CN112564748B - MIMO heterogeneous wireless network beam forming method considering hardware damage - Google Patents

MIMO heterogeneous wireless network beam forming method considering hardware damage Download PDF

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CN112564748B
CN112564748B CN202011412246.1A CN202011412246A CN112564748B CN 112564748 B CN112564748 B CN 112564748B CN 202011412246 A CN202011412246 A CN 202011412246A CN 112564748 B CN112564748 B CN 112564748B
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femtocell
user
hardware
macrocell
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CN112564748A (en
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徐勇军
谢豪
刘期烈
黄勇
谢超
黄东
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Guangzhou Tiancheng Weiye Communication Technology Co ltd
Shenzhen Hongyue Enterprise Management Consulting Co ltd
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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
    • H04B7/0452—Multi-user MIMO systems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/18—Network design, e.g. design based on topological or interconnect aspects of utility systems, piping, heating ventilation air conditioning [HVAC] or cabling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • 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
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
    • H04W16/24—Cell structures
    • H04W16/28—Cell structures using beam steering
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/02—CAD in a network environment, e.g. collaborative CAD or distributed simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/04—Constraint-based CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/08—Probabilistic or stochastic CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/10—Noise analysis or noise optimisation
    • 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 relates to a MIMO heterogeneous wireless network beam forming method considering hardware damage, and belongs to the technical field of wireless network resource allocation. The method comprises the following steps: s1: establishing a downlink signal transmission model of a macro cell user and a femto cell user with hardware damage; s2: respectively modeling hardware damage of a macro cell base station transmitter, a macro cell user receiver, a femtocell base station transmitter and a femtocell user receiver; s3: considering hardware damage at a base station transmitter and a user receiver, the maximum transmitting power constraint of each base station and the minimum signal-to-interference-and-noise ratio constraint of each user, and establishing a beam forming design problem of minimizing the total energy consumption of the system; s4: and converting the problem established in the step S3 into a convex optimization problem to solve based on an equivalent transformation method and a semi-definite relaxation method. The invention improves the robustness and the adaptability of the heterogeneous wireless network and reduces the interruption probability of the user.

Description

MIMO heterogeneous wireless network beam forming method considering hardware damage
Technical Field
The invention belongs to the technical field of wireless network resource allocation, and relates to a MIMO heterogeneous wireless network beam forming method considering hardware damage.
Background
With the increasing popularity of the fifth generation communication networks, the number of wireless smart devices is growing exponentially, which makes the wireless communication networks face serious challenges in terms of system capacity and network coverage. Multiple-input multiple-output (MIMO) technology and heterogeneous wireless networks have attracted attention as two key technologies for next-generation communication networks. MIMO technology can improve spectral efficiency and system energy efficiency by deploying large-scale antenna arrays at base stations or user terminals. Heterogeneous wireless networks greatly increase network coverage by deploying a large number of femto networks in a macro cellular network. Therefore, the new network (i.e. the MIMO heterogeneous wireless network) generated by combining the MIMO technology and the heterogeneous wireless network has very important theoretical significance and practical value. However, cross-layer interference caused by heterogeneous wireless networks and co-channel interference caused by MIMO technology may limit the performance of the communication network. Beamforming designs can significantly mitigate cross-layer interference and improve system throughput by flexibly adjusting the beamforming vectors. Therefore, the method has very important significance in the research of the beam forming of the MIMO heterogeneous wireless network.
The operating mode or state of the transceiver hardware equipment may change due to the effect of objective factors such as phase noise, amplifier nonlinearity, and in-phase/quadrature phase imbalance on the system. Especially in massive MIMO systems, communication device manufacturers may use inexpensive components in order to reduce hardware costs, which increases the likelihood of hardware damage. Although some transmitter calibration schemes and receiver compensation algorithms currently exist to mitigate the detrimental impact of hardware impairments on system performance. However, these schemes and algorithms have limited capabilities and do not completely eliminate the impact of hardware damage on the system. For example, the time-varying nature of the hardware still leaves the transceiver with some residual hardware impairments. Residual hardware impairment errors distort the desired signal, resulting in a large gap between the theoretical received signal and the actual received signal. Therefore, when the system is remodeled and the beam forming is designed in the MIMO heterogeneous wireless network, the consideration of hardware damage has important significance and practical value.
