CN113708811B - Hybrid precoding design method in millimeter wave large-scale MIMO system - Google Patents

Hybrid precoding design method in millimeter wave large-scale MIMO system Download PDF

Info

Publication number
CN113708811B
CN113708811B CN202110906384.3A CN202110906384A CN113708811B CN 113708811 B CN113708811 B CN 113708811B CN 202110906384 A CN202110906384 A CN 202110906384A CN 113708811 B CN113708811 B CN 113708811B
Authority
CN
China
Prior art keywords
matrix
precoding
analog
lobe
digital
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202110906384.3A
Other languages
Chinese (zh)
Other versions
CN113708811A (en
Inventor
李正权
李树梅
袁月
马可
李君�
陆波
丁文杰
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Ictehi Technology Development Jiangsu Co ltd
Jiangnan University
Original Assignee
Ictehi Technology Development Jiangsu Co ltd
Jiangnan University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Ictehi Technology Development Jiangsu Co ltd, Jiangnan University filed Critical Ictehi Technology Development Jiangsu Co ltd
Priority to CN202110906384.3A priority Critical patent/CN113708811B/en
Publication of CN113708811A publication Critical patent/CN113708811A/en
Application granted granted Critical
Publication of CN113708811B publication Critical patent/CN113708811B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station

Abstract

The invention discloses a hybrid precoding design method in a millimeter wave large-scale MIMO system, which aims to solve the problems of low system spectrum efficiency and high calculation complexity caused by a solving mode of a non-convex constrained optimization problem in the precoding design process of the millimeter wave large-scale MIMO system. According to the method, a lobe decomposition channel is adopted during system modeling, optimization problems containing non-convex constraints are converted, correlation between an analog precoding matrix and a digital precoding matrix is fully utilized, an own support set and a common support set of each data stream in each lobe are solved according to a hidden sparse structure of the digital precoding matrix, and accordingly mixed precoding is jointly designed to improve the spectral efficiency of the system.

