CN112865842B - 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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CN112865842B
CN112865842B CN202110002811.5A CN202110002811A CN112865842B CN 112865842 B CN112865842 B CN 112865842B CN 202110002811 A CN202110002811 A CN 202110002811A CN 112865842 B CN112865842 B CN 112865842B
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precoder
combiner
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column
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CN112865842A (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

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 precoder and a 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 that millimeter waves with higher bandwidth gradually become the key point of research of domestic and foreign scholars. 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, the 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, so real world analog beamformers are often implemented with a 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 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 GDA0003259425490000021
And analog combiner
Figure GDA0003259425490000022
1 st column vector of
Figure GDA0003259425490000023
And
Figure GDA0003259425490000024
Figure GDA0003259425490000025
Figure GDA0003259425490000026
wherein v is1＝V(:,1)，u1U (: 1), V (: 1) denotes a vector of the 1 st column in the matrix V, and U (: 1) denotes a vector of the 1 st column in the matrix U;
s3: let i be 2;
s4: adopt the first i-1
Figure GDA0003259425490000027
Constructing matrix F as a column vectori-1The first i-1 are adopted
Figure GDA0003259425490000028
Constructing W as a column vectori-1I ═ 1,2, …, i-1, and then the matrix E is calculatedi-1：
Figure GDA0003259425490000029
Figure GDA00032594254900000210
U (: 1: L) represents a submatrix formed by the 1 st to L th columns of the matrix U,
Figure GDA00032594254900000211
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 GDA00032594254900000212
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 GDA00032594254900000213
And
Figure GDA00032594254900000214
Figure GDA0003259425490000031
Figure GDA0003259425490000032
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 D;
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 GDA0003259425490000033
As a column directionQuantity composition designed hybrid precoder
Figure GDA0003259425490000034
Will be L
Figure GDA0003259425490000035
Analog merger designed as column vector construction
Figure GDA0003259425490000036
S8: obtaining an effective baseband channel using the following equation
Figure GDA0003259425490000037
Figure GDA0003259425490000038
S9: for effective baseband channel
Figure GDA0003259425490000039
Performing singular value decomposition to obtain
Figure GDA00032594254900000310
Wherein
Figure GDA00032594254900000311
And
Figure GDA00032594254900000312
is an L multiplied by L dimensional unitary matrix,
Figure GDA00032594254900000313
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 GDA00032594254900000314
And digital merger
Figure GDA00032594254900000315
Figure GDA00032594254900000316
Figure GDA00032594254900000317
Wherein the content of the first and second substances,
Figure GDA00032594254900000318
representation matrix
Figure GDA00032594254900000319
Figure GDA00032594254900000319
1 to N ofsA sub-matrix of columns is formed,
Figure GDA00032594254900000320
representation matrix
Figure GDA00032594254900000321
Figure GDA00032594254900000321
1 to N ofsA sub-matrix of columns.
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 an analog precoder and an analog combiner, namely, a channel matrix is subjected to singular value decomposition, a final analog precoder and an analog 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 analog precoder and the 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 comparing the average spectral efficiency versus the 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
In order to better explain the technical scheme of the invention, firstly, the technical derivation process of the 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 GDA0003259425490000041
wherein, FRFRepresents NrX L dimensional low essenceDegree analog precoder, FBBRepresents L × NsDigital precoder of dimension, s being NsX 1-dimensional symbol vector, and satisfy
Figure GDA0003259425490000042
Where E represents the mathematical expectation that,
Figure GDA0003259425490000043
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 GDA0003259425490000051
||||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 GDA0003259425490000052
wherein y is NrX 1-dimensional signal vector, H being of size Nr×NtThe channel matrix of (a) is determined,
Figure GDA0003259425490000053
is a complex Gaussian noise vector, σ, of the interfering received signal2Represents the variance, INrRepresents 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 GDA0003259425490000054
wherein, WRFIs NrAnalog merger of x L dimension with elements of FRFSame constraint, WBBIs L × NsNumber of dimensionThe combiner, 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 where the phase shifter has 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 GDA0003259425490000055
wherein the content of the first and second substances,
Figure GDA0003259425490000056
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 GDA0003259425490000057
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 objective 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 GDA0003259425490000061
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 GDA0003259425490000062
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 GDA0003259425490000063
And (4) obtaining the product. Near optimal hybrid designs should also exhibit compatibility with FDThe same orthogonality, i.e.
Figure GDA0003259425490000064
Based on this result, it can be assumed that the digital precoder F isBBAre also approximately orthogonal, i.e.
