes for computing these MUCQI (s) have been described in detail in previous work [9], one of which sets a set of coscheduled interferences (for the subband basis if so configured) After the assumption, the PMI (s) determined by the SUCSI report to calculate the MUCQI (s) or determined using SUMIMO rules (hereinafter referred to as basePMI Quot;). ≪ / RTI > Here, the set of coscheduled interfering PMIs (i.e., transmission precoders assigned to other users that are coscheduled to be) that the user assumes for the subband is a function of the basePMI for which it is determined. Each set of coscheduled interfering PMIs that the user must assume can be set by the network in a quasistatic (and possibly userspecific) manner. The size of the set of interfering PMIs (for selection for each basePMI) may be greater than one. In order to reduce the overhead, the final MUCQI (s) computed for the subband basis may be combined into one (or up to two) wideband MUCQI (s) Detailed in task [10]), after which it is reported. To further improve performance, a plurality of such sets of interfering PMIs (for each basePMI) may be set. Thereafter, the user may report one (or at most two) wideband MUCQI (s) for each set of interfering PMIs, and the differential feedback may be leveraged to reduce the feedback overhead. Alternatively, the abovedescribed process may be repeated for several selections for basePMs, and the user may select one particular basePMI (using the appropriate selection rules, such as the rule to maximize the expected MU gain) , And report it with the associated MUCQI (s).
Return to the next codebook configuration.
Productoriented codebook configuration
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
Lt;
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 subband codebooks, while a smaller N selection could degrade performance in a closespaced crosspole 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.
here,
And Is the set of indices associated with the ith 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 rank1 outer (subband) codebook is defined as follows.
Here, e _{i} is the ith J × 1 column selection vector (ie, the ith column of the J × J identity matrix)
Is a commonphase term. Thus, the (maximum) size of the rank1 codebook is JS . A smaller size can be obtained by selecting only a subset of all these possible vectors. The commonphase terms can be obtained by optimizing the appropriate metric, such as the average covariance distance, after limiting it to being placed in the MPSK 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 commonphase terms is maintained. For rank2, 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 commonphase terms. The commonafter 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 commonphase 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 (18)
 A method implemented in a base station for use in a wireless communication system,
Layer, 2layer, 3layer, and 4layer codebooks 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
And transmitting the precoded data to a user equipment,
Wherein each of the onelayer and twolayer codebooks includes a first codebook and a second codebook,
Wherein each precoding matrix in the first codebook comprises a first index and a second index.  The method according to claim 1,
Wherein the first index is for a plurality of subbands and the second index is for each subband.  The method according to claim 1,
Wherein the second codebook comprises a legacy codebook or a householder codebook.  The method according to claim 1,
Wherein each of the 3layer and 4layer codebooks comprises a legacy codebook or a householder codebook.  A method implemented in a user equipment used in a wireless communication system,
Receiving precoded data from a base station,
Each of the 1layer, 2layer, 3layer, and 4layer codebooks for 4TX (4 transmit) antenna transmission includes a plurality of precoding matrices,
Wherein each of the onelayer and twolayer codebooks includes a first codebook and a second codebook,
Wherein each precoding matrix in the first codebook comprises a first index and a second index.  The method according to claim 6,
Wherein the first index is for a plurality of subbands and the second index is for each subband.  The method according to claim 6,
Wherein the second codebook comprises a legacy codebook or a householder codebook.  The method according to claim 6,
Wherein each of the 3layer and 4layer codebooks comprises a legacy codebook or a householder codebook.  1. A base station used in a wireless communication system,
And a transmitter for transmitting the precoded data to the user equipment,
Each of the 1layer, 2layer, 3layer, and 4layer codebooks for 4TX (4 transmit) antenna transmission includes a plurality of precoding matrices,
Wherein each of the onelayer and twolayer codebooks includes a first codebook and a second codebook,
Wherein each precoding matrix in the first codebook comprises a first index and a second index.  A user equipment for use in a wireless communication system,
Comprising: a receiver for receiving precoded data from a base station,
Each of the 1layer, 2layer, 3layer, and 4layer codebooks for 4TX (4 transmit) antenna transmission includes a plurality of precoding matrices,
Wherein each of the firstlayer and the secondlayer codebooks includes a first codebook and a second codebook,
Wherein each precoding matrix in the first codebook comprises a first index and a second index.  1. A wireless communication system,
Layer, 2layer, 3layer, and 4layer codebooks for transmitting 4TX (4 transmit) antennas, each codebook comprising a plurality of precoding matrices, wherein one of the plurality of precoding matrices A base station for precoding data into one;
And user equipment for receiving the precoded data from the base station,
Wherein each of the onelayer and twolayer codebooks includes a first codebook and a second codebook,
Wherein each precoding matrix in the first codebook comprises a first index and a second index.  A method implemented in a wireless communication system,
Precoding data; And
Transmitting the precoded data from a base station to a user equipment,
Each of the 1layer, 2layer, 3layer, and 4layer codebooks for 4TX (4 transmit) antenna transmission includes a plurality of precoding matrices,
Wherein each of the onelayer and twolayer codebooks includes a first codebook and a second codebook,
Wherein each precoding matrix in the first codebook comprises a first index and a second index.  15. The method of claim 14,
Wherein the first index is for a plurality of subbands and the second index is for each subband.  15. The method of claim 14,
Wherein the second codebook comprises a legacy codebook or a householder codebook.  15. The method of claim 14,
Wherein each of the 3layer and 4layer codebooks comprises a legacy codebook or a householder codebook.
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