Disclosure of Invention
In view of this, the present invention provides a beamforming method for a MIMO heterogeneous wireless network considering hardware damage, which establishes a network model and optimizes the network model under the condition that the MIMO heterogeneous wireless network has hardware damage, improves robustness and adaptability of the heterogeneous wireless network, and reduces interruption probability of a user.
In order to achieve the purpose, the invention provides the following technical scheme:
a MIMO heterogeneous wireless network beam forming method considering hardware damage specifically comprises the following steps:
s1: using an imperfect hardware transmitter and a receiver in a downlink of a two-layer MIMO heterogeneous wireless network, analyzing hardware damage sources in a macro cellular network and a femtocell network, and establishing a downlink signal transmission model of a macro cellular user and a femtocell user with hardware damage;
s2: respectively modeling hardware damage of a macro cell base station transmitter, a macro cell user receiver, a femtocell base station transmitter and a femtocell user receiver;
s3: considering hardware damage at a base station transmitter and a user receiver, the maximum transmitting power constraint of each base station and the minimum signal-to-interference-and-noise ratio constraint of each user, and establishing a beam forming design problem of minimizing the total energy consumption of the system;
s4: and (4) converting the problem established in the step (S3) into a convex optimization problem to solve based on an equivalent transformation method and a semi-positive definite relaxation method.
Further, in step S1, analyzing the sources of hardware damage in the macro cellular network and the femto cellular network includes: hardware impairments at the base station transmitter and the user receiver can be modeled as additive hardware impairment noise and amplified thermal noise;
establishing a downlink signal transmission model of the macro cell user with hardware damage, namely, a signal received by the mth macro cell user
Figure BDA0002815210630000021
Expressed as:
Figure BDA0002815210630000022
wherein the content of the first and second substances,
Figure BDA0002815210630000023
and
Figure BDA0002815210630000024
respectively representing a channel vector of the macrocell base station to the mth macrocell user and a channel vector of the nth femtocell base station to the mth macrocell user;
Figure BDA0002815210630000025
and s m Respectively representing beamforming vectors and information of the macrocell base station to the mth macrocell user;
Figure BDA0002815210630000026
and s n,k Respectively representing beamforming vectors and information of an nth femtocell base station to a kth femtocell user; wherein the content of the first and second substances,
Figure BDA0002815210630000027
N M indicating the total number of antennas, N, provided in the macrocell base station F Representing the total number of antennas equipped by the femtocell base station,
Figure BDA0002815210630000028
respectively represent N M X 1 dimension, N F A complex column vector of x 1 dimension;
Figure BDA0002815210630000029
and
Figure BDA00028152106300000210
additive hardware impairment noise for the macrocell base station transmitter, the nth femtocell base station transmitter and the mth macrocell user receiver,
Figure BDA00028152106300000211
means zero variance of mean at the mth macrocell user receiver
Figure BDA00028152106300000212
Amplified thermal noise.
Further, in step S1, a downlink signal transmission model of the femtocell user is established, where the downlink signal transmission model includes hardware impairments, that is, in the nth femtocell network, a signal from the base station to the kth femtocell user receiver may be represented as:
Figure BDA00028152106300000213
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00028152106300000214
and
Figure BDA00028152106300000215
respectively representing a channel vector of the nth femtocell base station to the kth femtocell user in the network and a channel vector of the macrocell base station to the kth femtocell user in the nth femtocell;
Figure BDA00028152106300000216
representing additive hardware impairment noise at a kth femtocell user receiver in an nth femtocell;
Figure BDA00028152106300000217
means that the mean at the k-th femtocell user receiver in the n-th femtocell is zero variance
Figure BDA0002815210630000031
Amplified thermal noise.
