CN114465643A - Mixed precoding method of millimeter wave large-scale MIMO antenna system based on gradient descent method - Google Patents

Mixed precoding method of millimeter wave large-scale MIMO antenna system based on gradient descent method Download PDF

Info

Publication number
CN114465643A
CN114465643A CN202210205437.3A CN202210205437A CN114465643A CN 114465643 A CN114465643 A CN 114465643A CN 202210205437 A CN202210205437 A CN 202210205437A CN 114465643 A CN114465643 A CN 114465643A
Authority
CN
China
Prior art keywords
precoder
radio frequency
signal
millimeter wave
hybrid
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.)
Granted
Application number
CN202210205437.3A
Other languages
Chinese (zh)
Other versions
CN114465643B (en
Inventor
楚彩虹
韦成杰
穆中华
李丽兰
李春莹
梁宏伟
李珊珊
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.)
Zhengzhou Railway Vocational and Technical College
Original Assignee
Zhengzhou Railway Vocational and Technical College
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 Zhengzhou Railway Vocational and Technical College filed Critical Zhengzhou Railway Vocational and Technical College
Priority to CN202210205437.3A priority Critical patent/CN114465643B/en
Publication of CN114465643A publication Critical patent/CN114465643A/en
Application granted granted Critical
Publication of CN114465643B publication Critical patent/CN114465643B/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
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/391—Modelling the propagation channel
    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention provides a mixed precoding method of a millimeter wave large-scale MIMO antenna system based on a gradient descent method, which comprises the steps of establishing a millimeter wave large-scale MIMO antenna system model, constructing a channel matrix by adopting an expanded Saleh-Valenzuaa channel model, establishing an objective function, and finally optimizing a mixed precoder by utilizing the gradient descent method, so that the performance of the mixed precoder is close to that of a pure digital precoder, and meanwhile, the design complexity and the cost are kept low.