Figure GDA0003259425490000065
Wherein tau is2Is the normalization factor of the precoder. Analogously, can be derived
Figure GDA0003259425490000066
And
Figure GDA0003259425490000067
in which ξ2Is the normalization factor of the combiner. Let gamma be2＝τ2ξ2Therefore, equation (6) can be further simplified as:
Figure GDA0003259425490000068
from equations (7) to (8), it is necessary to satisfy that the two decomposed matrices are squared matrices, so the analog precoder and combiner design with low-precision phase shifters can be redesigned roughly as:
Figure GDA0003259425490000069
wherein the content of the first and second substances,
Figure GDA00032594254900000610
representing a simulated precoder as designed,
Figure GDA00032594254900000611
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 GDA0003259425490000071
Wherein
Figure GDA0003259425490000072
U (: 1: L) represents a submatrix formed by the 1 st to L th columns of the matrix U,
Figure GDA0003259425490000073
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 GDA0003259425490000074
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 GDA0003259425490000075
Figure GDA0003259425490000076
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 GDA0003259425490000077
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 GDA0003259425490000078
wherein D isLIs term 2 in formula (13)
Figure GDA0003259425490000079
The following formula can be directly substituted for convenient expression. FRF,\L,L-1Is represented by FRFRemoving the column vector fRF,LAnd fRF,L-1The latter matrix, the recursion method omits the middle formulas to obtain:
Figure GDA0003259425490000081
f is to beRF,\L,L-1,…,iIs shown as Fi-1I.e. FRFThe first i-1 column of (a),
Figure GDA0003259425490000082
is represented by Wi-1I.e. WRFThe first i-1 column of (a).
Order to
Figure GDA0003259425490000083
Equation (15) can be varied as:
Figure GDA0003259425490000084
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 GDA0003259425490000085
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 GDA0003259425490000086
Namely when
Figure GDA0003259425490000087
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 GDA0003259425490000088
Figure GDA0003259425490000089
The problem can therefore be equated with:
Figure GDA00032594254900000810
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 GDA0003259425490000091
therefore, it can be minimized
Figure GDA0003259425490000092
To maximize
Figure GDA0003259425490000093
Re () represents the real component of (2), since v1And fRF,1Is fixed, so there are:
Figure GDA0003259425490000094
where j represents an imaginary unit, and angle () represents the phase.
The same principle is as follows:
Figure GDA0003259425490000095
to obtain
Figure GDA0003259425490000096
And
Figure GDA0003259425490000097
then, it can be calculated, and then the second term is optimized:
Figure GDA0003259425490000098
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 GDA0003259425490000099
other terms can be obtained in turn, finally
Figure GDA00032594254900000910
And
Figure GDA00032594254900000911
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 an embodiment of a design method of a 5G-oriented hybrid precoder and combiner according to the present invention. As shown in fig. 2, the specific steps of the design method for 5G 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 chainsL, 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 simulated precoder
Figure GDA0003259425490000101
And analog combiner
Figure GDA0003259425490000102
Figure GDA0003259425490000102
1 st column vector of
Figure GDA0003259425490000103
And
Figure GDA0003259425490000104
Figure GDA0003259425490000105
Figure GDA0003259425490000106
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 GDA0003259425490000107
and
Figure GDA0003259425490000108
adopt the first i-1
Figure GDA0003259425490000109
Constructing matrix F as a column vectori-1The first i-1 are adopted
Figure GDA00032594254900001010
Constructing W as a column vectori-1I ═ 1,2, …, i-1, and then the matrix E is calculatedi-1：
Figure GDA00032594254900001011
For matrix Ei-1Singular value decomposition is carried out to obtain Ei-1＝SVDHThen calculated to obtain
Figure GDA00032594254900001012
And
Figure GDA00032594254900001013
Figure GDA00032594254900001014
Figure GDA00032594254900001015
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 D.
