CN101635612B - Precoding code book constructing method and precoding code book constructing device of multi-input multi-output system - Google Patents

Abstract

The invention discloses a precoding code book constructing method of a multi-input multi-output system, comprising the following steps: selecting N 4*4 first orthogonal matrixes Un, and selecting N second orthogonal matrixes Kn; generating N 8*8 matrixes Mn according to the selected Un and Kn in a manner of a Kronecker product or analog Kronecker product; and selecting a row or multiple rows of matrixes Mn to construct partial code words in a subcode book of each rank under 8 antennae. The invention also discloses a precoding code book constructing device of a multi-input multi-output system. The method and the device enables the designed code book to satisfy an orthogonal characteristic, a constant modulus characteristic and a 8 PSK characteristic in 8 antennae and have better performance under correlation channels and noncorrelation channels.

Description

Precoding codebook construction method and device of multi-input multi-output system

Technical Field

The present invention relates to codebook construction technology, and more particularly, to a precoding codebook construction method and apparatus for a multiple-input multiple-output (MIMO) system.

Background

In a wireless communication Multiple-Input Multiple-output (MIMO) system, if Multiple antennas are used at both the transmitting end and the receiving end, a spatial multiplexing method can be adopted to obtain a higher rate: different data are transmitted at different antenna positions of the same time-frequency resource at the transmitting end, so that the transmission rate can be improved. Channel Information (CSI) between each transmitting and receiving antenna can be obtained through Channel estimation at a receiving end, and the CSI can be formed into a plurality of Channel matrices. Because the receiving end obtains the channel matrix that the transmitting signal passes through, even if each antenna transmits different data, the receiving end can still solve the different transmitting data on each antenna after passing through the channel matrix.

One enhanced approach is to use transmit precoding techniques, as opposed to methods that use channel matrices to directly resolve the transmitted data on each antenna. The concept of "layer" is defined at the transmitting end: on the same time frequency resource, each layer can transmit different data modulation symbols (i.e. data), and the number of layers is equal to the Rank (Rank) of the channel matrix corresponding to the time frequency resource. And carrying out precoding processing on the data on the layer, mapping the data to an antenna, and then sending the data to a receiving end through an air channel. If the complete and accurate CSI can be obtained at the transmitting end, Singular Value Decomposition (Singular Value Decomposition) can be performed on a channel matrix composed of the CSI, then a matrix composed of the decomposed right eigenvectors is used as a precoding matrix, and precoding processing is performed on data of each layer based on the matrix.

Based on complete and accurate CSI, optimal precoding processing can be performed on data of each layer. However, the CSI can only be directly and accurately obtained at the receiving end, and the CSI which is desired to be accurately obtained at the transmitting end can only be fed back to the transmitting end through the receiving end. It can be seen that an important issue in the precoding technique is how to acquire and utilize CSI. In the current mainstream standard, the capacity of a channel provided by the MIMO system for CSI feedback is limited, and the feedback amount of the entire CSI is very large, so the mainstream feedback method is based on a codebook, and the feedback content is a matrix composed of right eigenvectors of a channel matrix, i.e. a precoding matrix.

Precoding based on codebook feedbackThe basic principle is as follows: suppose the number of channel overhead bits for feeding back CSI is bps/Hz (B is a positive integer). Then the number of available codewords is N-2^B(ii) a All the quantized values of the precoding matrix form a codebookFN is code word, and the transmitting end and the receiving end jointly store the codebook. For each channel, H is realized, and the receiving end follows a certain criterionTo select an optimal codeword F_NAnd feeding back the code word serial number N corresponding to the code word serial number to the transmitting end. And the transmitting terminal finds out the corresponding code word according to the code word sequence number and carries out precoding on the transmitted data symbol block.

In general terms, the amount of the solvent to be used,the method can be further divided into a plurality of sub-codebooks corresponding to the ranks, and each Rank corresponds to a plurality of values to quantize a precoding matrix formed by the right eigenvector of the channel matrix under the Rank. Since the number of Rank and non-zero right eigenvector of the channel matrix is equal, the codeword with Rank N generally has N columns, so we can use the codebookDividing the codebook into a plurality of subcodebooks according to Rank, as shown in table 1:

TABLE 1

The performance of precoding is best when the CSI can be acquired completely accurately. Due to the limitation of feedback overhead (channel capacity for feedback), only codebook-based CSI feedback and precoding of transmitted data symbols can be employed. In an actual MIMO system, the design of a codebook is very important, and an important objective of codebook design is to ensure that quantization errors are as small as possible, and the codebook is simple to implement, reasonable in overhead, and small in storage.

In addition, considering some specific applications, the codebook design should also satisfy the following characteristics:

1. constant modulus property: in the design of the codebook, the row vectors in each pre-coding code word of the codebook are considered to have constant modulus characteristics, so that the Power distributed on each antenna is equal after pre-coding, the increase of the peak-to-average Power ratio (PAPR) is avoided, and the Power amplification balance among Power Amplifiers (PA) can be realized. Therefore, the fundamental requirement of constant modulus property is that each row of the precoding matrix has the same modulus, and when Rank is 1, the constant modulus property requires that the modulus of each element is equal.

2. Orthogonal property: after SVD decomposition of the channel matrix, the obtained right eigenvectors are always orthogonal. The codebook is designed to match the direction of the right eigenvector of the channel matrix, so the designed codeword should also conform to this characteristic, and in the precoding codeword with Rank > 1, the column vectors should be orthogonal. The orthogonality is an important principle, and no matter how the codebook is designed, the orthogonality is necessarily satisfied, so that the quantization precision of the codebook can be guaranteed.

3. 8PSK characteristics: considering the complexity of implementing precoding processing at the transmitting and receiving ends, it is necessary to limit the value of each element to be selected only from a point corresponding to 8 Phase Shift Keying (PSK), which is called 8PSK characteristic. The codebook is limited to have 8PSK characteristics, that is, before the codebook is normalized, the value of each element can only be selected from the alphabet set of 8 PSK: $\{1,-1,j,-j,\frac{1+j}{\sqrt{2}},\frac{-1+j}{\sqrt{2}},\frac{1-j}{\sqrt{2}},\frac{-1-j}{\sqrt{2}}\}$ to select.

When the codebook is designed, corresponding defects can be caused when any one of the characteristics is not satisfied, and quantization errors are large when the orthogonal characteristic is not satisfied; not meeting the constant modulus characteristic can cause the power imbalance among the PAs of the antenna; the non-satisfaction of the 8PSK characteristic increases the complexity of the precoding at the transmitting end. At this time, it may be considered to increase the value of each element to be 0 in some scenarios, so that the complexity of precoding is not affected.

Currently, the prior art designs of codebooks have the following schemes:

firstly, a codebook based on Household transform is adopted in the 4-antenna (4Tx) codebook design of the existing mainstream standard third Generation partnership project (3 GPP) Long Term Evolution (LTE), and the idea is as follows: select 16 vectors u₀～u₁₅(ii) a The 16 vectors are subjected to Household conversion to obtain a Household matrix W_n(W₀～W₁₅)， $W_n=I-2u_n{u}_n^H/u_n^H{u}_n$ (n is 0 to 15); from W_nAll or part of the columns are extracted to form a codebook under each Rank

When the 4Tx codebook is designed, the method can well ensure the orthogonal characteristic, the constant modulus characteristic and the 8PSK characteristic by selecting the u vector, and has the advantages of less memory and good performance. However, in the 8Tx codebook design, the method cannot satisfy the constant modulus characteristic, and the power amplifiers between the antennas are unbalanced, so the method cannot be well applied to the 8Tx codebook design.

Secondly, the performance is better under the relevant channel and is poorer under the non-relevant channel based on the codebook design idea of other transformations, such as the codebook design based on Discrete Fourier Transform (DFT); in 8Tx codebook design, the DFT transform based codebook still has the disadvantage of better performance under correlated channels under single polarized antennas, but worse performance under correlated channels under dual polarized antennas and uncorrelated channels under single and dual polarized antennas, and does not meet 8PSK characteristics.

At present, no scheme in the prior art can ensure that the orthogonal characteristic, the constant modulus characteristic and the 8PSK characteristic can be met when a codebook is designed, and the better performance can be met under both relevant channels and non-relevant channels.

Disclosure of Invention

In view of the above, the main objective of the present invention is to provide a method and an apparatus for constructing a precoding codebook of a MIMO system, so that the designed codebook can satisfy the orthogonal characteristic, the constant modulus characteristic, and the 8PSK characteristic, and also satisfy the requirement of having better performance in both the correlated channel and the uncorrelated channel.

In order to achieve the purpose, the technical scheme of the invention is realized as follows:

the invention provides a precoding codebook construction method of a multi-input multi-output system, which comprises the following steps:

selecting N4 x 4 first orthogonal matrixes U_nAnd N second orthogonal matrices K are selected_n；

According to the selected U_nAnd K_nN8 x 8 matrices M are constructed by or similar to the Kronecker product_n；

Slave matrix M_nOne or more columns are selected to generate partial code words in the sub-codebook of each Rank under 8 antennas.

Wherein N is less than or equal to 2^BB is the channel overhead bit number of the feedback channel information CSI and is a positive integer;

the N U_nFrom orthogonal matrix W_nSelecting; the above-mentioned $W_n=I-2u_n{u}_n^H/u_n^H{u}_n,$ u_nIs a vector, including u₀～u₁₅。

The method further comprises the following steps: the N U_nThe orthogonal matrix comprises k orthogonal matrixes adaptive to related channels, and is arranged as O according to the size sequence of an index number n₁，O₂......O_kAnd O is₁，O₂......O_kFrom the W_nW of (2)₀～W₇Wherein k is less than or equal to N.

Said O is₁，O₂......O_kFrom W₀～W₇The method specifically comprises the following steps:

when the direction vectors need to be uniformly distributed within 120 degrees, O₁，O₂......O_kFrom W₀～W₃Selecting;

or, when the direction vectors need to be uniformly distributed within 180 degrees, O₁，O₂......O_kFrom W₄～W₇Selecting;

or, O₁，O₂......O_kComprising W₀～W₇；

The direction vector is O₁，O₂......O_kThe first column of the vector.

