CN110730022A - MIMO precoding codebook construction method based on MacQueen clustering - Google Patents

MIMO precoding codebook construction method based on MacQueen clustering Download PDF

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CN110730022A
CN110730022A CN201911044093.7A CN201911044093A CN110730022A CN 110730022 A CN110730022 A CN 110730022A CN 201911044093 A CN201911044093 A CN 201911044093A CN 110730022 A CN110730022 A CN 110730022A
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邓宏贵
杨凯
封雨鑫
马松山
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Central South University
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Abstract

The invention discloses a MIMO precoding codebook construction method based on MacQueen clustering, which comprises the following steps of: randomly selecting Q channel samples H; step 2: performing SVD decomposition on the first N (Q > > N) channel matrices H in the Q channel samples to obtain corresponding N precoding matrices F, and using the N precoding matrices as an initial codebook F0= { F1, F2, …, fN }, where each codeword fi (i =1,2, …, N) is an initial centroid of N classes; according to the invention, a MacQueen clustering algorithm is adopted to replace the Lloyd clustering algorithm in the Lloyd vector quantization codebook, so that the selection of an error threshold value is avoided, and the centroid is updated after each channel matrix H is classified, so that the classification is more accurate, and better system error rate performance can be realized, thereby improving the reliability of a communication system.

Description

MIMO precoding codebook construction method based on MacQueen clustering
Technical Field
The invention relates to the technical field of mobile communication systems, in particular to a MIMO precoding codebook construction method based on MacQueen clustering.
Background
A Multiple Input Multiple Output (MIMO) system architecture is widely applied as a key technology in 4G-LTE, and the latest 5G standard for discharge still continues to adopt the MIMO technology as its physical layer architecture. When the MIMO technology is adopted, because a plurality of antennas are deployed at a base station end and a large number of users exist in a cell, the MIMO system has serious inter-stream interference and inter-user interference, precoding is used as an effective means for solving the problem, becomes a core functional module of the MIMO system architecture, is widely applied, and is also deeply researched by academia and various large communication enterprises.
At present, the precoding mainly comprises two types of linear precoding and nonlinear precoding, the nonlinear precoding is high in complexity and difficult to realize, the linear precoding is low in complexity and simple in principle, and the linear precoding is generally applied to an actual communication system. In the existing linear precoding scheme, the scheme can be divided into non-codebook and codebook-based precoding, but the actual communication system is limited by the bandwidth of a feedback link, so that ideal Channel State Information (CSI) feedback cannot be realized, and for feedback of part of CSI, the 3GPP specifies that a codebook-based precoding scheme is adopted. The codebook-based precoding scheme is mainly divided into two parts: the codebook structure and the code word selection, and the codebook structure method are many, such as DFT codebook, Householder codebook, layer structure codebook, and Lloyd vector quantization codebook. The Lloyd vector quantization codebook is constructed by adopting an Lloyd clustering algorithm, but the performance of the code book error rate generated by the method is limited by the selection of an initial code book and the setting of an error threshold, so that the performance of the code book error rate is unstable.
Disclosure of Invention
The invention aims to provide an MIMO precoding codebook construction method based on MacQueen clustering, which replaces an Lloyd clustering algorithm in an Lloyd vector quantization codebook by adopting the MacQueen clustering algorithm, so that the error threshold setting similar to Lloyd iteration is not involved in the calculation process, the influence of the selection of an error threshold value on the error rate performance of the codebook is avoided, and simultaneously, the centroid is updated after each channel matrix H is classified, so that more accurate classification basis is provided for the classification of the next channel matrix, the error rate performance of an MIMO system is further improved, and the reliability of a communication system is improved.
In order to achieve the purpose, the invention provides the following technical scheme: a MIMO precoding codebook construction method based on MacQueen clustering comprises the following steps:
step 1: randomly selecting Q channel samples H;
step 2: for the first N (Q) of Q channel samples>>N) channel matrixes H are subjected to SVD to obtain corresponding N precoding matrixes F, and the N precoding matrixes are used as an initial codebook F0＝{f1,f2,…,fNAre each codeword fi(i-1, 2, …, N) is the initial centroid of the N classes;
and step 3: selecting the next channel matrix H, calculating the square of the Frobenius norm multiplied by each code word matrix fi, and distributing the channel matrix H to the class corresponding to the code word matrix fi with the maximum Frobenius norm square;
and 4, step 4: recalculating the centroid f of the class updated in step 3i；
And 5: repeating the step 3 and the step 4 until all Q channel samples are distributed;
step 6: and taking the centroids corresponding to the final N classes as a precoding codebook F.
Preferably, the SVD decomposition is performed on the first N (Q > > N) channel matrices H in the Q channel samples to obtain corresponding N precoding matrices f, wherein the precoding matrices are obtained according to the following formula:
H＝U∑V
f＝V(j)
the U matrix, the sigma matrix and the V matrix are respectively a left singular matrix obtained by SVD of a channel matrix, a diagonal matrix formed by singular values and a right singular matrix, and V (j) is a matrix formed by the front j columns of the matrix V.
Preferably, the channel matrices are classified one by one in sequence, and after each channel matrix H is assigned, the centroid f of the class added with the new channel matrix is recalculated, wherein the centroid f is calculated according to the following formula:
Figure 3
wherein
Figure RE-GDA0002281260670000032
To representAnd (4) a class consisting of precoding matrices f obtained by SVD decomposition of each channel matrix H.
Preferably, the next channel matrix H selected in step 3 is the N +2, N +3, …, Q channel matrices H in sequence from the N +1 channel matrix H.
Preferably, the calculation expression for calculating the square of the Frobenius norm of H multiplied by each codeword matrix fi in step 3 is as follows:
Figure 2
wherein
Figure RE-GDA0002281260670000035
Representing a center of mass of fkThe channel matrix H of (a).
The invention provides a MIMO precoding codebook construction method based on MacQueen clustering, which has the following beneficial effects:
according to the invention, the MacQueen clustering algorithm is adopted to replace the Lloyd clustering algorithm in the Lloyd vector quantization codebook, so that the error threshold setting similar to that in Lloyd iteration is not involved in the calculation process, the influence of the selection of the error threshold value on the error rate performance of the codebook is avoided, and simultaneously the centroid is updated after each channel matrix H is classified, so that more accurate classification basis is provided for the classification of the next channel matrix, therefore, the error rate performance of the MIMO system is further improved, and the reliability of the communication system is improved.
Drawings
FIG. 1 is a block diagram of a MIMO-OSTBC system;
FIG. 2 is a flow chart of codebook-based precoding operation;
FIG. 3 is a flow chart of a MIMO precoding codebook construction method based on MacQueen clustering provided by the invention;
fig. 4 is a schematic diagram illustrating a Bit Error Rate (BER) performance curve comparison between a MIMO precoding codebook construction method based on MacQueen clustering and a Lloyd vector quantization codebook and DFT codebooks provided by the present invention when a precoding codebook size L is 64;
fig. 5 is a schematic diagram illustrating a Bit Error Rate (BER) performance curve comparison between a MIMO precoding codebook construction method based on MacQueen clustering and a Lloyd vector quantization codebook according to the present invention when the precoding codebook size L is 16.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
In this example, the communication system adopted in the simulation is a MIMO-OSTBC system, 4-QAM modulation and Alamouti space-time coding are adopted, the number Tx of transmitting antennas is 4, the number Rx of receiving antennas is 2, and the system block diagram is shown in fig. 1, where the precoding part adopts a codebook-based precoding scheme, and the specific working flow is shown in fig. 2.
Example 1
A MIMO precoding codebook construction method based on MacQueen clustering comprises the following steps:
step 1: randomly selecting 10000 channel matrixes H;
step 2: SVD (singular value decomposition) is carried out on the first 64 channel matrixes, H is U sigma V, the first two columns of the right singular matrix V are selected as precoding matrixes according to F is V (2), corresponding 64 precoding matrixes F are obtained, and the 64 precoding matrixes are used as initial codebooks F0＝{f1,f2,…,f64Codebook size L64, each codeword fi(i is 1,2, …,64), that is, 64
Figure RE-GDA0002281260670000051
The initial center of mass of the class,
Figure RE-GDA0002281260670000052
representing a center of mass of fiA class of channel matrix H;
and step 3: selecting the 65 th channel matrix H65Calculating the matrix and each codeword matrix fiSquares of multiplied Frobenius norms, i.e.
Figure RE-GDA0002281260670000053
Then the channel matrix H65Assigning the value to the class corresponding to the codeword matrix f with the largest value, and assuming that the value is the largest when i is m for the sake of clarity, H is the same as H65Is distributed to
Figure RE-GDA0002281260670000054
Class (c);
and 4, step 4: recalculating the values updated in step 3 according to the following equation
Figure RE-GDA0002281260670000055
Centroid f of classm：
Figure 4
Wherein the formula represents the calculation
Figure RE-GDA0002281260670000057
Each of class f andall channel matrix H calculation in class
Figure RE-GDA0002281260670000059
And find their expectation, and then select f that minimizes the expectation as the valueThe new center of mass of the class,to represent
Figure RE-GDA00022812606700000512
Each channel matrix H is subjected to SVD to obtain a class consisting of precoding matrixes f;
and 5: respectively selecting the channel matrixes 66,67, … and 10000, and repeating the step 3 and the step 4;
step 6: after the final allocation is completed, each
Figure RE-GDA00022812606700000513
Centroid f of classiThe precoding codebook F that we need is composed as a codeword.
Example 2
A MIMO precoding codebook construction method based on MacQueen clustering comprises the following steps:
step 1: randomly selecting 10000 channel matrixes H;
step 2: SVD (singular value decomposition) is carried out on the first N-16 channel matrixes to obtain H-U-Sigma V, the first two columns of the right singular matrix V are selected as precoding matrixes according to F-V (2), corresponding 64 precoding matrixes F are obtained, and the 64 precoding matrixes are used as initial codebooks F0＝{f1,f2,…,f16Codebook size L16, each codeword fi(i-1, 2, …,16) i.e. 16
Figure RE-GDA0002281260670000061
The initial center of mass of the class,representing a center of mass of fiA class of channel matrix H;
and step 3: selecting the 17 th channel matrix H17Calculating the matrix and each codeword matrix fiSquares of multiplied Frobenius norms, i.e.
Figure RE-GDA0002281260670000063
Then the channel matrix H17Is assigned to the class corresponding to the codeword matrix f with the largest value asIt is more clear to state that, assuming that when i ═ m, the value is the largest, then H17Is distributed to
Figure RE-GDA0002281260670000064
Class (c);
and 4, step 4: recalculating the values updated in step 3 according to the following equationCentroid f of classm：
Figure 5
Wherein the formula represents the calculation
Figure RE-GDA0002281260670000067
Each of class f and
Figure RE-GDA0002281260670000068
all channel matrix H calculation in class
Figure RE-GDA0002281260670000069
And find their expectation, and then select f that minimizes the expectation as the value
Figure RE-GDA00022812606700000610
The new center of mass of the class,
Figure RE-GDA00022812606700000611
to represent
Figure RE-GDA00022812606700000612
Each channel matrix H is subjected to SVD to obtain a class consisting of precoding matrixes f;
and 5: respectively selecting 18 th, 19 th, … th and 10000 th channel matrixes, and repeating the step 3 and the step 4;
step 6: after the final allocation is completed, each
Figure RE-GDA00022812606700000613
Centroid f of classiThe precoding codebook F that we need is composed as a codeword.
The bit error rate performance of the embodiment 1 of the present invention and the existing precoding codebook in the communication system is simulated and compared to obtain fig. 4, and the bit error rate performance of the embodiment 1 of the present invention and the existing precoding codebook in the communication system is simulated and compared to obtain fig. 5.
And (4) conclusion:
(1) as can be seen from fig. 4 and fig. 5, under the same condition, compared with the existing precoding codebook scheme, the present invention can further reduce the error rate of the system without increasing the feedback overhead, i.e., under the condition of the same codebook size, and under the condition of high signal-to-noise ratio, the present invention exhibits more excellent error rate performance.
(2) It can be seen from the specific examples described herein that the method of the present invention does not involve setting an error threshold similar to that in Lloyd iteration in the calculation process, thereby avoiding the influence of the selection of the error threshold on the error rate performance of the codebook, and simultaneously updating the centroid after each channel matrix H is classified, so that the classification is more accurate, the error rate performance of the MIMO system is further improved, and the reliability of the communication system is enhanced.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (5)

1. A MIMO precoding codebook construction method based on MacQueen clustering is characterized by comprising the following steps:
step 1: randomly selecting Q channel samples H;
step 2: for the first N (Q) of Q channel samples>>N) channel matrixes H are subjected to SVD to obtain corresponding N precoding matrixes F, and the N precoding matrixes are used as an initial codebook F0＝{f1,f2,…,fNAre each codeword fi(i-1, 2, …, N) is the initial centroid of the N classes;
and step 3: selecting the next channel matrix H, calculating the square of the Frobenius norm multiplied by each code word matrix fi, and distributing the channel matrix H to the class corresponding to the code word matrix fi with the maximum Frobenius norm square;
and 4, step 4: recalculating the centroid f of the class updated in step 3i；
And 5: repeating the step 3 and the step 4 until all Q channel samples are distributed;
step 6: and taking the centroids corresponding to the final N classes as a precoding codebook F.
2. The method of claim 1, wherein the method comprises the following steps: performing SVD on the first N (Q > > N) channel matrixes H in the Q channel samples to obtain corresponding N precoding matrixes f, wherein the precoding matrixes are obtained according to the following formula:
H＝U∑V
f＝V(j)
the U matrix, the sigma matrix and the V matrix are respectively a left singular matrix obtained by SVD of a channel matrix, a diagonal matrix formed by singular values and a right singular matrix, and V (j) is a matrix formed by the front j columns of the matrix V.
3. The method of claim 1, wherein the method comprises the following steps: the channel matrixes are classified one by one in sequence, and after one channel matrix H is distributed, the centroid f of the class added with the new channel matrix is recalculated, wherein the centroid f is calculated according to the following formula:
Figure 1
wherein
Figure RE-FDA0002281260660000022
To represent
Figure RE-FDA0002281260660000023
And (4) a class consisting of precoding matrices f obtained by SVD decomposition of each channel matrix H.
4. The method of claim 1, wherein the method comprises the following steps: in the step 3, the next channel matrix H is selected from the N +1 th channel matrix H, which is the N +2 th channel matrix, the N +3 th channel matrix, the … th channel matrix and the Q channel matrices H in sequence.
5. The method of claim 1, wherein the method comprises the following steps: the calculation expression for calculating the square of the Frobenius norm multiplied by H and each codeword matrix fi in step 3 is as follows:
wherein
Figure RE-FDA0002281260660000025
Representing a center of mass of fkThe channel matrix H of (a).
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