Further, in step S2, additive hardware impairment noise at the macrocell base station transmitter, the femtocell base station transmitter, the macrocell user receiver, and the femtocell user receiver can be modeled as:
Figure BDA0002815210630000032
Figure BDA0002815210630000033
where ψ represents the covariance matrix of additive hardware impairment noise at the macrocell base station transmitter, Φ n A covariance matrix representing additive hardware impairment noise at the nth femtocell base station transmitter,
Figure BDA0002815210630000034
represents the variance of additive hardware impairment noise at the mth macrocell user receiver,
Figure BDA0002815210630000035
representing the variance of additive hardware impairment noise at the kth femtocell user receiver in the nth femtocell.
Further, in step S3, a beamforming design problem that minimizes the total energy consumption of the system is constructed, which is expressed as:
Figure BDA0002815210630000036
Figure BDA0002815210630000037
Figure BDA0002815210630000038
Figure BDA0002815210630000039
Figure BDA00028152106300000310
wherein, C 1 And C 2 Representing maximum transmit power constraints, P, for the macrocell base station and the nth femtocell base station, respectively max And
Figure BDA00028152106300000311
representing maximum transmit power thresholds for the macrocell base station and the nth femtocell base station, respectively; c 3 Represents a minimum signal-to-interference-and-noise ratio constraint for each femtocell user,
Figure BDA00028152106300000312
representing a minimum signal-to-interference-and-noise ratio threshold for a kth femtocell user in the nth femtocell; c 4 Represents the minimum signal-to-interference-and-noise ratio constraint for the mth macrocell user,
Figure BDA00028152106300000313
a minimum signal-to-interference-and-noise ratio threshold representing an mth macrocell user; p is C Represents the circuit power consumption of the macro cell and all femtocells, and ζ ≧ 1 represents the power amplification factor.
Further, in step S4, P1 is a non-convex optimization problem, and P1 is converted into a convex optimization problem by using an equivalent transformation method and a semi-definite relaxation method to solve, and the specific conversion step includes:
s41: definition of
Figure BDA00028152106300000314
Converting the optimization problem P1 into a form that is easy to handle;
s42: introducing an auxiliary matrix S t And S l Covariance matrices psi and phi to process hardware impairment vectors n In which S is t And S l Respectively representing the t-th diagonal element and the l-th diagonal element as 1, and the rest elements as 0;
s43: processing the constraint with the coupling variable by using an equivalent transformation method, and converting the non-convex optimization problem P1 into a convex optimization problem to solve; based on the interior point method, the optimal solution of the convex optimization problem can be obtained
Figure BDA00028152106300000315
And
Figure BDA00028152106300000316
decomposition method by using eigenvalueTo obtain the optimal beam forming vector
Figure BDA00028152106300000317
And
Figure BDA00028152106300000318
the invention has the beneficial effects that: the invention considers the maximum transmitting power constraint of the macro cellular base station, the maximum transmitting power constraint of each femtocell base station, the minimum signal to interference plus noise ratio constraint of macro cellular users and femtocell users, takes the total energy consumption minimization of the system as an optimization target, and establishes a network model and optimizes the problem under the condition that the MIMO heterogeneous wireless network has hardware damage. And converting the original non-convex optimization problem into a convex optimization problem by using an equivalent transformation method and a semi-positive definite relaxation method, and solving an optimal solution by using an interior point method. Compared with the traditional ideal hardware algorithm, the method has the characteristics of low calculation complexity, low user interruption probability, high robustness and high adaptability.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
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For the purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
FIG. 1 is a diagram of a system model of the present invention;
FIG. 2 is a flow chart of the algorithm of the present invention;
FIG. 3 is a diagram showing the relationship between the total energy consumption of the system and the SINR threshold of the user under different algorithms;
fig. 4 shows the average outage probability of a macrocell user versus the user signal-to-interference-and-noise ratio threshold under different algorithms.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.