Description

Hybrid precoding design method in millimeter wave large-scale MIMO system
Technical Field
The invention relates to a hybrid precoding design method in a millimeter wave large-scale MIMO system, and belongs to the technical field of wireless communication.
Background
With the explosive increase of wireless data volume, millimeter wave large-scale MIMO systems are receiving more and more attention, and have the significant advantages of high data transmission rate and high reliability as one of the key technologies of the fifth-generation mobile communication technology. In a traditional MIMO system, a sending end eliminates part or all interference among data streams in advance through a digital pre-coding technology, so that the spatial distribution characteristic of a sending signal is matched with a channel condition, and better spectrum efficiency and error rate performance are obtained. However, for a large-scale MIMO system, the scale of the antenna array is greatly increased, and if a conventional all-digital precoding technology is adopted, a large number of Radio Frequency (RF) links are required, which increases the hardware design difficulty and design cost. Researchers apply the analog precoding technology to a large-scale MIMO system, only a small number of RF links are needed, and hardware cost and power consumption are low. However, this application has a certain loss of spectral efficiency performance and weak anti-interference capability, so researchers have proposed a hybrid precoding structure combining a low-dimensional digital precoding technique and a high-dimensional analog precoding technique, which can fully utilize the gain brought by a large-scale antenna array while reducing the RF link.
Because of the high frequency and short wavelength of the millimeter wave, the millimeter wave will generate serious loss due to the influence of environmental factors in the transmission process, and the scattering of the millimeter wave is limited, so line-of-sight transmission is the main transmission mode, and the channel characteristics are specifically expressed as the sparsity of the channel. Meanwhile, based on the constant modulus constraint and the discrete characteristic of a codeword in a simulated precoding codebook, researchers convert a mixed precoding design problem into an optimization problem containing non-convex constraint in order to maximize the system spectral efficiency, and adopt an Orthogonal Matching Pursuit (OMP) to reconstruct sparse signals to design a mixed precoding matrix, but the OMP algorithm needs Singular Value Decomposition (SVD) and inversion operation of a high-dimensional matrix, which leads to obviously increased computational complexity. Some scholars improve the spectrum efficiency and the error rate performance of the system by designing a precoding codebook, improving an RF connection structure, optimizing an iterative algorithm and the like, but balance among the spectrum efficiency, the error rate performance and the calculation complexity of the system is difficult to realize.
In addition, most of the existing hybrid precoding technologies are based on a time cluster channel model, and the angle sparse characteristic of a millimeter wave communication transmission path is ignored. Research shows that the Angle of Arrival (AOA) and Angle of Departure (AOD) of the millimeter wave transmission path have the characteristic of lobe decomposition, and the channel can be decomposed into a plurality of orthogonal lobe subchannels, so that SVD of a high-dimensional matrix is avoided, but partial system performance is sacrificed by the method. Therefore, if a hybrid precoding design in a millimeter wave massive MIMO system needs to be performed based on a lobe decomposition channel model, the system spectrum efficiency and the bit error rate performance also need to be improved.
Disclosure of Invention
The invention provides a hybrid precoding design method in a millimeter wave large-scale MIMO system, aiming at solving the problems of low system spectrum efficiency and error rate performance and high calculation complexity caused by a solving mode of a non-convex constraint optimization problem in the precoding design process of the millimeter wave large-scale MIMO system. The method of the invention adopts a lobe decomposition channel model to design mixed precoding in a millimeter wave large-scale MIMO system, and improves the system spectrum efficiency and the error rate performance while ensuring the calculation complexity.
According to the design method of the hybrid precoding, N is contained in a millimeter wave large-scale MIMO systemsAfter the transmitting end carries out digital pre-coding processing on the transmitting signal s of each data stream through the digital pre-coding module, the transmitting signal s is transmitted to the receiving end
Figure GDA0003262766920000021
The analog pre-coding module is composed of a radio frequency chain, a phase shifter and a radio frequency adder, and after analog pre-coding processing is carried out by the analog pre-coding module, the data stream is mapped to NtTransmitting to a noisy lobe decomposition channel for data transmission and receptionTerminal through NrThe receiving antenna receives data, and the data are processed by the analog combining module and the digital combining module in sequence to obtain a receiving signal y, so that multi-path data stream transmission is realized.
However, the analog precoding module only adjusts the deflection phase of each phase shifter to realize analog precoding, so the analog precoding matrix has a constant modulus constraint condition, and in addition, due to the limitation of the phase shifter hardware design, the phase resolution of the phase shifters is often constant, and the number of code words in the analog precoding codebook is constant and has a discrete characteristic, so that the mixed precoding design problem including the digital precoding design and the analog precoding design is an optimization problem including non-convex constraint based on the above characteristics of the analog precoding codebook.
According to the method, a lobe decomposition channel is adopted during system modeling, optimization problems containing non-convex constraints are converted, correlation between an analog pre-coding matrix and a digital pre-coding matrix is fully utilized, an own support set and a common support set of each data stream in each lobe are solved according to an implicit sparse structure of the digital pre-coding matrix, and accordingly mixed pre-coding is jointly designed, so that the spectral efficiency and the error rate performance of a system are improved.
In order to solve the technical problems, the invention provides the following technical scheme:
a hybrid precoding optimization design method in a millimeter wave large-scale MIMO system, wherein the millimeter wave large-scale MIMO system comprises NsAfter the transmitting end carries out digital pre-coding processing on the transmitting signal s of each data stream through the digital pre-coding module, the transmitting signal s is transmitted to the receiving end
Figure GDA0003262766920000022
The analog pre-coding module is composed of a radio frequency chain, a phase shifter and a radio frequency adder, and after analog pre-coding processing is carried out by the analog pre-coding module, the data stream is mapped to NtTransmitting the data to a noisy lobe decomposition channel for data transmission on a root transmitting antenna, and transmitting the data to a receiving end through NrThe root receiving antenna receives data and sequentially passes through the analog combining module and the digital combining modulePerforming line processing to obtain a received signal y, and realizing multi-path data transmission containing a plurality of data streams; in the millimeter wave large-scale MIMO system, N is assumed at the transmitting endtThe number of the transmitting antennas is the same as,
Figure GDA0003262766920000031
a radio frequency chain, a receiving end has NrThe antenna is received at the root of the antenna,
Figure GDA0003262766920000032
a radio frequency chain, the number of transmission data streams is Ns. In order to ensure multiplexing gain and realize multi-path data stream communication, the number of radio frequency chains at the transmitting end and the receiving end respectively satisfies
Figure GDA0003262766920000033
Is transmitting a signal vector and satisfies
Figure GDA0003262766920000034
In the formula (I), the compound is shown in the specification,
Figure GDA0003262766920000035
is a noise covariance matrix;
Figure GDA0003262766920000036
is transmitting a signal vector and satisfies
Figure GDA00032627669200000320
FRFTo represent
Figure GDA0003262766920000037
Dimension simulation precoding matrix, FBBRepresent
Figure GDA0003262766920000038
Dimension digital precoding matrix, WRFTo represent
Figure GDA0003262766920000039
Analog combiner matrix of dimensions, WBBTo represent
Figure GDA00032627669200000310
Number merger matrix of dimensions, F ═ FRFFBBFor the hybrid precoding matrix, the total transmission power is satisfied
Figure GDA00032627669200000311
W＝WRFWBBRepresenting a combiner matrix;
Figure GDA00032627669200000312
for channel noise vector, σ2Is the power of the noise or noise,
Figure GDA00032627669200000313
for the channel matrix, ρ represents the average received power; the method comprises the following steps:
the method comprises the following steps: in order to maximize the spectral efficiency of a system, the design of a digital pre-coding module, an analog merging module and a digital merging module is optimized, and the optimization problem containing non-convex constraint in the design process of mixed pre-coding comprising an analog pre-coding matrix, a digital pre-coding matrix, an analog merger matrix and a digital merger matrix is converted into the problem of solving the minimum Euclidean distance;
under the lobe decomposition channel model, the received signal is y,
Figure GDA00032627669200000314
taking the gaussian signal as the transmission signal s, the system spectrum efficiency is:
Figure GDA00032627669200000315
in the formula
Figure GDA00032627669200000316
Is a noise covariance matrix. With the goal of maximizing spectral efficiency, the formula for hybrid precoding design is as follows:
Figure GDA00032627669200000317
wherein omega is an analog precoding codebook with constant modulus constraint and satisfies
Figure GDA00032627669200000318
In order to simplify the design, the formula (3) is converted into the problem of solving the euclidean distance minimum as shown in the formula (4), and the optimal code word is searched in the analog precoding codebook Ω to form an analog precoding matrix:
Figure GDA00032627669200000319
in the formula, FoptIs an optimal precoding reference matrix, and can be decomposed by singular values of a channel matrix, H ═ U ∑ VHTo obtain i.e. Fopt＝V(：，1：Ns)。
Step two: according to mutual independence among the lobes, the lobe channel is decomposed into a plurality of independent lobe sub-channels, the problem (4) in the first step can be converted into a mixed precoding design problem based on the independent lobe sub-channels, and an analog precoding matrix and a digital precoding matrix are respectively designed;
respectively designing an analog precoding matrix and a digital precoding matrix aiming at the L lobe sub-channels:
Figure GDA0003262766920000041
in the formula
Figure GDA0003262766920000042
For the optimal precoding reference matrix corresponding to the l-th lobe subchannel,
Figure GDA0003262766920000043
and
Figure GDA0003262766920000044
respectively corresponding to the l sub-channel, an analog pre-coding matrix and a digital pre-coding matrix, omegalRepresents the ith analog precoding subcodebook, and
Figure GDA0003262766920000045
the invention assumes power averaging distribution, GlIs the sum of the powers of all transmission paths in the first lobe.
Step three: solving analog precoding matrix corresponding to each lobe subchannel
Figure GDA0003262766920000046
And a digital precoding matrix
Figure GDA0003262766920000047
Selecting antenna array response A for each lobe subchanneltlAs a precoding reference matrix FresConstructing an analog precoding codebook according to the hardware limitation of a phase shifter in the analog precoding module; at each analog precoding codebook
Figure GDA0003262766920000048
Searching the position of the best code word to form an analog precoding matrix
Figure GDA0003262766920000049
Self-supported set Ψl。
More than two single antennas working at the same frequency are arranged according to a certain space to form an antenna array; and mapping the transmission signals to the transmission antenna after precoding to form antenna array response. To avoid high complexity matrix operations, an antenna array response A is selectedtAs a precoding reference matrix Fres. The channel matrix H can be abbreviated as:
Figure GDA00032627669200000410
Figure GDA00032627669200000411
in order for the transmitting end antenna array to respond,
Figure GDA00032627669200000412
and responding by the antenna array at the receiving end. The multiplexing gain of each data transmission path is
Figure GDA00032627669200000413
For each lobe subchannel, the antenna array response corresponds to L sub-antenna array responses, with a transmit side at＝[At1，At2，...，AtL]The receiving end is Ar＝[Ar1，Ar2，...，ArL]，ArlAnd AtlDenotes the L-th antenna array response, where L1, 2.
And constructing an analog precoding codebook according to the hardware limit of a phase shifter in the analog precoding module. Assume an analog precoding codebook size of Nθ＝2bAnd b represents that the phase resolution of the phase shifter is b-bit, the analog precoding codebook is as follows:
Figure GDA00032627669200000414
in the formula (I), the compound is shown in the specification,
Figure GDA0003262766920000051
Figure GDA0003262766920000052
representing the quantization azimuth of the ith codeword in the analog precoding codebook. The analog precoding codebook may be divided into L sub-codebooks corresponding to the L lobe subchannels
Figure GDA0003262766920000053
Setting the position of the code word forming the analog precoding matrix to be the self-supporting set psi of the analog precoding matrix, because of the analog precoding matrix of each lobe subchannel
Figure GDA0003262766920000054
Digital precoding matrix
Figure GDA0003262766920000055
Are independent of each other, and for each lobe corresponding to the simulated precoding matrix, there is a corresponding set of self-supporting ΨslDifferent analog precoding matrices
Figure GDA0003262766920000056
There is no identical support set between the self-supporting sets, i.e. the common support set is
Figure GDA0003262766920000057
And satisfies Ψ ═ Ψ { Ψ1，Ψ2，...，ΨL}. Because paths among different lobes are independent, when a simulation precoding matrix is designed, the search of all codebooks is converted into the search of a plurality of subcodebooks, namely a precoding reference matrix F is searchedresIn-analog precoding codebook
Figure GDA0003262766920000058
The largest codeword is up-projected. The target solution problem is:
Figure GDA0003262766920000059
in the formula (I), the compound is shown in the specification,
Figure GDA00032627669200000510
is the L-th analog precoding codebook, where L is 1, 2. The reference precoding matrix is an antenna array response, AtlRepresenting the transmit antenna array response for the l-th lobe subchannel.
Step four: simulating a precoding matrix for solving the corresponding problem of each lobe subchannel in the step three
Figure GDA00032627669200000511
Self-supported set ΨlA joint sparse method is introduced, the correlation between the analog pre-coding matrix and the digital pre-coding matrix is utilized, and a pre-coding reference matrix F is calculated according to the implicit sparse structure of the digital pre-coding matrixresIn-analog precoding codebook
Figure GDA00032627669200000512
The size of the projection is recorded, and the position of the code word with strong projection is recorded, so that a common support set among different data stream simulation pre-coding matrixes is obtained
Figure GDA00032627669200000513
Analog precoding matrix corresponding to each data stream
Figure GDA00032627669200000514
Self-supported set ΨlpThe two constitute psi corresponding to each lobe subchannell。
Forming an analog precoding matrix FRFIs located in the analog precoding matrix FRFDue to the analog precoding matrix of each lobe subchannel
Figure GDA00032627669200000515
Digital precoding matrix
Figure GDA00032627669200000516
Are independent of each other. Similarly, for each lobe, a corresponding analog precoding matrix is used
Figure GDA00032627669200000517
All have corresponding self-supporting sets psilWherein L is 1, 2. Different analog precoding matrices
Figure GDA00032627669200000518
There is no identical support set between the self-supporting sets, i.e. the common support set is
Figure GDA00032627669200000519
And satisfies Ψ ═ Ψ { Ψ1，Ψ2，...，ΨL}. Analog precoding matrix for each data stream
Figure GDA00032627669200000520
With its own supporting set of ΨlpEach data stream simulating a precoding matrix
Figure GDA00032627669200000521
There is a common supporting set between
Figure GDA00032627669200000522
Satisfy the requirement of
Figure GDA00032627669200000523
The first lobe simulates a precoding matrix
Figure GDA00032627669200000524
Self-supporting set of
Figure GDA0003262766920000061
And (3) actual solving: in a lobe, each data stream is shared
Figure GDA0003262766920000062
Corresponding psi of each data streamlpThe two constitute psi for each lobe pairlFinally, psi corresponding to all lobes is obtained. Correspondingly, the analog precoding matrix of each data stream is solved first
Figure GDA0003262766920000063
Analog precoding matrix for each lobe subchannel
Figure GDA0003262766920000064
Thereby obtaining a complete simulationPrecoding matrix FRF。
Because the digital precoding matrix has a hidden sparse structure, the projection sizes of column vectors of the precoding reference matrix on different code words are different, and the analog precoding matrix for the p data stream of the ith lobe
Figure GDA0003262766920000065
Design, consider that there are multiple strong projection cases for the precoded reference matrix column vector. To simplify the design, consider each
Figure GDA0003262766920000066
Designed to have the same number of projections
Figure GDA0003262766920000067
Are integers. If a common support set exists among the simulation precoding matrixes of different data streams
Figure GDA0003262766920000068
Searching
Figure GDA0003262766920000069
A code word, wherein
Figure GDA00032627669200000610
The expression is rounded down so that the column vectors of at least two pre-coding reference matrices have a strong projection on the selected code words, the positions of the code words are set as the analog pre-coding matrix
Figure GDA00032627669200000611
Common supporting set of
Figure GDA00032627669200000612
Simulating precoding matrix for designing p-th data stream
Figure GDA00032627669200000613
Searching
Figure GDA00032627669200000614
The position of each code word and the common support set
Figure GDA00032627669200000615
Form a
Figure GDA00032627669200000616
Self-supported set Ψlp. Thus, the formula (10) is converted into,
Figure GDA00032627669200000617
wherein
Figure GDA00032627669200000618
Representing the set ΨlpThe cardinality of (c), i.e., the number of elements in the set.
In order to solve the problems, the invention provides a combined sparse mixed precoding optimization algorithm based on a lobe decomposition channel. Since each lobe mixing precoding design is independent and the method is the same, only the first lobe mixing precoding matrix design is introduced below. Firstly, designing a common supporting set
Figure GDA00032627669200000619
Precoding reference matrix FresAntenna array response A for the l lobetlCalculating a correlation matrix of the reference matrix and the codebook,
Figure GDA00032627669200000620
searching
Figure GDA00032627669200000621
A code word such that a reference matrix F is precodedresThe column vectors have a strong projection on the selected codeword, and if the selected codeword can be used as a common support, the condition needs to be satisfied,
Figure GDA0003262766920000071
making a precoding reference matrix FresExcept for j0There are still other column vectors in the ith column vector in addition to the individual column vector0Having a strong projection on each codeword, then the ith0The individual code words being common supports, the code word position i being recorded0Updating common supporting set
Figure GDA0003262766920000072
Self-supporting set Ψ of p-th data stream analog precoding matrixlp. To design for
Figure GDA0003262766920000073
Selecting a single antenna array response column vector Atl(p) as a reference matrix FresCalculating a correlation matrix R, similar to the common support setcSearch for
Figure GDA0003262766920000074
Forming an analog precoding matrix from the individual codewords and updating ΨlpModeling the self-supporting set Ψ of the precoding matrix with the l-th lobel。
Step five: modeling the self-supporting set Ψ of the precoding matrix according to each lobelOptimizing the column vector distribution of the simulation pre-coding matrix to obtain the simulation pre-coding matrix