The N number of K_nIs a 2 × 2 orthogonal matrix, or a 4 × 4 orthogonal matrix;

K_nin the case of a 2 × 2 orthogonal matrix, the corresponding Kronecker product mode specifically includes:or

K_nIn the case of a 4 × 4 orthogonal matrix, the corresponding Kronecker product-like manner is specifically: $\left[\begin{array}{cc}{a}_n{U}_n& c_n{K}_n\\ b_n{U}_n& d_n{K}_n\end{array}\right],$ or $\left[\begin{array}{cc}{a}_n{K}_n& c_n{U}_n\\ b_n{K}_n& {\text{d}}_n{U}_n\end{array}\right],$ Or $\left[\begin{array}{cc}{a}_n{K}_n& c_n{K}_n\\ b_n{U}_n& d_n{U}_n\end{array}\right],$ Or $\left[\begin{array}{cc}{a}_n{U}_n& c_n{U}_n\\ b_n{K}_n& d_n{K}_n\end{array}\right],$ The above-mentioned $\left(\begin{array}{cc}{a}_n& c_n\\ b_n& d_n\end{array}\right)$ Is an orthogonal matrix, a_n、b_n、c_n、d_nIs 8PSK alphabet set $\{1,-1,j,-j,\frac{1+j}{\sqrt{2}},\frac{-1+j}{\sqrt{2}},\frac{1-j}{\sqrt{2}},\frac{-1-j}{\sqrt{2}}\}$ Of (a) or_n、d_nAt the same time, 0, or b_n、c_nAnd is also 0.

When the value of N is larger than a preset threshold value, K_nThe matrix for the non-correlated channel matching includes both a 2 × 2 orthogonal matrix and a 4 × 4 orthogonal matrix.

If K is_nIs a 4 × 4 orthogonal matrix, K_nFrom W₀～W₁₅Selecting the following specific components:

if it is desired to generate a codeword suitable for the associated channel, K_nFrom W₀～W₇Selecting;

if it is desired to generate a codeword suitable for an uncorrelated channel, K_nFrom W₈～W₁₅Selecting.

Said K_nIn the case of a 2 × 2 orthogonal matrix, the method further includes: the 2 × 2 orthogonal matrix is selected from the following eight mathematical model matrices:

$K_n=\left[\begin{array}{cc}{w}_1& w_1\\ w_2& -w_2\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_2& -w_2\\ w_1& w_1\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_1& w_2\\ w_1& -w_2\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_2& w_1\\ {-w}_2& w_1\end{array}\right],$

$K_n=\left[\begin{array}{cc}{w}_3& {w_4}^{*}\\ -w_4& {w_3}^{*}\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_3& {w_4}^{*}\\ w_4& -{w_3}^{*}\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_3& 0\\ 0& w_4\end{array}\right],$ $K_n=\left[\begin{array}{cc}0& w_3\\ w_4& 0\end{array}\right];$

wherein, w₁，w₂Is 8PSK alphabet set $\{1,-1,j,-j,\frac{1+j}{\sqrt{2}},\frac{-1+j}{\sqrt{2}},\frac{1-j}{\sqrt{2}},\frac{-1-j}{\sqrt{2}}\}$ Element of (5), w₃，w₄Are elements in a 4PSK alphabet {1, -1, j, -j }.

The method further comprises the following steps: the 2 x 2 orthogonal matrix is selected from the expansion of the eight mathematical model matrices;

the expansion of the eight mathematical models specifically comprises the following steps: multiplying each column of the matrix by an element in the same or a different 8PSK alphabet set; or multiplying each row of the matrix by an element in the same or a different 8PSK alphabet set; or multiplying the matrix by a constant.

When generating the code words in the sub-codebook of each Rank under 8 antennas, the method further includes: from matrix M, according to the nested property_nOne or more columns are selected to generate partial code words in the sub-codebook of each Rank under 8 antennas.

The invention also provides a precoding codebook construction device of the multi-input multi-output system, which comprises the following steps: a matrix selecting module, a matrix generating module and a codebook generating module, wherein,

the matrix selection module is used for selecting N4 multiplied by 4 first orthogonal matrixes U_nAnd N second orthogonal matrices K_nAnd will select U_nAnd K_nProviding to the matrix generation module;

the matrix generation module is used for generating a matrix according to the selected U_nAnd K_nN8 x 8 matrices M are generated by means of or similar to the Kronecker product_n；

The codebook generating module is used for generating a matrix M_nAnd selecting 1 or more columns to generate code words in the sub-codebook of each Rank under 8 antennas.

The matrix selection module is further configured to select the matrix from orthogonalMatrix W_nIn which N U's are selected_nAnd is and $W_n=I-2u_n{u}_n^H/u_n^H{u}_n,$ u_nis a vector, n is 0-15;

the W is_nThe 8-phase shift keying PSK characteristic, the constant modulus characteristic and the quadrature characteristic are satisfied.

Said K_nIn the case of a 4 x 4 matrix, the matrix selection module is further adapted to select from W_nW of (2)₀～W₁₅In the selection of K_n

Said K_nIn the case of a 2 × 2 matrix, the matrix selection module is further configured to select K from the following eight mathematical model matrices_n： $K_n=\left[\begin{array}{cc}{w}_1& w_1\\ w_2& -w_2\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_2& -w_2\\ w_1& w_1\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_1& w_2\\ w_1& -w_2\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_2& w_1\\ {-w}_2& w_1\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_3& {w_4}^{*}\\ -w_4& {w_3}^{*}\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_3& {w_4}^{*}\\ w_4& -{w_3}^{*}\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_3& 0\\ 0& w_4\end{array}\right],$ $K_n=\left[\begin{array}{cc}0& w_3\\ w_4& 0\end{array}\right];$

Wherein, w₁，w₂Is 8PSK alphabet set $\{1,-1,j,-j,\frac{1+j}{\sqrt{2}},\frac{-1+j}{\sqrt{2}},\frac{1-j}{\sqrt{2}},\frac{-1-j}{\sqrt{2}}\}$ Element of (5), w₃，w₄Are elements in a 4PSK alphabet {1, -1, j, -j }.

The precoding codebook construction scheme based on the MIMO system provided by the invention is based on the orthogonal matrix such as the Household matrix which satisfies the orthogonal characteristic, the constant modulus characteristic and the 8PSK characteristic $W_n=I-2u_n{u}_n^H/u_n^H{u}_n$ Selecting a first orthogonal matrix and a second orthogonal matrix, and providing eight mathematical model matrixes for selecting the second orthogonal matrix; and generating the required matrix M by a Kronecker product or a similar Kronecker product mode based on the selected first orthogonal matrix and the second orthogonal matrix_nFinally from M_nSelecting 1 or more columns to form code words in the sub-codebooks of the ranks; due to the fact that $W_n=I-2u_n{u}_n^H/u_n^H{u}_n$ The matrix M meets the requirements of orthogonal property, constant modulus property and 8PSK property, and the first orthogonal matrix and the second orthogonal matrix are expanded by a Kronecker product or a similar Kronecker product mode, so that the matrix M obtained by the method_nThe orthogonality characteristic, the constant modulus characteristic, and the 8PSK characteristic are also satisfied.

In addition, when the first orthogonal matrix and the second orthogonal matrix are selected, the first orthogonal matrix and the second orthogonal matrix may be selected as needed $W_n=I-2u_n{u}_n^H/u_n^H{u}_n$ Selecting a matrix matched with a relevant channel or a non-relevant channel from the orthogonal matrixes, so that the method has better performance aiming at the relevant channel and the non-relevant channel; the codebook constructed by the invention meets the nesting characteristic, has good compatibility compared with the subsequent standard of LTE, can effectively utilize the existing storage capacity of LTE, can construct the codebook with more code words by increasing a small amount of storage, and has small calculation amount of the construction method.

Drawings

FIG. 1 is a flowchart of a precoding codebook construction method of a MIMO system according to the present invention;

fig. 2 is a schematic diagram of a structure of a precoding codebook constructing apparatus of a MIMO system according to the present invention.

Detailed Description

The technical solution of the present invention is further elaborated below with reference to the drawings and the specific embodiments.

The invention constructs an 8Tx codebook by using a Kronecker product or a similar Kronecker product, and the flow of the method is shown as figure 1 and comprises the following steps:

step 101, selecting N4 × 4 first orthogonal matrixes U_n(U₀，U₁......U_N-1)。

102, selecting N second orthogonal matrixes K_n(K₀，K₁......K_N-1)。

Step 103, according to the selected U_nAnd K_nN8 x 8 matrices M are generated by means of or similar to the Kronecker product_n。

Step 104, slave matrix M_nOne or more columns are selected to generate code words in the sub-codebook of each Rank under 8 antennas.

The flow shown in FIG. 1 is described in detail below:

step 101: selecting N4 x 4 first orthogonal matrixes U_n(U₀，U₁......U_N-1)。

In the step, N is less than or equal to 2^BWherein, B is a positive integer, which means the number of channel overhead bits (bits) for feeding back CSI, and U can be set according to the requirement_nThe index number N is 0 to N-1.

First orthogonal matrix U_n(U₀，U₁......U_N-1) Any one of them can be selected from orthogonal matrix satisfying 8PSK characteristic, orthogonal characteristic and constant modulus characteristic, so as to ensure U_nHas 8PSK characteristic, orthogonal characteristic and constant modulus characteristic. The orthogonal matrix satisfying the 8PSK characteristic, the orthogonal characteristic, and the constant modulus characteristic may be a Household matrix $W_n=I-2u_n{u}_n^H/u_n^H{u}_n,$ Other orthogonal matrices satisfying the above three characteristics are also possible.

