CN105187107A

CN105187107A - Method And Apparatus For Transmitting Uplink Signals Using Multi-antenna

Info

Publication number: CN105187107A
Application number: CN201510593436.0A
Authority: CN
Inventors: 卢柳珍; 金沂濬; 卢东昱; 姜秉祐; 李大远; 金奉会; 徐东延
Original assignee: LG Electronics Inc
Current assignee: LG Electronics Inc
Priority date: 2008-08-11
Filing date: 2009-08-11
Publication date: 2015-12-23
Anticipated expiration: 2029-08-11
Also published as: KR20100019929A; JP2014132763A; ES2576728T3; CN105187107B; JP2016028492A; KR20100019974A; JP6196268B2; KR101612103B1; CN105141348A; MX2011000996A; CN102119494B; CA2731210A1; JP5814394B2; CN102119494A; JP5702282B2; CA2731210C; CN105141348B; JP2011530207A

Abstract

A method and apparatus for allowing a UE to transmit uplink signals using a MIMO scheme are disclosed. In order to maintain good Peak power to Average Power Ratio (PAPR) or Cubic Metric (CM) properties when the UE transmits uplink signals using the MIMO scheme, the UE uses a precoding scheme based on a precoding matrix established in a manner that one layer is transmitted to each antenna in specific rank transmission.

Description

Method and apparatus for transmitting uplink signal using multiple antennas

The present application is a divisional application of the patent application entitled "method and apparatus for transmitting uplink signals using multiple antennas" filed on 2/11/2011 with application number 200980131273.7(PCT/KR2009/004468) filed on 8/11/2009, international application date.

Technical Field

The present invention relates to a wireless mobile communication system, and more particularly, to a communication system based on a Multiple Input Multiple Output (MIMO) scheme.

Background

MIMO technology is an abbreviation of multiple input multiple output technology. The MIMO technology improves efficiency of transmission and reception (Tx/Rx) of data using a plurality of transmit (Tx) antennas and a plurality of receive (Rx) antennas. In other words, the MIMO technology allows a transmitting end or a receiving end of a wireless communication system to use a plurality of antennas (hereinafter, referred to as multiple antennas), so that capacity or performance can be improved. For convenience of description, the term "MIMO" may also be considered a multi-antenna technique.

In more detail, MIMO technology does not rely on a single antenna path to receive a single overall message. Alternatively, the MIMO technique collects a plurality of data pieces received via a plurality of antennas, combines the collected data pieces, and completes overall data. As a result, the MIMO technology can increase a data transmission rate within a cell area of a predetermined size, or can increase system coverage while guaranteeing a specific data transmission rate. In this case, the MIMO technology can be widely applied to mobile communication terminals, repeaters (repeaters), and the like. The MIMO technology can extend the range of data communication so that the limited amount of transmission (Tx) data of a mobile communication system can be overcome.

Fig. 1 is a block diagram illustrating a general MIMO communication system.

Referring to fig. 1, the number of transmit (Tx) antennas in a transmitter is N_TAnd the number of receive (Rx) antennas in the receiver is N_R. In this way, the theoretical channel transmission capacity of the MIMO communication system when both the transmitter and the receiver use a plurality of antennas is larger than that in the other case where only the transmitter or the receiver uses a plurality of antennas. The theoretical channel transmission capacity of the MIMO communication system increases in proportion to the number of antennas. Thus, the data transfer frequency and the frequency efficiency can be greatly increased. It is assumed that the maximum data transfer rate obtained when a single antenna is used is set to R_oThe data transfer rate obtained when using a plurality of antennas can theoretically be increased by a predetermined amount multiplied by the rate of increase R₁Maximum data transfer rate (R)_o) And correspondingly. Rate of increase (R)₁) Can be represented by the following equation 1.

[ equation 1]

R₁＝min(N_T，N_R)

For example, assuming that a MIMO system uses four transmit (Tx) antennas and four receive (Rx) antennas, the MIMO system can theoretically obtain a very high data transfer rate four times higher than that of a single antenna system. After demonstrating the above theoretical capacity increase of the MIMO system in the mid-nineties, many developers have started intensive research into various technologies capable of sufficiently increasing a data transfer rate using the theoretical capacity increase. Some of the above techniques are reflected in various wireless communication standards, such as third-generation mobile communication or next-generation wireless LAN, and the like.

The above MIMO technology can be classified into a spatial diversity scheme (also referred to as a transmit diversity scheme) and a spatial multiplexing scheme. The spatial diversity scheme increases transmission reliability using symbols through various channel paths. The spatial multiplexing scheme simultaneously transmits a plurality of data symbols via a plurality of transmit (Tx) antennas, so that a transmission rate of data is increased. In addition, a combination of a spatial diversity scheme and a spatial multiplexing scheme has been recently developed to appropriately obtain the characteristic advantages of both schemes.

With respect to MIMO technology, many companies or developers intensively study various MIMO-related technologies, for example, studies on information theory related to MIMO communication capacity calculation under various channel environments or multiple access environments, studies on Radio Frequency (RF) channel measurement and modeling of a MIMO system, and studies on a space-time signal processing technology for increasing transmission reliability and data transfer rate.

In the third generation partnership project long term evolution (3gpp lte) system, the above-described MIMO scheme is applied only to downlink signal transmission of the 3gpp lte system. MIMO technology may also be applied to uplink signal transmission. In this case, the transmitter structure is changed to implement the MIMO technique so that a peak to average power ratio (PAPR) or Cubic Metric (CM) characteristic may be deteriorated. Thus, a new technology capable of effectively applying the MIMO scheme to uplink signal transmission is required.

Disclosure of Invention

Accordingly, the present invention is directed to a method and apparatus for transmitting an uplink signal via multiple antennas that substantially obviate one or more problems due to limitations and disadvantages of the related art.

An object of the present invention is to provide a technique for efficiently performing uplink signal transmission according to a MIMO scheme.

Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.

To achieve these objects and other advantages and in accordance with the purpose of the invention, as embodied and broadly described herein, a method for a User Equipment (UE) to transmit uplink signals via a plurality of antennas includes: mapping an uplink signal to a predetermined number of layers; performing Discrete Fourier Transform (DFT) spreading on each of a predetermined number of layer signals; precoding the DFT-spread layer signal by selecting a specific precoding matrix from a pre-stored codebook, the specific precoding matrix being established in such a manner that one layer signal is transmitted to each of a plurality of antennas; and performing a predetermined process for constructing a single carrier-frequency division multiple access (SC-FDMA) symbol on the precoded signal; and transmitting the processed signal to a Base Station (BS) via a plurality of antennas.

The specific precoding matrix may be a precoding matrix established in such a manner that a transmission power is uniform among a plurality of antennas. The specific precoding matrix may be a precoding matrix established in such a manner that a predetermined number of layers have uniform transmission power therebetween.

The codebook may include a first type precoding matrix, wherein the first type precoding matrix is different from the first type precoding matrixThe type precoding matrix may be configured to

[\begin{matrix} 1 & 0 \\ X & 0 \\ 0 & 1 \\ 0 & Y \end{matrix}]

Is a rank-2 precoding matrix utilized when the number of the plurality of antennas is 4 and the rank is set to 2, and may satisfy the condition

<math> <mrow> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> <mo>.</mo> </mrow> </math>

The rank-2 precoding matrix may further include a precoding matrix generated when a position of each row of the first type precoding matrix is changed.

The rank 2 precoding matrix may further include: to be provided with

[\begin{matrix} 1 & 0 \\ 0 & 1 \\ X & 0 \\ 0 & Y \end{matrix}]

Formally configured second-type precoding matrix, and

[\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & Y \\ X & 0 \end{matrix}]

a third type of precoding matrix configured formally, wherein each row of the precoding matrix may correspond to four antennas of the plurality of antennas, respectively, and each column may correspond to a layer, respectively.

The rank-2 precoding matrix may further include a precoding matrix generated when a position of each column of the first type precoding matrix is changed.

The codebook may include a first-type precoding matrix, wherein the first-type precoding matrix (serving as a rank-3 precoding matrix utilized when the number of the plurality of antennas is 4 and the rank is set to 3) is configured to be a precoding matrix of a rank-3

[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ X & 0 & 0 \end{matrix}],

And satisfies the condition

<math> <mrow> <mi>X</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> <mo>.</mo> </mrow> </math>

The rank 3 precoding matrix may further include a precoding matrix generated when a position of each row of the first type precoding matrix is changed. The rank 3 precoding matrix may further include a precoding matrix generated when a position of each column of the first type precoding matrix is changed. That is, the codebook may include a precoding matrix configured to alternatively map the first layer to the first and second antennas and map the second and third layers to the third and fourth antennas, respectively, as a precoding matrix used in the case when the number of antennas is 4 and the rank is 3.

When the number of antennas is 4, the rank is 3, and the number of codewords is 2, one codeword is mapped to a single layer and another codeword is mapped to two layers. The precoding matrix may be configured such that the total transmit power may be different from the layer perspective in order to implement uniform transmit power among the multiple antennas. In this case, a precoding matrix column having a large effective transmission power is mapped to layers separately mapped to a single codeword. Thus, in

[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ X & 0 & 0 \end{matrix}]

In the case of formal precoding matrix columns, the first column is mapped to a layer that is mapped separately to a single codeword, and the second and third columns are mapped to a layer that is mapped to another codeword.

The codebook may include a different number of precoding matrices for each rank.

Each uplink signal may be input in units of codewords, and the mapping step of the uplink signal to a predetermined number of layers may periodically change a layer mapped to a specific codeword to another layer. One example of the periodicity may be 1 SC-FDMA symbol.

In another aspect of the present invention, a User Equipment (UE) transmitting an uplink signal via a plurality of antennas includes: a plurality of antennas for transmitting and receiving signals; a memory for storing a codebook having a precoding matrix established in such a manner that one layer signal is transmitted to a plurality of antennas; and a processor connected to the plurality of antennas and the memory to process the uplink signal transmission. The processor includes: a layer mapper for mapping the uplink signal to a predetermined number of layers corresponding to a specific rank; a Discrete Fourier Transform (DFT) module for performing DFT spreading on each of a predetermined number of layer signals; a precoder for precoding each of the DFT spread layer signals received from the DFT module by selecting a specific precoding matrix from a codebook stored in the memory, the specific precoding matrix being established in such a manner that one layer signal is transmitted to each of the plurality of antennas; and a transmission module for performing a predetermined process for constructing a single carrier-frequency division multiple access (SC-FDMA) symbol on the precoded signal, and transmitting the processed signal to a Base Station (BS) via a plurality of antennas.

In this case, the memory may store a codebook. The processor may perform antenna switching (shift) and/or layer switching in a different manner from precoding of a precoder or by row permutation and/or column permutation of a precoding matrix.

It is to be understood that both the foregoing general description and the following detailed description of the present invention are exemplary and explanatory and are intended to provide further explanation of the invention as claimed.

Drawings

The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention, in which:

fig. 1 is a schematic diagram illustrating a general MIMO communication system.

Fig. 2 and 3 show a general structure of a transmitter based on the MIMO technique.

Fig. 4 is a schematic diagram illustrating a method for precoding information of each layer and transmitting the precoded information via antennas.

Fig. 5 is a diagram illustrating a general SC-FDMA scheme.

Fig. 6 is a schematic diagram illustrating a method for mapping codewords to multiple layers.

Fig. 7 is a schematic diagram illustrating a method for performing DFT on each layer after codeword-to-layer mapping (i.e., codeword-to-layer mapping) is performed to prevent a CM value for each antenna from increasing.

Fig. 8 is a schematic diagram illustrating a method for performing permutation on positions of rows or columns of a precoding matrix.

Fig. 9 is a schematic diagram showing a chord distance (chord distance).

Fig. 10 is a block diagram illustrating a general Base Station (BS) and a general User Equipment (UE).

Fig. 11 and 12 illustrate an SC-FDMA scheme for transmitting an uplink signal in a 3gpp lte system and an OFDMA scheme for transmitting a downlink signal in the 3gpp lte system.

Fig. 13 is a block diagram illustrating a processor for a Base Station (BS) to transmit a downlink signal using a MIMO scheme in a 3gpp lte system.

Fig. 14 is a processor illustrating a UE according to one embodiment of the present invention.

Detailed Description

Reference will now be made in detail to the preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts.

The detailed description set forth below in connection with the appended drawings is intended as a description of exemplary embodiments of the present invention and is not intended to represent the only embodiments in which the present invention may be practiced. The following detailed description includes specific details in order to provide a thorough understanding of the invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced without such specific details. For example, the following description is given focusing on specific terms, but the present invention is not limited thereto and any other terms may be used to represent the same meanings. Moreover, wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts.

The peak-to-average power ratio (PAPR) is a parameter representing the characteristics of a waveform. The PAPR is a specific value obtained when the peak amplitude of a waveform is divided by the time-averaged Root Mean Square (RMS) value of the waveform. The PAPR is a dimensionless (dimensionless) value. Generally, the PAPR of a single carrier signal is better than that of a multi-carrier signal.

The LTE-Advanced scheme may implement a MIMO technique using single carrier-frequency division multiple access (SC-FDMA) to maintain good CM performance. When general precoding is used, a signal including information corresponding to a plurality of layers is multiplexed and transmitted via a single antenna, so that the signal transmitted via the antenna can be regarded as a kind of multicarrier signal. The PAPR is related to a dynamic range that a power amplifier of a transmitter must support, and the CM value is another value that can be used as a substitute for the PAPR.