Description

Mixed precoding method of millimeter wave large-scale MIMO antenna system based on gradient descent method
Technical Field
The invention relates to the technical field of multiple-input multiple-output antennas, in particular to a mixed pre-coding method of a millimeter wave large-scale MIMO antenna system based on a gradient descent method.
Background
Millimeter wave and massive MIMO are two new technologies in 5G communication systems, the combination of which is to provide bandwidth and spectral efficiency at millimeter wave frequencies using large antenna arrays. However, in the design of the millimeter wave massive MIMO system, the excessive power consumption and hardware cost caused by operating multiple antennas on the frequency band need to be considered, and if a pure digital precoder is used, the higher cost and power consumption must be spent, so that each antenna corresponds to one radio frequency chain; if the analog precoder is used, the cost and power consumption can be reduced, and the analog precoder can control the phase of a signal transmitted by each antenna through a phase shifter, so that the defects of a radio frequency chain are overcome, but the performance of the radio frequency chain is far from that of a pure digital precoder. To solve this problem, a relatively good solution is a hybrid precoding scheme combining analog and digital, where the hybrid precoder includes a low-dimensional digital precoder and a high-dimensional analog precoder, which are connected by a small number of radio frequency links, thereby reducing the implementation cost and energy consumption of the system.
Although the hybrid precoding scheme reduces hardware cost and power consumption, the performance of the system is also reduced, and the problem that the solution of the optimization problem is complex exists in the design process, so that how to design a hybrid precoder with better performance under the conditions of low complexity and low cost is an urgent problem to be solved.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a mixed precoding method of a millimeter wave large-scale MIMO antenna system based on a gradient descent method, which can keep lower design complexity and cost and simultaneously make the performance of a mixed precoder close to a pure digital precoder.
The technical scheme of the invention is as follows:
a mixed pre-coding method of a millimeter wave large-scale MIMO antenna system based on a gradient descent method comprises the following steps:
step 1: establishing a millimeter wave large-scale MIMO antenna system model, and constructing a channel matrix by adopting an expanded Saleh-Vallenzuela channel model; the specific construction mode of the millimeter wave large-scale MIMO antenna system model is as follows:
in a millimeter-wave massive MIMO antenna system, a base station configures NtRoot transmitting antenna and Nt RFTransmitting K data streams according to the radio frequency link, and simultaneously serving K User Equipment (UE) at a receiving end, wherein N is configured for each UErRoot receiving antenna and a radio frequency link, and receiving only one data stream, Nr RFRepresenting the total number of radio links of all users, the system must satisfy
Figure BDA0003529087700000021
The transmission signal x of the base station is represented as:
Figure BDA0003529087700000022
wherein, the transmitting symbol vector s is a group of random numbers, elements of which are independent from each other and satisfy zero average value and unit energy,
Figure BDA0003529087700000023
and is
Figure BDA0003529087700000024
And P is the total transmit power, FRFIs an analog radio frequency precoding matrix in the form of
Figure BDA0003529087700000025
FBBIs a digital precoding matrix of the form
Figure BDA0003529087700000026
FRFAnd FBBShould satisfy power control, i.e.
Figure BDA0003529087700000027
After being sent from a transmitting antenna, a signal is transmitted to a receiving end through a channel, and the mixed pre-coding millimeter wave large-scale MIMO system model is represented as follows:
Figure BDA0003529087700000028
wherein H is Nr RF*Nt RFChannel fading matrix, WRFIs a receiving end simulating a radio frequency decoding matrix and WBBIs a receiving end digital radio frequency decoding matrix, n-CN (0, sigma)2INr) Representing a mean of 0 and a variance of σ2The elements of the channel noise vector of (a) are independent of each other and have the same distribution characteristics, and are independent of the transmitted symbol vector s;
step 2: establishing a target function according to the achievable total transmission rate of the system after the pre-coding processing of the base station;
the kth user receives the signal ykThen passing through the analog radio frequency decoding matrix
Figure BDA0003529087700000029
After that, the receiving end signal is expressed as:
Figure BDA00035290877000000210
wherein the content of the first and second substances,
Figure BDA00035290877000000211
the representation corresponds to the k-th user skThe transmitting end and the receiving end both have perfect channel state information; the equation (3) is composed of three terms, i.e., the desired signal of the kth user, the interference signal from other users, and the noise signal, and the achievable sum transmission rate (ASR) of the system is represented as:
Figure BDA0003529087700000031
wherein, γkFor the interference of the k-th userA noise ratio (SINR), which is expressed as:
Figure BDA0003529087700000032
the precoding design optimization problem is equivalent to the following:
Figure BDA0003529087700000033
Figure BDA0003529087700000034
Figure BDA0003529087700000035
Figure BDA0003529087700000036
wherein, the simulating is performed by using phase shifters in both the RF precoder and the decoder, fRF，k(i) Representing an analog radio frequency precoding matrix FRFThe ith element of the line vector corresponding to the kth user normalized to satisfy
Figure BDA0003529087700000037
For a feasible set, the quantization phase is
Figure BDA0003529087700000038
For a fixed initial weight magnitude, phase
Figure BDA0003529087700000039
B is the resolution of the phase shifter; w is aRF，k(j) Representing an analog radio frequency decoding matrix WRFFor the jth element of the kth user, the normalization is satisfied
Figure BDA00035290877000000310
To a feasible set, phase
Figure BDA00035290877000000311
Quantizing the phase to
Figure BDA00035290877000000312
For a fixed initial weight size, feasible set
Figure BDA00035290877000000313
Is limited to
Figure BDA00035290877000000314
Each radio frequency link of the transmitting end is limited to MtA root antenna;
and step 3: optimizing the structure of the hybrid precoder;
3-1, designing precoder by using orthogonal matching pursuit OMP algorithm, wherein mutual information is mixed precoder FRFFBBThe achieved information gain, then the mutual information is expressed as:
Figure BDA0003529087700000041
where I (X, Y) is mutual information between the pair variables (X, Y), Ns is the transmitted data traffic, ρ represents the transmission power per unit time, σn 2Is a variance of σ2Because of the channel noise vector of FRFFBBIs provided with
Figure BDA0003529087700000042
Resulting in the best precoder FoptCannot be directly denoted as FRFFBBOptimization cannot be achieved within the millimeter wave channel, but hybrid precoder F is assumedRFFBBAnd an optimal precoder FoptClose enough to pass FoptAnd FRFFBBThe generated mutual information is compared, so the precoder design problem can be optimized as follows:
Figure BDA0003529087700000043
Figure BDA0003529087700000044
wherein the content of the first and second substances,
Figure BDA0003529087700000045
for a feasible set of elements of constant size, the constraint is Nr RF*Nt RFOf the hybrid precoder F, thus according to the hybrid precoder FRFFBBInformation gain and optimal precoder F achievedoptThe minimum residual error between the two is used for solving a suboptimal solution by using a formula (8) to design a hybrid precoder;
3-2, optimizing the hybrid precoder based on a gradient descent method:
first, find out
Figure BDA0003529087700000046
To FRFAnd FBBGradient of
Figure BDA0003529087700000047
Defined as the error ε, then
Figure BDA0003529087700000048
To FBBGradient (2):
Figure BDA0003529087700000049
similarly, calculate
Figure BDA00035290877000000410
To FRFGradient (2):
Figure BDA00035290877000000411
after the two gradient values are obtained through calculation, F is designed by utilizing a gradient descent methodRFAnd FBBThe method specifically comprises the following steps:
random generation analog precoder FRFAnd a digital precoder FBBSince the analog precoder is limited by the phase shifter, only the phase of the signal can be changed, but not the amplitude of the signal, so the amplitude of the analog precoder has to be a fixed magnitude:
Figure BDA00035290877000000412
wherein, i-1, …, Nt，j＝1，…，Nt RF；
Updating F with step ηRFAnd FBBEta is set as required:
Figure BDA0003529087700000051
Figure BDA0003529087700000052
using updated FRFAnd FBBError epsilon is calculated and set as an error threshold, F, every time an update is completedRFAnd FBBIf the calculated error is larger than the error threshold, carrying out secondary iteration and recalculating the gradient until the error is smaller than the error threshold; after the iteration is completed, FBBNormalization is carried out to obtain the final simulation precoder FRFAnd digital precoder FBB。
Preferably, an optimal precoder FoptIs a pure digital precoder.
Preferably, the hybrid precoder is a fully-connected hybrid precoder architecture, with each radio frequency chain connected to all antennas by phase shifters.
The technical effect that this application realized is as follows:
the invention optimizes the hybrid precoder by using the gradient descent method, simplifies the optimal design problem of the existing hybrid precoder, and changes solving the optimal solution into searching a suboptimal solution, and then uses the gradient descent method and an iterative updating mode to ensure that the performance of the hybrid precoder is as close to a pure digital precoder as possible, thereby effectively balancing the restriction problem of the choice between the performance and the complexity on the basis of keeping lower design complexity and cost.
Drawings
Fig. 1 is a diagram of a fully connected antenna architecture.
Fig. 2 is a model structure of a millimeter-wave massive MIMO antenna system to which the present invention is applied.
Fig. 3 is an algorithm code for designing an analog precoder and a digital precoder using a gradient descent method according to the present invention.
Detailed Description
