CN112865842A - Design method of 5G-oriented hybrid precoder and combiner - Google Patents

Design method of 5G-oriented hybrid precoder and combiner Download PDF

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CN112865842A
CN112865842A CN202110002811.5A CN202110002811A CN112865842A CN 112865842 A CN112865842 A CN 112865842A CN 202110002811 A CN202110002811 A CN 202110002811A CN 112865842 A CN112865842 A CN 112865842A
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matrix
precoder
combiner
analog
column
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CN112865842B (en
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张崇富
罗晨萌
孔谦
周李梦男
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University of Electronic Science and Technology of China
University of Electronic Science and Technology of China Zhongshan Institute
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University of Electronic Science and Technology of China Zhongshan Institute
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    • 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
    • H04B7/0615—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 of weighted versions of same signal
    • H04B7/0617—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 of weighted versions of same signal for beam forming
    • 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
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining

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Abstract

The invention discloses a design method of a 5G-oriented hybrid precoder and a combiner, which adopts a recursive algorithm based on matrix decomposition to design an analog precoder and an analog combiner, namely, singular value decomposition is carried out on a channel matrix, then a final analog precoder and an analog combiner are designed through a recursive thought, and then a digital precoder and a digital combiner are calculated based on effective baseband signals associated with the obtained optimal analog precoder and the obtained combiner. The invention improves the performance of the hybrid precoder and the combiner on the premise of controlling the cost and the energy consumption as much as possible, and the frequency spectrum efficiency of the millimeter wave MIMO system can approach the performance of a full digital beam forming system by adopting the hybrid precoder and the combiner designed by the invention.

Description

Design method of 5G-oriented hybrid precoder and combiner
Technical Field
The invention belongs to the technical field of 5G communication, and particularly relates to a design method of a 5G-oriented hybrid pre-encoder and combiner.
Background
The fifth Generation mobile communication technology (5th Generation mobile networks or 5th Generation with less systems, 5th-Generation, 5G or 5G technology for short) is the latest Generation cellular mobile communication technology, and is also an extension following 4G (LTE-A, WiMax), 3G (UMTS, LTE) and 2G (gsm) systems. Under the 5G technical framework, higher requirements are placed on system capacity and energy efficiency, and the bandwidth of the traditional frequency band is difficult to meet the increasing requirements of users, so millimeter waves with higher bandwidth gradually become the key point of research of scholars at home and abroad. However, the millimeter wave has a shorter wavelength, and the transmission loss is more serious than that of the conventional frequency band, so that a large number of antennas are required to be arranged at the transmitting end and the receiving end to compensate for the path loss of the millimeter wave channel, thereby improving the channel transmission quality. The combination of millimeter wave and Multiple Input Multiple Output (MIMO) technology can greatly improve the transmission efficiency of the system, and therefore is considered as one of the emerging technologies of 5G.
For MIMO systems operating over the conventional cellular band, an all-digital precoder and combiner can be fully implemented in the digital domain by adjusting the amplitude and phase of the baseband signals. But when the millimeter wave communication system operates at higher carrier frequencies and wider bandwidths, the enormous cost and power consumption of the required RF chains and ADC/DAC make the millimeter wave system incapable of adopting an all-digital precoding and combining scheme.
Recently, an economical and energy-saving analog/digital hybrid precoder and combiner have been advocated as a promising approach to solve this problem. The hybrid precoder method employs a large number of Phase Shifters (PS) to implement a high-dimensional analog precoder to compensate for severe path loss over the millimeter-wave band, and a small number of RF chains and DACs to implement a low-dimensional digital precoder to achieve the flexibility needed to perform several multiplexing/multiuser techniques.
Existing hybrid precoder and combiner designs typically assume an infinite or high precision PS for implementing an analog beamformer, however implementing an infinite/high precision PS over the millimeter wave band would greatly increase the power consumption and complexity of the required hardware circuitry, and thus analog beamformers in the real world are often implemented with low precision PS. However, the existing low-precision PS schemes do not perform satisfactorily in terms of computational complexity, and further improvement is needed.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a design method of a 5G-oriented hybrid precoder and combiner, which adopts a recursive idea to continuously design a low-precision analog precoder and combiner pair so as to conditionally maximize spectral efficiency, and then calculates a digital precoder and a combiner based on an obtained effective baseband channel so as to further improve the spectral efficiency.