$W_n=I-2u_n{u}_n^H/u_n^H{u}_n,$ n is 0 to 15, I is a 4 × 4 identity matrix, u_nIs a vector of 16 in total, including u₀～u₁₅(ii) a The 16 vectors are subjected to Household conversion to obtain a Household matrix W_nAnd 16 in total: w₀～W₁₅。u_nAs shown in table 2:

TABLE 2

W_nThe codebook is a sub-codebook with Rank being 4 in a 4Tx lower precoding codebook in the 3GPP LTE standard, and has a plurality of good characteristics. W in the invention_nCan still better inherit to M in step 103_nSuch as larger minimum chord distance, larger average chord distance, and the presence of uniformly distributed direction vectors in the relevant channelsEqual characteristics can be transferred to M_n。

For a fixed precoding codebook, the generation process of each codeword in the codebook is similar, and all codewords can be divided into two types: codewords that match correlated channels, and codewords that match uncorrelated channels. For the orthogonal matrix U of the invention_n(U₀，U₁......U_N-1) In other words, a part of the matrix is expanded in step 103 to generate a matrix adapted to the correlated channel (and thus a codeword adapted to the correlated channel), and a part of the matrix is expanded in step 103 to generate a matrix adapted to the uncorrelated channel (and thus a codeword adapted to the uncorrelated channel), and these two parts of the matrix form the matrix M in step 103_n(M₀，M₁......M_N-1). It can be seen that U_n(U₀，U₁......U_N-1) The method can comprise an orthogonal matrix adapting to a relevant channel and can also comprise an orthogonal matrix adapting to an irrelevant channel, namely, the performance of the codebook under the relevant channel and the irrelevant channel is ensured. Where the orthogonal matrix matching the associated channel may be selected from W_nW of (2)₀～W₇Selecting; the orthogonal matrix matching the uncorrelated channels may be from W_nW of (2)₈～W₁₅Selecting.

Suppose U_n(U₀，U₁......U_N-1) Includes k orthogonal matrices adapted to the associated channels, k being a constant (k ≦ N), preferably k being 1/2 or 1/4 of N. Arranging the k orthogonal matrixes according to the size sequence of the index numbers, and marking the k orthogonal matrixes as O₁，O₂......O_k，O_kIs a 4 x 4 orthogonal matrix and adapts to the correlation channel, which can be selected from W₀～W₇Is selected from, in particular, O as required₁，O₂......O_kThe following method can be used for selection:

one is that when the direction vectors are required to be uniformly distributed within 120 degrees, O is₁，O₂......O_kCan be selected from W₀～W₃In this way, it is adapted to the available codesWord (i.e. matrix M generated after expansion in step 103)_n) Less frequently; first, when the direction vectors are required to be uniformly distributed within 180 degrees, O₁，O₂......O_kCan be selected from W₄～W₇This approach is also applicable to the case of fewer available codewords. Both of the above methods can ensure uniform distribution of the direction vectors. In addition, O₁，O₂......O_kMay also contain all of W₀～W₇The code word beam generated by the method has higher direction precision.

1/2 or 1/4 taking k as N, which takes into account the fact that for W_nSome columns of vector information (including vector direction and vector density). In step 103, W may be processed by the methods described herein_nThe four-dimensional direction vector is expanded to 8 dimensions, meanwhile, the vector direction can be kept not to change greatly, the beam can not generate larger side lobe, and the power loss and the interference caused by the beam can be avoided. In practical application, the general cells provide services for the terminal in the direction of 120 degrees or 180 degrees, and based on the method of the invention, W can be ensured_nThe vector direction information of (a) is not lost and is still uniformly distributed in the direction of 120 degrees or 180 degrees. When a codebook with a small number of codewords is designed, W can be reduced_nThe density of the medium direction vectors, but still needs to ensure a uniform distribution of the direction vectors.

Orthogonal matrix O₁，O₂......O_kAfter the first column vector in (1) is precoded, the first column vector has a better beam direction (beam under 4Tx) under a relevant channel, and the better beam characteristic under 4Tx can still be maintained after the expansion in step 103, and a better beam direction under 8Tx can be formed; at the same time due to O₁，O₂......O_kAre matched to the associated channel, the resulting matrix is expanded after step 103 to produce a codeword suitable for the associated channel.

It should be noted that U is selected_nThen, W matching the related channel can be selected₀～W₇Or all of them can be selectedSelecting W matching uncorrelated channels₈～W₁₅It is also possible to select W matching correlated and uncorrelated channels simultaneously₀～W₁₅(ii) a Thereby M from step 103_nThe selected code words may be all adaptive to the correlated channel, or all adaptive to the uncorrelated channel, or may include both adaptive and uncorrelated channels.

102, selecting N second orthogonal matrixes K_n(K₀，K₁......K_N-1)。

In the invention K_n(K₀，K₁......K_N-1) May be a 2 × 2 or 4 × 4 orthogonal matrix, in particular, K_nThe following method can be adopted for selection:

firstly, determining K according to requirements_nIn the case of a 4 × 4 orthogonal matrix, it is preferably selected from W₀～W₁₅Selecting. Further, K is used to generate codewords suitable for uncorrelated channels if needed₀，K₁......K_N-1Can be selected from W₈～W₁₅Selecting; if it is desired to generate code words suitable for the associated channel, it is possible to select from W₀～W₇Selecting.

Due to K of 4X 4_n(K₀，K₁......K_N-1) Is from W_nIs selected so that each K_nThe 8PSK characteristic, the constant modulus characteristic, and the quadrature characteristic are satisfied.

Secondly, determining K according to needs_nIn the case of a 2 × 2 orthogonal matrix, K_nThe matrix has the following characteristics:

if K is_nThere is no zero element, and after each element of the matrix is converted into a complex exponential form, the phase difference between the 1 st element and the 2 nd element of the first column is different from the phase difference between the 1 st element and the 2 nd element of the second column, and this feature may be referred to as a phase difference rule. This enables M generated in step 103_n(M₀，M₁......M_N-1) InThere are more column vectors to match the dual polarized antenna characteristics and to quantify the phase differences that exist in the horizontal and vertical polarization directions of the dual polarized antenna.

Preferably, the phase difference between the 1 st element and the 2 nd element of the first column differs by pi or-pi from the phase difference between the 1 st element and the 2 nd element of the second column.

In determining K_nIn the case of a 2 × 2 orthogonal matrix, the following method may be preferably used: k_nWith neutralization of O₁，O₂......O_kThe k matrices matched are 2 x 2 orthogonal matrices. So-called K_nAnd O₁，O₂......O_kThe matching is as follows: determination of and O_kEqual U_nThe index number of (1) is K which is the same as the index number_nAnd O_kAre matched, e.g. O₁Corresponding to U₅Then K is₅And O₁Are matched.

Determination of K_nIn the case of a 2 × 2 orthogonal matrix, K can be selected as follows_n：K_nThe following six mathematical models can be selected:

$K_n=\left[\begin{array}{cc}{w}_1& w_1\\ w_2& -w_2\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_2& -w_2\\ w_1& w_1\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_1& w_2\\ w_1& -w_2\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_2& w_1\\ {-w}_2& w_1\end{array}\right],$

$K_n=\left[\begin{array}{cc}{w}_3& {w_4}^{*}\\ -w_4& {w_3}^{*}\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_3& {w_4}^{*}\\ w_4& -{w_3}^{*}\end{array}\right].$

wherein w₁，w₂Is a set of 8PSK letters {1, -1, j, -j, s₀，s₁，s₂，s₃The elements in (a) are (b) in (b), $s_0=(1+j)/\sqrt{2},$ $s_1=(1-j)/\sqrt{2},$ $s_2=(-1+j)/\sqrt{2},$ $s_3=-(1+j)/\sqrt{2},$ j is an imaginary number; w is a₃，w₄Are elements in the 4PSK alphabet {1, -1, j, -j }. These six data model matrices conform to the phase difference rules described above.

In addition, considering that in some dual polarization scenarios, such as vertical and horizontal polarization at the transmitting end and vertical and horizontal polarization at the receiving end, from the viewpoint of channel eigenvalue decomposition, the eigenvector always has 0 element, and in order to better match the channel in this case, 0 element should also exist in the codebook, and at this time K is K_nThe performance is very good when the following two models are satisfied.

$K_n=\left[\begin{array}{cc}{w}_3& 0\\ 0& w_4\end{array}\right],$ $K_n=\left[\begin{array}{cc}0& w_3\\ w_4& 0\end{array}\right].$

Based on the two models, part of elements in the matrix (codeword) obtained by the expansion in step 103 satisfy 8PSK characteristics, and the other part of 0 elements that do not satisfy 8PSK characteristics do not increase the complexity of precoding, and can satisfy constant modulus characteristics and orthogonal characteristics.

It is noted that K_nThe method can also be selected from the extensions of the eight mathematical model matrixes, and the specific extensions of the eight data model matrixes are as follows: multiplying each column of the matrix by an element in the same or different 8PSK alphabet set; or multiplying each row of the matrix by an element in the same or different 8PSK alphabet set; or multiplying the matrix by a set constant.

Due to 2X 2K_n(K₀，K₁......K_N-1) Is selected based on 8PSK alphabet set or 4PSK alphabet set, so that 2 x 2K can be ensured_nThe orthogonality characteristic, the 8PSK characteristic and the constant modulus characteristic are satisfied.

It should be noted that if a codeword is to be generated that matches the associated channel, preferably K_nThe matrix of the medium matching correlation channel can be a 2 x 2 matrix; if a codeword is to be generated that matches the uncorrelated channel, K_nThe matrix of the non-correlated channels may comprise a 2 x 2 and/or 4 x 4 matrix; when the value of N is large (preferably, a threshold value may be set as required, and N is larger than the threshold value), and when a codeword matching the uncorrelated channel needs to be generated, preferably, K_nThe matrix of the matched uncorrelated channels comprises both 2 x 2 and 4 x 4 matrices.

The above steps 101 and 102 describe the first orthogonal matrix U respectively_nAnd a second orthogonal matrix K_nThe selection of (1) may be, if the first orthogonal matrix and the second orthogonal matrix include a matrix matching the uncorrelated channel, determined not only according to the selection of the matching uncorrelated matrix of the present invention but also according to other codebook design rules in the prior art; in addition, the selection may be performed in advance in practical applicationK_nThen, U is selected_n. When K is_nWhen the matrix is 2 x 2 and the code word of the related channel needs to be generated, U_nAnd K_nThe following conditions are satisfied: if U is_e＝U_fThen K is_e≠K_f(e, f is less than or equal to N).