The technical solution of the present invention will be further explained with reference to the attached drawings and tables.
The analog portion of hybrid beamforming is typically implemented with simple analog components such as adders and phase shifters, where the analog phase shifters can only change the phase of the signal. The analog beamforming matrix has a constraint limit of fixed element mode values in consideration of the limit of the mode part element architecture. The existing literature mainly studies two widely used analog beamforming architectures: fully connected and partially connected architectures.
FIG. 1 shows a fully connected architecture, under which N isRFEach of the radio frequency chains (RF chain) is connected to all transmit antennas NtIn other words, each transmit antenna is also connected to all of the radio frequency chains. However, because the millimeter wave band has a higher frequency, the spacing between the antennas is smaller, so that more antennas can be placed on an area of the same size for higher-rate transmission, and the performance is closest to that of a pure digital precoder, but because the number of antennas is increased, the power consumption becomes larger, even though hybrid beamforming is more than pure digital precoderDigital beamforming power consumption is reduced, but hybrid beamforming based on a fully connected architecture still consumes considerable power.
FIG. 2 shows a millimeter-wave MIMO antenna system model structure with a base station configuration NtRoot transmitting antenna and Nt RFRoot radio frequency link (RF chain), FBBAs a digital precoder matrix, FRFFor simulating a radio frequency precoder matrix, K data streams are transmitted and a receiving end is simultaneously served by K User Equipment (UE) which are all same in configuration with NrRoot receiving antenna and a radio frequency link (RF chain) and receiving only one data stream, Nr RFRepresenting the total number of radio links of all users, the system must satisfy
Figure BDA0003529087700000061
The transmission signal x of the base station is represented as:
Figure BDA0003529087700000062
wherein, the transmitting symbol vector s is a group of random numbers, elements of which are independent from each other and satisfy zero average value and unit energy,
Figure BDA0003529087700000063
and is
Figure BDA0003529087700000064
And P is the total transmit power, FRFIs an analog radio frequency precoding matrix in the form of
Figure BDA0003529087700000065
FBBIs a digital precoding matrix of the form
Figure BDA0003529087700000066
FRFAnd FBBShould satisfy power control, i.e.
Figure BDA0003529087700000067
After being sent from a transmitting antenna, a signal is transmitted to a receiving end through a channel, and the mixed pre-coding millimeter wave large-scale MIMO system model is represented as follows:
Figure BDA0003529087700000068
wherein H is Nr RF*Nt RFChannel fading matrix, WRFA receiving end analog radio frequency decoding matrix and a WBB digital radio frequency decoding matrix, wherein n-CN (0, sigma 2INr) represents a channel noise vector with the mean value of 0 and the variance of sigma 2, the elements of the channel noise vector are independent of each other, have the same distribution characteristic and are independent of a transmitting symbol vector s;
the millimeter wave massive MIMO system channel adopts a geometric Saleh-Vallenzuela model, the design mode of the millimeter wave massive MIMO system channel has various design modes in the prior art, and the millimeter wave massive MIMO system channel can be selected according to the design requirement.
The kth user receives the signal ykThen passing through the analog radio frequency decoding matrix
Figure BDA0003529087700000071
After that, the receiving end signal is expressed as:
Figure BDA0003529087700000072
wherein the content of the first and second substances,
Figure BDA0003529087700000073
the representation corresponds to the k-th user skThe transmitting end and the receiving end both have perfect channel state information; the equation (6) is composed of three terms, i.e., the desired signal of the kth user, the interference signal from other users, and the noise signal, and the achievable sum transmission rate (ASR) of the system is represented as:
Figure BDA0003529087700000074
wherein, γkThe signal-to-interference-and-noise ratio (SINR) for the kth user, which is expressed as:
Figure BDA0003529087700000075
the precoding design optimization problem is equivalent to the following:
Figure BDA0003529087700000076
Figure BDA0003529087700000077
Figure BDA0003529087700000078
Figure BDA0003529087700000079
wherein, the simulating is performed by using phase shifters in both the RF precoder and the decoder, fRF，k(i) Representing an analog radio frequency precoding matrix FRFThe ith element of the line vector corresponding to the kth user normalized to satisfy
Figure BDA00035290877000000710
For a feasible set, the quantization phase is
Figure BDA00035290877000000711
For a fixed initial weight magnitude, phase
Figure BDA00035290877000000712
B is the resolution of the phase shifter; wRF，k(j) Representing an analog radio frequency decoding matrix WRFFor the jth element of the kth user, the normalization is satisfied
Figure BDA0003529087700000081
To a feasible set, phase
Figure BDA0003529087700000082
Quantizing the phase to
Figure BDA0003529087700000083