In order to achieve the above object, the design method of the 5G-oriented hybrid precoder and combiner of the present invention comprises the following steps:
s1: obtaining millimeter wave MIMO system parameters including the number of transmit antennas NtNumber of RF chains L, number of receiving antennas NrAnd a channel matrix H;
s2: performing singular value decomposition on the channel matrix H to obtain H ═ U Σ VHThen calculating to obtain the designed simulated precoder
Figure BDA0002881916720000021
And analog combiner
Figure BDA0002881916720000022
1 st column vector of
Figure BDA0002881916720000023
And
Figure BDA00028819167200000214
Figure BDA0002881916720000024
Figure BDA0002881916720000025
wherein v is1＝V(:,1)，u1U (: 1), V (: 1) represents the vector of the 1 st column in the matrix V, and U (: 1) represents the vector of the 1 st column in the matrix U;
s3: let i be 2;
s4: adopt the first i-1
Figure BDA0002881916720000026
Constructing matrix F as a column vectori-1The first i-1 are adopted
Figure BDA0002881916720000027
Constructing W as a column vectori-1I ═ 1,2, …, i-1, and then the matrix E is calculatedi-1：
Figure BDA0002881916720000028
Figure BDA0002881916720000029
U (: 1: L) represents a submatrix formed by the 1 st to L th columns of the matrix U,
Figure BDA00028819167200000210
a sub-matrix is formed by the row numbers 1 to L and the column numbers 1 to L in the matrix sigma,
Figure BDA00028819167200000211
v (: 1: L) represents a submatrix formed by the 1 st to L th columns of the matrix V;
for matrix Ei-1Singular value decomposition is carried out to obtain Ei-1＝SVDHThen calculated to obtain
Figure BDA00028819167200000212
And
Figure BDA00028819167200000213
Figure BDA0002881916720000031
Figure BDA0002881916720000032
wherein s is1＝S(:,1),d1D (: 1), S (: 1) represents the vector of the 1 st column in the matrix S, D (: 1) represents the vector of the 1 st column in the matrix S;
s5: and judging whether i is less than L, if so, entering step S6, and otherwise, entering step S7.
S6: returning to step S4 by making i + 1;
s7: will be L
Figure BDA0002881916720000033
Hybrid precoder designed as column vector construction
Figure BDA0002881916720000034
Will be L
Figure BDA0002881916720000035
Analog merger designed for column vector construction
Figure BDA0002881916720000036
S8: obtaining an effective baseband channel using the following equation
Figure BDA0002881916720000037
Figure BDA0002881916720000038
S9: for effective baseband channel
Figure BDA0002881916720000039
Go to oddDecomposing the abnormal value to obtain
Figure BDA00028819167200000310
Wherein
Figure BDA00028819167200000311
And
Figure BDA00028819167200000312
is an L multiplied by L dimensional unitary matrix,
Figure BDA00028819167200000313
is an L multiplied by L dimensional diagonal matrix of singular values;
the following formula is adopted to calculate and obtain the digital precoder
Figure BDA00028819167200000314
And digital merger
Figure BDA00028819167200000315
Figure BDA00028819167200000316
Figure BDA00028819167200000317
Wherein,
Figure BDA00028819167200000318
representation matrix
Figure BDA00028819167200000319
Figure BDA00028819167200000319
1 to N ofsA sub-matrix of columns is formed,
Figure BDA00028819167200000320
representation matrix
Figure BDA00028819167200000321
Figure BDA00028819167200000321
1 to N ofsStructure of columnForming a sub-matrix.
The invention relates to a design method for a 5G hybrid precoder and a combiner, which adopts a recursive algorithm based on matrix decomposition to design a simulated precoder and a simulated combiner, namely, singular value decomposition is carried out on a channel matrix, a final simulated precoder and a final simulated combiner are designed through a recursive idea, and then a digital precoder and a digital combiner are calculated based on effective baseband signals associated with the obtained optimal simulated precoder and the obtained combined combiner. The invention improves the performance of the hybrid precoder and the combiner on the premise of controlling the cost and the energy consumption as much as possible, and the frequency spectrum efficiency of the millimeter wave MIMO system can approach the performance of a full digital beam forming system by adopting the hybrid precoder and the combiner designed by the invention.