Below is combined with U_nDetailed description of the invention K_nSelecting:

i, if U_e＝U_f，U_e、U_fIs O₁，O₂......O_kIs matched to the associated channel, and O₁，O₂......O_kWithout other matrix and U_e、U_fEqual, then K_e≠K_fThus, the expanded matrix M can be ensured_nThere are more column vectors available; in addition, K_e，K_fShould be spatially uniform to ensure that the chordal distance of the matrix expanded in step 103 is large.

At this time, K_e，K_fThe first list of rules that need to be further satisfied is: if K is_e，K_fDoes not contain zero elements, and_e，K_fafter each element of the matrix is converted into a complex exponential form, a phase difference exists between the 1 st element and the 2 nd element in the 1 st column of each matrix, and 2 phase differences of the 2 matrices should be uniformly distributed within 0-2 pi. At the same time K_e，K_fAre also spatially uniformly distributed, such that K_e，K_fThe method can have the best quantization performance under the conditions of a mainstream dual-polarized antenna scene and a related channel.

With respect to K_e，K_fPreferred manner of selection of the first column of (1):

K_e，K_fcolumn 1 of $p*\left[\begin{array}{c}1\\ -1\end{array}\right],p*\left[\begin{array}{c}1\\ 1\end{array}\right]$ Selecting;

or K_e，K_fColumn 1 of $p*\left[\begin{array}{c}1\\ q3\end{array}\right],p*\left[\begin{array}{c}1\\ q1\end{array}\right]$ Selecting;

or K_e，K_fColumn 1 of $p*\left[\begin{array}{c}1\\ q2\end{array}\right],p*\left[\begin{array}{c}1\\ q0\end{array}\right]$ Selecting;

or K_e，K_fColumn 1 of $p*\left[\begin{array}{c}1\\ -j\end{array}\right],p*\left[\begin{array}{c}1\\ j\end{array}\right]$ Selecting.

Where p is a constant, preferably an element in the 8PSK alphabet, where q0 is s 0; q1 ═ s 2; q2 ═ s 3; q3 ═ s 1; it is noted that K_e，K_fIs not equal.

Based on K_e，K_fThe selection of the first column, preferably,

K_e，K_fcan be selected from $\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right],\left[\begin{array}{cc}1& 1\\ -1& 1\end{array}\right]$ Selecting;

or K_e，K_fCan be selected from $\left[\begin{array}{cc}1& j\\ 1& -j\end{array}\right],\left[\begin{array}{cc}1& j\\ -1& j\end{array}\right]$ Selecting;

or K_e，K_fCan be selected from $\left[\begin{array}{cc}1& 1\\ j& -j\end{array}\right],\left[\begin{array}{cc}1& 1\\ -j& j\end{array}\right]$ Selecting;

or K_e，K_fCan be selected from $\left[\begin{array}{cc}1& j\\ j& 1\end{array}\right],\left[\begin{array}{cc}1& -j\\ -j& 1\end{array}\right]$ Selecting;

or K_e，K_fCan be selected from $\left[\begin{array}{cc}1& 1\\ q0& q2\end{array}\right],\left[\begin{array}{cc}1& 1\\ q2& q0\end{array}\right]$ Selecting;

or K_e，K_fCan be selected from $\left[\begin{array}{cc}1& q3\\ q0& 1\end{array}\right],\left[\begin{array}{cc}1& q1\\ q2& 1\end{array}\right]$ Selecting;

or K_e，K_fCan be selected from $\left[\begin{array}{cc}1& 1\\ q1& q3\end{array}\right],\left[\begin{array}{cc}1& 1\\ q3& q1\end{array}\right]$ Selecting;

or K_e，K_fCan be selected from $\left[\begin{array}{cc}1& q0\\ q3& 1\end{array}\right],\left[\begin{array}{cc}1& q2\\ q1& 1\end{array}\right]$ Selecting.

It should be noted that as long as K is guaranteed_e，K_fSatisfies the selection rule of the first column and conforms to the first six models, K, of the eight mathematical models_e，K_fAny selection from the above matrix is possible, and the combinations are not limited to the above two combinations. And due to K_e，K_fIs based on the phase difference and therefore can multiply any column of the matrix by a constant p, with the same effect as the matrix.

Based on the above K_e，K_fThe selection of (3) can ensure that the generated code word matches the related channel, and can also be applied to the generation of the code word under the non-related channel, and the minimum chordal distance between every two matrixes generated in the step 103 can be well controlled to be maximized, so that the performance of the code word under the non-related channel is ensured. It should be noted that when applied to the generation of codewords in uncorrelated channels, or K_nIn a 4 × 4 matrix, U_nAnd K_nThe above is not necessarily satisfied: u shape_e＝U_fThen K is_e≠K_fThe conditions of (1).

II, if U_e＝U_f＝U_g＝U_h，U_e、U_f、U_g、U_hIs O₁，O₂......O_kIs matched to the associated channel, and O₁，O₂......O_kWithout other matrix and U_e、U_f、U_g、U_hEqual, then K_e≠K_f≠K_g≠K_hTherefore, more available column vectors of the expanded matrix can be ensured, and the minimum chord distance of the matrix can be ensured not to be 0. In addition K_e、K_f、K_g、K_hShould be distributed evenly in space to ensure that the minimum chord distance and the average chord of the matrix expanded in step 103 are large. If U is present_e、U_f、U_g、U_hAll belong to O₁，O₂......O_kThen U is_e、U_f、U_g、U_hAre matched to the associated channel.

At this time, K_e、K_f、K_g、K_hThe first list of rules that need to be further satisfied is: will K_e、K_f、K_g、K_hAfter each element of the matrix is converted into a complex exponential form, a phase difference exists between the 1 st element and the 2 nd element of the 1 st column of each matrix, and 4 phase differences of the 4 matrices should be uniformly distributed in space. Therefore, the phase difference of the two polarization directions can be uniformly distributed and optimally quantized, and the dual-polarization antenna has better performance under the relevant channels of the dual-polarization antenna scene.

With respect to K_e、K_f、K_g、K_hSelection of the first column:

K_e、K_f、K_g、K_hthe first column of (A) can be from $\left[\begin{array}{c}1\\ -1\end{array}\right],\left[\begin{array}{c}1\\ 1\end{array}\right],\left[\begin{array}{c}1\\ -j\end{array}\right],\left[\begin{array}{c}1\\ j\end{array}\right]$ Selecting;

or K_e、K_f、K_g、K_hThe first column of (A) can be from $\left[\begin{array}{c}1\\ s_0\end{array}\right],\left[\begin{array}{c}1\\ s_1\end{array}\right],\left[\begin{array}{c}1\\ s_2\end{array}\right],\left[\begin{array}{c}1\\ s_3\end{array}\right]$ Selecting.

According to K_e、K_f、K_g、K_hThe principle of uniform distribution of the phase difference of the 1 st column of (1), preferably, K_e、K_f、K_g、K_hColumn 1 of $\left[\begin{array}{c}1\\ -1\end{array}\right],\left[\begin{array}{c}1\\ 1\end{array}\right],\left[\begin{array}{c}1\\ -j\end{array}\right],\left[\begin{array}{c}1\\ j\end{array}\right]$ Is selected from, and K_e、K_f、K_g、K_hAre each unequal. The selection mode can better adapt to the characteristics of the related channels under the single-polarized antenna, and some vectors in the matrix expanded in the way are in the related channels of the single-polarized antenna model, so that the beam directivity generated after precoding is obvious, and the distribution in space is uniform.

Based on K_e、K_f、K_g、K_hThe selection of the first column, preferably,

K_e、K_f、K_g、K_hfrom $\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right],\left[\begin{array}{cc}1& 1\\ -1& 1\end{array}\right],\left[\begin{array}{cc}1& -1\\ j& j\end{array}\right],\left[\begin{array}{cc}1& -1\\ -j& -j\end{array}\right]$ Selecting;

or K_e、K_f、K_g、K_hFrom $\left[\begin{array}{cc}1& -1\\ 1& 1\end{array}\right],\left[\begin{array}{cc}1& -1\\ -1& -1\end{array}\right],\left[\begin{array}{cc}1& 1\\ j& -j\end{array}\right],\left[\begin{array}{cc}1& 1\\ -j& j\end{array}\right]$ Selecting;

or K_e、K_f、K_g、K_hFrom $\left[\begin{array}{cc}1& j\\ 1& -j\end{array}\right],\left[\begin{array}{cc}1& -j\\ -1& -j\end{array}\right],\left[\begin{array}{cc}1& -1\\ j& j\end{array}\right],\left[\begin{array}{cc}1& 1\\ -j& j\end{array}\right]$ Selecting;

or K_e、K_f、K_g、K_hFrom $\left[\begin{array}{cc}1& -j\\ 1& j\end{array}\right],\left[\begin{array}{cc}1& j\\ -1& j\end{array}\right],\left[\begin{array}{cc}1& 1\\ j& -j\end{array}\right],\left[\begin{array}{cc}1& -1\\ -j& -j\end{array}\right]$ Selecting;

or K_e、K_f、K_g、K_hFrom $\left[\begin{array}{cc}1& j\\ 1& -j\end{array}\right],\left[\begin{array}{cc}1& j\\ -1& j\end{array}\right],\left[\begin{array}{cc}1& 1\\ j& -j\end{array}\right],\left[\begin{array}{cc}1& 1\\ -j& j\end{array}\right]$ Selecting;

or K_e、K_f、K_g、K_hFrom $\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right],\left[\begin{array}{cc}1& 1\\ -1& 1\end{array}\right],\left[\begin{array}{cc}1& 1\\ j& -j\end{array}\right],\left[\begin{array}{cc}1& 1\\ -j& j\end{array}\right]$ Selecting.

It should be noted that as long as K is guaranteed_e、K_f、K_g、K_hSatisfies the selection rule of the first column and conforms to the 6 mathematical models, K_e、K_f、K_g、K_hIt can be arbitrarily selected from the above-mentioned matrices, and is not limited to the combination of the above-described 4 matrices.