For a fixed initial weight size, feasible set
Figure BDA0003529087700000084
Is limited to
Figure BDA0003529087700000085
Each radio frequency link of the transmitting end is limited to MtA root antenna.
As can be seen from equation (9), this is a non-deterministic polynomial NP problem, FRF，FBB，WRFThe synchronization design is needed to maximize the hybrid precoder performance, but the computational complexity is high, plus FRF，FBBWith non-convex function constraints, the difficulty of optimization of the hybrid precoder is further exacerbated. Therefore, the solution to the problem of the present invention is to design the hybrid precoder by using the OMP algorithm, and the mutual information is the hybrid precoder FRFFBBThe achieved information gain, then the mutual information is expressed as:
Figure BDA0003529087700000086
where I (X, Y) is mutual information between the pair variables (X, Y), Ns is the transmitted data traffic, ρ represents the average received power, σ representsn 2Is a variance of σ2Because of the channel noise vector of FRFFBBIs provided with
Figure BDA0003529087700000087
Resulting in an optimal precoder FoptCannot be directly denoted as FRFFBBOptimization cannot be achieved within the millimeter wave channel, but hybrid precoder F is assumedRFFBBAnd the optimum precoder FoptClose enough to pass FoptAnd FRFFBBThe generated mutual information is compared, so the precoder design problem can be optimized as follows:
Figure BDA0003529087700000088
Figure BDA0003529087700000089
wherein the content of the first and second substances,
Figure BDA00035290877000000810
for a feasible set of elements of constant size, the constraint is Nr RF*Nt RFIs given by the matrix set, | | Fopt-FRFFBB||FIs a euclidean distance and is therefore according to the hybrid precoder FRFFBBInformation gain and optimal precoder (pure digital precoder) Fo achievedptThe minimum residual between the two is used for solving the suboptimal solution by using a formula (8) to design the hybrid precoder. Furthermore, the pure digital precoder FoptThe design method of (a) can adopt any method in the prior art according to the needs, and the invention is not limited to this.
And finally, optimizing the hybrid precoder based on a gradient descent method: the gradient descent method is a first-order optimization algorithm, and if a local minimum value of a function is found by using the gradient descent method, iterative search must be performed on a distance point with a specified step length in the reverse direction of the gradient of a current corresponding point on the function.
The gradient descent method is based on the following observations: if the real function F (x) is differentiable and defined at point a, the function F (x) is defined at point aIn the opposite direction of the gradient
Figure BDA0003529087700000091
The most degradation. Based on the above considerations, x may be estimated from the initial estimate of the local minimum of the function0Starting from, and considering the following sequence x0，x1，x2… are such that
Figure BDA0003529087700000092
n 0. Thus, F (x) can be obtained0)》F(x1)》F(x2) …, sequence (x)n) Smoothly converges to the desired local minimum, wherein the step size r is adjustable at each iteration.
Based on the concept, the invention adopts a gradient descent method to design an analog precoder and a digital precoder. First, find out
Figure BDA0003529087700000093
To FRFAnd FBBGradient of
Figure BDA0003529087700000094
Defined as the error epsilon, then calculated
Figure BDA0003529087700000095
To F is aligned withBBGradient (2):
Figure BDA0003529087700000096
similarly, calculate
Figure BDA0003529087700000097
To FRFGradient (2):
Figure BDA0003529087700000098
after the two gradient values are obtained through calculation, F is designed by utilizing a gradient descent methodRFAnd FBBThe method specifically comprises the following steps:
random generation analog precoder FRFAnd a digital precoder FBBSince the analog precoder is limited by the phase shifter, only the phase of the signal can be changed, but not the amplitude of the signal, so the amplitude of the analog precoder has to be a fixed magnitude:
Figure BDA0003529087700000099
wherein, i-1, …, Nt，j＝1，…，Nt RF；
Updating F with step ηRFAnd FBBEta is set as required:
Figure BDA00035290877000000910
Figure BDA00035290877000000911
using updated FRFAnd FBBError epsilon is calculated and set as an error threshold, F, every time an update is completedRFAnd FBBIf the calculated error is larger than the error threshold, carrying out secondary iteration and recalculating the gradient until the error is smaller than the error threshold; after the iteration is completed, FBBNormalization is carried out to obtain the final simulation precoder FRFAnd digital precoder FBB. Specific algorithm codes for designing analog precoders and digital precoders by using the gradient descent method are shown in fig. 3.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in the embodiments or some parts of the embodiments.
While one embodiment of the present invention has been described in detail, the description is only a preferred embodiment of the present invention and should not be taken as limiting the scope of the invention. All equivalent changes and modifications made within the scope of the present invention shall fall within the scope of the present invention.