Drawings
FIG. 1 is a block diagram of a point-to-point millimeter wave MIMO system of the present invention;
FIG. 2 is a flow chart of an embodiment of a design method of a 5G-oriented hybrid precoder and combiner according to the present invention;
FIG. 3 is a graph comparing average spectral efficiency versus SNR for 64x64 antenna array counts and multiple data streams for the present invention and comparison method;
FIG. 4 is a graph of average spectral efficiency versus number of antennas for multiple streams for the present invention and comparison method;
FIG. 5 is a graph comparing average spectral efficiency versus SNR for 64x16 antenna array counts and multiple data streams for the present invention and comparison method;
fig. 6 is a graph comparing average spectral efficiency versus SNR for a 64x16 antenna array count and a single data stream for the present invention and comparison method.
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
Examples
To better explain the technical solution of the present invention, first, the technical derivation process of the present invention is briefly explained.
The invention adopts a point-to-point millimeter wave MIMO system with a hybrid precoder and a combiner of a low-precision phase shifter. Fig. 1 is a structural diagram of a point-to-point millimeter wave MIMO system in the present invention. As shown in FIG. 1, the transmitter in the point-to-point millimeter wave MIMO system uses NtThe root transmitting antenna and L RF chains simultaneously transmit NsSending a data stream to the equipment NrA receiver that receives the antenna and the L RF chains.
After the data stream is processed by the hybrid precoder, the transmission signal at the transmitting end can be represented as:
Figure BDA0002881916720000041
wherein, FRFRepresents NrxL-dimensional low-precision analog precoder, FBBRepresents L × NsDigital pre-encoder of dimension, s being NsX 1-dimensional symbol vector, and satisfy
Figure BDA0002881916720000042
Where E represents the mathematical expectation that,
Figure BDA0002881916720000051
represents Ns×NsDimension unit matrix, P represents total transmission power, and is obtained by applying a pair of digital precoders FBBNormalization is performed to force the power to be constrained such that
Figure BDA0002881916720000052
|| ||FWhich means that a two-norm is found.
Considering the channel as a narrow-band slow fading propagation channel, the following received signals are generated:
Figure BDA0002881916720000053
wherein y is NrX 1-dimensional signal vector, H being of size Nr×NtThe channel matrix of (a) is determined,
Figure BDA0002881916720000054
is a complex Gaussian noise vector, σ, of the interfering received signal2The variance is represented as a function of time,
Figure BDA0002881916720000059
represents Nr×NrA dimension unit matrix.
The receiver employs an analog combiner implemented by PS and a digital combiner that processes the received signal using L RF chains. The spatially processed signal has the form:
Figure BDA0002881916720000055
wherein, WRFIs NrAnalog merger of x L dimension with elements of FRFSame constraint, WBBIs L × NsDimension number merger, superscript H denotes the conjugate transpose matrix.
Perfect timing and frequency recovery is generally assumed and both the transmitter and receiver have good knowledge of the Channel State Information (CSI).
The present invention contemplates a practical and hardware efficient solution for phase shifters with low precision to reduce power consumption and complexity. Under such hardware constraints, the hybrid precoder and combiner of the millimeter wave MIMO system are intended to be designed together. When transmitting gaussian symbols through a millimeter-wave MIMO channel, the achievable spectral efficiency is given by:
Figure BDA0002881916720000056
wherein,
Figure BDA0002881916720000057
the combined noise covariance matrix is obtained, and the superscript-1 indicates that the inverse matrix is obtained.
Therefore, a common design of the digital beamformer (including the digital precoder F) is requiredBBDigital combiner WBB) And a low resolution analog beamformer (including an analog precoder F)RFAnalog combiner WRF) To improve the spectrum efficiency to the maximum extent, the formula can be expressed as follows:
Figure BDA0002881916720000058
where the superscript denotes the optimum matrix, i ═ 1,2, …, Nt，j＝1,2,…,Nr。
Equation (5) is a multivariate problem whose globally optimal solution is difficult to obtain directly. Thus, the present invention decomposes the target problem into two separate optimizations, focusing first on the simulated precoder FRFAnd a combiner WRFThen calculates a digital precoder F based on the effective baseband channel associated with the obtained optimal analog precoder and combinerBBAnd a combiner WBBTo further maximize spectral efficiency.