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 GDA00032594254900001016
Hybrid precoder designed as column vector construction
Figure GDA00032594254900001017
Namely, it is
Figure GDA00032594254900001018
Will be L
Figure GDA00032594254900001019
Analog merger designed as column vector construction
Figure GDA00032594254900001020
Namely, it is
Figure GDA00032594254900001021
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 GDA00032594254900001022
Figure GDA00032594254900001023
Wherein
Figure GDA00032594254900001024
And is
Figure GDA00032594254900001025
S209: determining a digital precoder and digital combiner:
for the design of digital precoder and digital combiner, the effective baseband channel is selected
Figure GDA0003259425490000111
Performing singular value decomposition to obtain
Figure GDA0003259425490000112
Wherein
Figure GDA0003259425490000113
And
Figure GDA0003259425490000114
is an L multiplied by L dimensional unitary matrix,
Figure GDA0003259425490000115
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 GDA0003259425490000116
And digital merger
Figure GDA0003259425490000117
Figure GDA0003259425490000118
Figure GDA0003259425490000119
Wherein the content of the first and second substances,
Figure GDA00032594254900001110
representation matrix
Figure GDA00032594254900001111
Figure GDA00032594254900001111
1 to N ofsA sub-matrix of columns is formed,
Figure GDA00032594254900001112
representation matrix
Figure GDA00032594254900001113
Figure GDA00032594254900001113
1 to N ofsA sub-matrix of columns.
In general, the digital precoder can be normalized using the following equation:
Figure GDA00032594254900001114
in order to better illustrate the technical scheme of the invention, a specific example is adopted for simulation verification.
As shown in fig. 1, 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 also 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 space multiplexing and the efficiency of millimeter wave MIMO communication by 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 (a conventional low-resolution hybrid beamformer) is selected as the comparison method in the present embodiment, and the iterative phase matching algorithm has the best performance in the conventional low-resolution phase shifter scheme.
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 comparative method. The spectral efficiency of the present invention was evaluated in fig. 3 and 4 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. 3 and 4, 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. 5 is a graph of average spectral efficiency versus SNR for 64x16 antenna array counts and multiple data streams for the present invention and comparative method. As shown in fig. 5, compared to fig. 4, the performance of the inventive method is much better than the comparative method with 1-bit precision.
Fig. 6 is a graph 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. 6, the present invention performs much better with 1-bit precision than the contrast scheme, even with a macroscopic advantage over the 2-bit precision contrast scheme, compared to the multiple data stream case of fig. 4.
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 matters of the invention which utilize the inventive concepts 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 FDA0003259425480000011
And analog combiner
Figure FDA0003259425480000012
1 st column vector of
Figure FDA0003259425480000013
And
Figure FDA0003259425480000014
Figure FDA0003259425480000015
Figure FDA0003259425480000016
wherein v is1＝V(:,1)，u1U (: 1), V (: 1) denotes a vector of the 1 st column in the matrix V, and U (: 1) denotes a vector of the 1 st column in the matrix U;
s3: let i be 2;
s4: adopt the first i-1
Figure FDA0003259425480000017
Constructing matrix F as a column vectori-1The first i-1 are adopted
Figure FDA0003259425480000018
Constructing W as a column vectori-1I ═ 1,2, …, i-1, and then the matrix E is calculatedi-1：
Figure FDA0003259425480000019
Figure FDA00032594254800000110
U (: 1: L) represents a submatrix formed by the 1 st to L th columns of the matrix U,
Figure FDA00032594254800000111
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 FDA00032594254800000112
v (: 1: L) represents a submatrix formed by the 1 st to L th columns of the matrix V; α is a predetermined minimum scalar value, ILRepresenting an L × L dimensional identity matrix;
for matrix Ei-1Singular value decomposition is carried out to obtain Ei-1＝SVDHThen calculated to obtain
Figure FDA00032594254800000113
And
Figure FDA00032594254800000114
Figure FDA00032594254800000115
Figure FDA00032594254800000116
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 D;
s5: judging whether i is less than L, if so, entering step S6, otherwise, entering step S7;
s6: returning to step S4 by making i + 1;
s7: will be L
Figure FDA0003259425480000021
Hybrid precoder designed as column vector construction
Figure FDA0003259425480000022
Will be L
Figure FDA0003259425480000023
Analog merger designed as column vector construction
Figure FDA0003259425480000024
S8: obtaining an effective baseband channel using the following equation
Figure FDA0003259425480000025
Figure FDA0003259425480000026
S9: for effective baseband channel
Figure FDA0003259425480000027
Performing singular value decomposition to obtain
Figure FDA0003259425480000028
Wherein
Figure FDA0003259425480000029
And
Figure FDA00032594254800000210
is an L multiplied by L dimensional unitary matrix,
Figure FDA00032594254800000211
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 FDA00032594254800000212
And digital merger
Figure FDA00032594254800000213
Figure FDA00032594254800000214
Figure FDA00032594254800000215
Wherein the content of the first and second substances,
Figure FDA00032594254800000216
representation matrix
Figure FDA00032594254800000217
1 to N ofsA sub-matrix of columns is formed,
Figure FDA00032594254800000218
representation matrix
Figure FDA00032594254800000219
1 to N ofsA sub-matrix of columns.
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