Claims (3)

1. A mixed precoding method of a millimeter wave large-scale MIMO antenna system based on a gradient descent method is characterized by comprising the following steps:
step 1: establishing a millimeter wave large-scale MIMO antenna system model, and constructing a channel matrix by adopting an expanded Saleh-Vallenzuela channel model; the specific construction mode of the millimeter wave large-scale MIMO antenna system model is as follows:
in a millimeter-wave massive MIMO antenna system, a base station configures NtRoot transmitting antenna and Nt RFTransmitting K data streams according to the radio frequency link, and simultaneously serving K User Equipment (UE) at a receiving end, wherein N is configured for each UErRoot receiving antenna and a radio frequency link, and receiving only one data stream, Nr RFRepresenting the total number of radio links of all users, the system must satisfy
Figure FDA0003529087690000011
The transmission signal x of the base station is represented as:
Figure FDA0003529087690000012
wherein the transmitted symbol vector s is a set of random numbers, the elements of whichThe elements are independent of each other and satisfy zero average value and unit energy,
Figure FDA0003529087690000013
and is
Figure FDA0003529087690000014
And P is the total transmit power, FRFIs an analog radio frequency precoding matrix in the form of
Figure FDA0003529087690000015
FBBIs a digital precoding matrix of the form
Figure FDA0003529087690000016
FRFAnd FBBShould satisfy power control, i.e.
Figure FDA0003529087690000017
After being sent from a transmitting antenna, a signal is transmitted to a receiving end through a channel, and the mixed pre-coding millimeter wave large-scale MIMO system model is represented as follows:
Figure FDA0003529087690000018
wherein H is Nr RF*Nt RFChannel fading matrix, WRFIs a receiving end simulating a radio frequency decoding matrix and WBBIs a receiving end digital radio frequency decoding matrix, n-CN (0, sigma)2INr) Representing a mean of 0 and a variance of σ2The elements of the channel noise vector of (a) are independent of each other and have the same distribution characteristics, and are independent of the transmitted symbol vector s;
step 2: establishing a target function according to the achievable total transmission rate of the system after the pre-coding processing of the base station;
the kth user receives the signal ykThen passing through the analog radio frequency decoding matrix
Figure FDA0003529087690000019
After that, the receiving end signal is expressed as:
Figure FDA0003529087690000021
wherein the content of the first and second substances,
Figure FDA0003529087690000022
the representation corresponds to the k-th user skThe transmitting end and the receiving end both have perfect channel state information; the equation (3) is composed of three terms, i.e., the desired signal of the kth user, the interference signal from other users, and the noise signal, and the achievable sum transmission rate (ASR) of the system is represented as:
Figure FDA0003529087690000023
wherein, γkThe signal-to-interference-and-noise ratio (SINR) for the kth user, which is expressed as:
Figure FDA0003529087690000024
the precoding design optimization problem is equivalent to the following:
Figure FDA0003529087690000025
Figure FDA0003529087690000026
Figure FDA0003529087690000027
Figure FDA0003529087690000028
wherein, the simulating is performed by using phase shifters in both the RF precoder and the decoder, fRF，k(i) Representing an analog radio frequency precoding matrix FRFThe ith element of the line vector corresponding to the kth user normalized to satisfy
Figure FDA0003529087690000029
Figure FDA00035290876900000210
For a feasible set, the quantization phase is
Figure FDA00035290876900000211
Figure FDA00035290876900000212
For a fixed initial weight magnitude, phase
Figure FDA00035290876900000213
B is the resolution of the phase shifter; w is aRF，k(j) Representing an analog radio frequency decoding matrix WRFFor the jth element of the kth user, the normalization is satisfied
Figure FDA00035290876900000214
Figure FDA00035290876900000215
To a feasible set, phase
Figure FDA00035290876900000216
Quantizing the phase to
Figure FDA00035290876900000217
Figure FDA00035290876900000218
For a fixed initial weight size, feasible set
Figure FDA00035290876900000219
Is limited to
Figure FDA0003529087690000031
Each radio frequency link of the transmitting end is limited to MtA root antenna;
and step 3: optimizing the structure of the hybrid precoder;
3-1, designing precoder by using orthogonal matching pursuit OMP algorithm, wherein mutual information is mixed precoder FRFFBBThe achieved information gain, then the mutual information is expressed as:
Figure FDA0003529087690000032
where I (X, Y) is mutual information between the pair variables (X, Y), Ns is the transmitted data traffic, ρ represents the transmission power per unit time, σn 2Is a variance of σ2Because of the channel noise vector of FRFFBBIs provided with
Figure FDA0003529087690000033
Resulting in the best precoder FoptCannot be directly denoted as FRFFBBOptimization cannot be achieved within the millimeter wave channel, but hybrid precoder F is assumedRFFBBAnd an optimal precoder FoptClose enough to pass FoptAnd FRFFBBThe generated mutual information is compared, so the precoder design problem can be optimized as follows:
Figure FDA0003529087690000034
Figure FDA0003529087690000035
wherein the content of the first and second substances,
Figure FDA0003529087690000036
for a feasible set of elements of constant size, the constraint is Nr RF*Nt RFOf the hybrid precoder F, thus according to the hybrid precoder FRFFBBAchieved information gain and optimal precoder FoptThe minimum residual error between the two is used for solving a suboptimal solution by using a formula (8) to design a hybrid precoder;
3-2, optimizing the hybrid precoder based on a gradient descent method:
first, find out
Figure FDA0003529087690000037
To FRFAnd FBBGradient of
Figure FDA0003529087690000038
Defined as the error ε, then
Figure FDA0003529087690000039
To FBBGradient (2):
Figure FDA00035290876900000310
similarly, calculate
Figure FDA00035290876900000311
To FRFGradient (2):
Figure FDA00035290876900000312
after the two gradient values are obtained through calculation, F is designed by utilizing a gradient descent methodRFAnd FBBThe method specifically comprises the following steps:
random generation analog precoder FRFAnd a digital precoder FBBSince the analog precoder is limited by the phase shifter, and can only change the phase of the signal but not the amplitude of the signal, the amplitude of the analog precoder must be a fixed magnitude:
Figure FDA0003529087690000041
wherein, i-1, …, Nt，j＝1，…，Nt RF；
Updating F with step ηRFAnd FBBEta is set as required:
Figure FDA0003529087690000042
Figure FDA0003529087690000043
using updated FRFAnd FBBError epsilon is calculated and set as an error threshold, F, every time an update is completedRFAnd FBBIf the calculated error is larger than the error threshold, carrying out secondary iteration and recalculating the gradient until the error is smaller than the error threshold; after the iteration is completed, FBBNormalization is carried out to obtain the final simulation precoder FRFAnd a digital precoder FBB。
2. The method of claim 1, wherein: the best precoder FoptIs a pure digital precoder.
3. The method of claim 1, wherein: the hybrid precoder is a fully-connected hybrid precoder architecture, with each radio frequency chain connected to all antennas through phase shifters.
CN202210205437.3A 2022-03-02 2022-03-02 Mixed precoding method of millimeter wave large-scale MIMO antenna system based on gradient descent method Active CN114465643B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210205437.3A CN114465643B (en) 2022-03-02 2022-03-02 Mixed precoding method of millimeter wave large-scale MIMO antenna system based on gradient descent method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210205437.3A CN114465643B (en) 2022-03-02 2022-03-02 Mixed precoding method of millimeter wave large-scale MIMO antenna system based on gradient descent method