Thus, under the assumption of high signal-to-noise ratio (SNR), the achievable spectral efficiency in equation (4) can be approximated as:
Figure BDA0002881916720000061
although the SNR per antenna in a millimeter wave system is low, the combined SNR should be high enough to justify this approximation. Furthermore, it has been demonstrated in the literature that for massive MIMO systems, the optimal analog beamformers are approximately orthogonal, i.e. the
Figure BDA0002881916720000062
ILRepresenting an L × L dimensional identity matrix.
Furthermore, it is well known that the optimal all-digital precoder FDIs a single right singular vector sum from the channel matrix H
Figure BDA0002881916720000063
And (4) obtaining the product. Near optimal hybrid designs should also exhibit compatibility with FDThe same orthogonality, i.e.
Figure BDA0002881916720000064
Based on this result, it can be assumed that the digital precoder F isBBAre also approximately orthogonal, i.e.
Figure BDA0002881916720000065
Wherein tau is2Is the normalization factor of the precoder. Analogously, can be derived
Figure BDA0002881916720000066
And
Figure BDA0002881916720000067
in which ξ2Is the normalization factor of the combiner. Let gamma be2＝τ2ξ2So equation (6) can be further simplified as:
Figure BDA0002881916720000068
from equations (7) to (8), it is necessary to satisfy that the two decomposed matrices are square matrices, so the analog precoder and combiner design with low-precision phase shifters can be redesigned roughly as:
Figure BDA0002881916720000069
wherein,
Figure BDA00028819167200000610
representing a simulated precoder as designed,
Figure BDA00028819167200000611
representing the designed combiner.
Unfortunately, the optimization problem (9) remains an NP-hard problem and has exponential complexity. The present invention therefore further decomposes this difficult optimization problem into a series of sub-problems, in which each transmit/receive RF chain pair is considered one by one, and the analog precoders and combiners for each pair are designed in turn.
The Singular Value Decomposition (SVD) of the channel matrix H is defined as:
H＝UΣVH (10)
wherein U is Nr×NrUnitary matrix of dimension V being one Nt×NtThe unitary matrix of dimension, Σ, is a singular value rectangular diagonal matrix. The channel matrix H is typically low rank due to the sparsity of the millimeter wave channels. In particular, the effective rank of a channel serves as an upper limit on the number of data streams that the channel can support. In case of a limited number of RF chains, it is assumed that only N is reservedRFThe channel matrix H can be well approximated by the strongest components, i.e. the channel matrix H
Figure BDA0002881916720000071
Wherein
Figure BDA0002881916720000072
U (: 1: L) represents a submatrix formed by the 1 st to L th columns of the matrix U,
Figure BDA0002881916720000073
a sub-matrix composed of rows with serial numbers of 1 to L and columns with serial numbers of 1 to L in the matrix Σ is shown,
Figure BDA0002881916720000074
v (: 1: L) represents a submatrix formed by the 1 st to L th columns of the matrix V. Thus, the target (9) can be transformed into:
Figure BDA0002881916720000075
wherein f isRF,LRepresenting an analog precoder FRFVector of the L-th column, FRF,\LRepresenting an analog precoder FRFRemoving the matrix of the L-th column vector, WRF,\LRepresenting an analog combiner WRFThe matrix of the L-th column vector is removed. α is a preset minimum scalar.
Based on equation (12), the present invention provides a thought and solution to derive a new derivation:
Figure BDA0002881916720000076
it can be seen that the first term in equation (13) has exactly the same form as equation (11), and therefore, with the idea of recursion, we further conclude that equation (13) is equal to:
Figure BDA0002881916720000077
wherein D isLIs term 2 in formula (13)
Figure BDA0002881916720000078
The following formula may be directly substituted for convenience of expression. FRF,\L,L-1Is represented by FRFRemoving the column vector fRF,LAnd fRF,L-1And the subsequent matrix, the recursion method omits the middle formulas to obtain:
Figure BDA0002881916720000081
f is to beRF,\L,L-1,…,iIs shown as Fi-1I.e. FRFThe first i-1 column of (a),
Figure BDA0002881916720000082
is represented by Wi-1I.e. WRFThe first i-1 column of (a).