Fig. 2 shows a general structure of a transmitter based on the MIMO technique.

In fig. 2, one or more codewords are mapped to multiple layers. In this case, the mapping information is mapped to each physical antenna through a precoding process and then transmitted via each physical antenna.

Fig. 3 is a detailed block diagram illustrating the MIMO-based transmitter shown in fig. 2.

The term "codeword" means that Cyclic Redundancy Check (CRC) bits are appended to data information and then encoded by a specific encoding method. There are various encoding methods such as Turbo code, tail-biting convolutional code (tailbiting convolutional code), and the like. Each codeword is mapped to one or more layers (i.e., one or more virtual layers), and the total number of mapped layers is equal to the rank value. In other words, if the transmission rank is 3, the total number of transmission layers is also set to 3. The information mapped to each layer is precoded. In this case, data information mapped to each layer is mapped to a physical layer through a precoding process (here, the term "layer" means an actual layer as long as it particularly designates the physical layer). Information is sent to each antenna via each physical layer. In the case where a specific explanation is not shown in fig. 3, precoding is performed in the frequency domain, and an OFDM information transmission scheme is used for information mapped to the physical layer. The information mapped to the physical layer is mapped to a specific frequency domain and then IFFT processing is performed. Thereafter, a Cyclic Prefix (CP) is appended to the IFFT result. Thereafter, the information is sent to each antenna via a Radio Frequency (RF) chain (chain).

The precoding process may be performed by matrix multiplication. At each oneIn the matrix, the number of rows is equal to the number of physical layers (i.e., the number of antennas), and the number of columns is equal to the rank value. The rank value is equal to the number of layers, so that the number of columns is equal to the number of layers. Referring to the following equation 2, the information mapped to a layer (i.e., virtual layer) is x₁And x₂Each element p of the (4 × 2) matrix_ijAre weights used for precoding. y is₁、y₂、y₃And y₄Is information mapped to a physical layer and is transmitted via respective antennas using respective OFDM transmission schemes.

[ equation 2]

In the following description, a virtual layer will be referred to as a layer hereinafter as long as such use does not cause confusion. The operation for mapping the virtual layer signal to the physical layer will hereinafter be referred to as an operation for mapping the layer directly to the antenna.

The precoding method can be largely classified into two methods, i.e., a wideband precoding method and a subband precoding method.

The wideband precoding method is as follows. According to the wideband precoding method, when precoding is performed in the frequency domain, the same precoding matrix is applied to all information transmitted to the frequency domain.

Referring to fig. 4, it can be appreciated that information corresponding to a plurality of layers is precoded while being classified according to subcarriers of each frequency domain, and the precoded information is transmitted via each antenna. All precoding matrices 'P' used in the wideband precoding method are equal to each other.

The subband precoding method is provided by an extension of the wideband precoding method. The subband precoding method applies a plurality of precoding matrices to each subcarrier without applying the same precoding matrix to all subcarriers. In other words, according to the subband precoding method, a precoding matrix "P" is used in a specific subcarrier and another precoding matrix "M" is used in the remaining subcarriers except the specific subcarrier. Here, the element values of the precoding matrix "P" are different from those of another precoding matrix "M".

Uplink signaling is relatively sensitive to PAPR or CM performance compared to downlink signaling. The increase in filter cost caused by the improvement of PAPR or CM performance may cause more serious problems in a User Equipment (UE). Thus, the SC-FDMA scheme is used for uplink signal transmission.

Fig. 5 is a diagram illustrating a general SC-FDMA scheme.

As shown in fig. 5, the OFDM scheme and the SC-FDMA scheme are considered to be identical to each other because they all convert a serial signal into a parallel signal and map the parallel signal to subcarriers, perform IDFT or IFFT processing on the mapped signal, convert the IDFT or IFFT-processed signal into a serial signal, append a Cyclic Prefix (CP) to the resulting serial signal, and transmit a CP-synthesized signal via a Radio Frequency (RF) module. However, compared to the OFDM scheme, the SC-FDMA scheme converts a parallel signal into a serial signal and performs DFT spreading on the serial signal, so that the influence of the next IDFT or IFFT process is reduced and the individual signal characteristics are maintained above a predetermined level.

Meanwhile, the reason why the CM value is lowered when the MIMO scheme is applied to the uplink signal transmission is as follows. If a plurality of single carrier signals each having a good CM characteristic overlap each other at the same time, the overlapping signals may have a poor CM characteristic. Therefore, if the SC-FDMA system multiplexes output information of a plurality of layers using a minimum number of single carrier signals or one single carrier signal on a single physical antenna, a transmission signal having good CM can be generated.

A codeword-to-layer mapping process may be performed before precoding information to be transmitted. Since the SC-FDMA scheme is generally used for one transmission mode (1Tx), the number of layers is 1. However, if the SC-FDMA scheme supports the MIMO scheme, the number of layers is complex, and a codeword consisting of a single transport block may be mapped to a plurality of layers.

Fig. 6 is a schematic diagram illustrating a method of mapping codewords to a plurality of layers.

Referring to fig. 6, if codeword-layer mapping is performed after performing DFT processing for the SC-FDMA scheme, the CM value may increase. That is, since the output signal of the DFT block is subjected to other processes before entering the IFFT module, that is, since the output signal of the DFT block is divided into two layers, the CM value may increase.

Fig. 7 is a schematic diagram illustrating a method of performing DFT on each layer after codeword-to-layer mapping (i.e., codeword-to-layer mapping) is performed to prevent a CM value per antenna from increasing.

Therefore, if the number of DFT blocks is changed while being classified according to the number of layers based on the rank value, the CM value can be maintained low. That is, the output signal of the DFT block is directly input to the IFFT block without undergoing other processing, so that the low CM value can be maintained. In the case of an actual implementation, multiple layers may share a single DFT block.

If a plurality of layer signals are transmitted via a single antenna by applying the MIMO scheme to uplink signal transmission, PAPR or CM performance may deteriorate. In order to overcome the above problems, the following embodiments of the present invention will describe a method for designing a codebook based on a precoding matrix, by which only one layer signal is transmitted via a single antenna.

For convenience of description and better understanding of the present invention, in a transmission system, it is assumed that a set of signals transmitted to a pre-encoded block is set to "x" and a set of pre-encoded signals is set to "y". In this case, if the precoding matrix is "P", the following equation 3 is obtained.

[ equation 3]

Y＝P·x

In equation 3, the dimension of "P" is N_T×N_LThe dimension of "x" is N_LThe dimension of x 1, y being N_TX 1. In this case, N_TIs the number of antennas, and N_LIs the number of layers.

In the following description, the principle of designing a codebook that can be applied to uplink signal transmission using a MIMO scheme by a UE will first be described in chapter (I), and then the detailed format of the codebook will be described in chapter (II).

I. Principle of codebook design

<2Tx codebook >

Various embodiments according to the structure of a precoding matrix included in a codebook used in the 2Tx mode will be described below.

The method according to the embodiment of the invention comprises the following steps: generating a plurality of streams by mapping a codebook to a plurality of layers; and precoding the generated streams, mapping the precoded streams to a plurality of antennas, and transmitting the mapped result via the antennas. In this case, the codebook may be configured as follows. The precoding matrix used in rank 1 and the precoding matrix used in rank 2 will be described in different ways.

2 Tx-rank 1 precoding matrix

In the case of 2 Tx-rank 1, equation 3 may be rewritten as the following equation 4 according to an embodiment of the present invention.

[ equation 4]

In general, if it is assumed that a wideband precoding scheme is used, according to a rank-1 precoding scheme, a specific constant value is multiplied by a signal of each layer, and a PAPR and a CM value of a signal transmitted via each antenna in a 2Tx mode are equal to those in a 1Tx mode. Therefore, when wideband precoding is used, PAPR and CM are not affected by the value of the 2 Tx-rank 1 precoding matrix.

Precoding is a method for changing channels to obtain structural influence (constructive effect) between signals transmitted via each channel. Thus, the transmission performance of each signal is improved. Accordingly, "a" representing the first element of the precoding matrix P shown in equation 4 is set to "1", and the precoding matrix P isThe second element "b" may be set to an arbitrary value. The signals transmitted via the respective antennas have the same power so that all power amplifiers included in each antenna can be maximally used. For this purpose, the above-mentioned second element "b" may be a complex number having an absolute value of 1. In other words, P shown in equation 4 may be represented by

And (4) showing.

There is a limit to the number of precoding matrices included in a codebook for precoding because a transmitting end and a receiving end must have a codebook and transmit information about a predetermined precoding matrix between the transmitting end and the receiving end. Therefore, the transmitting end and the receiving end must use a limited number of precoding matrices. For this operation, a complex number having an absolute value of 1 and a phase corresponding to any one of +0 °, +45 °, +90 °, +135 °, +180 °, -135 °, -90 °, and-45 ° may be used as each element of the precoding matrix. Namely, in the above expression

In, theta can be represented byAnd (4) showing. In other words, P may be represented by

<math> <mrow> <mi>P</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>j</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>j</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mtd> </mtr> </mtable> </mfenced> </mrow> <mo>}</mo> </mrow> </mrow> </math>

And (4) showing.

2 Tx-rank 2 precoding matrix

In the case of 2 Tx-rank 2, equation 3 may be rewritten as the following equation 5.

[ equation 5]

In equation 5, a signal y transmitted via each antenna_kFrom a plurality of input signals x_iSo that the CM value can be increased.

In this case, if p₁₂And p₂₁Is set to zero "0", or if p is₁₁And p₂₂Is set to "0", only one signal can be transmitted via each antenna. Thus, if signal x is assumed_iThe CM value of the precoded signal becomes good if the CM value of (c) is considered good. With regard to fig. 7, in the case where a codeword is mapped to each layer, DFT spreading is applied to the resulting signal mapped to each layer, and precoding processing that allows only one layer signal to be transmitted per antenna is performed, the same effect as IDFT or IFFT processing performed as soon as DFT processing is performed can be obtained, and PAPR or CM characteristics can be maintained in a good state. A detailed description thereof will be explained in the following description.

In this case, if p₁₂And p₂₁Is set to zero "0", signals corresponding to each layer are transmitted via each antenna after being multiplied by a constant complex value. As a result, although the above-described constant complex value is set to 1, the performance is not affected by the constant complex value of 1.

Thus, equation 5 may be represented by equation 6 below.

[ equation 6]

<math> <mrow> <mi>y</mi> <mo>=</mo> <mfenced open = '[' close = ']'> <mtable> <mtr> <mtd> <msub> <mi>y</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mn>2</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mi>P</mi> <mo>·</mo> <mi>x</mi> <mo>=</mo> <mfenced open = '[' close = ']'> <mtable> <mtr> <mtd> <msub> <mi>p</mi> <mn>11</mn> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>p</mi> <mn>22</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>·</mo> <mfenced open = '[' close = ']'> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mn>2</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = '[' close = ']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>·</mo> <mfenced open = '[' close = ']'> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mn>2</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = '[' close = ']'> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mn>2</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>P</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mfenced open = '[' close = ']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>}</mo> </mrow> </mrow> </math>

<4Tx codebook >

Various embodiments according to the structure of a precoding matrix included in a codebook used in the 4Tx mode will be described below.

The method according to the embodiment of the invention comprises the following steps: generating a plurality of streams by mapping codewords to a plurality of layers; and precoding the generated streams, mapping the precoded streams to a plurality of antennas, and transmitting the mapping result via the antennas. In this case, the codebook may be configured as follows. Precoding matrices used in rank 1, rank 2, rank 3, and rank 4, respectively, will be described in different ways.

4 Tx-rank 1 precoding matrix

In the case of 4 Tx-rank 1, equation 3 may be rewritten as the following equation 7.

[ equation 7]

In the case of using the wideband precoding scheme in the same manner as the 2 Tx-rank 1 codebook, the CM of a signal transmitted via each antenna is processed by 4 Tx-rank 1 precoding is equal to the CM of a signal used in the 1Tx mode. Therefore, all types of precoding matrices can be freely applied to such CM without any problem.

4 Tx-rank 2 precoding matrix

In the case of 4 Tx-rank 2, equation 3 may be rewritten as the following equation 8.

[ equation 8]

In the 4 Tx-rank 2 codebook, in a similar manner to the 2 Tx-rank 2 codebook, a specific element of a precoding matrix is set to zero "0" so that the overlap of signals transmitted via respective antennas is minimized, and thus the CM can be maintained at a low value.

In equation 8, if a signal (p) transmitted via each antenna is assumed_k1x₁+p_k2x₂) P in (1)_k1Or p_k2Is set to zero "0", the signal transmitted via each antenna becomes equal to the signal transmitted from a single layer, and thus the CM of the signal transmitted via each antenna can be maintained at a low value.

In one embodiment of the present invention, "P" included in equation 8 may be represented by

P = [\begin{matrix} p_{11} & 0 \\ p_{21} & 0 \\ 0 & p_{32} \\ 0 & p_{42} \end{matrix}]

And (4) showing. Equation 8 can be rewritten as the following equation 9.

[ equation 9]

Referring to equation 9, only one layer is mapped to a signal transmitted via each antenna. From the perspective of a single layer, it is considered that 2 Tx-rank 1 precoding is applied to information transmitted via the single layer. Thus, a 4 Tx-rank 2 precoding matrix may be configured using a 2 Tx-rank 2 precoding matrix. In other words, the 4 Tx-rank 2 precoding matrix may be a super matrix (supermatrix) of a 2 Tx-rank 1 precoding matrix.