Figure GDA0003262766920000075
Obtaining the matrix of the analog combiner in the same way
Figure GDA0003262766920000076
Accordingly, ΨlEmbodies the correlation between the analog pre-coding matrix and the digital pre-coding matrix, so equivalent sub-channels are obtained
Figure GDA0003262766920000077
Performing singular value decomposition to obtain
Figure GDA0003262766920000078
That is, a digital precoding matrix can be obtained
Figure GDA0003262766920000079
The row vectors of the digital pre-coding matrix and the column vectors of the analog pre-coding matrix are in one-to-one correspondence to realize the joint optimization of the hybrid pre-coding, and the digital combiner matrix is obtained in the same way
Figure GDA00032627669200000710
Step six: repeating the first step to the fifth step, designing an own support set of the simulation precoding matrix corresponding to each lobe subchannel to obtain a simulation precoding matrix FRFIs self-supporting set Ψ ═ Ψ { Ψ ═ Ψ1，Ψ2，...，ΨL}. The analog precoding matrix is
Figure GDA00032627669200000711
Similarly, the combiner matrix is simulated
Figure GDA00032627669200000712
Corresponding digital precoding matrix is
Figure GDA00032627669200000713
The digital combiner matrix is
Figure GDA00032627669200000714
The method also comprises the steps of constructing an analog precoding codebook by adopting a uniform quantization and non-uniform quantization mode, and drawing the change condition of the communication performance index along with the signal-to-noise ratio by utilizing MATLAB simulation. The communication performance index of the millimeter wave large-scale MIMO system is the frequency spectrum efficiency.
The simulation pre-coding matrix F obtained according to the pre-coding design method of the inventionRFDigital precoding matrix FBBAnalog combiner matrix WRFDigital combiner matrix WBBThe frequency spectrum efficiency of the millimeter wave large-scale MIMO system can be improved. Moreover, the invention also provides a mixed pre-editing method designed by adopting the methodThe application of codes in the field of wireless communication technology.
The invention has the beneficial effects that:
according to the hybrid precoding design method, based on the lobe decomposition channel, the hybrid precoding optimization design is carried out by introducing the joint sparse method, the original hybrid precoding design problem is converted into the hybrid precoding design problem corresponding to a plurality of lobes and a plurality of data streams, the complexity of the precoding design process is simplified, the precoding design is optimized, and better system performance can be obtained in a large-scale MIMO system.
The hybrid precoding design method also reduces the requirement of the system on an analog precoding codebook, is more suitable for a practical large-scale MIMO system, fully utilizes the correlation between analog precoding and digital precoding, obtains the self-supporting set and the shared supporting set of each lobe and each data stream corresponding to the analog precoding matrix according to the implicit sparse structure of the digital precoding matrix, realizes the joint optimization of the analog precoding and the digital precoding, and improves the spectrum efficiency and the error rate performance of the system on the premise of ensuring the calculation complexity of the system.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a schematic diagram of a hybrid precoding structure in a millimeter wave massive MIMO system according to the present invention;
fig. 2 shows that in a 32 × 16, 128 × 32MIMO system with a lobe splitting channel, a millimeter wave frequency of 28GHz, and a bandwidth of 100MHz, the number of lobes L is 2, the number of paths in the lobes P is 2, and a radio frequency chain at a transmitting end is used as a transmit end
Figure GDA0003262766920000081
Receiving end radio frequency chain
Figure GDA0003262766920000082
Data stream NsUnder the condition that the phase resolution b of the phase shifter is 6, comparing the optimal pre-coding, an orthogonal matching pursuit algorithm (UQ-OMP) based on a uniform quantization codebook, a lobe decomposition algorithm (UQ-SLD) based on the uniform quantization codebook, a lobe decomposition algorithm (NUQ-SLD) based on a non-uniform quantization codebook and a schematic diagram of the change condition of the spectrum efficiency of the technical method of the invention along with the signal-to-noise ratio;
fig. 3(a) is a graph comparing the spectral efficiency variation of each algorithm when using non-uniform quantization codebooks under different phase resolutions of phase shifters, where b is 3, 4, and 5; fig. 3(b) is a graph comparing the spectral efficiency variation of each algorithm when uniform quantization and non-uniform quantization codebooks are used, wherein uniform quantization b is 6 and non-uniform quantization b is 4; the system is a 32 × 16MIMO system, the number of lobes L is 2, the number of paths in the lobes P is 2, and a radio frequency chain at a transmitting end
Figure GDA0003262766920000083
Receiving end radio frequency chain
Figure GDA0003262766920000084
Data stream Ns＝LP；
Fig. 4(a) is a comparison of the spectral efficiency variation of each algorithm when the present invention adopts a uniform quantization codebook in the case of different numbers of paths in lobes, where b is 6; fig. 4(b) is a comparison of the spectral efficiency variation of each algorithm when the number of paths in lobes is different and a non-uniform quantization codebook is used, where b is 4; in the 32 × 16MIMO system, the number of lobes L is 2, the number of paths in the lobes P is 2, and the transmitting-end radio frequency chain
Figure GDA0003262766920000091
Receiving end radio frequency chain
Figure GDA0003262766920000092
Data stream Ns＝LP；
FIG. 5(a) is the present inventionObviously comparing the error rate change conditions of each algorithm under the condition that the lobe path numbers are different and under the condition that a uniform quantization codebook is adopted, wherein b is 6; fig. 5(b) is a comparison of the bit error rate variation of each algorithm when the number of paths in lobes is different and a non-uniform quantization codebook is used, where b is 4; in the 32 × 16MIMO system, the number of lobes L is 2, the number of paths in the lobes P is 2, and the transmitting-side radio frequency link is configured as a transmit-side radio frequency link
Figure GDA0003262766920000093
Receiving end radio frequency chain
Figure GDA0003262766920000094
Data stream NsThe phase resolution b of the phase shifter is 6 for LP.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
The first embodiment is as follows:
this embodiment provides a method for designing hybrid precoding in a millimeter wave massive MIMO system, which combines the schematic diagram of a hybrid precoding structure shown in fig. 1, where the millimeter wave massive MIMO system includes NsAfter the transmitting end carries out digital pre-coding processing on the transmitting signal s of each data stream through a digital pre-coder, the transmitting signal s is transmitted to the receiving end
Figure GDA0003262766920000095
The analog pre-coder is composed of a radio frequency chain, a phase shifter and a radio frequency adder, and after analog pre-coding processing is carried out by the analog pre-coder, the data stream is mapped to NtTransmitting the data to a noisy lobe decomposition channel for data transmission on a root transmitting antenna, and transmitting the data to a receiving end through NrAnd the receiving antenna receives data and processes the data through the analog combiner and the digital combiner in sequence to obtain a receiving signal y, so that multi-path data transmission comprising a plurality of data streams is realized.
Assuming that N is arranged at a transmitting end in the millimeter wave massive MIMO systemtRoot transmitting antenna，
Figure GDA0003262766920000096
A radio frequency chain, a receiving end has NrThe antenna is received at the root of the antenna,
Figure GDA0003262766920000097
a radio frequency chain, the number of transmission data streams is Ns. In order to ensure multiplexing gain and realize data stream communication of multiple channels, the number of radio frequency chains at the transmitting end and the receiving end respectively satisfies
Figure GDA0003262766920000098
Is transmitting a signal vector and satisfies
Figure GDA0003262766920000099
In the formula (I), the compound is shown in the specification,
Figure GDA00032627669200000910
is a noise covariance matrix;
Figure GDA00032627669200000911
is transmitting a signal vector and satisfies
Figure GDA00032627669200000912
FRFTo represent
Figure GDA00032627669200000913
Dimension simulation precoding matrix, FBBTo represent
Figure GDA00032627669200000914
Dimension digital precoding matrix, WRFTo represent
Figure GDA00032627669200000915
Analog combiner matrix of dimensions, WBBTo represent
Figure GDA00032627669200000916
Number merger matrix of dimensions, F ═ FRFFBBFor the hybrid precoding matrix, the total transmission power is satisfied
Figure GDA00032627669200000917
W＝WRFWBBRepresenting a combiner matrix;
Figure GDA00032627669200000918
for channel noise vector, σ2Is the power of the noise(s),
Figure GDA00032627669200000919
for the channel matrix, ρ represents the average received power.
According to this embodiment, and as shown in fig. 1, the hybrid precoding design method includes the following specific steps:
the method comprises the following steps: in order to maximize the spectral efficiency of a system, the design of a digital precoder, an analog combiner and a digital combiner is optimized, and the optimization problem containing non-convex constraint in the design process of mixed precoding comprising an analog precoding matrix, a digital precoding matrix, an analog combiner matrix and a digital combiner matrix is converted into the problem of solving the minimum Euclidean distance;
under the lobe decomposition channel model, the received signal is y,
Figure GDA0003262766920000101
taking the gaussian signal as the transmission signal s, the system spectrum efficiency is:
Figure GDA0003262766920000102
in the formula (I), the compound is shown in the specification,
Figure GDA0003262766920000103
is a noise covariance matrix. With the goal of maximizing spectral efficiency, the formula for hybrid precoding design is as follows:
Figure GDA0003262766920000104
wherein omega is an analog precoding codebook with constant modulus constraint and satisfies
Figure GDA0003262766920000105