Referring to fig. 1 to 4, the MIMO heterogeneous wireless network beamforming method considering hardware impairments, as shown in fig. 2, specifically includes the following steps:
s1: and under an ideal transceiver hardware state, establishing a downlink signal transmission model of a macro cellular user and a femtocell user of the two-layer MIMO heterogeneous wireless network.
The present invention considers a downlink transmission scenario of a multi-cellular multi-user MIMO heterogeneous wireless network, as shown in fig. 1. The network comprises a network provided with N M Root antenna macrocell base station and N devices equipped with N F Femtocell base station with root antenna, where there are M single-antenna macrocell users in a macrocell network and K in each femtocell network n A single antenna femtocell user. Wherein the macrocell base station and the femtocell base station transmit information to the macrocell user and the femtocell user, respectively, over a downlink. Definition of
Figure BDA0002815210630000051
And
Figure BDA0002815210630000052
respectively, a set of macro cell users, femto cell users, and femto cell numbers. The femtocell user is supposed to use the frequency spectrum resource of the macrocell user in a underlay type frequency spectrum sharing mode, so that the total cross-layer interference of the femtocell user to any one macrocell user receiver is not more than a certain specific interference temperature threshold value, thereby improving the frequency spectrum utilization rate and the whole femtocell user receiverThe throughput of the network. The channel is assumed to be a block fading channel, i.e., the channel gain is a constant in the same time slot and varies in different time slots. According to the scenario description of 3GPP for heterogeneous wireless networks, since the femtocell base station generally has lower transmission power compared to the macrocell base station, in addition, indoor femtocell users generally suffer from strong wall penetration loss. Thus, as with most work, we assume that the mutual interference between different femtocells is negligible.
As can be seen from fig. 1, the reception of the signal from the macrocell base station by the mth macrocell user can be represented as:
Figure BDA0002815210630000053
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002815210630000054
and s m Respectively, the beamforming vectors and information for the macrocell base station to the mth macrocell user.
Figure BDA0002815210630000055
And s n,k Respectively, a beamforming vector and information for an nth femtocell base station to a kth femtocell user, wherein,
Figure BDA0002815210630000056
Figure BDA0002815210630000057
respectively represent N M X 1 dimension, N F Complex column vector of x 1 dimension.
Figure BDA0002815210630000058
And
Figure BDA0002815210630000059
representing channel vectors from macrocell base station to mth macrocell user and from nth femtocell base station to mth macrocell user, respectivelyA channel vector.
Figure BDA00028152106300000510
Means zero variance at the mth macrocell user
Figure BDA00028152106300000511
White additive gaussian noise.
In the nth femtocell network, the signal from the base station to the kth femtocell user receiver can be expressed as:
Figure BDA00028152106300000512
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00028152106300000513
and
Figure BDA00028152106300000514
representing the channel vector from the nth femtocell base station to the kth femtocell user in the network and the channel vector from the macrocell base station to the kth femtocell user in the nth femtocell, respectively.
Figure BDA00028152106300000515
Means that the mean value at the k-th femtocell user in the n-th femtocell is zero and the variance is
Figure BDA00028152106300000516
Is additive white gaussian noise.
S2: and using an imperfect hardware transmitter and a receiver in the two-layer MIMO heterogeneous wireless network, analyzing hardware damage sources in the macro cellular network and the femtocell network, and establishing downlink signal transmission models of the macro cellular user and the femtocell user again.
In practical systems, either the base station or the user equipment may be affected by hardware impairments to varying degrees, causing a distortion of the desired signal. Residual hardware impairment errors distort the desired signal, resulting in a large gap between the theoretical received signal and the actual received signal. To more truly describe the physical signal, the sources of hardware impairments in the macrocellular and femtocellular networks are analyzed, and the hardware impairments at the base station transmitter and the user receiver can be modeled as additive hardware impairment noise and amplified thermal noise. The reception of a signal from a macrocell base station by an mth macrocell user can be represented as:
Figure BDA0002815210630000061
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002815210630000062
and η r m Additive hardware impairment noise for the macrocell base station transmitter, the nth femtocell base station transmitter and the mth macrocell user receiver,
Figure BDA0002815210630000063
means zero variance of mean at the mth macrocell user receiver
Figure BDA0002815210630000064
Amplified thermal noise. According to equation (3), the mth macrocell user receives a signal-to-interference-and-noise ratio of
Figure BDA0002815210630000065
Wherein the content of the first and second substances,
Figure BDA0002815210630000066
analyzing the source of hardware impairments in a femtocell network, in an nth femtocell network, the signal from the base station to a kth femtocell user receiver can be represented as:
Figure BDA0002815210630000067
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002815210630000068
representing additive hardware impairment noise at the kth femtocell user receiver in the nth femtocell.
Figure BDA0002815210630000069
Means that the mean at the receiver of the kth femtocell user in the nth femtocell is zero and the variance is
Figure BDA00028152106300000610
Amplified thermal noise. According to equation (5), in the n femtocell networks, the signal to interference plus noise ratio received by the kth femtocell user is:
Figure BDA00028152106300000611
wherein the content of the first and second substances,
Figure BDA00028152106300000612
s3: hardware impairments of a macrocell base station transmitter, a macrocell user receiver, a femtocell base station transmitter and a femtocell user receiver are modeled respectively.
In general, the impact of hardware impairments can be partially mitigated by transmitter correction schemes or receiver compensation algorithms, but there will still be some residual hardware impairments at the transmitter and receiver. We model this portion of residual hardware impairments as additive hardware impairment noise, which describes the combined effect of various residual hardware impairments. In addition, additive hardware impairment noise can be modeled as a gaussian distributed random process. Thus, additive hardware impairment noise at a macrocell base station transmitter, a femtocell base station transmitter, a macrocell user receiver, and a femtocell user receiver can be modeled as
Figure BDA00028152106300000613
Figure BDA00028152106300000614
Where ψ represents the covariance matrix of additive hardware impairment noise at the macrocell base station transmitter, Φ n A covariance matrix representing additive hardware impairment noise at the nth femtocell base station transmitter,
Figure BDA0002815210630000071
represents the variance of additive hardware impairment noise at the mth macrocell user receiver,
Figure BDA0002815210630000072
representing the variance of additive hardware impairment noise at the kth femtocell user receiver in the nth femtocell. Definition of
Figure BDA0002815210630000073
Figure BDA0002815210630000074
Is provided with
Figure BDA0002815210630000075
Figure BDA0002815210630000076
Figure BDA0002815210630000077
Figure BDA0002815210630000078
Wherein the content of the first and second substances,
Figure BDA0002815210630000079
and
Figure BDA00028152106300000710
the degree of transmitter and receiver hardware impairment is described separately and is numerically expressed as the ratio of the variance of additive hardware impairment noise to the signal power. In practice, these parameters can be obtained by error vector magnitude measurements. In addition to this, the present invention is,
Figure BDA00028152106300000711
and
Figure BDA00028152106300000712
covariance matrix P of signal vector transmitted by macrocell base station and covariance matrix Q of signal vector transmitted by nth femtocell base station n The main diagonal element of (1). Comprises the following steps:
Figure BDA00028152106300000713
Figure BDA00028152106300000714
s4: and (3) considering hardware damage at a base station transmitter and a user receiver, the maximum transmitting power constraint of each base station and the minimum signal-to-interference-and-noise ratio constraint of each user, and establishing a beam forming design problem of minimizing the total energy consumption of the system.
Considering the constraints of the maximum transmission power of the macrocell base station and each femtocell base station, the constraint of the quality of service of each macrocell user and the constraint of the minimum signal-to-interference-and-noise ratio of each femtocell user, the beamforming design problem of minimizing the total energy consumption of the constructed system can be expressed as
Figure BDA00028152106300000715
Wherein, C 1 And C 2 Representing maximum transmit power constraints, P, for the macrocell base station and the nth femtocell base station, respectively max And
Figure BDA00028152106300000716
representing maximum transmit power thresholds for the macrocell base station and the nth femtocell base station, respectively; c 3 Represents a minimum signal-to-interference-and-noise ratio constraint for each femtocell user,
Figure BDA00028152106300000717
representing a minimum signal-to-interference-and-noise ratio threshold for a kth femtocell user in the nth femtocell; c 4 Representing the minimum signal-to-interference-and-noise ratio constraint for the mth macrocell user,
Figure BDA0002815210630000081
representing the minimum signal to interference plus noise ratio threshold for the mth macrocell user. P C Represents the circuit power consumption of the macro cell and all femtocells, and ζ ≧ 1 represents the power amplification factor.
S5: and (4) converting the original non-convex optimization problem established in the step (S4) into a convex optimization problem to solve based on an equivalent transformation method and a semi-positive definite relaxation method.
P1 is a non-convex optimization problem, and the P1 is converted into a convex optimization problem by using an equivalent transformation method and a semi-definite relaxation method to solve. The specific conversion steps include:
s51: definition of
Figure BDA0002815210630000082
Is provided with
Figure BDA0002815210630000083
Figure BDA0002815210630000084
According to equations (14) and (15), the optimization problem P1 can be transformed into:
Figure BDA0002815210630000085
s52: introducing an auxiliary matrix S t And S l Method and apparatus for handling hardware damageCovariance matrix psi and phi of vectors n In which S is t And S l Respectively, the t-th diagonal element and the l-th diagonal element are 1, and the rest elements are all 0. The optimization problem P2 can be converted into:
Figure BDA0002815210630000086
wherein the content of the first and second substances,
Figure BDA0002815210630000087
Figure BDA0002815210630000088
Figure BDA0002815210630000091
s53: processing constraints with coupling variables by using equivalent transformation method
Figure BDA0002815210630000092
And
Figure BDA0002815210630000093
in addition, rank-one constraint C is discarded based on a semi-positive definite relaxation method 6 The original non-convex optimization problem can be transformed into a convex optimization problem. The optimization problem P3 can be converted into:
Figure BDA0002815210630000094
based on the interior point method, the optimal solution of the convex optimization problem can be obtained
Figure BDA0002815210630000095
And
Figure BDA0002815210630000096
by using eigenvalue decomposition method, the optimal wave beam can be obtainedShaped vector
Figure BDA0002815210630000097
And
Figure BDA0002815210630000098
otherwise, an approximate solution can be obtained using gaussian randomness.
The application effect of the present invention will be described in detail with reference to the simulation.
1) Simulation conditions
Suppose there is one macro-cellular network, two femto-cellular networks, two macro-cellular users in the macro-cellular network, and two femto-cellular users in each femto-cellular network. The coverage radii of the macro network and each femtocell network are 500 m and 20 m respectively, with a minimum distance of 40 m between different femtocells. Assume that the number of femtocells and macrocells antennas is 4. The channel fading model is assumed to contain large-scale fading and small-scale fading. Large scale fading is modeled as D = A 0 (d/d 0 ) -α Wherein A is 0 =1,d represents the distance between the transmitter and the receiver, reference distance d 0 At 20 meters, α =3 represents the path loss exponent. The small scale fading coefficients follow a gaussian distribution with mean 0 and variance 1. Without loss of generality, it is assumed that the noise variance at all transceivers is equal, i.e.,
Figure BDA0002815210630000099
in addition, suppose
Figure BDA00028152106300000910
Different hardware damage levels are in the interval [0,0.3 ]]An internal change. Assume that the conventional algorithm is an ideal transceiver, i.e., κ t ＝κ r =0, the other parameters are given in table 1.
TABLE 1 simulation parameter Table
Figure BDA00028152106300000911
2) Simulation result
In the present embodiment, fig. 3 shows the relationship between the total energy consumption of the system and the minimum sir threshold of the user. Fig. 4 shows the average outage probability of a macro cell user versus a minimum signal to interference plus noise ratio threshold. As can be seen from fig. 3, the total energy consumption of the system increases as the user signal to interference plus noise ratio threshold increases. As the sir threshold of the user increases, the base station needs to allocate higher power for information transmission to meet the user minimum sir requirement, resulting in an increase in the total energy consumption of the system. On the other hand, under the same signal-to-interference-and-noise ratio threshold condition, the total energy consumption of the system of the algorithm is higher than that of the traditional algorithm. Since the conventional algorithm does not take into account the impact of hardware impairments on the transceiver. In order to reduce the occurrence of communication interruption events, the base station allocates higher power to overcome the influence of hardware damage parameters on the signal-to-interference-and-noise ratio of the user, and prevents the user from generating harmful interruption. Fig. 4 shows that as the minimum signal to interference plus noise ratio threshold of a macrocell user increases, the average outage probability for the macrocell user gradually increases. The reason for this is that the larger the minimum sir threshold is, the more difficult it is to satisfy the sir constraint of the macro-cell users, and the probability of interruption of the macro-cell users increases. On the other hand, the average outage probability is reduced by about 8.1% for the inventive algorithm compared to the conventional algorithm. This is because the algorithm herein greatly reduces the probability of interruption by allocating higher power to the user in order to overcome the adverse effects of hardware damage, but the total system power consumption increases. In addition, in the algorithm, when the hardware damage parameter is increased, the system considers larger hardware damage and has stronger hardware damage resistance. When the transceiver has more serious hardware damage, the system can still ensure the communication quality of the user without communication interruption.
Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.

Claims (6)

1. A MIMO heterogeneous wireless network beam forming method considering hardware damage is characterized by specifically comprising the following steps:
s1: using an imperfect hardware transmitter and a receiver in a downlink of a two-layer MIMO heterogeneous wireless network, analyzing hardware damage sources in a macro cellular network and a femtocell network, and establishing a downlink signal transmission model of a macro cellular user and a femtocell user with hardware damage;
s2: respectively modeling hardware damage of a macro cell base station transmitter, a macro cell user receiver, a femtocell base station transmitter and a femtocell user receiver;
s3: considering hardware damage at a base station transmitter and a user receiver, the maximum transmitting power constraint of each base station and the minimum signal-to-interference-and-noise ratio constraint of each user, and establishing a beam forming design problem of minimizing the total energy consumption of the system;
s4: based on an equivalent transformation method and a semi-positive definite relaxation method, the problem established in the step S3 is converted into a convex optimization problem to be solved, and the optimal beam forming vector from the macro cell base station to the mth macro cell user is solved
Figure FDA0003770020670000011
And beamforming vectors for the nth femtocell base station to the kth femtocell user
Figure FDA0003770020670000012
2. The method for beamforming a MIMO heterogeneous wireless network according to claim 1, wherein the step S1 of analyzing the sources of hardware impairments in the macro cellular network and the femto cellular network comprises: hardware damage at a base station transmitter and a user receiver is modeled as additive hardware damage noise and amplified thermal noise;
establishing a downlink signal transmission model of a macro-cell user with hardware impairments, i.e. for the mth macro-cellSignals received by the user
Figure FDA0003770020670000013
Expressed as:
Figure FDA0003770020670000014
wherein the content of the first and second substances,
Figure FDA0003770020670000015
and
Figure FDA0003770020670000016
respectively representing a channel vector of the macrocell base station to the m-th macrocell user and a channel vector of the n-th femtocell base station to the m-th macrocell user;
Figure FDA0003770020670000017
and s m Respectively representing beamforming vectors and information of the macrocell base station to the mth macrocell user;
Figure FDA0003770020670000018
and s n,k Respectively representing beamforming vectors and information of an nth femtocell base station to a kth femtocell user; wherein the content of the first and second substances,
Figure FDA0003770020670000019
N M indicating the total number of antennas provided in the macrocell base station, N F Representing the total number of antennas equipped by the femtocell base station,
Figure FDA00037700206700000110
respectively represent N M X 1 dimension, N F A complex column vector of x 1 dimension;
Figure FDA00037700206700000111
and
Figure FDA00037700206700000112
additive hardware impairment noise for the macrocell base station transmitter, the nth femtocell base station transmitter and the mth macrocell user receiver,
Figure FDA00037700206700000113
means zero variance of mean at the mth macrocell user receiver
Figure FDA00037700206700000114
Amplified thermal noise.
3. The method for beamforming a MIMO heterogeneous wireless network according to claim 2, wherein in step S1, a femtocell user downlink signal transmission model with hardware impairments is established, that is, in the nth femtocell network, a signal from the base station to the kth femtocell user receiver is represented as:
Figure FDA0003770020670000021
wherein the content of the first and second substances,
Figure FDA0003770020670000022
and
Figure FDA0003770020670000023
respectively representing a channel vector of the nth femtocell base station to the kth femtocell user in the network and a channel vector of the macrocell base station to the kth femtocell user in the nth femtocell;
Figure FDA0003770020670000024
representing additive hardware impairment noise at a kth femtocell user receiver in an nth femtocell;
Figure FDA0003770020670000025
means that the mean value at the k-th femtocell user receiver in the n-th femtocell is zero variance
Figure FDA0003770020670000026
Amplified thermal noise.
4. The MIMO heterogeneous wireless network beamforming method of claim 3, wherein in step S2, additive hardware impairment noise at the macro cell base station transmitter, the femto cell base station transmitter, the macro cell user receiver and the femto cell user receiver is modeled as:
Figure FDA0003770020670000027
where ψ represents the covariance matrix of additive hardware impairment noise at the macrocell base station transmitter, Φ n A covariance matrix representing additive hardware impairment noise at the nth femtocell base station transmitter,
Figure FDA0003770020670000028
represents the variance of additive hardware impairment noise at the mth macrocell user receiver,
Figure FDA0003770020670000029
representing the variance of additive hardware impairment noise at the kth femtocell user receiver in the nth femtocell.
5. The beamforming method for the MIMO heterogeneous wireless network according to claim 4, wherein in step S3, the beamforming design problem for minimizing the total energy consumption of the system is expressed as:
Figure FDA00037700206700000210
Figure FDA00037700206700000211
Figure FDA00037700206700000212
Figure FDA00037700206700000213
Figure FDA00037700206700000214
wherein, C 1 And C 2 Representing maximum transmit power constraints, P, for the macrocell base station and the nth femtocell base station, respectively max And
Figure FDA00037700206700000215
representing maximum transmit power thresholds for the macrocell base station and the nth femtocell base station, respectively; c 3 Represents a minimum signal-to-interference-and-noise ratio constraint for each femtocell user,
Figure FDA00037700206700000216
representing a minimum signal-to-interference-and-noise ratio threshold for a kth femtocell user in the nth femtocell; c 4 Representing the minimum signal-to-interference-and-noise ratio constraint for the mth macrocell user,
Figure FDA00037700206700000217
a minimum signal-to-interference-and-noise ratio threshold representing an mth macrocell user; p C Represents the circuit power consumption of the macro cell and all femtocells, and ζ ≧ 1 represents the power amplification factor.
6. The method for beamforming a MIMO heterogeneous wireless network according to claim 5, wherein in step S4, P1 is a non-convex optimization problem, and the P1 is transformed into a convex optimization problem by using an equivalent transformation method and a semi-definite relaxation method to solve, and the specific transformation step includes:
s41: definition of
Figure FDA00037700206700000218
S42: introducing an auxiliary matrix S t And S l Covariance matrices psi and phi to process hardware impairment vectors n In which S is t And S l Respectively representing the t-th diagonal element and the l-th diagonal element as 1, and the rest elements as 0;
s43: processing the constraint with the coupling variable by using an equivalent transformation method, and converting the non-convex optimization problem P1 into a convex optimization problem to solve; solving the optimal solution of the convex optimization problem based on the interior point method
Figure FDA0003770020670000031
And
Figure FDA0003770020670000032
obtaining optimal beam forming vector by using eigenvalue decomposition method
Figure FDA0003770020670000033
And
Figure FDA0003770020670000034
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