For example, "P" according to an embodiment of the present invention may be represented by equation 10.

[ equation 10]

<math> <mrow> <mi>P</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> </mtr> </mtable> </mfenced> </mtd> <mtd> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mtd> <mtd> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </math>

The above-described 2 Tx-rank 1 precoding matrix is used for a method of transmitting information by applying two antennas to a single layer signal. However, if it is assumed that there are four physical antennas, communication performance may vary depending on which combination of two antennas is used for data transmission. In this case, the selected combination of antennas may vary according to the value of the precoding matrix P.

For example, according to one embodiment of the present invention, the precoding matrix P may be configured into various formats. Each format may represent a different antenna combination.

[ equation 11]

<math> <mrow> <mi>P</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> <mo>}</mo> </mrow> </mrow> </math>

In equation 11, if an appropriate value is selected as the precoding matrix P, performance improvement due to precoding can be improved. If the precoding matrix is configured as above, signals corresponding to each layer use two antennas out of a total of four antennas, channel estimation performance among the respective layers becomes similar to each other, and a CM value for each antenna can be minimized.

In general, although a constant value is multiplied by a specific column vector of an arbitrary precoding matrix, the characteristics of the precoding matrix do not change. Therefore, although a constant value is multiplied by a specific column of the above precoding matrix, the characteristic of the precoding matrix does not change. As a result, the above-described operation for multiplying a constant value by a particular column vector of the precoding matrix does not depart from the scope of the present invention.

In addition, if a predetermined scaling factor (scalingfactor) is multiplied by the precoding matrix shown in equation 11, the result of the multiplication can be represented by the following equation 12.

[ equation 12]

<math> <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>P</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mi>k</mi> <mo>·</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>k</mi> <mo>·</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>k</mi> <mo>·</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> <mo>}</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>

4 Tx-rank 3 precoding matrix (1)

In the case of 4 Tx-rank 3, equation 3 may be rewritten as the following equation 13.

[ equation 13]

In the 4 Tx-rank 3 precoding matrix in a similar manner to the 4 Tx-rank 2 precoding matrix, a specific element of the precoding matrix is set to zero "0" so that the overlap of signals transmitted via the respective antennas is minimized, and thus the CM may be maintained at a low value.

In equation 13, if it is assumed that the signal p is transmitted via each antenna_k1x₁+p_k2x₂+p_k3x₃) P in (1)_k1、p_k2Or p_k3Set to "0", the CM of the signal transmitted via each antenna may be maintained at a low value.

In one embodiment of the present invention, "P" included in equation 12 may be represented by

P = [\begin{matrix} p_{11} & 0 & 0 \\ 0 & p_{22} & 0 \\ 0 & 0 & p_{33} \\ p_{41} & p_{42} & p_{43} \end{matrix}]

And (4) showing. Equation 13 can be rewritten as the following equation 14.

[ equation 14]

In rank 3, the number of layers to be transmitted is 3, and the number of physical antennas is 4. In this case, each of the three antennas may be independently mapped to a single layer. Here, only a signal of a single layer may be mapped to the remaining one antenna, or signals of at least two layers may be mapped to the remaining one antenna. If only a signal of a specific single layer is mapped to the remaining one antenna, a CM of a signal transmitted via the antenna may have a good characteristic, but communication performance of the specific single layer may be different from that of another layer. For example, in the case where information of a first layer (layer 1) is mapped to a first antenna (antenna 1) and a fourth antenna (antenna 4), information of a second layer (layer 2) is mapped to a second antenna (antenna 2), and information of a third layer (layer 3) is mapped to a third antenna (antenna 3), communication performance of layer 1 information may be different from that of layer 2 or layer 3.

In one embodiment of the present invention, in order to minimize a CM value for each antenna in a precoding process, a precoding matrix P may have a value P shown in the following equation 15₁、P₂And P₃Any one of them.

[ equation 15]

P_{1} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ X & 0 & 0 \end{matrix}], P_{2} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & Y & 0 \end{matrix}], P_{3} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & Z \end{matrix}]

Wherein,

<math> <mrow> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>,</mo> <mi>Z</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> <mo>.</mo> </mrow> </math>

using the above-mentioned precoding matrix P₁、P₂And P₃In the case of (2), the numbers of antennas used for the respective layers are different from each other. However, if a precoding matrix P is assumed₁、P₂And P₃Is uniformly used for transmitting specific information, instead of using the precoding matrix P₁、P₂And P₃Of the antenna elements, the number of antennas used for the respective layers may be normalized (normalized). Although the precoding matrix P may be used alternately in the frequency domain₁、P₂And P₃However, the single-carrier characteristic of a signal composed of a single carrier is destroyed, so that the CM value inevitably increases. Thus, if the precoding matrix P is₁、P₂And P₃Is alternately applied to each SC-FDMA symbol, there is no additional increase in CM. In the case of transmitting data, information may be decoded in units of one subframe. Thus, if the precoding matrix P is₁、P₂And P₃Alternately applied to each SC-FDMA symbol, each layer information of the entire information transmitted via a single subframe can be transmitted via the same number of antennas on average.

In another embodiment of the present invention, the position of the antenna used by each layer is changed so that the performance can be improved. The change in antenna position may occur over time. In particular, the antenna position may be changed at each SC-FDMA symbol. A detailed method for changing the position of the antenna will be described in detail below.

For example, the position of a value other than "0" in the precoding matrix is changed to another position within the range of the row vector, so that the position of an antenna via which each layer signal is transmitted can be changed to another position. As another example, the above method may be implemented by row/column permutation, since the position permutation is performed between rows or columns of a given precoding matrix.

In more detail, fig. 8(a) is a schematic diagram showing a method for performing permutation on the positions of rows, and fig. 8(b) is a schematic diagram showing a method for performing permutation on the positions of columns.

Among the precoding matrices shown in equation 15, a precoding matrix P₁May be row permuted and/or column permuted such that a precoding matrix P may be generated₂Or P₃. Thus, for example, in the precoding matrix P₁、P₂Or P₃In the structure of (3), a new unique precoding matrix can be obtained only by row permutation.

The row order changed by the row permutation available in the 4Tx mode can be represented by the following expression.

{1，2，3，4}，{1，2，4，3}，{1，3，2，4}，{1，3，4，2}，

{1，4，2，3}，{1，4，3，2}，{2，1，3，4}，{2，1，4，3}，

{2，3，1，4}，{2，3，4，1}，{2，4，1，3}，{2，4，3，1}，

{3，2，1，4}，{3，2，4，1}，{3，1，2，4}，{3，1，4，2}，

{3，4，2，1}，{3，4，1，2}，{4，2，3，1}，{4，2，1，3}，

{4，3，2，1}，{4，3，1，2}，{4，1，2，3}，{4，1，3，2}

In the above expression, { w, x, y, z } means that the row vectors 1, 2, 3, and 4 of the precoding matrix are in a given precoding matrix P_kAre rearranged in the order of numerals in parentheses where present.

By the row permutation, the signals corresponding to a particular row are mapped to different antennas. By column permutation, the same effect as switching information of different layers can be obtained. Systems requiring similar performance for each layer need not utilize column permutation if there is no need to distinguish the performance of each layer. Thus, only the line permutation can be used to obtain the effect corresponding to the antenna selection.

Meanwhile, in the case of multiplying a given scaling factor by each precoding matrix shown in equation 15, the result may be represented by the following equation 16.

[ equation 16]

<math> <mrow> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>,</mo> <mi>Z</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </math>

4 Tx-rank 3 precoding matrix (2)

In the case of 4 Tx-rank 3, if each antenna transmits information corresponding to only one layer, the CM value of a signal transmitted via each antenna may be maintained at a low value, however, information of only one layer is transmitted via only one antenna, so that communication performance is deteriorated. Thus, in 4 Tx-rank 3, a codebook designed in such a manner that at most two layers are multiplexed and transmitted via a single antenna is required so that the increment of CM can be minimized while communication performance can be improved.

According to an embodiment of the present invention, when information corresponding to two layers is transmitted via a single antenna, a precoding matrix P shown in equation 13 may be represented by P in equation 17₄Or P in equation 18₅And (4) showing.

[ equation 17]

<math> <mrow> <msub> <mi>P</mi> <mn>4</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Z</mi> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>X</mi> <mo>&NotEqual;</mo> <mi>Z</mi> <mo>,</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>,</mo> <mi>Z</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </math>

[ equation 18]

<math> <mrow> <msub> <mi>P</mi> <mn>5</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Z</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>,</mo> <mi>Z</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </math>

In equation 17, to satisfy rank 3, "X" must be associated with the precoding matrix P₄Is different from "Z" in (1).

Using a precoding matrix P₄Or P₅The method of (2) has a disadvantage in that only signals of a single layer are transmitted via other antennas, and signals of two layers are multiplexed and transmitted via a specific antenna.

In one embodiment of the present invention, to eliminate the above-mentioned problem, the precoding matrix P may have a value P shown in the following equation 19₆、P₇And P₈Any one of them.

[ equation 19]

P_{6} = [\begin{matrix} 1 & 0 & Z \\ X & 1 & 0 \\ 0 & Y & 1 \\ A & 0 & C \end{matrix}], P_{7} [\begin{matrix} 1 & 0 & Z \\ X & 1 & 0 \\ 0 & Y & 1 \\ 0 & B & C \end{matrix}], P_{8} = [\begin{matrix} 1 & 0 & Z \\ X & 1 & 0 \\ 0 & Y & 1 \\ A & B & 0 \end{matrix}]

Wherein,

<math> <mrow> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>,</mo> <mi>Z</mi> <mo>,</mo> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi>C</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </math>

with respect to precoding matrix P₄、P₅、P₆、P₇Or P₈Row permutation and/or column permutation may be performed on the 4 Tx-rank 3 precoding matrix. Since row permutation and column permutation are performed, an antenna selection function and a layer permutation function of causing signals of a specific layer to be transmitted via an arbitrary antenna can be realized by precoding.

In one embodiment of the present invention, the respective column vectors of the precoding matrix may be configured to be orthogonal to each other.

If respective column vectors of the precoding matrix are configured to be orthogonal to each other, the precoding matrix can satisfy the characteristics of a one-sided unitary matrix (onesideunitymatrix). That is, the precoding matrix P may have a characteristic represented by the following equation 20.

[ equation 20]

P^HP＝α·I≠PP^H

In one embodiment of the present invention, a precoding matrix of rank 3 may be configured in the form of the following equation 21. The precoding matrix P for satisfying the following equation 21 can satisfy the relationship shown in equation 20.

[ equation 21]

<math> <mrow> <mi>P</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>X</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </math>

In equation 21, the result is satisfied by

Expressed, it can be appreciated that the matrix P satisfies equation 20.

4 Tx-rank 4 precoding matrix (1)

In the case of 4 Tx-rank 4, equation 3 may be rewritten as the following equation 22.

[ equation 22]

In the case of 4 Tx-rank 4, signals from four layers are multiplexed and transmitted via respective antennas.

In one embodiment of the present invention, if a precoding matrix is configured in the form of an identity matrix, one antenna can transmit only a signal corresponding to a single layer. In this case, equation 22 may be rewritten as the following equation 23.

[ equation 23]

4 Tx-rank 4 precoding matrix (2)

In the 4 Tx-rank 4 codebook, if the number of rank-4 precoding matrices is increased, communication performance may also be increased. When the number of precoding matrices included in the codebook increases, a precoding matrix closer to an actual channel may be selected. Therefore, the larger the number of precoding matrices, the higher the performance. However, selecting a precoding matrix in a codebook becomes complicated, so that it is preferable to include an appropriate precoding matrix in such a codebookA number of precoding matrices. However, in case of 4 Tx-rank 4, in order to transmit only signals corresponding to a single layer via each antenna, the precoding matrix should be an identity matrix, so that in case of using a plurality of rank 4 precoding matrices, signals corresponding to two or more layers should be sometimes transmitted via a single antenna. Therefore, in order to minimize the CM value and increase the number of rank 4 precoding matrices in the codebook, a specific element of the precoding matrix may be set to zero "0". In equation 22, if a signal (p) transmitted via each antenna is assumed_k1x₁+p_k2x₂+p_k3x₃+p_k4x₄) P in (1)_k1、p_k2、p_k3And p_k4Is set to zero "0", respectively, the CM of the signal transmitted via each antenna can be maintained at a low value.

In one embodiment of the present invention, the precoding matrix may be set to P in the following equation 24₉P in the following equation 25₁₀Or P in the following equation 26₁₁。

[ equation 24]

<math> <mrow> <msub> <mi>P</mi> <mn>9</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mi>A</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mi>B</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mi>C</mi> </mtd> </mtr> <mtr> <mtd> <mi>D</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mn>1</mn> <mo>&NotEqual;</mo> <mi>A</mi> <mi>B</mi> <mi>C</mi> <mi>D</mi> <mo>,</mo> </mrow> </math>

<math> <mrow> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo>,</mo> <mi>C</mi> <mo>,</mo> <mi>D</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </math>

[ equation 25]

P_{10} = [\begin{matrix} 1 & 0 & 1 & 0 \\ A & 0 & C & 0 \\ 0 & 1 & 0 & 1 \\ 0 & B & 0 & D \end{matrix}]

Wherein A is not equal to C, B is not equal to D,

[ equation 26]

<math> <mrow> <msub> <mi>P</mi> <mn>11</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>A</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>A</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>B</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>B</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </math>

Precoding matrix P₉、P₁₀Or P₁₁Is an example of a precoding matrix for transmitting signals corresponding to at most two layers via each antenna. As described above, for the precoding matrix P₉、P₁₀Or P₁₁Row/column permutation is performed so that signals of different layers can be transmitted via different antennas.