In order to simplify the design, the formula (3) is converted into the problem of solving the euclidean distance minimum as shown in the formula (4), and the optimal code word is searched in the analog precoding codebook Ω to form an analog precoding matrix:
Figure GDA0003262766920000106
in the formula, FoptIs an optimal precoding reference matrix, and can be decomposed by singular values of a channel matrix, H ═ U ∑ VHTo obtain i.e. Fopt＝V(:，1：Ns)。
Step two: according to mutual independence among the lobes, the lobe channel is decomposed into a plurality of independent lobe sub-channels, the problem (4) in the first step can be converted into a mixed precoding design problem based on the independent lobe sub-channels, and an analog precoding matrix and a digital precoding matrix are respectively designed;
respectively designing an analog precoding matrix and a digital precoding matrix aiming at the L lobe sub-channels:
Figure GDA0003262766920000107
in the formula (I), the compound is shown in the specification,
Figure GDA0003262766920000108
for the optimal precoding reference matrix corresponding to the l-th lobe subchannel,
Figure GDA0003262766920000109
and
Figure GDA00032627669200001010
respectively corresponding to the l sub-channel, an analog pre-coding matrix and a digital pre-coding matrix, omegalRepresents the ith analog precoding subcodebook, and
Figure GDA00032627669200001011
the invention assumes power averaging distribution, GlIs the sum of the powers of all transmission paths in the first lobe.
Step three: solving analog precoding matrix corresponding to each lobe subchannel
Figure GDA0003262766920000111
And a digital precoding matrix
Figure GDA0003262766920000112
Selecting antenna array response A for each lobe subchanneltlAs a precoding reference matrix FresAnd constructing an analog precoding codebook according to the hardware limitation of a phase shifter in the analog precoding module. At each sub-codebook
Figure GDA0003262766920000113
Searching the position of the best code word to form an analog precoding matrix
Figure GDA0003262766920000114
Self-supported set Ψl。
To avoid high complexity matrix operations, an antenna array response A is selectedtAs a precoding reference matrix. The channel matrix H can be abbreviated as:
Figure GDA0003262766920000115
Figure GDA0003262766920000116
in order for the transmitting end antenna array to respond,
Figure GDA0003262766920000117
for the receiving endAn antenna array response. Each path has a multiplexing gain of
Figure GDA0003262766920000118
For each lobe subchannel, the antenna array response corresponds to L sub-antenna array responses, with a transmit side at＝[At1，At2，...，AtL]The receiving end is Ar＝[Ar1，Ar2，...，ArL]，ArlAnd AtlDenotes the L-th antenna array response, where L1, 2.
And constructing an analog precoding codebook according to the hardware limit of a phase shifter in the analog precoding module. Assume an analog precoding codebook size of Nθ＝2bAnd b represents that the phase resolution of the phase shifter is b-bit, the analog precoding codebook is as follows:
Figure GDA0003262766920000119
in the formula (I), the compound is shown in the specification,
Figure GDA00032627669200001110
Figure GDA00032627669200001111
representing the quantization azimuth of the ith codeword in the analog precoding codebook. The analog precoding codebook may be divided into L sub-codebooks
Figure GDA00032627669200001112
Setting the position of the code word forming the analog precoding matrix to be the self-supporting set psi of the analog precoding matrix, because of the analog precoding matrix of each lobe subchannel
Figure GDA00032627669200001113
Digital precoding matrix
Figure GDA00032627669200001114
Are independent of each other, and for each lobe corresponding to the simulated precoding matrix, there is a corresponding set of self-supporting ΨslWherein L is 1, 2. Different analog precoding matrices
Figure GDA00032627669200001115
There is no identical support set between the self-supporting sets, i.e. the common support set is
Figure GDA00032627669200001116
And satisfies Ψ ═ Ψ { Ψ1，Ψ2，...，ΨL}. Because paths among different lobes are independent, when a simulation precoding matrix is designed, the search of all codebooks is converted into the search of a plurality of subcodebooks, namely a precoding reference matrix A is searchedtlIn-analog precoding codebook
Figure GDA00032627669200001117
The largest codeword is up-projected. The target solution problem is:
Figure GDA0003262766920000121
in the formula (I), the compound is shown in the specification,
Figure GDA0003262766920000122
is the L-th analog precoding codebook, where L is 1, 2. The reference precoding matrix is an antenna array response, AtlRepresenting the transmit antenna array response for the l-th lobe subchannel.
Step four: simulating a precoding matrix for solving the corresponding problem of each lobe in the third step
Figure GDA0003262766920000123
Self-supported set ΨlIntroducing a joint sparse method, using an analog precoding matrix and digital precodingThe correlation between the coding matrixes is calculated, and a precoding reference matrix F is calculated according to the implicit sparse structure of the digital precoding matrixresIn-analog precoding codebook
Figure GDA0003262766920000124
The size of the projection is recorded, and the position of the code word with strong projection is recorded, so that a common support set among different data stream simulation pre-coding matrixes is obtained
Figure GDA0003262766920000125
Analog precoding matrix corresponding to each data stream
Figure GDA0003262766920000126
Self-supported set ΨlpThe two form Ψl。
Forming an analog precoding matrix FRFIs located at the position of the analog precoding FRFDue to the analog precoding matrix of each lobe subchannel
Figure GDA0003262766920000127
Digital precoding matrix
Figure GDA0003262766920000128
Are independent of each other. Similarly, for each lobe, a corresponding analog precoding matrix is used
Figure GDA0003262766920000129
All have corresponding self-supporting sets psilDifferent analog precoding matrices
Figure GDA00032627669200001210
There is no identical support set between the self-supporting sets, i.e. the common support set is
Figure GDA00032627669200001211
And satisfies Ψ ═ Ψ { Ψ1，Ψ2，...，ΨL}. Analog precoding matrix for each data stream
Figure GDA00032627669200001212
With its own supporting set of ΨlpEach data stream simulating a precoding matrix
Figure GDA00032627669200001213
There is a common supporting set between
Figure GDA00032627669200001214
Satisfy the requirement of
Figure GDA00032627669200001215
The first lobe simulates a precoding matrix
Figure GDA00032627669200001216
Self-supporting collector
Figure GDA00032627669200001217
Wherein
Figure GDA00032627669200001218
To represent
Figure GDA00032627669200001219
To ΨlpThe difference set of (2). And (3) actual solving: in a lobe, each data stream is shared
Figure GDA00032627669200001220
Corresponding psi of each data streamlpThe two constitute psi corresponding to each lobelFinally, psi corresponding to all lobes is obtained. Correspondingly, the analog precoding matrix of each data stream is solved first
Figure GDA00032627669200001221
Analog precoding matrix for each lobe subchannel
Figure GDA00032627669200001222
Thereby obtaining a complete analog precoding matrix FRF。
Because the digital precoding matrix has a hidden sparse structure, the projection sizes of column vectors of the precoding reference matrix on different code words are different, and the analog precoding matrix for the p data stream of the ith lobe
Figure GDA00032627669200001223
Design, consider that there are multiple strong projection cases for the precoded reference matrix column vector. To simplify the design, consider each
Figure GDA00032627669200001224
Designed to have the same number of projections
Figure GDA00032627669200001225
Is an integer. If a common support set exists among the simulation precoding matrixes of different data streams
Figure GDA00032627669200001226
Searching
Figure GDA00032627669200001227
A code word, wherein
Figure GDA0003262766920000131
The expression is rounded down so that the column vectors of at least two pre-coding reference matrices have a strong projection on the selected code words, the positions of the code words are set as the analog pre-coding matrix
Figure GDA0003262766920000132
Common supporting set of
Figure GDA0003262766920000133
Simulating precoding matrix for designing p-th data stream
Figure GDA0003262766920000134
Searching
Figure GDA0003262766920000135
The position of each code word and the common support set
Figure GDA0003262766920000136
Form a
Figure GDA0003262766920000137
Self-supported set Ψlp. Thus, the formula (10) is converted into,
Figure GDA0003262766920000138
wherein
Figure GDA0003262766920000139
Representing the set ΨlpThe cardinality of (c), i.e., the number of elements in the set.
In order to solve the problems, the invention provides a combined sparse mixed precoding optimization algorithm based on a lobe decomposition channel. Since each lobe mixing precoding design is independent and the method is the same, only the first lobe mixing precoding matrix design is introduced below. Firstly, designing a common supporting set
Figure GDA00032627669200001310
Precoding reference matrix FresAntenna array response A for the l lobetlCalculating a correlation matrix of the reference matrix and the codebook,
Figure GDA00032627669200001311
searching
Figure GDA00032627669200001312
A code word such that a reference matrix F is precodedresThe column vectors have a strong projection on the selected codeword, and if the selected codeword can be used as a common support, the condition needs to be satisfied,
Figure GDA00032627669200001313
making a precoding reference matrix FresExcept for j0There are still other column vectors in the ith column vector in addition to the individual column vector0Having a strong projection on each codeword, then the ith0With individual code words as common supports, recording the position i of the code word0Updating common supporting set
Figure GDA00032627669200001314
Self-supporting set Ψ of p-th data stream analog precoding matrixlp. To design for
Figure GDA00032627669200001315
Selecting a single antenna array response column vector Atl(p) as a reference matrix FresCalculating a correlation matrix R, similar to the common support setcSearch for
Figure GDA00032627669200001316
Forming an analog precoding matrix from the individual codewords and updating ΨlpModeling the self-supporting set Ψ of precoding matrix with the l-th lobel。
Step five: modeling the self-supporting set Ψ of the precoding matrix according to each lobelOptimizing the column vector distribution of the simulation pre-coding matrix to obtain the simulation pre-coding matrix
Figure GDA00032627669200001317
Obtaining the matrix of the analog combiner by the same method