Publications (2)

Publication Number Publication Date
CN114465643A true CN114465643A (en) 2022-05-10
CN114465643B CN114465643B (en) 2023-03-10

Family

ID=81416179

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210205437.3A Active CN114465643B (en) 2022-03-02 2022-03-02 Mixed precoding method of millimeter wave large-scale MIMO antenna system based on gradient descent method

Country Status (1)

Country Link
CN (1) CN114465643B (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115102590A (en) * 2022-06-21 2022-09-23 郑州铁路职业技术学院 Millimeter wave beam space mixed beam forming method and device
CN115276728A (en) * 2022-07-16 2022-11-01 西安邮电大学 Hybrid precoding method and system in millimeter wave system

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20120082259A1 (en) * 2010-10-04 2012-04-05 Nec Laboratories America, Inc. Precoding Selection for Retransmission in Uplink MIMO Hybrid ARQ
CN105610477A (en) * 2016-01-28 2016-05-25 西南交通大学 Enhancement signal multiplexing technique of multiple-input multiple-output system based on compressive sensing
CN106452535A (en) * 2016-11-24 2017-02-22 北京邮电大学 Hybrid beam forming method and device in blind channel
US20190044588A1 (en) * 2017-08-04 2019-02-07 Samsung Electronics Co., Ltd. Apparatus and method for uplink transmission in wireless communication system