Order to
Figure BDA0002881916720000083
Equation (15) can be varied as:
Figure BDA0002881916720000084
it can be seen that when fRF,1And wRF,1After it is known, E1I.e. a known value, can be given to fRF,2And wRF,2Optimized to obtain E2By analogy, f can be obtainedRF,LAnd wRF,L. Finally, the problem is expressed as:
Figure BDA0002881916720000085
the maximum value of each term in the formula (17) is specifically analyzed below. For the first term in equation (17), it can be changed to
Figure BDA0002881916720000086
Namely when
Figure BDA0002881916720000087
Take the first column of the left unitary matrix of the channel matrix H, fRF,1The first column of the right unitary matrix is taken to have the maximum value. However due to the limitation of constant modulus, i.e.
Figure BDA0002881916720000088
Figure BDA0002881916720000089
The problem can therefore be equated with:
Figure BDA00028819167200000810
wherein | | | purple hair2The method comprises the steps of obtaining two norms, wherein V (: 1) represents a vector of a 1 st column in a matrix V, and U (: 1) represents a vector of a 1 st column in a matrix U.
Let v1＝V(:,1)，u1U (: 1), then:
Figure BDA0002881916720000091
therefore, it can be minimized
Figure BDA0002881916720000092
To maximize
Figure BDA0002881916720000093
Re () represents the real component of (2), since v1And fRF,1Is fixed, so there are:
Figure BDA0002881916720000094
where j represents an imaginary unit, and angle () represents the phase.
The same principle is as follows:
Figure BDA0002881916720000095
to obtain
Figure BDA0002881916720000096
And
Figure BDA0002881916720000097
then, it can be calculated, and then the second term is optimized:
Figure BDA0002881916720000098
observing the same form as the optimized expression for the first term, the following can be concluded:
svd(E1)＝SVDH,s1＝S(:1),d1＝D(:1) (23)
Figure BDA0002881916720000099
other terms can be obtained in turn, finally
Figure BDA00028819167200000910
And
Figure BDA00028819167200000911
according to the derivation process, the invention provides a design method of a 5G-oriented hybrid precoder and a combiner. Fig. 2 is a flow chart of a specific embodiment of the design method of the 5G-oriented hybrid precoder and combiner of the present invention. As shown in fig. 2, the specific steps of the design method of the 5G-oriented hybrid precoder and combiner of the present invention include:
s201: obtaining millimeter wave MIMO system parameters:
obtaining millimeter wave MIMO system parameters including the number of transmit antennas NtNumber of RF chains L, number of receiving antennas NrAnd a channel matrix H.
S202: calculating the 1 st column vector of the matrix of the analog precoder and the analog combiner:
performing singular value decomposition on the channel matrix H to obtain H ═ U Σ VHThen calculating to obtain the designed analog precoder
Figure BDA0002881916720000101
And analog combiner
Figure BDA0002881916720000102
Figure BDA0002881916720000102
1 st column vector of
Figure BDA0002881916720000103
And
Figure BDA0002881916720000104
Figure BDA0002881916720000105
Figure BDA0002881916720000106
wherein v is1＝V(:,1)，u1＝U(:,1)。
S203: let i equal 2.
S204: calculating the ith column vector of the matrix of the analog precoder and the analog combiner:
Figure BDA0002881916720000107
and
Figure BDA0002881916720000108
adopt the first i-1
Figure BDA0002881916720000109
Constructing matrix F as a column vectori-1The first i-1 are adopted
Figure BDA00028819167200001010
Constructing W as a column vectori-1I ═ 1,2, …, i-1, and then the matrix E is calculatedi-1：
Figure BDA00028819167200001011
For matrix Ei-1Singular value decomposition is carried out to obtain Ei-1＝SVDHThen calculated to obtain
Figure BDA00028819167200001012
And
Figure BDA00028819167200001013
Figure BDA00028819167200001014
Figure BDA00028819167200001015
wherein s is1＝S(:,1),d1D (: 1), S (: 1) represents the vector of the 1 st column in the matrix S, and D (: 1) represents the vector of the 1 st column in the matrix S.