Figure GDA00032627669200001318
Accordingly, ΨlEmbodies the correlation between the analog pre-coding matrix and the digital pre-coding matrix, so equivalent sub-channels are obtained
Figure GDA0003262766920000141
Performing singular value decomposition to obtain
Figure GDA0003262766920000142
That is, a digital precoding matrix can be obtained
Figure GDA0003262766920000143
The row vectors of the digital pre-coding matrix and the column vectors of the analog pre-coding matrix are in one-to-one correspondence, the joint optimization of hybrid pre-coding is realized, and the matrix of the digital combiner is obtained in the same way
Figure GDA0003262766920000144
Step six: repeating the first step to the fifth step, designing an own support set of the simulation precoding matrix corresponding to each lobe subchannel to obtain a simulation precoding matrix FRFIs self-supporting set Ψ ═ Ψ { Ψ ═ Ψ1，Ψ2，...，ΨL}. The analog precoding matrix is
Figure GDA0003262766920000145
Corresponding digital precoding matrix is
Figure GDA0003262766920000146
The same can obtain the matrix of the analog combiner
Figure GDA0003262766920000147
Digital combiner matrix
Figure GDA0003262766920000148
In order to make the purpose, technical scheme and advantages of the present invention clearer, some classical precoding algorithms are compared with the proposed algorithm to show the superiority of the joint sparse mixed precoding optimization design method in the aspects of computational complexity, spectral efficiency and error rate performance.
The precoding algorithms used for comparison are respectively an optimal precoding algorithm (OPT), a uniform quantization orthogonal matching algorithm (UQ-OMP), a non-uniform quantization orthogonal matching algorithm (NUQ-OMP), a uniform quantization spatial lobe decomposition algorithm (UQ-SLD) and a non-uniform quantization spatial lobe decomposition algorithm (NUQ-SLD).
The optimal precoding algorithm is a classic precoding algorithm, and shows better spectrum efficiency performance in a large-scale MIMO system. The UQ-OMP algorithm and the NUQ-OMP algorithm respectively adopt a uniform quantization mode and a non-uniform quantization mode to construct a simulation precoding codebook, the OMP algorithm is used for solving the sparse reconstruction problem, the UQ-SLD algorithm and the NUQ-SLD algorithm reconstruct the original problem into a mixed precoding design problem of a plurality of sub-channels by utilizing the sparsity of azimuth angles of paths in space lobes, and respectively adopt the uniform quantization mode and the non-uniform quantization mode to construct the simulation precoding codebook.
Fig. 2 shows that in a 32 × 16, 128 × 32MIMO system with a lobe splitting channel, a millimeter wave frequency of 28GHz, and a bandwidth of 100MHz, the number of lobes L is 2, the number of paths in the lobes P is 2, and a radio frequency chain at a transmitting end is used as a transmit end
Figure GDA0003262766920000149
Receiving end radio frequency chain
Figure GDA00032627669200001410
Data stream NsUnder the condition that the phase resolution b of the phase shifter is 6, comparing the optimal pre-coding, an orthogonal matching pursuit algorithm (UQ-OMP) based on a uniform quantization codebook, a lobe decomposition algorithm (UQ-SLD) based on the uniform quantization codebook, a lobe decomposition algorithm (NUQ-SLD) based on a non-uniform quantization codebook and a schematic diagram of the change condition of the spectrum efficiency of the technical method of the invention along with the signal-to-noise ratio;
fig. 3(a) is a graph comparing the spectral efficiency variation of each algorithm when using non-uniform quantization codebooks under different phase resolutions of phase shifters, where b is 3, 4, and 5; fig. 3(b) is a graph comparing the spectral efficiency variation of each algorithm when uniform quantization and non-uniform quantization codebooks are used, wherein uniform quantization b is 6 and non-uniform quantization b is 4; the system is a 32 × 16MIMO system, the number of lobes L is 2, the number of paths in the lobes P is 2, and a radio frequency chain at a transmitting end
Figure GDA0003262766920000151
Receiving end radio frequency chain
Figure GDA0003262766920000152
Data stream Ns＝LP；
Fig. 4(a) is a comparison of the spectral efficiency variation of each algorithm when the present invention adopts a uniform quantization codebook in the case of different numbers of paths in lobes, where b is 6; fig. 4(b) is a comparison of the spectral efficiency variation of each algorithm when the number of paths in lobes is different and a non-uniform quantization codebook is used, where b is 4; in the 32 × 16MIMO system, the number of lobes L is 2, the number of paths in the lobes P is 2, and the transmitting-end radio frequency chain
Figure GDA0003262766920000153
Receiving end radio frequency chain
Figure GDA0003262766920000154
Data stream Ns＝LP；
Fig. 5(a) is a comparison of the bit error rate variation of each algorithm when the uniform quantization codebook is used in the case of different numbers of paths in lobes, where b is 6; fig. 5(b) is a comparison of the bit error rate variation of each algorithm when the number of paths in lobes is different and a non-uniform quantization codebook is used, where b is 4; in the 32 × 16MIMO system, the number of lobes L is 2, the number of paths in the lobes P is 2, and the transmitting-end radio frequency chain is configured to transmit data in the uplink
Figure GDA0003262766920000155
Receiving end radio frequency chain
Figure GDA0003262766920000156
Data stream NsThe phase resolution b of the phase shifter is 6 for LP.
As shown in fig. 2, the spectral efficiency of the above algorithm is improved with the increase of the signal-to-noise ratio. When N is presentt＝32、Nr＝16，
When the uniform quantization codebook is adopted, compared with the UQ-SLD algorithm, the spectral efficiency of the invention is improved by 0.68bps/Hz, and when the non-uniform quantization codebook is adopted, compared with the NUQ-SLD algorithm, the spectral efficiency of the invention is improved by 0.44bps/Hz, namely two typesUnder the condition, the spectral efficiency of the proposed algorithm reaches 89.6% and 99% of the OPT algorithm respectively. Likewise, when N ist＝128、NrWhen the value is 32 and the value b is 8, the frequency spectrum efficiency of the algorithm is obviously improved. Compared with the OMP algorithm, the algorithm has gap in spectrum efficiency performance, but the algorithm greatly reduces the calculation complexity, and the larger the number of the antennas is, the larger the reduction range of the calculation complexity is (see section 3.3). The algorithm and the SLD algorithm both select antenna array response as a reference matrix to avoid complex matrix operation and sacrifice the spectral efficiency performance of part of systems; compared with the SLD algorithm, under the condition of two quantization modes, the algorithm provided by the invention has the advantages that the spectrum efficiency difference is reduced, the influence of the analog precoding codebook quantization mode on the system spectrum efficiency is reduced, and the requirement on the phase resolution of the phase shifter is reduced.
Fig. 3(a) shows that the algorithm spectrum efficiency changes under different phase resolutions of phase shifters when the non-uniform quantization codebook is used. As can be seen from the figure, as the phase resolution b of the phase shifter is increased, the spectral efficiency of several algorithms is improved, and the spectral efficiency gradually approaches to the OPT algorithm. Fig. 3(b) is a comparison graph of the spectral efficiency of the algorithm under the conditions of uniform quantization and non-uniform quantization. As can be seen from the figure, the spectral efficiency when the non-uniform quantization b is 4 is similar to that when the uniform quantization b is 6, because the quantization precision of the non-uniform quantization is higher than that of the uniform quantization (see section 3.1), and when the phase resolution of the phase shifter is the same, the algorithm has higher spectral efficiency when the non-uniform quantization is used compared with the uniform quantization. When in non-uniform quantization
Figure GDA0003262766920000161
Then the total angulation angle
Figure GDA0003262766920000162
Is a uniform quantization of the total quantization angle
Figure GDA0003262766920000163
Therefore, when the two spectral efficiencies are close, the non-uniform quantization is less than the uniform quantization2 bits.
Fig. 4(a) and 4(b) are graphs comparing the changes of spectral efficiency in the case of different path numbers P, for uniform quantization and non-uniform quantization, respectively. As can be seen from the figure, regardless of whether a uniform quantization codebook or a non-uniform quantization codebook is used, the spectral efficiency of each algorithm is improved as the number of paths P increases, and the spectral efficiency when the non-uniform quantization b is 4 is close to that when the uniform quantization b is 6.
Fig. 5(a) and 5(b) show the bit error rate of each algorithm as a function of the signal-to-noise ratio when the quantization is uniform and non-uniform, respectively. As can be seen from the figure, when P is 1, the error rate of each algorithm is lower than that of P2, regardless of whether uniform quantization or non-uniform quantization is used. Since the smaller the number of paths P, the less interference between transmission paths within a lobe, the lower the system error rate. Under two quantification modes, the error rate performance of the algorithm is close to that of an OPT algorithm, and compared with an SLD algorithm, the error rate is 6 multiplied by 10-2When the signal-to-noise ratio gain is increased by about 2dB under the condition that P is 1, the error rate difference with the OMP algorithm is reduced by 50%; when the error rate is 5 x 10-1When P is 2, the snr gain is increased by about 3.7dB, and the snr loss from the OMP algorithm is only 0.3 dB.
As can be seen from the results of fig. 2 to fig. 5(b), the joint sparse hybrid precoding algorithm exhibits the advantages of higher spectral efficiency and bit error rate performance, and can still ensure the spectral efficiency and bit error rate performance of the large-scale MIMO system under the condition of lower phase shifter resolution.
Some steps in the embodiments of the present invention may be implemented by software, and the corresponding software program may be stored in a readable storage medium, such as an optical disc or a hard disk.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (10)