Precoding matrix P₁₁Is a unitary matrix so that the advantages of a unitary precoding matrix can be utilized.

4 Tx-rank 4 precoding matrix (3)

In the case of 4 Tx-rank 4, only one of the elements of each row of the precoding matrix may be set to zero "0". In the case of using the above method, signals corresponding to three layers may be multiplexed and transmitted via a single antenna, so that communication performance may be improved. However, in the case of using the above-described method, the CM value is further increased, but the increased CM value may be lower than another CM value obtained when all elements in the precoding matrix are set to any other value except zero "0". Thus, the above method can be effectively utilized in a good SNR state where the transmitter does not need to transmit data or information at the maximum transmission power.

In one embodiment of the present invention, the precoding matrix P may be represented by P in the following equation 27₁₂P in the following equation 28₁₃P in the following equation 29₁₄Or P in the following equation 30₁₅And (4) showing.

[ equation 27]

P_{12} = [\begin{matrix} 1 & m_{12} & m_{13} & 0 \\ 0 & 1 & m_{23} & m_{24} \\ m_{31} & 0 & 1 & m_{34} \\ m_{41} & m_{42} & 0 & 1 \end{matrix}],

<math> <mrow> <msub> <mi>m</mi> <mrow> <mi>i</mi> <mi>k</mi> </mrow> </msub> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> </mrow> </math>

[ equation 28]

P_{13} = [\begin{matrix} 1 & 0 & 1 & 1 \\ m_{21} & 0 & m_{23} & m_{24} \\ 0 & 1 & m_{33} & m_{34} \\ 0 & m_{42} & m_{43} & m_{44} \end{matrix}],

[ equation 29]

<math> <mrow> <msub> <mi>P</mi> <mn>14</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>m</mi> <mn>21</mn> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>m</mi> <mn>23</mn> </msub> </mtd> <mtd> <msub> <mi>m</mi> <mn>24</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>m</mi> <mn>31</mn> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <msub> <mi>m</mi> <mn>33</mn> </msub> </mtd> <mtd> <msub> <mi>m</mi> <mn>34</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <msub> <mi>m</mi> <mn>43</mn> </msub> </mtd> <mtd> <msub> <mi>m</mi> <mn>44</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>m</mi> <mrow> <mi>i</mi> <mi>k</mi> </mrow> </msub> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> </mrow> </math>

[ equation 30]

<math> <mrow> <msub> <mi>P</mi> <mn>15</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>c</mi> </mtd> <mtd> <mrow> <mo>-</mo> <mi>c</mi> </mrow> </mtd> <mtd> <mi>c</mi> </mtd> </mtr> <mtr> <mtd> <mi>a</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>a</mi> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mi>a</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>b</mi> </mtd> <mtd> <mrow> <mo>-</mo> <mi>b</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mi>b</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </math>

Precoding matrix P shown in equation 30₁₅Is a unitary matrix so that the advantages of a unitary precoding matrix can be utilized.

A matrix obtained when a constant is multiplied by a specific column of the precoding matrix or another matrix obtained when row/column permutation is performed on the above precoding matrix may be used as a part of the codebook.

The elements of the precoding matrix are selected from complex numbers having an absolute value of 1 and a phase corresponding to any one of +0 °, +45 °, +90 °, +135 °, +180 °, -135 °, -90 °, and-45 °. That is, the elements of the precoding matrix are selected fromFor example, the above selection is disclosed for illustrative purposes only, and the elements of the precoding matrix may be selected from a set of complex numbers having an absolute value of 1 and different phases. For example, each element of the precoding matrix may be selected from

<math> <mrow> <mo>{</mo> <mrow> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mi>θ</mi> <mo>+</mo> <mi>a</mi> </mrow> </msup> <mo>,</mo> <mi>θ</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>0</mn> <mo>,</mo> <mfrac> <mi>π</mi> <mn>4</mn> </mfrac> <mo>,</mo> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> <mo>,</mo> <mfrac> <mrow> <mn>3</mn> <mi>π</mi> </mrow> <mn>4</mn> </mfrac> <mo>,</mo> <mi>π</mi> <mo>,</mo> <mfrac> <mrow> <mn>5</mn> <mi>π</mi> </mrow> <mn>4</mn> </mfrac> <mo>,</mo> <mfrac> <mrow> <mn>6</mn> <mi>π</mi> </mrow> <mn>4</mn> </mfrac> <mo>,</mo> <mfrac> <mrow> <mn>7</mn> <mi>π</mi> </mrow> <mn>4</mn> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> <mo>}</mo> </mrow> </math>

(where α is an arbitrary constant).

Power balance (powerbalancing)

Meanwhile, the transmission power balance of the respective antennas and/or the transmission power balance of the respective layers may be regarded as an important issue in the codebook design. If the transmission power of each antenna is not adjusted for maximum uniformity (maximum), a performance difference occurs between each transmission antenna. Likewise, if the transmission power of each layer is not adjusted for maximum uniformity, performance differences occur between each codeword.

Accordingly, one embodiment of the present invention proposes a method of designing a precoding matrix in consideration of antenna power balance using norms of all elements corresponding to respective antennas of the precoding matrix (i.e., all elements of a specific row of the precoding matrix). In more detail, the precoding matrix shown in the following equation 31 may be utilized in the form of antenna power balancing shown in the following equation 32.

[ equation 31]

[ equation 32]

On the other hand, one embodiment of the present invention provides a method of designing a precoding matrix in consideration of layer power balance using norms of all elements of each layer (i.e., all elements of a specific column of the precoding matrix). In more detail, the precoding matrix shown in the following equation 33 may be utilized in the form of layer power balancing shown in the following equation 34.

[ equation 33]

[ equation 34]

In this case, unlike the rank-2 precoding matrix, the number of rows and columns in the 4 Tx-rank-3 precoding matrix are not suitable for simultaneously performing antenna power balancing and layer power balancing. However, in certain cases, for example, in a system using layer switching (which changes a layer used for transmission to another layer according to a specific pattern in a transmission mode), an effect is produced in which performance differences between layers are dispersed, and layer power balance may be relatively less important than antenna power balance. Accordingly, one embodiment of the present invention proposes to use a precoding matrix obtained when antenna balancing is first performed under the condition that antenna power balancing and layer power balancing cannot be performed simultaneously.

Meanwhile, the following precoding matrices among the above-mentioned 4 Tx-rank 3 precoding matrices are represented: since two symbols are transmitted to each layer, antenna power balancing may be performed as represented by equation 35 below.

[ equation 35]

Similarly, in case of the following precoding matrix among the 4 Tx-rank 3 precoding matrices, since only one symbol is transmitted to one antenna, only layer power balancing may be performed as shown in the following equation 36.

[ equation 36]

Meanwhile, according to another embodiment of the present invention, from the viewpoint of simultaneously performing antenna power balancing and layer power balancing, the present invention proposes a 4 Tx-rank 3 precoding matrix including the following precoding matrix represented by equation 37.

[ equation 37]

In other words, equation 37 shows a precoding matrix used as a 4 Tx-rank 3 precoding matrix, and each precoding matrix in equation 37 is established not to transmit a signal to a single specific antenna.

Meanwhile, an example of a precoding matrix obtained when performing layer power balancing on a 4 Tx-rank 3 precoding matrix may be represented by the following equation 38.

[ equation 38]

< codebook pruning > (codebook pruning)

In the 4Tx system, precoding matrices corresponding to rank 1, rank 2, rank 3, and rank 4 may be used as elements of a codebook used in a transmitting end and a receiving end. However, in the case where all the precoding matrices are used, the size of the codebook is excessively increased, so that the number of precoding matrices must be reduced while maintaining performance at an appropriate level. An embodiment capable of reducing the number of precoding matrices will be described in detail below. The method of limiting the following precoding matrix may be utilized independently or simultaneously.

Codebook element alphabet (alphabet) restriction

Each element in the above precoding matrix is selected from a complex number having an absolute value of 1 and a phase corresponding to any one of +0 °, +45 °, +90 °, +135 °, +180 °, -135 °, -90 °, and-45 °.

In one embodiment of the present invention, in order to reduce the number of precoding matrices, each element of the precoding matrices may be selected from complex numbers having an absolute value of 1 and a phase corresponding to any one of +0 °, +90 °, +180 °, and-90 °. That is, each element in the precoding matrix may be selected from {1, j, -1, -j }.

Otherwise, each element of the precoding matrix may be extracted from a subset of N alphabetical letters (letters) in an 8-letter table that are spaced at an angle of 45 ° from each other.

Restriction of unitary precoding matrices

In the case where respective column vectors included in the precoding matrix are orthogonal to each other, the precoding matrix may be a unitary matrix or a partially unitary matrix. If the precoding matrix has the above characteristics, an additional gain can be obtained.

Therefore, according to an embodiment of the present invention, unitary matrices or partial unitary matrices of all the aforementioned precoding matrices are collected so that a codebook is formed.

For example, row/column permutation is performed on a precoding matrix shown in the following equation 39 and a precoding matrix shown in the following equation 40 to obtain several matrices, and the obtained matrices are combined so that a codebook is generated.

[ equation 39]

P^{(1)} = [\begin{matrix} 1 \\ a \\ b \\ c \end{matrix}], P^{(2)} = [\begin{matrix} 1 & 0 \\ a & 0 \\ 0 & 1 \\ 0 & b \end{matrix}], P^{(3)} = [\begin{matrix} 1 & 0 & 1 \\ a & 0 & - a \\ 0 & 1 & 0 \\ 0 & b & 0 \end{matrix}],

P_{1}^{(4)} = [\begin{matrix} 1 & 0 & 1 & 0 \\ a & 0 & - a & 0 \\ 0 & 1 & 0 & 1 \\ 0 & b & 0 & - b \end{matrix}], P_{2}^{(4)} = [\begin{matrix} 1 & 1 & 1 & 0 \\ 0 & c & - c & c \\ a & 0 & - a & - a \\ b & - b & 0 & b \end{matrix}],

Wherein,

<math> <mrow> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </math>

constraints on nested structures

When constructing the precoding matrices of rank 1, rank 2, rank 3, and rank 4, in the case where a precoding matrix of rank 2 or rank 3 can be constructed with a column vector of a rank 4 precoding matrix, the constructed precoding matrix is referred to as a precoding matrix having a nested structure. If a specific rank 4 precoding matrix is used as a part of the precoding codebook, a rank 3 precoding matrix should be configured with a column vector of the specific rank 4 precoding matrix so that a restriction is generated in the construction of the precoding matrix. Thus, the codebook size may be limited according to the aforementioned norm or standard.

In one embodiment of the present invention, the precoding matrices of rank 1, rank 2, rank 3 and rank 4 have a nested structure.

For example, a codebook may be constructed with a combination of matrices obtained by performing row/column permutation on a precoding matrix shown in the following equation 40.

[ equation 40]

P^{(1)} = [\begin{matrix} 1 \\ a \\ b \\ c \end{matrix}], P^{(2)} = [\begin{matrix} 1 & 0 \\ a & 0 \\ 0 & 1 \\ 0 & b \end{matrix}], P^{(3)} = [\begin{matrix} 1 & 0 & 1 \\ a & 0 & - a \\ 0 & 1 & 0 \\ 0 & b & 0 \end{matrix}], P_{1}^{(4)} = [\begin{matrix} 1 & 0 & 1 & 0 \\ a & 0 & - a & 0 \\ 0 & 1 & 0 & 1 \\ 0 & b & 0 & - b \end{matrix}]

Wherein,

there may be other applicable matrices besides those shown in the above equations. It can be easily understood that an applicable matrix can be obtained by performing row permutation and/or column permutation on the above matrix. In the present invention, since the precoding matrix has an element having a value of 0, a specific antenna may not be mapped to a specific input stream. This operation may be considered an antenna selection function.

Detailed format of codebook

Hereinafter, in a case where the codebook is designed to satisfy the above-described codebook design rule, a method for deciding a precoding matrix for each rank included in the codebook in consideration of a chordal distance will be described in detail.

FIG. 9 is a schematic diagram showing chordal distances.

As is well known, chordal distance is one of the norms (or criteria) used to compare the performance of various codebook sets. Here, the term "chord" means a straight line between two points on the circumference. Thus, given a two-dimensional (2D) case, the chordal distance represents the distance between two points located on the circumference of a circle (e.g., a unit circle), as shown in fig. 9.

The 4 Tx-codebook needs to consider four-dimensional chordal distances so that the following equation 41 can be used as the chordal distance for selecting a codebook set.

[ equation 41]

d_{c} (P, Q) = \frac{1}{\sqrt{2}} | | {PP}^{H} - {QQ}^{H} | |_{F}

In equation 41, P is P ═ v₁v₂…v_N]And Q is Q ═ u₁u₂…u_N]Wherein v is_iAnd u_i(in the case of a 4Tx antenna, i = 1, 2, … N, N =4) are the principal vectors (principal vectors) of the matrices P and Q, respectively. In addition, the first and second substrates are,is the Frobenius norm of the matrix. The above chord distance can also be measured by the following equation 42.