Above K_e、K_f、K_g、K_hThe selection of the matrix takes into account the most uniform distribution of the 4 matrixes in the direction vector and the phase difference of the dual-polarized antenna, and can ensure that the M generated in the step 103₀，M₁......M_N-1The column vector of (2) can still have obvious directivity when the antenna is single-polarized, and can ensure that the direction vectors are uniformly distributed in the directions of 120 degrees and 180 degrees. Thus, the dual-polarized antenna can be adapted to the application of the dual-polarized antennaThe method can adapt to the application scene of the single-polarized antenna. And the minimum chord distance between the matrixes is larger, and the code words obtained by the matrix expansion can be ensured to be matched with the uncorrelated channels. It should be noted that the codeword matching the correlated channel can also be used for the uncorrelated channel as long as the chordal distance of the matrix is not 0.

Step 103, according to the selected U_nAnd K_nN8 x 8 matrices M are constructed by or similar to the Kronecker product_nMatrix M_n。

Based on U selected in the above steps_n、K_nIf K is_nFor a 2 × 2 matrix, the Kronecker product is used:orM of construction 8X 8_n(M₀，M₁......M_N-1) (ii) a If K is_nFor a 4 x 4 matrix, a similar manner to the Kronecker product is used $\left[\begin{array}{cc}{a}_n{U}_n& c_n{K}_n\\ b_n{U}_n& d_n{K}_n\end{array}\right],$ Or $\left[\begin{array}{cc}{a}_n{K}_n& c_n{U}_n\\ b_n{K}_n& d_n{U}_n\end{array}\right],$ Or $\left[\begin{array}{cc}{a}_n{K}_n& c_n{K}_n\\ b_n{U}_n& d_n{U}_n\end{array}\right],$ Or $\left[\begin{array}{cc}{a}_n{U}_n& c_n{U}_n\\ b_n{K}_n& d_n{K}_n\end{array}\right]$ M of construction 8X 8_n(M₀，M₁......M_N-1). Wherein, $\left(\begin{array}{cc}{a}_n& c_n\\ b_n& d_n\end{array}\right)$ is an orthogonal matrix, a_n、b_n、c_n、d_nMay be an element in the 8PSK alphabet set。

Is provided with $A_n=\left(\begin{array}{cc}{a}_n& c_n\\ b_n& d_n\end{array}\right),$ Then A is_nCan be selected from K_nThe first six models of (1) are arbitrarily selected.

Similarly, considering that in some dual polarization scenarios, such as vertical and horizontal polarization at the transmitting end, and vertical and horizontal polarization at the receiving end, there are always 0 elements in the eigenvector from the viewpoint of channel eigenvalue decomposition, and in order to better match the channel in this case, there should also be 0 elements in the codebook. At this time, a_n、b_n、c_n、d_nMay be an element of 0, a_n、d_nAt the same time, 0, or b_n、c_nAt the same time, is 0, but a_n、b_n、c_n、d_nNot simultaneously 0, at this time A_nCan be selected from K_nThe latter two models of (1) are arbitrarily chosen.

a_n、d_nAt the same time, 0, or b_n、c_nWhile being 0, the resulting 8 x 8 matrix M_nAnd a part of elements in the precoding matrix satisfy 8PSK characteristics, and the other part of 0 elements which do not satisfy 8PSK characteristics do not increase the complexity of precoding and can satisfy constant modulus characteristics and orthogonal characteristics.

It is to be noted that A_nOr can be selected from the extensions of the eight models, and the specific extensions of the eight models are as same as K_nThe extension of the eight models is not described herein.

Step 104: from M_nOne or more columns are extracted to form partial code words in the sub-codebook of each Rank under 8 Tx.

Preferably, from M_nWhen one or more columns of partial code words in the sub-codebook forming each Rank are extracted, the nesting characteristic needs to be satisfied, so that the storage capacity can be reduced, the Channel Quality Indicator (CQI) calculation amount can be reduced, and Rank adaptive change can be supported. Other codewords in the sub-codebook of Rank can be determined according to the codebook design method in the prior art.

The nested characteristic means that, for code words of the same index number under different ranks, a low-Rank code word is formed by extracting several columns from a high-Rank code word. The nesting characteristic can reduce the memory space of a transmitting end and a receiving end, the Rank is automatically changed frequently in practical application, the self-adaption of the Rank can be easier by meeting the nesting characteristic, and the complexity of CQI calculation can be reduced; in addition, at the UE end, the codebook stored therein only needs to acquire the codebook corresponding to the highest Rank, and other ranks only need to be extracted from the codebooks corresponding to the highest Rank, so that the storage overhead of the UE is saved.

The scheme of the invention is illustrated by the following specific examples:

example 1, N-16 was determined as needed.

1，U_nAnd (4) selecting.

If a matrix M is required to match the associated channels_nThe first 8 of (A), M₀，M₁......M₇Then, M can be determined₀，M₁......M₇From O₁，O₂......O_kGenerating, preferably, k is 8, O₁，O₂......O_kMay be U₀，U₁......U₇(ii) a Suppose U₈，U₉......U₁₅For matching the matrix of the uncorrelated channel, the selection method of the matrix of the matched uncorrelated channel in the first orthogonal matrix of the present invention may be adopted, or other codebook design rules in the prior art may be adopted to determine the matrix. It is to be noted that O₁，O₂......O_kCorresponding U_nOr may be discontinuous (index number discontinuous). Examples of the invention are represented by O₁，O₂......O_kIs U₀，U₁......U₇For example.

O₁，O₂......O_k(U₀，U₁......U₇) Is matched to the associated channel, i.e. from W₀，W₁......W₇Of selected, different O_kThe same W can be selected_n. If the number of the currently available code words is less and the quantization is more fine in the phase difference dimension of the dual-polarized antenna, less direction vectors should be used in the direction dimension, and further, when the direction vectors need to be uniformly distributed in the 120-degree direction, O₁，O₂......O_kCan be all selected from W₀，W₁......W₃Selecting; when it is necessary to ensure that the direction vectors are uniformly distributed in the 180-degree direction, O₁，O₂......O_kCan be all selected from W₄，W₅......W₇Selecting. From this, W₀，W₁......W₃Or W₄，W₅......W₇Wherein each matrix is at O₁，O₂......O_kWhich are equal to 2 matrices. This ensures that the beam directions are uniform over 120 degrees or 180 degrees and there are 2 identical basis matrices in each direction.

Preferably, U_nThe selection of the matrix for the matched correlation channel is shown in tables 3 and 4:

TABLE 3

TABLE 4

Preferably, U_nThe selection of the matrix for the non-correlated channel is shown in table 5:

TABLE 5

2，K_nAnd (4) selecting.

Suppose U₀，U₁......U₇Middle U₀＝U₁，U₂＝U₃，U₄＝U₅，U₆＝U₇Then K can be determined₀≠K₁，K₂≠K₃，K₄≠K₅，K₆≠K₇(ii) a Preferably, according to K described in step 102_nSelection rule, K₀～K₇The selection of (a) is shown in table 6:

TABLE 6

Preferably, K₈～K₁₅The selection of (b) is shown in table 7:

TABLE 7

Therefore, the minimum chord distance and the average chord distance between the N code words can be ensured to be larger, and the performance is better under the non-relevant channel.

3, generating M_n。

If K is_nIs a 2 × 2 matrix, and is selectedThen

<math> <mrow> <msub> <mi>M</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>K</mi> <mn>0</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mn>0</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>&CircleTimes;</mo> <msub> <mi>W</mi> <mn>0</mn> </msub> <mo>;</mo> </mrow> </math> <math> <mrow> <msub> <mi>M</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mn>1</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>&CircleTimes;</mo> <msub> <mi>W</mi> <mn>0</mn> </msub> <mo>;</mo> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mn>2</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mi>j</mi> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <mi>j</mi> </mtd> </mtr> </mtable> </mfenced> <mo>&CircleTimes;</mo> <msub> <mi>W</mi> <mn>1</mn> </msub> <mo>;</mo> </mrow> </math> <math> <mrow> <msub> <mi>M</mi> <mn>3</mn> </msub> <mo>=</mo> <msub> <mi>K</mi> <mn>3</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mn>3</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mi>j</mi> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mn>1</mn> </mtd> <mtd> <mi>j</mi> </mtd> </mtr> </mtable> </mfenced> <mo>&CircleTimes;</mo> <msub> <mi>W</mi> <mn>1</mn> </msub> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>K</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mi>j</mi> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mn>1</mn> </mtd> <mtd> <mi>j</mi> </mtd> </mtr> </mtable> </mfenced> <mo>&CircleTimes;</mo> <msub> <mi>W</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>.</mo> </mrow> </math>

And 4, generating a code word.

From M_nOne or more columns are selected to form a part of code words under each Rank:

from M₀，M₁......M_N-1The 1 st column is selected as the part code word of Rank 1

From M₀，M₁......M_N-1The 1 st and 5 th columns are selected as the partial code words of Rank 2

From M₀，M₁......M_N-1The 1 st, 2 nd and 5 th columns are selected as the partial code words of Rank 3

From M₀，M₁......M_N-1The partial code words with the 1 st, 2 nd, 5 th and 6 th columns as Rank 4 are selected from the code words

From M₀，M₁......M_N-1The 1 st, 2 nd, 3rd, 5 th and 6 th columns are selected as the partial code words with Rank being 5

From M₀，M₁......M_N-1The 1 st, 2 nd, 3rd, 5 th, 6 th and 7 th columns are selected as the partial code words of Rank 6

From M₀，M₁......M_N-1The 1 st, 2 nd, 3rd, 4 th, 5 th, 6 th and 7 th columns are selected as the partial code words with Rank equal to 7

From M₀，M₁......M_N-1The 1 st, 2 nd, 3rd, 4 th, 5 th, 6 th, 7 th and 8 th columns are selected as the partial code words of Rank 8.

The generated code word conforms to the nesting characteristic. It should be noted that the partial code word with Rank 1 needs to select M₀，M₁......M_N-1Column 1 of (1); the partial codeword of Rank 2 requires M₀，M₁......M_N-11, 5 columns of (a); the selection of the partial code words of Rank 3, 4, 5, 6, 7, and 8 is determined as needed, and is not limited to the selection listed in this embodiment.