S205: and judging whether i is less than L, if so, entering step S206, and otherwise, entering step S207.
S206: let i be i +1, return to step S204.
S207: determining an analog precoder and an analog combiner:
will be L
Figure BDA00028819167200001016
Hybrid precoder designed as column vector construction
Figure BDA00028819167200001017
Namely, it is
Figure BDA00028819167200001018
Will be L
Figure BDA00028819167200001019
Analog merger designed as column vector construction
Figure BDA00028819167200001020
Namely, it is
Figure BDA00028819167200001021
S208: obtaining an effective baseband channel:
after all analog precoder-combiner pairs are determined, the effective baseband channel is obtained using the following equation
Figure BDA00028819167200001022
Figure BDA00028819167200001023
Wherein
Figure BDA0002881916720000111
And is
Figure BDA00028819167200001116
S209: determining a digital precoder and digital combiner:
for the design of digital precoder and digital combiner, the effective baseband channel is selected
Figure BDA0002881916720000112
Performing singular value decomposition to obtain
Figure BDA0002881916720000113
Wherein
Figure BDA0002881916720000114
And
Figure BDA0002881916720000115
is an L multiplied by L dimensional unitary matrix,
Figure BDA0002881916720000116
is an L multiplied by L dimensional singular value pair angle array.
The following formula is adopted to calculate and obtain the digital precoder
Figure BDA0002881916720000117
And digital merger
Figure BDA0002881916720000118
Figure BDA00028819167200001114
Figure BDA0002881916720000119
Wherein,
Figure BDA00028819167200001110
representation matrix
Figure BDA00028819167200001115
Figure BDA00028819167200001115
1 to N ofsA sub-matrix of columns is formed,
Figure BDA00028819167200001111
representation matrix
Figure BDA00028819167200001112
Figure BDA00028819167200001112
1 to N ofsA sub-matrix of columns.
In general, the digital precoder can be normalized using the following equation:
Figure BDA00028819167200001113
in order to better illustrate the technical scheme of the invention, a specific example is adopted for simulation verification.
Fig. 3 is a structural diagram of a point-to-point millimeter wave MIMO system using a hybrid precoder and a combiner in the present embodiment. As shown in fig. 3, the sending-end base station mainly comprises a digital pre-coding part and a power distribution part at the back end of the radio frequency link and an analog pre-coding part at the front end of the radio frequency link; the receiving end user mainly comprises an analog merging part at the front end of the radio frequency link and a digital merging part at the rear end of the radio frequency link. Sending end equipment NtThe root antenna is connected to the L radio frequency links in a full connection subarray mode. Receiving end user equipment NrThe root antenna is connected to the L radio frequency links in a full-connection sub-array mode and simultaneously supports Ns(NsMore than or equal to 1) data stream transmission, in order to ensure the spatial multiplexing and efficiency of millimeter wave MIMO communication using a limited number of RF chains, the number of data streams and the number of RF chains should be limited to Ns≤L。
In order to better demonstrate the technical performance of the present invention, an iterative phase matching algorithm (an existing low-resolution hybrid beamformer) is selected as a comparison method in the present embodiment, and the iterative phase matching algorithm has the best performance in the existing low-resolution phase shifter scheme.
Fig. 4 is a graph comparing average spectral efficiency versus SNR for 64x64 antenna array counts and multiple data streams for the present invention and comparison method. Fig. 5 is a graph of average spectral efficiency versus number of antennas for multiple streams for the present invention and comparative method. The spectral efficiency of the present invention was evaluated in fig. 4 and 5 for the case of a 1-bit (B-1) precision phase shifter and a 2-bit (B-2) precision phase shifter. As shown in fig. 4 and 5, the method of the present invention is superior to the iterative phase matching algorithm, especially for the case of 1-bit precision phase shifters. Furthermore, it can be observed that the inventive method achieves near-optimal all-digital beamforming performance when using 2-bit precision phase shifters.
Fig. 6 is a plot of average spectral efficiency versus SNR for a 64x16 antenna array count and multiple data streams for the present invention and comparative method. As shown in fig. 6, compared to fig. 5, the performance of the inventive method is much better than the comparative method with 1-bit precision.