[ equation 42]

\begin{matrix} d_{c} (P, Q) = \frac{1}{\sqrt{2}} | | {PP}^{H} - {QQ}^{H} | |_{F} \\ = \sqrt{n - t r a c e ({AA}^{H} {BB}^{H})} \end{matrix}

Where A and B are orthogonal generator matrices for P and Q, respectively.

The above codebook design for a 4Tx system based on four transmit antennas will be described using the above chordal distance concept. For convenience of description and better understanding of the present invention, the following expressions omit factors related to power balancing.

Rank 2

First, assume that the following three sets of codebooks are used that can maintain good CM performance with respect to a 4 Tx-rank 2 system.

[ equation 43]

First group

<math> <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>(</mo> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>Y</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>X</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>X</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>Y</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> <mo>)</mo> </mrow> </mtd> <mtd> <mrow> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> </mrow> <mo>}</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>

Second group

<math> <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>(</mo> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>Y</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>X</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>X</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>Y</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> <mo>)</mo> </mrow> </mtd> <mtd> <mrow> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> </mrow> <mo>}</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>

Third group

<math> <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>(</mo> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>Y</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>X</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>Y</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>X</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> <mo>)</mo> </mrow> </mtd> <mtd> <mrow> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>

Although the number of precoding matrices satisfying the above-described format may be a considerably large number, it is preferable to design a codebook including a predetermined number of precoding matrices according to a reasonable norm. The following description proposes a method of limiting the number of precoding matrices for each rank to a predetermined number or less using the following norm.

First norm (norm 1): chord distance

Second norm (norm 2): a reference indicating whether the precoding matrix is uniformly selected from the respective groups. If the number of precoding matrices/vectors in the codebook is not divisible by the number of groups, the precoding matrices are most uniformly selected considering the first norm (norm 1).

The above norm may equally apply not only to rank 3 but also to rank 4 described later.

In more detail, one embodiment of the present invention proposes a method of selecting a set of precoding matrices from a codebook for a specific rank using norm 1. In the first step, chordal distances associated with all pairs of precoding matrices included in a single codebook are calculated using equation 42. For example, if there are four codebook sets, four minimum chord distance values may be represented by the following expression.

[ expression ]

d_{c, \min}^{1} = 1, d_{c, \min}^{2} = 0.56, d_{c, \min}^{3} = 0.71 a n d d_{c, \min}^{4} = 1

In the above expression, the expression,(where i is the number of codebook sets) the higher the value, the higher the system performance. Therefore, it is preferable that the first and fourth codebooks enter the next selection step.

In the second step, in order to support various wireless channel environments, the present invention proposes a method of selecting a precoding matrix most uniformly for each group. For example, according to the proposed method of the present invention, if there are three codebook groups and 16 precoding matrices are required as a rank-2 codebook, 5 precoding matrices are selected from two groups and 6 precoding matrices are selected from the remaining one group. For example, according to the proposed inventive method, 5 precoding matrices are selected from the first two groups and 6 precoding matrices are selected from the last group. One embodiment of the present invention may consider the above-described method for limiting the alphabet for each precoding matrix, wherein, for example, the alphabet "X" may be limited to X ═ 1, j, -1, or-j. The following description shows an exemplary 4Tx rank-2 codebook that can be configured by the above steps.

[ Table 1]

Rank-2 codebook set 1-1

\begin{matrix} [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - j & 0 \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}] \end{matrix}

Rank-2 codebook set 2-1

\begin{matrix} [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 1 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & - j \end{matrix}] \end{matrix}

Rank-2 codebook set 3-1

\begin{matrix} [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - j & 0 \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}] \end{matrix}

Rank-2 codebook set 4-1

\begin{matrix} [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & j \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & j \end{matrix}] \end{matrix}

Rank-2 codebook set 5-1

\begin{matrix} [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - 1 \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - j \end{matrix}] \end{matrix}

Rank-2 codebook set 6-1

\begin{matrix} [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - j \end{matrix}] \end{matrix}

Rank-2 codebook set 7-1

\begin{matrix} [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - j \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ - 1 & 0 \end{matrix}] \end{matrix}

Rank-2 codebook set 8-1

\begin{matrix} [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - j & 0 \end{matrix}] \end{matrix}

Rank-2 codebook set 9-1

\begin{matrix} [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - 1 \end{matrix}] \end{matrix}

Rank-2 codebook set 10-1

\begin{matrix} [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ 1 & 0 \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - 1 & 0 \end{matrix}] \end{matrix}

Rank-2 codebook set 11-1

\begin{matrix} [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ - 1 & 0 \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - j & 0 \end{matrix}] \end{matrix}

Rank-2 codebook set 12-1

\begin{matrix} [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ j & 0 \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}] \end{matrix}

The above-described codebook shown in table 1 is disclosed for illustrative purposes only, and row permutation and/or column permutation may be applied to all precoding matrices or some precoding matrices.

If the 4Tx rank-2 codebook includes 15 precoding matrices, one precoding matrix may be removed from a group in which the maximum number of precoding matrices is selected among respective precoding matrix groups. The following description shows an exemplary 4Tx rank-2 codebook configured by the above-described scheme.

[ Table 2]

Rank-2 codebook set 1-2

\begin{matrix} [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - j & 0 \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}] \end{matrix}

Rank-2 codebook set 2-2

\begin{matrix} [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & - j \end{matrix}] \end{matrix}

Rank-2 codebook set 3-2

\begin{matrix} [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 1 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - j & 0 \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ - 1 & 0 \end{matrix}] \end{matrix}

Rank-2 codebook set 4-2

\begin{matrix} [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & j \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & j \end{matrix}] \end{matrix}

Rank-2 codebook set 5-2

\begin{matrix} [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - 1 \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - j \end{matrix}] \end{matrix}

Rank-2 codebook set 6-2

\begin{matrix} [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - j \end{matrix}] \end{matrix}

Rank-2 codebook set 7-2

\begin{matrix} [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - j \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ - 1 & 0 \end{matrix}] \end{matrix}

Rank-2 codebook set 8-2

\begin{matrix} [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - j & 0 \end{matrix}] \end{matrix}

Rank-2 codebook set 9-2

\begin{matrix} [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - 1 \end{matrix}] \end{matrix}

Rank-2 codebook set 10-2

\begin{matrix} [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ 1 & 0 \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - 1 & 0 \end{matrix}] \end{matrix}

Rank-2 codebook set 11-2

\begin{matrix} [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ - 1 & 0 \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ - j & 0 \end{matrix}] \end{matrix}

Rank-2 codebook set 12-2

\begin{matrix} [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - 1 & 0 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - j \\ j & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ - j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & j \\ j & 0 \end{matrix}], \\ [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & 1 \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ - j & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ - 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 0 & 1 \\ 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ j & 0 \\ 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 0 & - 1 \\ 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 \\ 0 & 1 \\ 1 & 0 \\ 0 & j \end{matrix}], [\begin{matrix} 1 & 0 \\ j & 0 \\ 0 & 1 \\ 0 & - j \end{matrix}] \end{matrix}

The codebook shown in table 2 is also disclosed for illustrative purposes only, and row permutation and/or column permutation may be performed on all or some of the precoding matrices in the codebook.

Rank 3-first embodiment

In order to design a 4Tx rank-3 codebook to maintain good CM characteristics, it is assumed that the following three precoding matrix groups are used. For convenience of description, factors related to power balance are omitted herein.

[ equation 44]

Group 1

<math> <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>(</mo> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>X</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>X</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>Y</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>Y</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>X</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>Y</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> <mo>)</mo> </mrow> </mtd> <mtd> <mrow> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>

Group 2

<math> <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>(</mo> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>X</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>X</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>Y</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>Y</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>X</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>Y</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> <mo>)</mo> </mrow> </mtd> <mtd> <mrow> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>

Group 3

<math> <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>(</mo> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>X</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>Y</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>X</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>Y</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>Y</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>X</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> <mo>)</mo> </mrow> </mtd> <mtd> <mrow> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>

In the case of rank 3, the present invention proposes a method of constructing a codebook from the above-described norm 1 and norm 2 in the same manner as rank 2. In more detail, the chordal distances associated with all precoding matrix combinations available in the codebook are calculated using equation 42, and then the set with the minimum number of the largest chordal distances may be selected. In addition, the invention providesA method of selecting a precoding matrix most uniformly from each group (group 1, group 2, or group 3) is presented. If the letters represented by the precoding matrix components of each group are limited to (1, j, -1, -j), a minimum chordal distance d that can be satisfied is obtained_c，The following codebook of 0.707.

[ Table 3]

Rank-3 codebook set 1-1

\begin{matrix} [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & j & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & - j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \end{matrix}], \\ [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & j & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & j & 0 \end{matrix}] \end{matrix}

Rank-3 codebook set 2-1

\begin{matrix} [\begin{matrix} 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & j & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & - j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & - j & 0 \end{matrix}], \\ [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - 1 & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & j & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{matrix}] \end{matrix}

Rank-3 codebook set 3-1

\begin{matrix} [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - j & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & - 1 & 0 \end{matrix}], \\ [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & - j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - 1 & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & - 1 \end{matrix}] \end{matrix}

Rank-3 codebook set 4-1

\begin{matrix} [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - j & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], \\ [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & j & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & - j & 0 \end{matrix}] \end{matrix}

Rank-3 codebook set 5-1

\begin{matrix} [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & j & 0 \\ j & 0 & - j \end{matrix}], \\ [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \end{matrix}] \end{matrix}

Rank-3 codebook set 6-1

\begin{matrix} [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - j & 0 \\ j & 0 & - j \end{matrix}], \\ [\begin{matrix} 0 & 1 & 0 \\ 0 & j & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & - 1 & 0 \end{matrix}] \end{matrix}

Rank-3 codebook set 7-1

\begin{matrix} [\begin{matrix} 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ j & 0 & - j \end{matrix}], \\ [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & j & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - j & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & - j & 0 \end{matrix}] \end{matrix}

Rank-3 codebook set 8-1

\begin{matrix} [\begin{matrix} 0 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & j & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & - j & 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & j & 0 \end{matrix}], \\ [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - j & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & j & 0 \\ j & 0 & - j \end{matrix}] \end{matrix}

It should be noted that row permutation and/or column permutation may be performed on all or some of the precoding matrices of the above codebook shown in table 3.

If only 15 precoding matrices are included in the rank-3 codebook, one precoding matrix of groups for which the maximum number of precoding matrices is selected among the respective groups is removed from the codebook shown in table 3, so that the removed result may be configured as shown in table 4 below.

[ Table 4]

Rank-3 codebook set 1-2

\begin{matrix} [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & j & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & - j & 0 \end{matrix}], \\ [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & j & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \end{matrix}] [\begin{matrix} 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}] [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & j & 0 \end{matrix}] \end{matrix}

Rank-3 codebook set 2-2

\begin{matrix} [\begin{matrix} 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & j & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & - j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & - j & 0 \end{matrix}], \\ [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - 1 & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{matrix}] \end{matrix}

Rank-3 codebook set 3-2

\begin{matrix} [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - j & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & - 1 & 0 \end{matrix}], \\ [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & - j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - 1 & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & - 1 \end{matrix}] \end{matrix}

Rank-3 codebook set 4-2

\begin{matrix} [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - j & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], \\ [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & j & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & - j & 0 \end{matrix}] \end{matrix}

Rank-3 codebook set 5-2

\begin{matrix} [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & j & 0 \\ j & 0 & - j \end{matrix}], \\ [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \end{matrix}], \end{matrix}

Rank-3 codebook set 6-2

\begin{matrix} [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & j & 0 \end{matrix}], \\ [\begin{matrix} 0 & 1 & 0 \\ 0 & j & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & - 1 & 0 \end{matrix}] \end{matrix}

Rank-3 codebook set 7-2

\begin{matrix} [\begin{matrix} 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \\ j & 0 & - j \end{matrix}], \\ [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & j & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & - j & 0 \end{matrix}] \end{matrix}

Rank-3 codebook set 8-2

\begin{matrix} [\begin{matrix} 0 & 1 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & - j \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & j & 0 \\ 1 & 0 & 1 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & - j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & j & 0 \end{matrix}], \\ [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 1 & 0 & - 1 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & - j & 0 \\ j & 0 & - j \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ j & 0 & - j \\ 0 & 1 & 0 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & - 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & - j & 0 \\ 1 & 0 & - 1 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & - 1 \\ 0 & j & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & j & 0 \\ j & 0 & - j \end{matrix}] \end{matrix}

It should be noted that row permutation and/or column permutation may be performed on all or some of the above precoding matrices shown in table 4.

Rank 3-secondTwo embodiments

In one embodiment of the present invention, a method of constructing a codebook using 6 precoding matrix groups capable of maintaining good CM characteristics will be described below. The six 4Tx rank-3 precoding matrix groups for maintaining good CM characteristics may be represented by the following equation 45.

[ equation 45]

Group 1

[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ X & 0 & 0 \end{matrix}],

Group 2

[\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ X & 0 & 0 \end{matrix}],

Group 3

[\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ X & 0 & 0 \end{matrix}],

Group 4

[\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \\ X & 0 & 0 \end{matrix}]

Group 5

[\begin{matrix} 1 & 0 & 0 \\ X & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix}],

Group 6

[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ X & 0 & 0 \\ 0 & 0 & 1 \end{matrix}]

Wherein,

<math> <mrow> <mi>X</mi> <mo>&Element;</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>}</mo> </mrow> </math>

an example of a rank-3 codebook including 24 precoding matrices in 6 groups shown in equation 45 is shown in table 5 below. To reduce complexity, in the example shown in Table 5, the letters represented by the precoding matrix elements are limited to 1, -j, -1, and-j.