Example 2, N-32 was determined as needed.

1，U_nAnd (4) selecting.

If a matrix M is required to match the associated channels_nThe first 16 of (A), M₀，M₁......M₁₅Then, M can be determined₀，M₁......M₁₅From O₁，O₂......O_kGenerating, preferably, k is 16, O₁，O₂......O_kMay be U₀，U₁......U₁₅(ii) a Suppose U₁₆，U₁₇......U₃₁For matching the matrix of the uncorrelated channels, the method for selecting the matrix of the matched uncorrelated channels in the first orthogonal matrix of the present invention may be used, or other codebook design rules in the prior art may be usedThen it is determined. It is to be noted that O₁，O₂......O_kCorresponding U_nOr may be discontinuous (index number discontinuous).

O₁，O₂......O_k(U₀，U₁......U₁₅) Is matched to the associated channel, i.e. from W₀，W₁......W₇Of selected, different O_kThe same W can be selected_n. If the number of the currently available code words is considered to be less and the quantization needs to be finer in the phase difference dimension of the dual-polarized antenna, fewer direction vectors should be used in the direction dimension, and further, when the direction vectors need to be ensured to be uniformly distributed in the 120-degree direction, O₁，O₂......O_kCan be all selected from W₀，W₁......W₃Selecting; when it is necessary to ensure that the direction vectors are uniformly distributed in the 180-degree direction, O₁，O₂......O_kCan be all selected from W₄，W₅......W₇Selecting. From this, W₀，W₁......W₃Or W₄，W₅......W₇Wherein each matrix is at O₁，O₂......O_kThere are 4 matrices equal to it. This ensures that the beam directions are uniform over 120 degrees or 180 degrees and there are 4 identical basis matrices in each direction.

Preferably, U_nMatrix U of medium-matched correlated channels₀～U₁₅Table 8 table 9 shows the selection of: let m be 0-3

TABLE 8

TABLE 9

Preferably, U_nMatrix U for intermediate matched uncorrelated channels₁₆～U₃₁The selection of (a) is shown in table 10: setting m to be 8-15

Watch 10

2，K_nAnd (4) selecting.

Suppose U₀，U₁......U₁₅Middle U_4m＝U_4m+1＝U_4m+2＝U_4m+3Then K can be determined_4m≠K_4m+1≠K_4m+2≠K_4m+3M is 0 to 3; preferably, according to K described in step 102_nSelection rule, K₀～K₁₅The selection of (a) is shown in table 11:

TABLE 11

K₁₆～K₃₁The determination of (c) may be based on the selection of the matrix matching the uncorrelated channels in the second orthogonal matrix in the present invention, or may be based on other codebook design methods in the prior art.

3, generating M_n。

If K is_nIs a 2 × 2 matrix, and is selectedThen

<math> <mrow> <msub> <mi>M</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mn>0</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>W</mi> <mn>0</mn> </msub> <mo>&CircleTimes;</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow> </math> <math> <mrow> <msub> <mi>M</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mn>1</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>W</mi> <mn>0</mn> </msub> <mo>&CircleTimes;</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mn>2</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>W</mi> <mn>1</mn> </msub> <mo>&CircleTimes;</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mi>j</mi> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <mi>j</mi> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow> </math> <math> <mrow> <msub> <mi>M</mi> <mn>3</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mn>3</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mn>3</mn> </msub> <mo>=</mo> <msub> <mi>W</mi> <mn>1</mn> </msub> <mo>&CircleTimes;</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mi>j</mi> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mn>1</mn> </mtd> <mtd> <mi>j</mi> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>U</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>W</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&CircleTimes;</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mi>j</mi> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mn>1</mn> </mtd> <mtd> <mi>j</mi> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow> </math>

And 4, generating a code word.

The codeword structure of embodiment 1 may be adopted, and will not be described herein again.

Example 3, N-16 or 32 was determined as needed.

If the matrix in which the associated channels are matched is M_nAll 16 of them (N ═ 16), or the first 16 (N ═ 32), i.e., M₀，M₁......M₁₅When k is 16, M₀，M₁......M₁₅From O₁，O₂......O_kGenerating, i.e. U₀，U₁......U₁₅Other U values are determined by other codebook design methods known in the art. Of course, if the matrix matching the associated channels is not so regularly distributed, O₁，O₂......O_kAt U_nMay also be discontinuous.

O₁，O₂......O_k(U₀，U₁......U₇) The matrix in (1) is from W₀，W₁......W₇Of selected, different O_kThe same W can be selected_n. To ensure uniform distribution in the 120 or 180 degree direction, W₀，W₁......W₇Wherein each matrix is at O₁，O₂......O_kWhich are equal to 2 matrices.

Preferably, U₀～U₁₅The choices of (2) are shown in table 12: m is 0 to 7

TABLE 12

Preferably, U₁₆～U₃₁The choices of (2) are shown in table 13: m is 8 to 15

Watch 13

Preferably, K_nThe selection of (2) is as follows:

wherein K_2m≠K_2m+1，m＝0，1，2，3......7

Of course, the selection can be made

Or

Or

It should be noted that here K_2mAnd K_2m+1The selection of (2) is not limited to all being selected from the same set of matrices, and when m ═ r, it is also possible to select:

when m is 1, the following can be selected:

M_nthe generation is the same as in embodiment 1 described above and will not be described again here.

From M_nOne or more columns are selected to form a part of code words under each Rank: (the following example shows the same selection rule for codewords corresponding to different Index numbers (indexes))

From M₀Selecting the 1 st column as a partial code word with Index of 0 in Rank 1;

from M₁Selecting the 2 nd column as a partial code word with Index being 1 in Rank ═ 1;

from M_N-1Selecting 8 th column as a partial code word with Index of N-1 in Rank ═ 1;

or,

from M₀Selecting the 1 st and 5 th columns as partial code words with Index of 0 in Rank 2;

from M₁Selecting the 5 th and 1 st columns as partial code words with Index being 1 in Rank 2;

from M_N-1Selecting the 2 nd and 6 th columns as the partial code words with Index of N-1 in Rank 2;

or

From M₀Selecting the 1 st, 2 nd and 5 th columns as the partial code words with Index of 0 in Rank 2;

from M₁Selecting the 5 th, 1 th and 6 th columns as the partial code words with Index being 1 in Rank 2;

from M_N-1Selecting the 5 th, 2 nd and 6 th columns as the partial code words with Index N-1 in Rank 2;

or,

other ranks are similar to this, and it is sufficient that the nesting characteristic is maintained for the codewords of different ranks in each Index.

Example 4, N-16 or 32 was determined as needed.

If the matrix matching the associated channel is M₀，M₁......M_N-1All 16 of them (N ═ 16), or the first 16 (N ═ 32), i.e., M₀，M₁......M₁₅Then k is determined to be 16.

Can be given first, K_nThe selection of (2) is as follows:

wherein K_2m≠K_2m+1，m＝0～7。

Then gives the corresponding U_nSelection of (U)₀～U₁₅Selection of (2): m is 0 to 7

TABLE 14

In the case where N is 32, U₁₆～U₃₁Selection of (2): m is 8 to 15

Watch 15

M_nThe generation is the same as in the previously described embodiment and is not described in detail here.

From M_nOne or more columns are selected to form a part of code words under each Rank: the selection is the same as that of embodiment 2, and the description is omitted.

Example 5, N-16 or 32 was determined as needed.

If the matrix matching the associated channel is M₀，M₁......M_N-1All 16 of them (N ═ 16), or the first 16 (N ═ 32), i.e., M₀，M₁......M₁₅Then k is determined to be 16.

Preferably, U₀～U₁₅Selection of (2): m is 0 to 7

TABLE 16

If N is 32, then U is present₁₆～U₃₁Preferably, U₁₆～U₃₁It is possible to select: m is 8 to 15

TABLE 17

Preferably, K_n(K₀～K₁₅) The following were selected:

watch 18

Wherein K_2m≠K_2m+1，m＝0，1，2，3......7

K₁₆～K₃₁The requirements for 8PSK characteristics, orthogonal characteristics and constant modulus characteristics are met; wherein K_2m≠K_2m+1，m＝8～15。

M_nThe generation is the same as in the previously described embodiment and is not described in detail here.

From M_nOne or more columns are selected to form a part of code words under each Rank: the selection is the same as that of embodiment 2, and the description is omitted.

Example 6, N-16 or 32 was determined as needed.

If the matrix matching the associated channel is M₀，M₁......M_N-1All 16 of them (N ═ 16), or the first 16 (N ═ 32), i.e., M₀，M₁......M₁₅Then k is determined to be 16.