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20120082259A1 (en) * 2010-10-04 2012-04-05 Nec Laboratories America, Inc. Precoding Selection for Retransmission in Uplink MIMO Hybrid ARQ
CN105610477A (en) * 2016-01-28 2016-05-25 西南交通大学 Enhancement signal multiplexing technique of multiple-input multiple-output system based on compressive sensing
CN106452535A (en) * 2016-11-24 2017-02-22 北京邮电大学 Hybrid beam forming method and device in blind channel
US20190044588A1 (en) * 2017-08-04 2019-02-07 Samsung Electronics Co., Ltd. Apparatus and method for uplink transmission in wireless communication system

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
AHMED NADHIM MOHAMMED: "Low computational complexity and minimizing training overhead for hybrid precoding in millimeter wave systems" *
冯湘云;周小平;王培培;汪洋;: "基于格拉斯曼流形的多用户大规模混合预编码" *
张煜: "毫米波MIMO系统中基于自适应梯度算法的混合预编码" *

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115102590A (en) * 2022-06-21 2022-09-23 郑州铁路职业技术学院 Millimeter wave beam space mixed beam forming method and device
CN115276728A (en) * 2022-07-16 2022-11-01 西安邮电大学 Hybrid precoding method and system in millimeter wave system
CN115276728B (en) * 2022-07-16 2023-12-05 西安邮电大学 Mixed pre-coding method and system in millimeter wave system

Also Published As

Publication number Publication date
CN114465643B (en) 2023-03-10

Similar Documents

Publication Publication Date Title
Gao et al. Machine learning inspired energy-efficient hybrid precoding for mmWave massive MIMO systems
CN107809274B (en) Hybrid precoding method based on novel phase-shifting switch network
CN114465643B (en) Mixed precoding method of millimeter wave large-scale MIMO antenna system based on gradient descent method
CN110011712B (en) Millimeter wave large-scale multi-input multi-output-oriented hybrid precoding method
Liu et al. Energy-efficient hybrid precoding with low complexity for mmWave massive MIMO systems
CN107809275B (en) Finite feedback hybrid precoding method based on millimeter wave MIMO system
Vlachos et al. Energy efficient transmitter with low resolution DACs for massive MIMO with partially connected hybrid architecture
CN113193893B (en) Millimeter wave large-scale MIMO intelligent hybrid beam forming design method
Zhu et al. Adaptive beamforming design for millimeter-wave line-of-sight MIMO channel
CN109981154A (en) Low complex degree array antenna multi-input multi-output system mixing precoding algorithms
CN113852402B (en) IRS (intelligent communications system) -assisted NOMA-MIMO (non-multiple input multiple output) high-capacity access method
CN105721029A (en) Multi-user scheduling method based on double-codebook limited feedback in 3D MU-MIMO FDD system
Bereyhi et al. PAPR-limited precoding in massive MIMO systems with reflect-and transmit-array antennas
CN107104719B (en) Millimeter wave digital-analog hybrid precoding design method based on geometric construction
Kabalci et al. Hybrid precoding for mmWave massive MIMO systems with generalized triangular decomposition
CN112398513A (en) Beam forming method of massive MIMO system
Bo et al. Deep learning based low-resolution hybrid precoding design for mmWave MISO systems
Qiao et al. Eigen decomposition-based hybrid precoding for millimeter wave MIMO systems with low-resolution ADCs/DACs
Fang et al. Improper gaussian signaling for IRS assisted multiuser SWIPT systems with hardware impairments
Magueta et al. Non linear space-time equalizer for single-user hybrid mmWave massive MIMO systems
Shahjehan et al. A sparse optimization approach for beyond 5G mmwave massive mimo networks
Zhang et al. ADMM enabled hybrid precoding in wideband distributed phased arrays based MIMO systems
Du et al. HP‐SPC algorithm with dynamic partially connected structure for mmWave MIMO systems
CN112468201B (en) Overlapping sub-connection hybrid precoding method based on millimeter wave large-scale MIMO antenna system
CN112468200B (en) Overlapping sub-connection hybrid precoding device based on millimeter wave large-scale MIMO antenna 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