Fig. 7 is a plot of average spectral efficiency versus SNR for a 64x16 antenna array count and a single data stream for the present invention and comparative method. As shown in fig. 7, the present invention performs much better at 1-bit precision than the contrast scheme, and even has a macroscopic advantage over the 2-bit precision contrast scheme, compared to the multiple data stream case of fig. 5.
In addition, the complexity analysis of the method and the iterative phase matching algorithm can obtain that the complexity of the method is one forty times of that of the iterative phase matching algorithm, and resources can be effectively saved.
In summary, the overall performance of the present invention is superior to that of the comparison method, and especially, the performance advantage is more obvious under the condition that the number of antennas at the receiving end is small and the number of data streams is small, so that the present invention is an effective design method of a hybrid precoder and a combiner under a fully concatenated subarray structure.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all inventions utilizing the inventive concept are protected.

Claims (1)

1. A design method of a 5G-oriented hybrid precoder and combiner, characterized by comprising the steps of:
s1: obtaining millimeter wave MIMO system parameters including the number of transmit antennas NtNumber of RF chains L, number of receiving antennas NrAnd a channel matrix H;
s2: performing singular value decomposition on the channel matrix H to obtain H ═ U Σ VHThen calculating to obtain the designed simulated precoder
Figure FDA0002881916710000011
And analog combiner
Figure FDA0002881916710000012
1 st column vector of
Figure FDA0002881916710000013
And
Figure FDA0002881916710000014
Figure FDA0002881916710000015
Figure FDA0002881916710000016
wherein v is1＝V(:,1)，u1＝U(:,1) V (: 1) represents the vector of the 1 st column in the matrix V, and U (: 1) represents the vector of the 1 st column in the matrix U;
s3: let i be 2;
s4: adopt the first i-1
Figure FDA0002881916710000017
Constructing matrix F as a column vectori-1The first i-1 are adopted
Figure FDA0002881916710000018
Constructing W as a column vectori-1I ═ 1,2, …, i-1, and then the matrix E is calculatedi-1：
Figure FDA0002881916710000019
Figure FDA00028819167100000110
U (: 1: L) represents a submatrix formed by the 1 st to L th columns of the matrix U,
Figure FDA00028819167100000111
a sub-matrix composed of rows with serial numbers of 1 to L and columns with serial numbers of 1 to L in the matrix Σ is shown,
Figure FDA00028819167100000112
v (: 1: L) represents a submatrix formed by the 1 st to L th columns of the matrix V;
for matrix Ei-1Singular value decomposition is carried out to obtain Ei-1＝SVDHThen calculated to obtain
Figure FDA00028819167100000113
And
Figure FDA00028819167100000114
Figure FDA00028819167100000115
Figure FDA00028819167100000116
wherein s is1＝S(:,1),d1D (: 1), S (: 1) represents the vector of the 1 st column in the matrix S, D (: 1) represents the vector of the 1 st column in the matrix S;
s5: and judging whether i is less than L, if so, entering step S6, and otherwise, entering step S7.
S6: returning to step S4 by making i + 1;
s7: will be L
Figure FDA00028819167100000117
Hybrid precoder designed as column vector construction
Figure FDA00028819167100000118
Will be L
Figure FDA00028819167100000119
Analog merger designed as column vector construction
Figure FDA0002881916710000021
S8: obtaining an effective baseband channel using the following equation
Figure FDA0002881916710000022
Figure FDA0002881916710000023
S9: for effective baseband channel
Figure FDA0002881916710000024
Performing singular value decomposition to obtain
Figure FDA0002881916710000025
Wherein
Figure FDA0002881916710000026
And
Figure FDA0002881916710000027
is an L multiplied by L dimensional unitary matrix,
Figure FDA0002881916710000028
is an L multiplied by L dimensional diagonal matrix of singular values;
the following formula is adopted to calculate and obtain the digital precoder
Figure FDA0002881916710000029
And digital merger
Figure FDA00028819167100000210
Figure FDA00028819167100000211
Figure FDA00028819167100000212
Wherein,
Figure FDA00028819167100000213
representation matrix
Figure FDA00028819167100000214
1 to N ofsA sub-matrix of columns is formed,
Figure FDA00028819167100000215
representation matrix
Figure FDA00028819167100000216
1 to N ofsA sub-matrix of columns.
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