1. A mixed precoding design method in a millimeter wave large-scale MIMO system is characterized in that the millimeter wave large-scale MIMO system comprises NsAfter the transmitting end carries out digital pre-coding processing on the transmitting signal s of each data stream through the digital pre-coding module, the transmitting signal s is transmitted to the receiving end
Figure FDA0003545747940000011
The analog pre-coding module is composed of a radio frequency chain, a phase shifter and a radio frequency adder, and after analog pre-coding processing is carried out by the analog pre-coding module, the data stream is mapped to NtTransmitting the data to a noisy lobe decomposition channel for data transmission on a root transmitting antenna, and transmitting the data to a receiving end through NrThe root receiving antenna receives data, and the data are processed by the analog combining module and the digital combining module in sequence to obtain a receiving signal y, so that multi-path data transmission comprising a plurality of data streams is realized; the method comprises the following steps:
the method comprises the following steps: in order to maximize the spectral efficiency of a system, the design of a digital pre-coding module, an analog merging module and a digital merging module is optimized, and the optimization problem containing non-convex constraint in the design process of mixed pre-coding comprising an analog pre-coding matrix, a digital pre-coding matrix, an analog merger matrix and a digital merger matrix is converted into the problem of solving the minimum Euclidean distance;
step two: because of the independence among the lobes, the lobe channel is decomposed into L independent lobe sub-channels, the problem of solving the minimum Euclidean distance in the step one is simplified into a mixed precoding design aiming at each lobe sub-channel, and an analog precoding matrix and a digital precoding matrix are respectively designed aiming at each lobe sub-channel;
step three: solving analog precoding matrix corresponding to each lobe subchannel
Figure FDA0003545747940000012
And a digital precoding matrix
Figure FDA0003545747940000013
Selecting antenna array response A for each lobe subchanneltlAs a precoding reference matrix FresAccording to the hardness of the phase shifters in the analog precoding blockLimiting the part, and constructing an analog precoding codebook; and at each analog precoding codebook
Figure FDA0003545747940000014
Searching the position of the best code word to obtain an analog pre-coding matrix
Figure FDA0003545747940000015
Self-supported set Ψl；
Step four: solving the analog precoding matrix corresponding to each lobe subchannel in the third step
Figure FDA0003545747940000016
Self-supported set ΨlIntroducing a joint sparse method, calculating a precoding reference matrix F by utilizing the correlation between the analog precoding matrix and the digital precoding matrix and according to the implicit sparse structure of the digital precoding matrixresIn-analog precoding codebook
Figure FDA0003545747940000017
Projection of (2) onto (F)resThe positions of the code words with strong projection are obtained, thereby obtaining a common support set among the analog pre-coding matrixes of different data streams
Figure FDA0003545747940000018
Analog precoding matrix corresponding to each data stream
Figure FDA0003545747940000019
Self-supported set ΨlpFrom
Figure FDA00035457479400000110
And ΨlpForm Ψl；
Step five: according to the analog precoding matrix corresponding to each lobe subchannel
Figure FDA0003545747940000021
Self-supported set ΨlOptimizing the column vector distribution of the simulation pre-coding matrix to obtain the simulation pre-coding matrix
Figure FDA0003545747940000022
Obtaining the matrix of the analog combiner by the same method
Figure FDA0003545747940000023
Accordingly, ΨlEmbodies the correlation between the analog pre-coding matrix and the digital pre-coding matrix, so equivalent sub-channels are obtained
Figure FDA0003545747940000024
Performing singular value decomposition to obtain
Figure FDA0003545747940000025
A digital precoding matrix can be obtained
Figure FDA0003545747940000026
The row vectors of the digital pre-coding matrix and the column vectors of the analog pre-coding matrix are in one-to-one correspondence, and the joint optimization of hybrid pre-coding is realized;
step six: repeating the first step to the fifth step, designing an own support set of the simulation precoding matrix corresponding to each lobe subchannel, and obtaining a simulation precoding matrix FRFIs self-supporting set Ψ ═ Ψ { Ψ ═ Ψ1，Ψ2，...，ΨL}; simulating a precoding matrix
Figure FDA0003545747940000027
The same can obtain the matrix of the analog combiner
Figure FDA0003545747940000028
Accordingly, the digital precoding matrix is
Figure FDA0003545747940000029
Digital mergerThe matrix is
Figure FDA00035457479400000210
2. The hybrid precoding design method of claim 1, wherein in step one of the method,
under the lobe decomposition channel model, the received signal y is:
Figure FDA00035457479400000211
taking the gaussian signal as the transmission signal s, the spectral efficiency of the system is:
Figure FDA00035457479400000212
in the formula (I), the compound is shown in the specification,
Figure FDA00035457479400000213
is a noise covariance matrix;
Figure FDA00035457479400000214
to transmit a signal vector and satisfy
Figure FDA00035457479400000215
FRFTo represent
Figure FDA00035457479400000216
Dimension simulation precoding matrix, FBBTo represent
Figure FDA00035457479400000217
Dimension digital precoding matrix, WRFTo represent
Figure FDA00035457479400000218
Of dimensionAnalog combiner matrix, WBBTo represent
Figure FDA00035457479400000219
Number merger matrix of dimensions, F ═ FRFFBBFor the hybrid precoding matrix, the total transmission power is satisfied
Figure FDA0003545747940000031
W＝WRFWBBRepresenting a combiner matrix;
Figure FDA0003545747940000032
for channel noise vector, σ2Is the power of the noise or noise,
Figure FDA0003545747940000033
for the channel matrix, ρ represents the average received power; with the goal of maximizing the spectral efficiency of the system, the formula for hybrid precoding design is as follows:
Figure FDA0003545747940000034
wherein Ω is an analog precoding codebook with constant modulus constraint and satisfies
Figure FDA0003545747940000035
3. The hybrid precoding design method of claim 2, wherein in step one of the method,
in order to simplify the design, the formula (3) is converted into the problem of solving the euclidean distance minimum as shown in the formula (4), and the optimal code word is searched in the analog precoding codebook Ω to form an analog precoding matrix:
Figure FDA0003545747940000036
in the formula, FoptIs an optimal precoding reference matrix, which can be decomposed by singular value of channel matrix HHTo obtain i.e. Fopt＝V(：，1：NS)。
4. The hybrid precoding design method of claim 1, wherein the second step further comprises:
respectively designing an analog precoding matrix and a digital precoding matrix aiming at the L lobe sub-channels:
Figure FDA0003545747940000037
in the formula (I), the compound is shown in the specification,
Figure FDA0003545747940000038
for the optimal precoding reference matrix corresponding to the l-th lobe subchannel,
Figure FDA0003545747940000039
and
Figure FDA00035457479400000310
respectively corresponding to the l sub-channel, an analog pre-coding matrix and a digital pre-coding matrix, omegalRepresents the ith analog precoding subcodebook, and
Figure FDA00035457479400000311
assuming power averaging distribution, GlIs the sum of the powers of all transmission paths in the first lobe.
5. The hybrid precoding design method of claim 4, wherein the third step further comprises:
to avoid high complexity matrix operations, an antenna array response A is selectedtAs a precoding reference matrix; the channel matrix H can be abbreviated as:
Figure FDA0003545747940000041
Figure FDA0003545747940000042
in order for the transmitting end antenna array to respond,
Figure FDA0003545747940000043
responding to the receiving end antenna array; the multiplexing gain of each data transmission path is:
Figure FDA0003545747940000044
for each lobe subchannel, the antenna array response corresponds to L sub-antenna array responses, with a transmit side at＝[At1，At2，...，AtL]The receiving end is Ar＝[Ar1，Ar2，...，ArL]，ArlAnd AtlDenotes the L-th antenna array response, where L1, 2.
6. The hybrid precoding design method of claim 5, wherein in step three of the method,
constructing an analog pre-coding codebook according to the hardware limit of a phase shifter in the analog pre-coding module; assume an analog precoding codebook size of Nθ＝2bAnd b represents that the phase resolution of the phase shifter is b-bit, the analog precoding codebook is as follows:
Figure FDA0003545747940000045
in the formula (I), the compound is shown in the specification,
Figure FDA0003545747940000046
Figure FDA0003545747940000047
representing a quantization azimuth of an ith codeword in the analog precoding codebook; the analog precoding codebook may be divided into L sub-codebooks corresponding to the L lobe subchannels
Figure FDA0003545747940000048
7. The hybrid precoding design method of claim 6, wherein in step three of the method,
setting the position of the code word forming the analog precoding matrix to be the self-supporting set psi of the analog precoding matrix, because of the analog precoding matrix of each lobe subchannel
Figure FDA0003545747940000051
Digital precoding matrix
Figure FDA0003545747940000052
Are independent of each other, and for each lobe corresponding to the simulated precoding matrix, there is a corresponding set of self-supporting ΨslWherein L is 1, 2.. L; different analog precoding matrices
Figure FDA0003545747940000053
Does not have the same support set and satisfies psi ═ psi1，Ψ2，...，ΨL}; because paths among different lobes are mutually independent, when a simulation precoding matrix is designed, the search of all codebooks is converted into the search of a plurality of subcodebooks, and the problem of target solution is as follows:
Figure FDA0003545747940000054
in the formula (I), the compound is shown in the specification,
Figure FDA0003545747940000055
an L-th analog precoding codebook, wherein L is 1, 2.. L; the precoding reference matrix is an antenna array response, AtlRepresenting the transmit antenna array response for the l-th lobe subchannel.
8. The hybrid precoding design method of claim 7, wherein the fourth step further comprises:
self-supporting set Ψ of analog precoding matrices for different data streamslpThere is a common supporting set between
Figure FDA0003545747940000056
And satisfy
Figure FDA0003545747940000057
The first lobe simulates the self-supporting set of the precoding matrix as
Figure FDA0003545747940000058
Wherein
Figure FDA0003545747940000059
To represent
Figure FDA00035457479400000510
To ΨlpA difference set of;
because the digital precoding matrix has a hidden sparse structure, the projection sizes of column vectors of the precoding reference matrix on different code words are different, and the analog precoding matrix for the p data stream of the ith lobe
Figure FDA00035457479400000511
Designing, wherein a plurality of strong projection conditions of a precoding reference matrix column vector are considered; to simplify the design, consider each
Figure FDA00035457479400000512
Designed to have the same number of projections
Figure FDA00035457479400000513
Is an integer; if a common support set exists among the simulation precoding matrixes of different data streams
Figure FDA00035457479400000514
Searching
Figure FDA00035457479400000515
A code word, wherein
Figure FDA0003545747940000061
The expression is rounded down so that the column vectors of at least two pre-coding reference matrices have a strong projection on the selected code words, the positions of the code words are set as the analog pre-coding matrix
Figure FDA0003545747940000062
Common supporting set of
Figure FDA0003545747940000063
Simulating precoding matrix for designing p-th data stream
Figure FDA0003545747940000064
Searching
Figure FDA0003545747940000065
The position of each code word and the common support set
Figure FDA0003545747940000066
Form a
Figure FDA0003545747940000067
Of itself hasSupport set Ψlp(ii) a Thus, formula (10) is converted to:
Figure FDA0003545747940000068
wherein
Figure FDA0003545747940000069
Representing the set Ψ of self-supportlpThe cardinality of (a), i.e., the number of elements in the set;
in order to solve the problems, a hybrid pre-coding optimization algorithm based on joint sparsity is adopted; because each lobe mixing precoding design is independent and the method is the same, only the first lobe mixing precoding matrix design is introduced: firstly, designing a common supporting set
Figure FDA00035457479400000610
Precoding reference matrix FresAntenna array response A for the l lobetlAnd calculating a correlation matrix of the reference matrix and the codebook:
Figure FDA00035457479400000611
searching
Figure FDA00035457479400000612
A code word such that a reference matrix F is precodedresThe column vectors have a strong projection on the selected codeword, and if the selected codeword can be used as a common support, the condition is satisfied:
Figure FDA00035457479400000613
making a precoding reference matrix FresExcept for j0There are still other column vectors in the ith column vector in addition to the individual column vector0Having a strong projection on each codeword, then the ith0Each code word is commonWith support, recording the position i of the code word0Updating common supporting set
Figure FDA00035457479400000614
Self-supporting set Ψ of p-th data stream analog precoding matrixlp(ii) a To design for
Figure FDA0003545747940000071
Selecting a single antenna array response column vector Atl(p) as a reference matrix FresCalculating a correlation matrix R, similar to the common support setcSearch for
Figure FDA0003545747940000072
Forming an analog precoding matrix from the individual codewords and updating ΨlpModeling the self-supporting set Ψ of the precoding matrix with the l-th lobel。
9. The hybrid precoding design method of claim 1, wherein the analog precoding codebook in the fourth step is constructed by using a uniform quantization mode and a non-uniform quantization mode.
10. Hybrid precoding design method according to one of claims 1 to 9, characterized in that the analog precoding matrix F obtained according to said methodRFDigital precoding matrix FBBAnalog combiner matrix WRFDigital combiner matrix WBBThe frequency spectrum efficiency and the error rate performance of the millimeter wave large-scale MIMO system are improved.
CN202110906384.3A 2021-08-06 2021-08-06 Hybrid precoding design method in millimeter wave large-scale MIMO system Active CN113708811B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110906384.3A CN113708811B (en) 2021-08-06 2021-08-06 Hybrid precoding design method in millimeter wave large-scale MIMO system