Preferably, U₀～U₁₅Selection of (2): m is 0 to 7

Watch 19

If N is 32 then U is present₁₆～U₃₁Preferably, U₁₆～U₃₁It is possible to select: m is 8 to 15

Watch 20

Preferably, K_n(K₀～K₁₅) The selection of (2) is as follows:

TABLE 21

Wherein, K_2m≠K_2m+1，m＝0，1，2，3......7

K₁₆～K₃₁The requirements for 8PSK characteristics, orthogonal characteristics and constant modulus characteristics are met; wherein K_2m≠K_2m+1，m＝8～15。

K_nIn a 2 × 2 matrix, M_nCan mix the choices <math> <mrow> <msub> <mi>M</mi> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi>K</mi> <mi>n</mi> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mi>n</mi> </msub> </mrow> </math> Or <math> <mrow> <msub> <mi>M</mi> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi>U</mi> <mi>n</mi> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mi>n</mi> </msub> <mo>:</mo> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mi>m</mi> </msub> <mo>=</mo> <msub> <mi>K</mi> <mi>m</mi> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mi>m</mi> </msub> <mo>,</mo> </mrow> </math> m＝0，1，2，…15：

<math> <mrow> <msub> <mi>M</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>K</mi> <mn>0</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mn>0</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>&CircleTimes;</mo> <msub> <mi>W</mi> <mn>0</mn> </msub> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mn>1</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>&CircleTimes;</mo> <msub> <mi>W</mi> <mn>0</mn> </msub> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mn>2</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>&CircleTimes;</mo> <msub> <mi>W</mi> <mn>1</mn> </msub> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mn>3</mn> </msub> <mo>=</mo> <msub> <mi>K</mi> <mn>3</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mn>3</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>&CircleTimes;</mo> <msub> <mi>W</mi> <mn>1</mn> </msub> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mi>l</mi> </msub> <mo>=</mo> <msub> <mi>U</mi> <mi>l</mi> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mi>l</mi> </msub> <mo>,</mo> </mrow> </math> l＝16，17，18，…31

<math> <mrow> <msub> <mi>M</mi> <mn>16</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mn>16</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mn>16</mn> </msub> <mo>=</mo> <msub> <mi>W</mi> <mn>8</mn> </msub> <mo>&CircleTimes;</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mn>17</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mn>17</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mn>17</mn> </msub> <mo>=</mo> <msub> <mi>W</mi> <mn>8</mn> </msub> <mo>&CircleTimes;</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mn>18</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mn>18</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mn>18</mn> </msub> <mo>=</mo> <msub> <mi>W</mi> <mn>9</mn> </msub> <mo>&CircleTimes;</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mn>19</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mn>19</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mn>19</mn> </msub> <mo>=</mo> <msub> <mi>W</mi> <mn>19</mn> </msub> <mo>&CircleTimes;</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>

From M_nOne or more columns are selected to form a part of code words under each Rank: the selection is the same as that of embodiment 2, and the description is omitted.

Example 7, N-16 or 32 was determined as needed.

U_nAnd K_nThe selection of (A) is the same as that of embodiment 6, and the description thereof is omitted.

K_nWhen the matrix includes both 4 × 4 and 2 × 2, M_nThe configuration of (A) can be selected from:orOr $\left[\begin{array}{cc}{a}_n{U}_n& c_n{K}_n\\ b_n{U}_n& d_n{K}_n\end{array}\right],$ Or $\left[\begin{array}{cc}{a}_n{K}_n& c_n{U}_n\\ b_n{K}_n& d_n{U}_n\end{array}\right],$ Or $\left[\begin{array}{cc}{a}_n{K}_n& c_n{K}_n\\ b_n{U}_n& d_n{U}_n\end{array}\right],$ Or $\left[\begin{array}{cc}{a}_n{U}_n& c_n{U}_n\\ b_n{K}_n& d_n{K}_n\end{array}\right].$ The method specifically comprises the following steps:

<math> <mrow> <msub> <mi>M</mi> <mi>m</mi> </msub> <mo>=</mo> <msub> <mi>K</mi> <mi>m</mi> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mi>m</mi> </msub> <mo>,</mo> </mrow> </math> m＝0，1，2，…15

<math> <mrow> <msub> <mi>M</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>K</mi> <mn>0</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mn>0</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>&CircleTimes;</mo> <msub> <mi>W</mi> <mn>0</mn> </msub> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mn>1</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>&CircleTimes;</mo> <msub> <mi>W</mi> <mn>0</mn> </msub> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mn>2</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>&CircleTimes;</mo> <msub> <mi>W</mi> <mn>1</mn> </msub> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mn>15</mn> </msub> <mo>=</mo> <msub> <mi>K</mi> <mn>15</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mn>15</mn> </msub> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>&CircleTimes;</mo> <msub> <mi>W</mi> <mn>7</mn> </msub> </mrow> </math>

M₁₆～M₃₁the generation of (d) may be:

$M_{16}=\left[\begin{array}{cc}{a}_{16}{U}_{16}& c_{16}{K}_{16}\\ b_{16}{U}_{16}& d_{16}{K}_{16}\end{array}\right]$

$M_{17}=\left[\begin{array}{cc}{a}_{17}{K}_{17}& c_{17}{U}_{17}\\ b_{17}{K}_{17}& d_{17}{U}_{17}\end{array}\right]$

$M_{18}=\left[\begin{array}{cc}{a}_{18}{K}_{18}& c_{18}{U}_{18}\\ b_{18}{U}_{18}& d_{18}{K}_{18}\end{array}\right]$

$M_{19}=\left[\begin{array}{cc}{a}_{19}{U}_{19}& c_{19}{K}_{19}\\ b_{19}{K}_{19}& d_{19}{U}_{19}\end{array}\right]$

<math> <mrow> <msub> <mi>M</mi> <mn>20</mn> </msub> <mo>=</mo> <msub> <mi>W</mi> <mn>10</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mn>20</mn> </msub> </mrow> </math>

from M_nOne or more columns are selected to form a part of code words under each Rank: the selection is the same as that of embodiment 2, and the description is omitted.

Example 8, N-16 or 32 was determined as needed.

If the matrix matching the associated channel is M₀，M₁......M_N-1The first 16, M₀，M₁......M₁₅Then, determining k as 16; m₀，M₁......M₁₅From the corresponding O₁，O₂......O_kGenerating, i.e. U₀，U₁......U₁₅If N is 16, then there is no other U value; if N is 32, other U values are matched with the uncorrelated channels, and may be determined by other codebook design methods in the prior art, or may be selected by the method of the present invention.

O₁，O₂......O_k(U₀，U₁......U₇) From W₀，W₁......W₇In the selection, when the direction vectors need to be ensured to be uniformly distributed in the 120-degree direction, O₁，O₂......O_kCan be all selected from W₀，W₁......W₃Selecting; when it is necessary to ensure that the direction vectors are uniformly distributed in the 180-degree direction, O₁，O₂......O_kCan be all selected from W₄，W₅......W₇Selecting. From this, W₀，W₁......W₃Or W₄，W₅......W₇Wherein each matrix is at O₁，O₂......O_kWhich are equal to 2 matrices. This ensures that the beam directions are uniform over 120 degrees or 180 degrees and there are 2 identical basis matrices in each direction.

Preferably, U_nThe matrix for the medium matching correlation channel is selected as follows:

TABLE 25

U_nThe other matrices need to satisfy 8PSK characteristics when selected.

Preferably, K_n(n is 0 to 15)

Watch 26

Wherein [ a ]_n b_n]^TAnd K_nIs orthogonal to the first column of a_n、b_nThe elements n in the 8PSK letter set are 0-15.

M_nThe generation is the same as in embodiment 2 and is not described here.

From M_nOne or more columns are selected to form a part of code words under each Rank: the selection is the same as that of embodiment 2, and the description is omitted.

For U_nAnd K_nThis embodiment is a preferred option.

Example 9, N-16 or 32 was determined as required.

If the matrix matching the uncorrelated channels is M₀，M₁......M_N-1The first 16, M matrices matching the associated channels₀，M₁......M_N-1The other 16 of; or all 16 matrices matching the uncorrelated channels. Then U of the uncorrelated channel is matched_nFrom W₈，W₉......W₁₅The method comprises the following steps:

watch 27

Preferably, K_n(n is 0 to 15) is selected as follows:

watch 28

M_nThe generation is the same as in embodiment 2 and is not described here.

From M_nOne or more columns are selected to form a part of code words under each Rank: the selection is the same as that of embodiment 2, and the description is omitted.

Example 10, N — 16 was determined as needed.

If the matrix in which the associated channels are matched is M₀，M₁......M_N-1The first 8, M matrices for matching uncorrelated channels₀，M₁......M_N-1The other 8 of them. Then U of the uncorrelated channel is matched_nFrom W₈，W₉......W₁₅The method comprises the following steps:

watch 29

It should be noted that U matching the uncorrelated channels does not necessarily correspond to U₀～U₇And the specific determination is determined according to the needs.

It is assumed here that K_nIs a 4 × 4 matrix, then K_nThe selection is as follows:

watch 30

The method can ensure that the minimum chord distance and the average chord distance are very uniform, and has better performance under the non-correlated channels.

Generating M_nThen, can select $M_n=\left[\begin{array}{cc}{a}_n{U}_n& c_n{K}_n\\ b_n{U}_n& d_n{K}_n\end{array}\right],$ Or $\left[\begin{array}{cc}{a}_n{K}_n& c_n{U}_n\\ b_n{K}_n& d_n{U}_n\end{array}\right],$ Or $\left[\begin{array}{cc}{a}_n{K}_n& c_n{K}_n\\ b_n{U}_n& d_n{U}_n\end{array}\right],$ Or $\left[\begin{array}{cc}{a}_n{U}_n& c_n{U}_n\\ b_n{K}_n& d_n{K}_n\end{array}\right]$ One or more of them.

From M_nOne or more columns are selected to form a part of code words under each Rank: the selection is the same as that of embodiment 2, and the description is omitted.

Example 11, N-32 was determined as needed.

1，U_nAnd (4) selecting.

If a matrix M is required to match the associated channels_nThe first 8 of (A), M₀，M₁......M₇Then, M can be determined₀，M₁......M₇From O₁，O₂......O_kGenerating, preferably, k is 8, O₁，O₂......O_kMay be U₀，U₁......U₇(ii) a Then U is₈，U₉......U₃₁For matching the matrix of the uncorrelated channel, the selection method of the matrix of the matched uncorrelated channel in the first orthogonal matrix of the present invention may be adopted, or other codebook design rules in the prior art may be adopted to determine the matrix. It is to be noted that O₁，O₂......O_kCorresponding U_nOr may be discontinuous (index number discontinuous).

O₁，O₂......O_k(U₀，U₁......U₇) Is matched to the associated channel, i.e. from W₀，W₁......W₇Of (1) selected

Preferably, the matrix U of the associated channels is matched₀，U₁，…U₇The selection is as follows: $U_n=W_m=I-2u_m{u}_m^H/u_m^H{u}_m,$ wherein m is 0-7.

2，K_nAnd (4) selecting.

Preferably, according to K described in step 102_nSelection rules, increasing performance considerations in certain scenarios of dual-polarized antennas, K₀～K₇Can be arbitrarily selected from the following four matrixes:

$\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],$ or $\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right],$ Or $\left[\begin{array}{cc}1& 1\\ j& -j\end{array}\right],$ Or $\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right].$

K₈，K₉，…K₃₁The determination of (c) may be based on the selection of the matrix matching the uncorrelated channels in the second orthogonal matrix in the present invention, or may be based on other codebook design methods in the prior art.

3, generating M_n。

If K is_nIs a 2 × 2 matrix, and is selectedThen

<math> <mrow> <msub> <mi>M</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mn>0</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mn>0</mn> </msub> <mo>=</mo> <msub> <mi>W</mi> <mn>0</mn> </msub> <mo>&CircleTimes;</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow> </math> <math> <mrow> <msub> <mi>M</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mn>1</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>W</mi> <mn>0</mn> </msub> <mo>&CircleTimes;</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mn>2</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>W</mi> <mn>1</mn> </msub> <mo>&CircleTimes;</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mi>j</mi> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>-</mo> <mi>j</mi> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow> </math> <math> <mrow> <msub> <mi>M</mi> <mn>3</mn> </msub> <mo>=</mo> <msub> <mi>U</mi> <mn>3</mn> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mn>3</mn> </msub> <mo>=</mo> <msub> <mi>W</mi> <mn>1</mn> </msub> <mo>&CircleTimes;</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mi>j</mi> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mn>1</mn> </mtd> <mtd> <mi>j</mi> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow> </math>

<math> <mrow> <msub> <mi>M</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>U</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&CircleTimes;</mo> <msub> <mi>K</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>W</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>&CircleTimes;</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mi>j</mi> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mn>1</mn> </mtd> <mtd> <mi>j</mi> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow> </math>

Other ways are also possible, e.g. <math> <mrow> <msub> <mi>M</mi> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi>K</mi> <mi>n</mi> </msub> <mo>&CircleTimes;</mo> <msub> <mi>U</mi> <mi>n</mi> </msub> <mo>.</mo> </mrow> </math>

And 4, generating a code word.

The codeword structure of embodiment 1 may be adopted, and will not be described herein again.

In order to implement the method for constructing the precoding codebook of the mimo system, the present invention further provides a precoding codebook apparatus of the mimo system, as shown in fig. 2, including: a matrix selection module 10, a matrix generation module 20, and a codebook generation module 30, wherein,

a matrix selection module 10 for selecting N4 × 4 first orthogonal matrices U_nAnd N second orthogonal matrices K_nAnd will select U_nAnd K_nProviding the matrix to a matrix generation module;

a matrix generation module 20 for generating a matrix according to the selected U_nAnd K_nN8 x 8 matrices M are generated by means of or similar to the Kronecker product_n；

A codebook generating module 30 for generating a codebook from the matrix M_nAnd selecting 1 or more columns to generate partial code words in the sub-code book of each Rank under 8 antennas.

The matrix selection module 10 is further configured to select the orthogonal matrix W from the orthogonal matrix_nIn which N U's are selected_nAnd is and $W_n=I-2u_n{u}_n^H/u_n^H{u}_n,$ u_nis a vector, including u₀□u₁₅。

K_nIn the case of a 4 x 4 matrix, the matrix selection module 10 is further adapted to select from W_nW of (2)₀～W₁₅In the selection of K_n。

K_nIn the case of a 2 × 2 matrix, the matrix selection module 10 is further configured to select K from the following eight mathematical model matrices_n：

$K_n=\left[\begin{array}{cc}{w}_1& w_1\\ w_2& {-w}_2\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_2& -w_2\\ w_1& w_1\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_1& w_2\\ w_1& -w_2\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_2& w_1\\ {-w}_2& w_1\end{array}\right],$

$K_n=\left[\begin{array}{cc}{w}_3& {w_4}^{*}\\ -w_4& {w_3}^{*}\end{array}\right],$ $K_n=\left[\begin{array}{cc}{w}_3& {w_4}^{*}\\ w_4& {{-w}_3}^{*}\end{array}\right];$ $K_n=\left[\begin{array}{cc}{w}_3& 0\\ 0& w_4\end{array}\right],$ $K_n=\left[\begin{array}{cc}0& w_3\\ w_4& 0\end{array}\right].$

Wherein, w₁，w₂Is 8PSK alphabet set $\{1,-1,j,-j,\frac{1+j}{\sqrt{2}},\frac{-1+j}{\sqrt{2}},\frac{1-j}{\sqrt{2}},\frac{-1-j}{\sqrt{2}}\}$ Element of (5), w₃，w₄Are elements in a 4PSK alphabet {1, -1, j, -j }.

The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention.

Claims (11)

1. A precoding codebook construction method of a multi-input multi-output system is characterized by comprising the following steps:

from orthogonal matrix W_nN4 x 4 first orthogonal matrixes U are selected_nAnd N second orthogonal matrices K are selected_n(ii) a N is less than or equal to 2^BB is the channel overhead bit number of the feedback channel information CSI and is a positive integer; the above-mentionedu_nIn the form of a vector, the vector,n is 0-15; the W is_nThe 8 phase shift keying PSK characteristic, the constant modulus characteristic and the quadrature characteristic are met;

according to the selected U_nAnd K_nN8 x 8 matrices M are constructed by or similar to the Kronecker product_n；

Slave matrix M_nOne or more columns are selected to generate partial code words in the sub-codebook of each Rank under 8 antennas.

2. The precoding codebook construction method for MIMO system as claimed in claim 1, wherein the method further comprises: the N U_nThe orthogonal matrix comprises k orthogonal matrixes adaptive to related channels, and is arranged as O according to the size sequence of an index number n₁，O₂……O_kAnd O is₁，O₂……O_kFrom the W_nW of (2)₀～W₇Wherein k is less than or equal to N.

3. The precoding codebook construction method for MIMO system as claimed in claim 2, wherein the O is₁，O₂……O_kFrom W₀～W₇The method specifically comprises the following steps:

when the direction vectors need to be uniformly distributed within 120 degrees, O₁，O₂……O_kFrom W₀～W₃Selecting;

or, when the direction vectors need to be uniformly distributed within 180 degrees, O₁，O₂……O_kFrom W₄～W₇Selecting;

or, O₁，O₂……O_kComprising W₀～W₇；

The direction vector is O₁，O₂……O_kThe first column of the vector.

4. The precoding codebook construction method for a mimo system according to claim 1,wherein the N numbers of K_nIs a 2 × 2 orthogonal matrix, or a 4 × 4 orthogonal matrix;

K_nin the case of a 2 × 2 orthogonal matrix, the corresponding Kronecker product mode specifically includes:or

K_nIn the case of a 4 × 4 orthogonal matrix, the corresponding Kronecker product-like manner is specifically:orOrOrThe above-mentionedIs an orthogonal matrix, a_n、b_n、c_n、d_nIs 8PSK alphabet setOf (a) or_n、d_nAt the same time, 0, or b_n、c_nAnd is also 0.

5. The precoding codebook construction method for MIMO system as claimed in claim 4, wherein K is greater than a preset threshold when N is greater than the preset threshold_nThe matrix for the intermediate matched uncorrelated channels includes both 2 x 2 orthogonal matrices andcontaining a 4 x 4 orthogonal matrix.

6. The precoding codebook construction method for MIMO systems as claimed in claim 4 or 5, wherein if K is_nIs a 4 × 4 orthogonal matrix, K_nFrom W₀～W₁₅Selecting the following specific components:

if it is desired to generate a codeword suitable for the associated channel, K_nFrom W₀～W₇Selecting;

if it is desired to generate a codeword suitable for an uncorrelated channel, K_nFrom W₈～W₁₅Selecting.

7. The precoding codebook construction method for MIMO system according to claim 4 or 5, wherein the K is_nIn the case of a 2 × 2 orthogonal matrix, the method further includes: the 2 × 2 orthogonal matrix is selected from the following eight mathematical model matrices:

wherein, w₁，w₂Is 8PSK alphabet setElement of (5), w₃，w₄Are elements in a 4PSK alphabet {1, -1, j, -j }.

8. The precoding codebook construction method for MIMO system as claimed in claim 7, wherein the method further comprises: the 2 x 2 orthogonal matrix is selected from the expansion of the eight mathematical model matrices;

the expansion of the eight mathematical models specifically comprises the following steps: multiplying each column of the matrix by an element in the same or a different 8PSK alphabet set; or multiplying each row of the matrix by an element in the same or a different 8PSK alphabet set; or multiplying the matrix by a constant.

9. The precoding codebook construction method for mimo system according to claim 1, wherein when generating the codeword in the sub-codebook for each Rank under 8 antennas, the method further comprises: from matrix M, according to the nested property_nOne or more columns are selected to generate partial code words in the sub-codebook of each Rank under 8 antennas.

10. An apparatus for constructing precoding codebook of mimo system, the apparatus comprising: a matrix selecting module, a matrix generating module and a codebook generating module, wherein,

the matrix selection module is used for selecting the orthogonal matrix W_nN4 x 4 first orthogonal matrixes U are selected_nAnd N second orthogonal matrices K_nAnd will select U_nAnd K_nProviding to the matrix generation module; n is less than or equal to 2^BB is the channel overhead bit number of the feedback channel information CSI and is a positive integer; the above-mentionedu_nIs a vector, n is 0-15; the W is_nThe 8 phase shift keying PSK characteristic, the constant modulus characteristic and the quadrature characteristic are met;

the matrix generation module is used for generating a matrix according to the selected U_nAnd K_nN8 x 8 matrices M are generated by means of or similar to the Kronecker product_n；

The codebook generating module is used for generating a matrix M_nAnd selecting 1 or more columns to generate code words in the sub-codebook of each Rank under 8 antennas.

11. The precoding codebook construction apparatus for a MIMO system according to claim 10,

said K_nIn the case of a 4 x 4 matrix, the matrix selection module is further adapted to select from W_nW of (2)₀～W₁₅In the selection of K_n；

Said K_nIn the case of a 2 × 2 matrix, the matrix selection module is further configured to select K from the following eight mathematical model matrices_n：

Wherein, w₁，w₂Is 8PSK alphabet setElement of (5), w₃，w₄Are elements in a 4PSK alphabet {1, -1, j, -j }.