[ Table 5]

\begin{matrix} [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ - 1 & 0 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ j & 0 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ - j & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ - 1 & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ j & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ - j & 0 & 0 \end{matrix}], \\ [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ - 1 & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ j & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ - j & 0 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \\ - 1 & 0 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \\ j & 0 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \\ - j & 0 & 0 \end{matrix}], \\ [\begin{matrix} 1 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ - 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ j & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ - j & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ - 1 & 0 & 0 \\ 0 & 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ j & 0 & 0 \\ 0 & 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ - j & 0 & 0 \\ 0 & 0 & 1 \end{matrix}] \end{matrix}

For another example, the present invention proposes a method of using the remaining groups except for the fourth group (group 4), which is generated by applying column permutation to the first group (group 1) among all the groups shown in equation 45. In general, if three column vectors are represented by [ c1, c2, c3], 5 column permutation matrices such as [ c1, c3, c2], [ c2, c1, c3], [ c2, c3, c1], [ c3, c2, c1], and [ c3, c1, c2] may be generated, so that 6 matrices may be obtained.

The reason why the specific vector permutation matrix is not used as described above is that the coded sequence is mapped to a specific column vector (or a specific layer) of the precoding matrix. It is assumed that two independently coded codewords in the above precoding matrix group are mapped to different layers, as described below.

(1) The first codeword is mapped to a first layer.

(2) The second codewords are uniformly distributed and mapped to the second layer and the third layer.

Given the above codeword-to-layer mapping, a particular column permutation does not produce a difference in average SINR between different codewords. For example, a permutation from column vector [ c1, c2, c3] to another column vector [ c1, c3, c2] may indicate that only the levels of the second codeword are swapped. In this way, the exchange between the two layers (where the same second codewords are evenly distributed and mapped) does not result in a performance change. For systems utilizing SIC receivers, correct decoding of codewords results in improved performance given the transmission of multiple codewords. This is because the codeword is correctly decoded at one time. Therefore, the correctly decoded codeword information can be used to cancel spatial layer interference. In the case where the transmission power of the plurality of antennas is uniformly normalized, some column vectors of the precoding matrix may have a large transmission power. In the absence of layer switching/permutation between all transmission layers, a specific layer corresponding to a column vector of a precoding matrix whose column vector has a larger transmission power may have better performance. In the absence of layer switching/permutation on all transmitted layers, in order to fully utilize the SIC receiver, a first layer to which a first codeword is separately mapped is mapped to a precoding matrix column vector having a larger transmission power, and second codewords mapped to second and third layers are mapped to precoding matrix columns having a relatively smaller transmission power than the first layer. With the above codeword-to-layer mapping, the precoding matrix shown in [ equation 46] can be used to further improve performance with the Successive Interference Cancellation (SIC) receiver algorithm.

[ equation 46]

Group 1

[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ X & 0 & 0 \end{matrix}],

Group 2

[\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ X & 0 & 0 \end{matrix}],

Group 3

[\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ X & 0 & 0 \end{matrix}],

Group 4

[\begin{matrix} 1 & 0 & 0 \\ X & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix}],

Group 5

[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ X & 0 & 0 \\ 0 & 0 & 1 \end{matrix}],

Wherein,

<math> <mrow> <mi>X</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </math>

the following codebooks are exemplary 4Tx rank-3 codebooks, each of which limits the letters included in each of the above precoding matrices to 1, j, -1, and-j, and includes 20 precoding matrices.

[ Table 6]

\begin{matrix} [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ - 1 & 0 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ j & 0 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ - j & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ - 1 & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ j & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ - j & 0 & 0 \end{matrix}], \\ [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ 1 & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ - 1 & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ j & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ - j & 0 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ - 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ j & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ - j & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix}] \\ [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ - 1 & 0 & 0 \\ 0 & 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ j & 0 & 0 \\ 0 & 0 & 1 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ - j & 0 & 0 \\ 0 & 0 & 1 \end{matrix}] \end{matrix}

Meanwhile, according to another embodiment of the present invention, the number of precoding matrices required to obtain the best performance from a high rank is smaller than the number of precoding matrices required to obtain the best performance from a low rank, so that the present invention can limit a rank-3 codebook to a codebook having less than 24 precoding matrices. In this case, the present invention can uniformly select a precoding matrix from the 6 precoding matrix groups using norm 2.

[ Table 7]

\begin{matrix} [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{matrix}] [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ - 1 & 0 & 0 \end{matrix}] [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ j & 0 & 0 \end{matrix}] [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ - j & 0 & 0 \end{matrix}] \\ [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix}] [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & - 1 & 0 \end{matrix}] [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & j & 0 \end{matrix}] [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & - j & 0 \end{matrix}] \\ [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & - 1 \end{matrix}] [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & j \end{matrix}] [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & - j \end{matrix}] \end{matrix}

As can be seen from the example of Table 7, if e^-jθBy multiplying by a specific column vector, column permutation in the precoding matrix has no influence on improvement of performance, so that the number of precoding matrices included in the codebook is limited to 12. Meanwhile, according to an embodiment of the present invention, antenna permutation may be performed to obtain an antenna selection gain. The antenna permutation may also be implemented by a row permutation of the precoding matrix included in the above codebook.

Rank 3-third embodiment

In the third embodiment of the present invention, it is assumed that the following 6 precoding matrix groups are considered as precoding matrices capable of maintaining good CM performance.

[ equation 47]

Group 1

[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ X & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & X & 0 \end{matrix}], [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & X \end{matrix}]

Group 2

[\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ X & 0 & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & X & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 0 & X \end{matrix}]

Group 3

[\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ X & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & X & 0 \end{matrix}], [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & X \end{matrix}]

Group 4

[\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & X & 0 \end{matrix}], [\begin{matrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & X \end{matrix}]

Group 5

[\begin{matrix} 1 & 0 & 0 \\ X & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 0 & X & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{matrix}], [\begin{matrix} 0 & 0 & 1 \\ 0 & 0 & X \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{matrix}]

Group 6

[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ X & 0 & 0 \\ 0 & 0 & 1 \end{matrix}], [\begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & X & 0 \\ 0 & 0 & 1 \end{matrix}], [\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 0 & X \\ 1 & 0 & 0 \end{matrix}]

Wherein,

in the case of the first group (group 1) in equation 47, it can be appreciated that the three permutation matrices are selected from [ c1, c3, c2], [ c2, c1, c3], [ c2, c3, c1], [ c3, c2, c1] and [ c3, c1, c2 ]. In the case of the fourth group (group 4), it can be recognized that one constituent precoding matrix is excluded because the excluded precoding matrix is already included in the first group (group 1). It is preferable to utilize the third embodiment when the layer switching operation is not performed. The third embodiment can implement layer conversion using a codebook including a set of precoding matrices on which column permutation is performed. Thus, the information sequence may be mapped to all layers so that the SINR difference between the layers may be normalized.

The third embodiment may select a precoding matrix using the first norm (norm 1) and the second norm (norm 2).

Rank 3-fourth embodiment

The fourth embodiment considers the following three groups as precoding matrix groups for maintaining good CM characteristics.

[ equation 48]

Wherein,

<math> <mrow> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>&Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mrow> <mo>}</mo> </mrow> </mrow> </math>

the last column vector in the set of precoding matrices shown in equation 48

May be different precoding momentsAn array, such as a DFT-based precoding vector/matrix or a hausehold (household) -based precoding vector/matrix. For example, the last vector instance may be the rank-1 codebook of the 3gpp lte system (release 8 system). Preferably, in order to maintain the matrix

[\begin{matrix} 1 & 0 & a \\ X & 0 & b \\ 0 & 1 & c \\ 0 & Y & d \end{matrix}]

Orthogonal/partially unitary character of, matrix

[\begin{matrix} 1 & a \\ X & b \end{matrix}]

And

[\begin{matrix} 1 & c \\ Y & d \end{matrix}]

unitary characteristics must be satisfied. Similarly, the matrix

Of (2) matrix

Sum matrix

And a matrix

Of (2) matrix

And

unitary characteristics must be satisfied. This means that the parameters must satisfy the following relationship.

[ equation 49]

In group 1: a is 1, b is-X, and c is-d-Y^*

In group 2: a '═ 1, b' ═ -X, and c '═ -d' · Y^*

In group 3: a ″ -1, b ″ -X, and c ″ -d ″, Y^*

In this case, although a specific complex constant is multiplied by each column vector of a specific precoding matrix, this means that the multiplication result represents the same precoding matrix, so it is assumed that a, a', or a ″ is set to 1.

Preferably, the fourth embodiment can be applied to the case when layer replacement is performed. The layer permutation operation means that a specific information sequence is circularly mapped and transmitted to all layers so that SINR performance differences of the respective layers are normalized. If the same power is used in different layers, the data sequence of the last layer corresponding to the last column without a 0 value has the highest power from the viewpoint of precoding the output signal.

Without using layer permutation and using the enhanced SIC receiver algorithm, the layer to which the first codeword is mapped should preferably correspond to a precoding vector column with relatively higher transmit power than other precoding vector columns. In the case of [ equation 48], the third column may have a greater transmit power than the other columns. For the case where the first column is mapped to the first layer, the second column is mapped to the second layer, and the third column is mapped to the third layer, [ equation 48a ] may be used instead of [ equation 48 ]. Such a precoding matrix structure would allow improved performance without using layer permutation and with SIC receivers, since the probability of correct decoding of the entire codeword is improved given multiple codeword transmissions.

[ equation 48a ]

Wherein,

rank 3-fifth embodiment

In the fifth embodiment, it is assumed that the following group shown in equation 50 is used as a precoding matrix group that maintains good CM performance.

[ equation 50]

G 1 = ([\begin{matrix} 1 & 0 & a \\ X & 0 & b \\ 0 & 1 & c \\ 0 & Y & d \end{matrix}] [\begin{matrix} 0 & 1 & a \\ 0 & X & b \\ 1 & 0 & c \\ Y & 0 & d \end{matrix}] [\begin{matrix} a & 0 & 1 \\ b & 0 & X \\ c & 1 & 0 \\ d & Y & 0 \end{matrix}])

Wherein,

the precoding matrix group shown in equation 50 is constituted by a plurality of precoding matrices obtained when row permutation or column permutation is performed on the structure of the fourth embodiment. The column vectors in the set of precoding matrices shown in equation 50

Different precoding matrices may be possible, such as DFT-based precoding vectors/matrices or hausler-based precoding vectors/matrices. For example, the example of the above column vector may be a rank-1 codebook of a 3gpp lte system (release 8 system).

Similar to the fourth embodiment, in the fifth embodiment, it is preferable that precoding matrix vectors are orthogonal to each other, and elements other than the first value of 0 in all column vectors of each precoding matrix group are set to 1.

The codebook according to the fifth embodiment includes precoding matrices generated when column permutation is performed on the precoding matrices of the fourth embodiment. As described above, the precoding matrix having the column vector [ c1, c2, c3] may have 6 column permutated precoding matrices, such as [ c1, c3, c2], [ c2, c1, c3], [ c2, c3, c1], [ c3, c2, c1], [ c3, c1, c2] and [ c3, c1, c2 ].

The reason why the specific column permutation is not included is that the second and third column permutations of the precoding matrix in the system in which the first codeword is mapped to the first layer and the second codeword is distributed and mapped to the second layer and the third layer do not cause a difference in performance.

Rank 3-sixth embodiment

The precoding matrix according to the sixth embodiment is configured in a format obtained when row permutation is performed on the precoding matrix of the codebook shown in the fourth embodiment, because the precoding matrix of the sixth embodiment can be obtained by antenna switching.

The precoding matrix according to the sixth embodiment can be represented by the following equation 51.

[ equation 51]

G 1 = ([\begin{matrix} 1 & 0 & a \\ X & 0 & b \\ 0 & 1 & c \\ 0 & Y & d \end{matrix}] [\begin{matrix} X & 0 & b \\ 1 & 0 & a \\ 0 & 1 & c \\ 0 & Y & d \end{matrix}] [\begin{matrix} 0 & 1 & c \\ X & 0 & b \\ 1 & 0 & a \\ 0 & Y & d \end{matrix}] [\begin{matrix} 0 & Y & d \\ X & 0 & b \\ 0 & 1 & c \\ 1 & 0 & a \end{matrix}] [\begin{matrix} 1 & 0 & a \\ 0 & 1 & c \\ X & 0 & b \\ 0 & Y & d \end{matrix}] [\begin{matrix} 1 & 0 & a \\ 0 & Y & d \\ 0 & 1 & c \\ X & 0 & b \end{matrix}] [\begin{matrix} 1 & 0 & a \\ X & 0 & b \\ 0 & Y & d \\ 0 & 1 & c \end{matrix}])

[ equation 51]

Column vector

Or their row permutation formats may be different precoding matrices such as DFT-based precoding vectors/matrices or hausler-based precoding vectors/matrices. For example, the example of the above column vector may be a rank-1 codebook of a 3gpp lte system (release 8 system).

Similar to the fourth embodiment, in the sixth embodiment, it is preferable that the column vectors of the precoding matrix are orthogonal to each other, and the element a, a', or a ″ is set to 1. An example of the codebook according to the sixth embodiment can be represented by the following equation 52.

[ equation 52]

Wherein,

rank 3-seventh embodiment

The codebook according to the seventh embodiment is configured in a line-permutated format of the codebook shown in the fifth embodiment. An example of the codebook according to the seventh embodiment can be represented by the following equation 53.

[ equation 53]

G 1 = (\begin{matrix} [\begin{matrix} 1 & 0 & a \\ X & 0 & b \\ 0 & 1 & c \\ 0 & Y & d \end{matrix}], [\begin{matrix} X & 0 & b \\ 1 & 0 & a \\ 0 & 1 & c \\ 0 & Y & d \end{matrix}], [\begin{matrix} 0 & 1 & c \\ X & 0 & b \\ 1 & 0 & a \\ 0 & Y & d \end{matrix}], [\begin{matrix} 0 & Y & d \\ X & 0 & b \\ 0 & 1 & c \\ 1 & 0 & a \end{matrix}], [\begin{matrix} 1 & 0 & a \\ 0 & 1 & c \\ X & 0 & b \\ 0 & Y & d \end{matrix}], [\begin{matrix} 1 & 0 & a \\ 0 & Y & d \\ 0 & 1 & c \\ X & 0 & b \end{matrix}], [\begin{matrix} 1 & 0 & a \\ X & 0 & b \\ 0 & Y & d \\ 0 & 1 & c \end{matrix}] \\ [\begin{matrix} 0 & 1 & a \\ 0 & X & b \\ 1 & 0 & c \\ Y & 0 & d \end{matrix}], [\begin{matrix} 0 & X & b \\ 0 & 1 & a \\ 1 & 0 & c \\ Y & 0 & d \end{matrix}], [\begin{matrix} 1 & 0 & c \\ 0 & X & b \\ 0 & 1 & a \\ Y & 0 & d \end{matrix}], [\begin{matrix} Y & 0 & d \\ 0 & X & b \\ 1 & 0 & c \\ 0 & 1 & a \end{matrix}], [\begin{matrix} 0 & 1 & a \\ 1 & 0 & c \\ 0 & X & b \\ Y & 0 & d \end{matrix}], [\begin{matrix} 0 & 1 & a \\ Y & 0 & d \\ 1 & 0 & c \\ 0 & X & b \end{matrix}], [\begin{matrix} 0 & 1 & a \\ 0 & X & b \\ Y & 0 & d \\ 1 & 0 & c \end{matrix}] \\ [\begin{matrix} a & 0 & 1 \\ b & 0 & X \\ c & 1 & 0 \\ d & Y & 0 \end{matrix}], [\begin{matrix} b & 0 & X \\ a & 0 & 1 \\ c & 1 & 0 \\ d & Y & 0 \end{matrix}], [\begin{matrix} c & 1 & 0 \\ b & 0 & X \\ a & 0 & 1 \\ d & Y & 0 \end{matrix}], [\begin{matrix} d & Y & 0 \\ b & 0 & X \\ c & 1 & 0 \\ a & 0 & 1 \end{matrix}], [\begin{matrix} a & 0 & 1 \\ c & 1 & 0 \\ b & 0 & X \\ d & Y & 0 \end{matrix}], [\begin{matrix} a & 0 & 1 \\ d & Y & 0 \\ c & 1 & 0 \\ b & 0 & X \end{matrix}], [\begin{matrix} a & 0 & 1 \\ b & 0 & X \\ d & Y & 0 \\ c & 1 & 0 \end{matrix}] \end{matrix})

Wherein,

column vector

Similar to the fourth embodiment, in the seventh embodiment, it is preferable that the column vectors of the precoding matrix are orthogonal to each other, and the element a, a', or a ″ is set to 1. It is preferable to use the codebook according to the present embodiment when antenna permutation is not performed because when the codebook of the seventh embodiment is used, an antenna permutation effect can be achieved by a precoding matrix that performs row permutation.

An example of the codebook according to the seventh embodiment can be represented by the following equation 54.

[ equation 54]

\begin{matrix} G 1 = \\ (\begin{matrix} [\begin{matrix} 1 & 0 & 1 \\ X & 0 & - X \\ 0 & 1 & c \\ 0 & Y & d \end{matrix}] [\begin{matrix} X & 0 & - X \\ 1 & 0 & 1 \\ 0 & 1 & c \\ 0 & Y & d \end{matrix}] [\begin{matrix} 0 & 1 & c \\ X & 0 & - X \\ 1 & 0 & 1 \\ 0 & Y & d \end{matrix}] [\begin{matrix} 0 & Y & d \\ X & 0 & - X \\ 0 & 1 & c \\ 1 & 0 & 1 \end{matrix}] [\begin{matrix} 1 & 0 & 1 \\ 0 & 1 & c \\ X & 0 & - X \\ 0 & Y & d \end{matrix}] [\begin{matrix} 1 & 0 & 1 \\ 0 & Y & d \\ 0 & 1 & c \\ X & 0 & - X \end{matrix}] [\begin{matrix} 1 & 0 & 1 \\ X & 0 & - X \\ 0 & Y & d \\ 0 & 1 & c \end{matrix}] \\ [\begin{matrix} 0 & 1 & 1 \\ 0 & X & - X \\ 1 & 0 & c \\ Y & 0 & d \end{matrix}] [\begin{matrix} 0 & X & - X \\ 0 & 1 & 1 \\ 1 & 0 & c \\ Y & 0 & d \end{matrix}] [\begin{matrix} 1 & 0 & c \\ 0 & X & - X \\ 0 & 1 & 1 \\ Y & 0 & d \end{matrix}] [\begin{matrix} Y & 0 & d \\ 0 & X & - X \\ 1 & 0 & c \\ 0 & 1 & 1 \end{matrix}] [\begin{matrix} 0 & 1 & 1 \\ 1 & 0 & c \\ 0 & X & - X \\ Y & 0 & d \end{matrix}] [\begin{matrix} 0 & 1 & 1 \\ Y & 0 & d \\ 1 & 0 & c \\ 0 & X & - X \end{matrix}] [\begin{matrix} 0 & 1 & 1 \\ 0 & X & - X \\ Y & 0 & d \\ 1 & 0 & c \end{matrix}] \\ [\begin{matrix} 1 & 0 & 1 \\ - X & 0 & X \\ c & 1 & 0 \\ d & Y & 0 \end{matrix}] [\begin{matrix} - X & 0 & X \\ 1 & 0 & 1 \\ c & 1 & 0 \\ d & Y & 0 \end{matrix}] [\begin{matrix} c & 1 & 0 \\ - X & 0 & X \\ 1 & 0 & 1 \\ d & Y & 0 \end{matrix}] [\begin{matrix} d & Y & 0 \\ - X & 0 & X \\ c & 1 & 0 \\ 1 & 0 & 1 \end{matrix}] [\begin{matrix} 1 & 0 & 1 \\ c & 1 & 0 \\ - X & 0 & X \\ d & Y & 0 \end{matrix}] [\begin{matrix} 1 & 0 & 1 \\ d & Y & 0 \\ c & 1 & 0 \\ - X & 0 & X \end{matrix}] [\begin{matrix} 1 & 0 & 1 \\ - X & 0 & X \\ d & Y & 0 \\ c & 1 & 0 \end{matrix}] \end{matrix}) \end{matrix}

Wherein,

reference for selecting a further precoding matrix

In addition to norm 1 and norm 2, the present embodiment is designed to consider another norm. In the norm, elements represented by letters included in each precoding matrix group are not selected from eight values but limited to 1, j, -1, and-j, thereby reducing the number of precoding matrices included in the codebook.

According to the present embodiment, a codebook set including 16 precoding matrices is considered. For example, a rank 1DFT vector for a 4Tx antenna may be represented as follows.

N × NDFT matrix (or fourier matrix) F based on a given component_NSuch as being normalized toF of (A)_N＝e^-j·2π/NRepresented by the following equation 55.

[ equation 55]

The rank 1DFT vector for the 4Tx antenna is composed of 16 column vectors located in the first four rows of equation 55.

[ Table 8]

Next, the 4Tx rank 1 hause hall vector (HH vector) may be represented by the following table 9.

[ Table 9]

[\begin{matrix} 1 \\ 1 \\ 1 \\ 1 \end{matrix}] [\begin{matrix} 1 \\ - j \\ - 1 \\ j \end{matrix}] [\begin{matrix} 1 \\ - 1 \\ 1 \\ - 1 \end{matrix}] [\begin{matrix} 1 \\ j \\ - 1 \\ - j \end{matrix}] [\begin{matrix} 1 \\ \frac{1 - j}{\sqrt{2}} \\ - j \\ \frac{- 1 - j}{\sqrt{2}} \end{matrix}] [\begin{matrix} 1 \\ \frac{- 1 - j}{\sqrt{2}} \\ j \\ \frac{1 - j}{\sqrt{2}} \end{matrix}] [\begin{matrix} 1 \\ \frac{- 1 + j}{\sqrt{2}} \\ - j \\ \frac{1 + j}{\sqrt{2}} \end{matrix}] [\begin{matrix} 1 \\ \frac{1 + j}{\sqrt{2}} \\ j \\ \frac{- 1 + j}{\sqrt{2}} \end{matrix}] [\begin{matrix} 1 \\ 1 \\ - 1 \\ - 1 \end{matrix}] [\begin{matrix} 1 \\ - j \\ 1 \\ - j \end{matrix}] [\begin{matrix} 1 \\ - 1 \\ - 1 \\ 1 \end{matrix}] [\begin{matrix} 1 \\ j \\ 1 \\ j \end{matrix}] [\begin{matrix} 1 \\ 1 \\ 1 \\ - 1 \end{matrix}] [\begin{matrix} 1 \\ 1 \\ - 1 \\ 1 \end{matrix}] [\begin{matrix} 1 \\ - 1 \\ 1 \\ 1 \end{matrix}] [\begin{matrix} 1 \\ - 1 \\ - 1 \\ - 1 \end{matrix}]

Codebook size limitation

At least one of the first to third norms (norm 1, norm 2 and norm 3) may be used to limit the number of precoding matrices included in the codebook. In the present embodiment, the codebook size restriction for each rank, in particular, the size restriction of the rank 1 codebook will be described in detail.

Currently, the downlink 4Tx codebook for the 3gpp lte system specifies that each rank has the same number of vectors/matrices (i.e., 16 vectors/matrices). However, it is well known in the art that the number of precoding matrices required to obtain the best performance from a high rank is less than the number of precoding matrices required to obtain the best performance from a low rank. To this end, this embodiment of the present invention proposes a new codebook format in which the number of precoding matrices of a low rank is higher than that of precoding matrices of a high rank, so that each rank has a different number of precoding matrices.

Meanwhile, the mobile communication system may support a plurality of transmission modes. It is assumed that the xth transmission mode can be effectively used for a UE located at a cell edge so that the UE can support a closed loop operation using a rank 1 Precoding Matrix Indicator (PMI). In this case, the rank-1 PMI vector may be selected from rank-1 precoding matrices included in an entire codebook consisting of a plurality of precoding matrices of all ranks supporting the Y-th transmission mode (such as open-loop MIMO or closed-loop MIMO). In this case, it is assumed that the xth transmission mode is different from the yth transmission mode. For the Y-th transmission mode, the size of the rank-1 codebook need not be configured as a power of two. In addition, although the rank-1 codebook size is configured as a power of two, only the codebook size can be increased without higher performance improvement. Therefore, this embodiment proposes a method of rationally limiting the size of the codebook while having appropriate performance, so that the codebook can be represented with a smaller amount of feedback information.

First, it is assumed that the number of precoding matrices of each rank supporting the Yth transmission mode is set to A-rank 1, B-rank 2, C-rank 3, and D-rank 4 (where D ≦ C ≦ B ≦ A). In this case, the size of the entire codebook is equal to the sum of A, B, C and D. To support the above codebook size, m-bit signaling for satisfying the following condition shown in equation 56 is required.

[ equation 56]

A+B+C+D≤2^m

The UE can use rank 1PMI information if the UE is configured to use the xth transmission mode. Preferably redefining 2ⁿRank 1PMI (where n<m) to reduce the number of bits required for signaling. A number of methods (1), (2), (3), (4), (5) and (6) can be used to reduce the number of signaling bits.

(1) Method 1

If so, the even index is selected.

(2) Method 2

If so, an odd number of indices is selected.

(3) Method 3

Select the first 2ⁿAn index.

(4) Method 4

Select the last 2ⁿAn index.

(5) Method 5

The index is arbitrarily selected.

(6) Method 6

The construction is achieved by signaling.

For example, for the Y-th transmission mode, 33 precoding matrices are given for rank 1, 15 precoding matrices are given for rank 2, 15 precoding matrices are given for rank 3, and 4 precoding matrices are given for rank 4.

In this case, various methods (1), (2), (3), (4), (5), and (6) for constructing a rank 1 codebook for representing only 16 precoding matrices may be used.

(1) Method 1

If possible, select the even number of indices

(2) Method 2

If so, an odd number of indices is selected

(3) Method 3

The first 16 indices are selected.

(4) Method 4

The last 16 indices are selected.

(5) Method 5

The index is arbitrarily selected.

(6) Method 6

The construction is achieved by signaling.

Meanwhile, various methods (1), (2), (3), and (4) for constructing a rank 1 codebook, which is used to represent only 32 precoding matrices, may be used.

(1) Method 1

The first 32 indices are selected.

(2) Method 2

The last 32 indices are selected.

(3) Method 3

The index is arbitrarily selected.

(4) Method 4

The construction is achieved by signaling.

If 16 downlink rank 1 vectors are included in a rank 1 codebook including 32 precoding matrices, the following restriction methods (I) and (II) may be used.

The restriction method (I) corresponding to the case of constructing a 16-size rank 1 codebook and a detailed description thereof will be described in detail below.

A) 16 downlink rank 1 vectors are selected.

B) A 16-size rank 1 codebook is selected without considering the downlink rank 1 vector.

(1) The first 16 indices are selected.

(2) The last 16 indices are selected.

(3) The index is arbitrarily selected.

(4) The construction is achieved by signaling.

Another restriction method (II) corresponds to another case of constructing a 32-size rank 1 codebook, and a detailed description thereof will be described in detail below.

A) 16 downlink rank 1 vectors + further vectors are selected.

(1) The first 16 indices are selected.

(2) The last 16 indices are selected.

(3) The index is arbitrarily selected.

(4) The construction is achieved by signaling.

B) A 32-size rank 1 codebook is selected without regard to the downlink rank 1 vector.

(1) The first 32 indices are selected.

(2) The last 32 indices are selected.

(3) The index is arbitrarily selected.

(4) The construction is achieved by signaling.

The number of codebooks for each rank can be efficiently constructed according to the above-described scheme.

Device configuration

Chapter III will disclose an improved structure included in the UE in the following, wherein the improved structure can maintain good PAPR or CM characteristics while applying the MIMO scheme to uplink signaling.

Referring to fig. 10, a Base Station (BS)10 includes a processor 11, a memory 12, and a Radio Frequency (RF) module 13. The RF module 13 is used as a transmission/reception module that receives an uplink signal and transmits a downlink signal. The processor 11 may control downlink signal transmission using downlink signal transmission information (e.g., a specific precoding matrix included in a codebook for downlink signal transmission) stored in the memory 12. Otherwise, as a reverse process of the precoding process, the processor 11 may control the signal reception process by multiplying uplink signal reception information (e.g., uplink signals) stored in the memory 12 by a hermitian matrix of the same precoding matrix as the precoding matrix used in the UE 20.

The UE20 may include a processor 21 serving as a transmission/reception module that transmits uplink signals and receives downlink signals, a memory 22, and an RF module 23. The processor 21 may control uplink signal transmission using uplink signal transmission information (e.g., a specific precoding matrix included in the above-described codebook for uplink signal transmission) stored in the memory 22. Otherwise, as a reverse process of the precoding process, the processor 21 may control the signal reception process by multiplying the downlink signal reception information (for example, downlink signal) stored in the memory 22 by a hermitian matrix of the same precoding matrix as the precoding matrix used in the UE 20.

Meanwhile, a detailed description will be described below with respect to a processor of the UE20 (or BS10), particularly, a structure for transmitting a signal using the SC-FDMA scheme. A processor for transmitting a signal based on the SC-FDMA scheme in the 3gpp lte system and a processor for transmitting a signal based on the OFDM scheme in the 3gpp lte system will be described below, and a processor for causing the UE to transmit an uplink signal using the SC-FDMA scheme as well as the MIMO scheme will be described below.

Referring to fig. 11, not only a UE for transmitting an uplink signal but also a Base Station (BS) for transmitting a downlink signal includes: serial-to-parallel converter 401, subcarrier mapper 403, M-point IDFT module 404, parallel-to-serial converter 405, etc. However, the UE transmitting a signal using the SC-FDMA scheme further includes an N-point DFT module 402 and compensates for the IDFT processing influence of a predetermined portion of an M-point IDFT module 404 so that the transmitted signal can have a single carrier characteristic.

Fig. 12 shows a relationship between a block diagram of uplink signal processing specified in TS36.211 including the 3gpp lte system specification and a processor transmitting a signal using the SC-FDMA scheme. According to TS36.211, each UE scrambles a transmission signal using a specific scrambling sequence to transmit an uplink signal, and the scrambled signal is modulated such that complex symbols are generated. Thereafter, transform precoding for performing DFT spread processing on the complex symbols is performed. That is, the transform precoder specified in TS36.211 may correspond to an N-point DFT module. Thereafter, the DFT-spread signal may be mapped to a specific resource element according to a Resource Block (RB) -based mapping rule through a resource element mapper, and it can be appreciated that this operation corresponds to the subcarrier mapper shown in fig. 11. The signals mapped to the resource elements are subjected to M-point IDFT or IFFT processing by an SC-FDMA signal generator, parallel-to-serial conversion is performed on the IDFT or IFFT processing results, and then a Cyclic Prefix (CP) is added to the P/S conversion results.

Meanwhile, fig. 12 further shows a processor of a Base Station (BS) for receiving a signal that has been received in the base station through the above-described process.

Thus, a processor for SC-FDMA transmission in a 3gpp lte system does not include a structure using the MIMO scheme. Thus, a BS processor for MIMO transmission in a 3gpp lte system will be described first, and then a processor for transmitting an uplink signal by using the above BS processor in combination with the SC-FDMA scheme and the MIMO scheme will be described.

A Base Station (BS) in a 3gpp lte system may transmit one or more codewords via a downlink. Thus, the one or more codewords may be processed into complex symbols through the scrambling module 301 and the modulation mapper 302 in the same manner as the uplink operation shown in fig. 12. Thereafter, the complex symbols are mapped to a plurality of layers by the layer mapper 303, and each layer is multiplied by a predetermined precoding matrix selected according to a channel state and then allocated to each transmission antenna by the precoding module 304. The processed transmission signals of the respective antennas are mapped to time-frequency resource elements to be transmitted for data by the resource element mapper 305. Thereafter, after passing through the OFDMA signal generator 306, the result of the mapping may be transmitted via each antenna.

However, if the downlink signal scheme shown in fig. 13 is used in the 3gpp lte system, the PAPR or CM characteristic deteriorates. Therefore, the UE must effectively combine the SC-FDMA scheme maintaining good PAPR and CM performance described in fig. 11 and 12 with the MIMO scheme shown in fig. 13, and must construct a UE that performs precoding using a precoding matrix capable of maintaining good PAPR and CM characteristics described in the above embodiments.

According to one embodiment of the present invention, it is assumed that a UE transmitting an uplink signal via a plurality of antennas (multi-antenna) includes a plurality of antennas (not shown) for transmitting and receiving signals. Referring to fig. 10, the UE20 includes: a memory 22 for storing a codebook, and a processor 21 connected to the plurality of antennas (not shown) and the memory 22 to process uplink signal transmission. In this case, the codebook stored in the memory 22 includes a precoding matrix established in such a manner that a single layer signal is transmitted to each of the plurality of antennas. The processor 21 of the UE configured as described above will be described in detail below.

FIG. 14 illustrates a processor according to one embodiment of the invention.

Referring to fig. 14, a processor of a UE20 according to one embodiment of the invention includes: a codeword to layer mapper 1401 for mapping the uplink signal to a predetermined number of layers corresponding to a specific rank; a predetermined number of DFT modules 1402 for performing Discrete Fourier Transform (DFT) spreading on each of the predetermined number of layer signals; and a precoder 1043. The precoder 1043 selects a specific precoding matrix established in such a manner that one layer signal is transmitted to each antenna 1405, so as to precode the layer signal resulting from DFT spreading received from the DFT module 1402. In particular, in this embodiment of the present invention, each DFT module 1402 performs spreading of each layer signal, and this DFT module 1402 for spreading each layer signal is located just before the precoder 1043. When the precoder 1043 performs precoding, the precoder 1403 is configured such that each layer signal is mapped to one antenna and then transmitted via the mapped antenna, so that the single carrier characteristic of each layer signal is maintained and good PAPR and CM characteristics are maintained. Meanwhile, the UE20 further includes a transmitting module. The transmission module performs a process of constructing SC-FDMA symbols based on the precoded signals, and transmits the resulting precoded signals to a Base Station (BS) via a plurality of antennas 1405.

Meanwhile, the precoder 1403 selects a precoding matrix to be used for signal transmission from a codebook stored in the memory 22 and performs precoding on the selected precoding matrix. Preferably, the precoding matrices may be precoding matrices established to equalize transmission power of a plurality of antennas and/or transmission power of each layer.

The number of the plurality of antennas 1045 may be 2 or 4. The processor of the UE according to an embodiment of the present invention may further perform not only a layer switching function for periodically or aperiodically changing a layer mapped to a specific codeword but also an antenna switching function for periodically or aperiodically changing an antenna transmitting a specific layer signal. The layer conversion function may be performed by the layer mapper 1401 separately from the precoding of the precoder 1403, or may also be performed by column permutation of a precoding matrix when the precoder 1403 performs precoding. In addition, the antenna switching function may also be performed separately from the precoding of the precoder 1403, or may also be performed by row permutation of a precoding matrix.

The exemplary embodiments described above are combinations of elements and features of the present invention. Elements or features may be considered optional unless otherwise mentioned. Each element or feature may be implemented without being combined with other elements or features. Also, the embodiments of the present invention may be configured by combining some of the elements and/or features. The order of operations described in the embodiments of the present invention may be rearranged. Some of the structures or features of any one embodiment may be included in another embodiment and may be replaced with corresponding structures or features of another embodiment. It is obvious that the present invention can be embodied as a combination of claims not having an explicit reference in the appended claims, or can include new claims modified after filing.

Embodiments of the invention may be implemented by various means, such as hardware, firmware, software, or a combination thereof. In a hardware configuration, embodiments of the invention may be implemented by one or more Application Specific Integrated Circuits (ASICs), Digital Signal Processors (DSPs), Digital Signal Processing Devices (DSPDs), Programmable Logic Devices (PLDs), Field Programmable Gate Arrays (FPGAs), processors, controllers, micro-controllers, microprocessors, and the like.

In a firmware or software configuration, the embodiments of the present invention may be implemented by a module, a process, a function, etc. performing the above-described functions or operations. The software codes may be stored in memory units and driven by processors. The memory unit may be located inside or outside the processor, and may transmit and receive data to and from the processor via various known means.

It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the invention. Accordingly, the foregoing detailed description should be regarded as illustrative in nature and not as restrictive. The scope of the invention must be determined by reasonable analysis of the claims and all modifications within the equivalent scope of the invention are included in the scope of the invention. It is obvious that the present invention can be embodied as a combination of claims not having an explicit citation relationship in the appended claims or can include new claims modified after filing the application.

As apparent from the above description, the present invention can maintain PAPR or CM characteristics while transmitting uplink signals using a MIMO scheme.

In addition, the present invention uniformly controls or adjusts antenna/layer transmission power, minimizes signaling overhead required for precoding matrix information, and obtains maximum diversity gain.

The present invention can be applied to a broadband wireless mobile communication system.

It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.

Claims

1. A method for a transmitting device to transmit a signal using an SC-fdmammo (single carrier-frequency division multiple access multiple input multiple output) scheme, the method comprising:

precoding signals of 2 layers by multiplying a specific precoding matrix P by a predetermined constant value, wherein,

<math> <mrow> <mi>P</mi> <mo>&Element;</mo> <mo>{</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>}</mo> <mo>,</mo> </mrow> </math>

and,

<math> <mrow> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>&Element;</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>}</mo> <mo>;</mo> </mrow> </math>

and is

The precoded signal is transmitted to a receiving device via 4 transmit antennas.

2. The method according to claim 1, wherein the specific precoding matrix P multiplied by the predetermined constant value is denoted as P',

<math> <mrow> <msup> <mi>P</mi> <mo>′</mo> </msup> <mo>&Element;</mo> <mo>{</mo> <mi>k</mi> <mo>·</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>k</mi> <mo>·</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>k</mi> <mo>·</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>}</mo> <mo>,</mo> </mrow> </math>

wherein "k" represents the predetermined constant value.

3. The method of claim 1, wherein "X" and "Y" are selected from {1, j, -1, -j }.

4. The method according to claim 1, wherein the specific precoding matrix P is selected from a rank 2 codebook, and

wherein the number of precoding matrices of the rank 2 codebook is 16.

5. The method of claim 1, wherein the signal is an uplink signal, the transmitting apparatus is a User Equipment (UE) and the receiving apparatus is a Base Station (BS).

6. An apparatus for transmitting a signal using an SC-fdmammo (single carrier-frequency division multiple access multiple input multiple output) scheme, the apparatus comprising:

a plurality of transmission antennas for transmitting signals;

a memory for storing codebooks of all ranks; and

a processor connected to the plurality of transmit antennas and the memory to process the transmission of the signals,

wherein a rank 2 codebook among the codebooks stored in the memory has a codebook order of

<math> <mrow> <mi>P</mi> <mo>&Element;</mo> <mo>{</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>Y</mi> </mtd> </mtr> <mtr> <mtd> <mi>X</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>}</mo> </mrow> </math>

The selected pre-coding matrix P is selected,

wherein,

<math> <mrow> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>&Element;</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>-</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>,</mo> <mo>-</mo> <mi>j</mi> <mo>,</mo> <mfrac> <mrow> <mo>-</mo> <mn>1</mn> <mo>+</mo> <mi>j</mi> </mrow> <msqrt> <mn>2</mn> </msqrt> </mfrac> <mo>}</mo> <mo>.</mo> </mrow> </math>

7. the apparatus according to claim 6, wherein the processor is configured to use the precoding matrix P multiplied by a predetermined constant value for precoding the signal.

8. The apparatus of claim 6, wherein "X" and "Y" are selected from {1, j, -1, -j }.

9. The apparatus of claim 6, wherein the number of precoding matrices of the rank 2 codebook is 16.

10. The apparatus of claim 6, wherein the apparatus is configured to operate as a User Equipment (UE) to transmit an uplink signal.