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110906384.3A CN113708811B (en) 2021-08-06 2021-08-06 Hybrid precoding design method in millimeter wave large-scale MIMO system

Publications (2)

Publication Number Publication Date
CN113708811A CN113708811A (en) 2021-11-26
CN113708811B true CN113708811B (en) 2022-05-10

Family

ID=78651886

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110906384.3A Active CN113708811B (en) 2021-08-06 2021-08-06 Hybrid precoding design method in millimeter wave large-scale MIMO system

Country Status (1)

Country Link
CN (1) CN113708811B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114665929B (en) * 2022-03-15 2023-05-05 江南大学 Hybrid precoding method based on dynamic connection structure and MIMO system
CN115001545A (en) * 2022-05-10 2022-09-02 江南大学 Hybrid precoding method in millimeter wave large-scale MIMO system

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108933745A (en) * 2018-07-16 2018-12-04 北京理工大学 A kind of broad-band channel estimation method estimated based on super-resolution angle and time delay
CN109547071A (en) * 2018-11-15 2019-03-29 北京大学 A kind of list cell MU-MISO mixing pre-coding system and its analog beam selection method
CN111654456A (en) * 2020-06-09 2020-09-11 江南大学 Millimeter wave large-scale MIMO angular domain channel estimation method and device based on dimension reduction decomposition
CN111786706A (en) * 2020-07-02 2020-10-16 电子科技大学 Joint channel information acquisition and beam forming method
CN113163422A (en) * 2021-04-06 2021-07-23 江南大学 Random node joint probability distribution optimization method based on hexagonal cell

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2018058262A1 (en) * 2016-09-27 2018-04-05 Intel Corporation Communication device and a method for hybrid beamforming

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108933745A (en) * 2018-07-16 2018-12-04 北京理工大学 A kind of broad-band channel estimation method estimated based on super-resolution angle and time delay
CN109547071A (en) * 2018-11-15 2019-03-29 北京大学 A kind of list cell MU-MISO mixing pre-coding system and its analog beam selection method
CN111654456A (en) * 2020-06-09 2020-09-11 江南大学 Millimeter wave large-scale MIMO angular domain channel estimation method and device based on dimension reduction decomposition
CN111786706A (en) * 2020-07-02 2020-10-16 电子科技大学 Joint channel information acquisition and beam forming method
CN113163422A (en) * 2021-04-06 2021-07-23 江南大学 Random node joint probability distribution optimization method based on hexagonal cell

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
A Low Complexity Precoding Algorithm Based on Parallel Conjugate Gradient for Massive MIMO Systems;Geng Chen 等;《IEEE Access》;20180918(第6期);第54010-54017页 *
Analysis of SVD-Based Hybrid Schemes for Massive MIMO With Phase Noise and Imperfect Channel Estimation;Roberto Corvaja 等;《IEEE Transactions on Vehicular Technology》;20200427;第69卷(第7期);第7325-7338页 *
基于STBC-VBLAST系统的预编码传输方案;刘海涛等;《中国民航大学学报》;20100215(第01期);全文 *

Also Published As

Publication number Publication date
CN113708811A (en) 2021-11-26

Similar Documents

Publication Publication Date Title
CN110557177A (en) DenseNet-based hybrid precoding method in millimeter wave large-scale MIMO system
CN112039565B (en) Large-scale MIMO mixed pre-coding method based on distributed part connection
CN110943768B (en) Mixed precoding codebook joint design method of millimeter wave large-scale MIMO system
CN113708811B (en) Hybrid precoding design method in millimeter wave large-scale MIMO system
CN112737647B (en) Millimeter wave large-scale MIMO precoding method based on hybrid connection
CN107294590B (en) Digital-analog hybrid beam forming method based on uplink training
CN111049557B (en) Millimeter wave MIMO system hybrid precoding method based on statistical channel information
CN110661555B (en) Hybrid precoding algorithm for partially connected phase shifter networks for massive MIMO
CN111953393B (en) Large-scale MIMO hybrid precoder and matching method
CN109120316B (en) Hybrid beam forming method based on maximized minimum phase difference value
CN107809275B (en) Finite feedback hybrid precoding method based on millimeter wave MIMO system
CN112653496B (en) Mixed precoding method of millimeter wave large-scale MIMO system
CN110518952B (en) Adaptive grouping broadband hybrid beam forming design method based on codebook
CN106972876B (en) Digital-analog hybrid beam forming method suitable for wireless communication common channel
CN112468202A (en) Low-complexity millimeter wave large-scale MIMO hybrid precoding method
CN113572503B (en) Low-complexity improved mixed beam forming method based on GP
CN110233649B (en) Dynamic subarray design method based on millimeter wave MIMO system
CN108566236B (en) User terminal, base station, and hybrid beamforming transmission method and system
CN107104719B (en) Millimeter wave digital-analog hybrid precoding design method based on geometric construction
CN107707284B (en) Mixed precoding method based on channel statistic codebook quantization feedback
CN112398513A (en) Beam forming method of massive MIMO system
CN112054827A (en) Combined hybrid precoding method based on channel equivalence
CN114039638B (en) Combined design method of hybrid beam shaper and analog-to-digital converter
CN108683441B (en) Multi-user beam forming method in hybrid pre-coding
CN115001545A (en) Hybrid precoding method in millimeter wave large-scale MIMO system

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant