CN111756424B - Millimeter wave cloud wireless access network beam design method based on secure transmission - Google Patents

Millimeter wave cloud wireless access network beam design method based on secure transmission Download PDF

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CN111756424B
CN111756424B CN202010149997.2A CN202010149997A CN111756424B CN 111756424 B CN111756424 B CN 111756424B CN 202010149997 A CN202010149997 A CN 202010149997A CN 111756424 B CN111756424 B CN 111756424B
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CN111756424A (en
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郝万明
赵少柯
孙钢灿
赵飞
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Zhengzhou University Industrial Research Institute Co ltd
Zhengzhou University
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Zhengzhou University
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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
    • H04B7/06—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
    • H04B7/022—Site diversity; Macro-diversity
    • H04B7/024—Co-operative use of antennas of several sites, e.g. in co-ordinated multipoint or co-operative multiple-input multiple-output [MIMO] systems
    • 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
    • H04B7/0426—Power distribution
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/06—Selective distribution of broadcast services, e.g. multimedia broadcast multicast service [MBMS]; Services to user groups; One-way selective calling services
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/06—TPC algorithms
    • H04W52/14—Separate analysis of uplink or downlink
    • H04W52/143—Downlink power control
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/26—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service]
    • H04W52/267—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service] taking into account the information rate
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/30—TPC using constraints in the total amount of available transmission power
    • H04W52/32—TPC of broadcast or control channels
    • H04W52/327—Power control of multicast channels
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/30—TPC using constraints in the total amount of available transmission power
    • H04W52/34—TPC management, i.e. sharing limited amount of power among users or channels or data types, e.g. cell loading
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/38—TPC being performed in particular situations
    • H04W52/42—TPC being performed in particular situations in systems with time, space, frequency or polarisation diversity
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/04—Wireless resource allocation
    • H04W72/044—Wireless resource allocation based on the type of the allocated resource
    • H04W72/0473—Wireless resource allocation based on the type of the allocated resource the resource being transmission power
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/50—Allocation or scheduling criteria for wireless resources
    • H04W72/54—Allocation or scheduling criteria for wireless resources based on quality criteria
    • H04W72/542—Allocation or scheduling criteria for wireless resources based on quality criteria using measured or perceived quality

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Abstract

The invention relates to the field of network transmission, in particular to a millimeter wave cloud wireless access network beam design method based on safe transmission, which comprises the following steps: establishing a system model, and the second step: analog beam design, and the third step: secret rate transmission problems; through the design of each step, the secret rate of maximizing information transmission is achieved.

Description

Millimeter wave cloud wireless access network beam design method based on secure transmission
Technical Field
The invention relates to the field of network transmission, in particular to a millimeter wave cloud wireless access network beam design method based on safe transmission.
Background
With the rapid rise of mobile internet services, various mobile applications have higher and higher requirements on data rates, and a Cloud radio access network (C-RAN) technology is proposed as an effective solution. In the C-RAN, a Central processing unit (CP) performs resource optimization configuration by using Channel State Information (CSI), so as to improve Spectral Efficiency (SE) of the system. In addition, with the deployment of ultra-dense base stations, interference among the base stations can be effectively solved by using a Coordinated multiple-point (CoMP) technology, that is, adjacent base stations are used to form a base station cluster and are combined to provide services for users. In the C-RAN, a CP transmits data to a base station through a forward link, while a plurality of base stations cooperate to collectively provide a service to a user. At this time, two basic issues need to be considered: forward/access link selection and data sharing schemes. In consideration of the characteristics of different frequency carriers and forward/access links, low-frequency microwaves and high-frequency millimeter waves are respectively adopted as carriers of the forward link and the access link. In addition, for data sharing between the CP and the base station cluster, when multiple base stations cooperatively serve one user, the CP must send information required by the user to all the cooperative base stations, and such point-to-multipoint forward transmission can be implemented by multicast technology. Therefore, the invention combines the forward microwave multicast transmission technology to establish a millimeter wave C-RAN system based on the cooperation of the base station. A Physical Layer Security (PLS) is proposed to enhance security of wireless communication because an Eavesdropper (Eve) may eavesdrop user information due to a broadcasting characteristic of wireless communication, and its core idea is to prevent an illegal user from eavesdropping information by designing a beam using randomness of a wireless channel. Although various designs for PLS exist today, there are still some other challenges, such as hybrid analog/digital Beamforming (BF) design, artificial noise, multicast BF design, etc. In order to solve the challenges, the invention researches the design problem of safe millimeter wave C-RAN safe BF based on microwave multicast forwarding, and aims to invent a combined beam design scheme to maximize the confidentiality rate of information transmission.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and designs a millimeter wave cloud wireless access network beam design method based on safe transmission.
The aim of the invention is achieved by the following measures: a millimeter wave cloud wireless access network beam design method based on secure transmission comprises the following steps:
the first step is as follows: system model building
In the microwave multicast forward link, the forward link channel vector from the CP to the l base station is recorded as
Figure GDA0003003818690000021
The multicast BF vector sent from CP to base station cluster is recorded as
Figure GDA0003003818690000022
x0Is E { | x0|2The multicast signal of 1, the signal received by the l base station is shown as (1), nlIs satisfied with CN (0, N)0) Independently equally distributed Additive White Gaussian Noise (AWGN),
Figure GDA0003003818690000023
let the downlink microwave bandwidth be WmcThen the forward rate available to the ith base station is:
Figure GDA0003003818690000024
since the forward multicast rate is limited by the base station under the worst channel conditions, the CP provides the forward rate as:
Figure GDA0003003818690000025
wherein L ═ { 1.., L } represents a set of base stations;
in the millimeter wave access link, the received signal of the kth user is:
Figure GDA0003003818690000026
wherein
Figure GDA0003003818690000031
Representing the channel vectors from the L base stations to the k user,
Figure GDA0003003818690000032
representing the channel vectors from the l base station to the k user,
Figure GDA0003003818690000033
representing artificial noise vectors sent by a base station cluster, assuming that q belongs to CN (0, A), A represents an artificial noise covariance matrix to be optimized,
Figure GDA0003003818690000034
and xiRespectively representing the digital BF vector and the signal required by the k-th user, nkIs an AWGN that satisfies the independent same distribution,
Figure GDA0003003818690000035
is a simulated BF, in a specific form as shown in (5), wherein
Figure GDA0003003818690000036
Represents an analog BF vector designed by the l-th base station, and flAll elements of (a) have the same amplitude but different phases, i.e.
Figure GDA0003003818690000037
M ═ { 1.. M } is the set of antennas for each base station, fl(m) represents flThe mth element of (1);
Figure GDA0003003818690000038
the achievable rate for the kth user is:
Figure GDA0003003818690000039
Wmmrepresents a millimeter wave bandwidth;
in this context, a millimeter wave channel model with C scattering clusters is employed, wherein each scattering cluster comprises a propagation path, and thus, a millimeter wave channel
Figure GDA00030038186900000310
Can be expressed as:
Figure GDA00030038186900000311
wherein
Figure GDA00030038186900000312
The complex gain of the c-th path is shown,
Figure GDA00030038186900000313
is the azimuth of arrival of the c-th path,
Figure GDA00030038186900000314
the antenna array steering vector is represented, the concrete form is shown as (11), d and lambda respectively represent the distance between antennas and the signal wavelength; further, the channel model expression of Eve is similar to (10).
Figure GDA0003003818690000041
The second step is that: analog beam design
In practice only quantized phase can be achieved, so we assume that a B-bit quantization phase shifter is used and that the non-zero elements of F should belong to
Figure GDA0003003818690000042
According to (5), analog BF must be designed for L base stations, respectively, and for the k-th user,
Figure GDA0003003818690000043
the array can thus be re-maximized by appropriate selection of the best quantization phase from (12)
Figure GDA0003003818690000044
For example, the analog BF vector f of the l-th base stationlIs shown as (13), where & (·) represents the angle:
Figure GDA0003003818690000045
thus, f can be obtainedl(m) As shown in (14):
Figure GDA0003003818690000046
in order to ensure fairness of users, the BF designed for L base stations should not only maximize array gain of a single user, but also allocate at least one base station to each user to maximize array gain thereof;
the third step: secret rate transmission problem
Firstly, a Secret Rate Maximization (SRM) problem is formulated under the constraint of total base station transmitting power and CP transmitting power, then a convex approximation technology and Semi-definite programming (SDP) relaxation are adopted to convert the problem, an iterative algorithm is adopted to carry out joint optimization, and an original solution and a dual optimal solution of the SDP relaxation problem are utilized to construct a solution of the original problem.
Preferably, in the first step of system modeling, Eve tries to eavesdrop the information of the kth user, and the signal received by the z-th Eve is:
Figure GDA0003003818690000051
wherein
Figure GDA0003003818690000052
Showing the channel vectors from the lth base station to the z-th Eve,
Figure GDA0003003818690000053
representing the channel vectors from the l base station to the z-th Eve;
the interception capacity of the kth user intercepted by the z-th Eve is as follows:
Figure GDA0003003818690000054
finally, the privacy rate that the kth user can achieve is:
Figure GDA0003003818690000055
wherein
Figure GDA00030038186900000511
Representing an Eve set.
Preferably, in the third step of secret rate transmission, the iterative SRM algorithm involved comprises the following specific steps:
the method comprises the following steps: problem planning under total base station transmit power constraint
After designing the analog BF, the equivalent channel of the kth user can be obtained
Figure GDA0003003818690000056
The z-th Eve equivalent channel is
Figure GDA0003003818690000057
Assuming that the multicast forward transmission time frame includes K time slots, and each time slot is used for transmitting a message of a single user from the CP to the L cooperative base stations, it is assumed that the frame length and the K-th time slot length are 1 and t, respectivelyk，
Figure GDA0003003818690000058
Then, according to certain constraints, the achievable capacity of the kth user must be smaller than the capacity provided by the CP for the kth userThe transfer capacity, and therefore (15),
Figure GDA00030038186900000510
representing a set of users:
Figure GDA0003003818690000059
from (15), a constraint (16) can be derived:
Figure GDA0003003818690000061
finally, the design problem of combining BF and artificial noise variance of the maximized secret keeping rate is provided;
Figure GDA0003003818690000062
Figure GDA0003003818690000063
Figure GDA0003003818690000064
Figure GDA0003003818690000065
wherein (17b) represents the fronthaul capacity constraint, (17c) is the total transmit power constraint of the L cooperative base stations, and (17d) represents the CP transmit power constraint, but the direct solution (17) is difficult due to the non-convexity of the objective function (17a) and the constraint (17 b);
step two: transformation and solution of problem (17)
First, the objective function (17a) is converted into the form (18):
Figure GDA0003003818690000066
wherein, { beta ]kAnd
Figure GDA0003003818690000067
is an introduced auxiliary variable, the form of which is shown in (19):
Figure GDA0003003818690000068
Figure GDA0003003818690000069
then define BF matrix
Figure GDA00030038186900000610
And
Figure GDA00030038186900000611
restating the problem (17) as a problem (20), wherein
Figure GDA00030038186900000612
||Fvk||2＝Tr(FHFVk)＝Tr(Vk)；
Figure GDA00030038186900000613
Figure GDA0003003818690000071
Figure GDA0003003818690000072
Figure GDA0003003818690000073
Figure GDA0003003818690000074
Figure GDA0003003818690000075
Figure GDA0003003818690000076
Figure GDA0003003818690000077
However, due to the non-convexity of (20a), (20b), (20c), (20f) and (20h), the problem (20) is difficult to solve, the transformation (20b) is first transformed into a convex constraint, by introducing the auxiliary variable { εkThe following transformations can be obtained:
Figure GDA0003003818690000078
Figure GDA0003003818690000079
βkεkas shown in (22) is the upper bound of,
Figure GDA00030038186900000710
and
Figure GDA00030038186900000711
is represented by betakAnd εkThe nth iteration:
Figure GDA00030038186900000712
it is thus possible to convert (21a) into a convex constraint (23):
Figure GDA00030038186900000713
next, an auxiliary variable is introduced
Figure GDA00030038186900000714
And
Figure GDA00030038186900000715
and decomposing (20c) into constraints (24):
Figure GDA0003003818690000081
Figure GDA0003003818690000082
Figure GDA0003003818690000083
it can be seen that (24a) is a convex constraint, for (24b), the quadratic term is developed by a first order Taylor series
Figure GDA0003003818690000084
May be (25):
Figure GDA0003003818690000085
thus (24b) can be converted into a convex constraint (26),
Figure GDA0003003818690000086
to represent
Figure GDA0003003818690000087
The nth iteration:
Figure GDA0003003818690000088
the nonlinear constraint (24c) may be converted to a convex Linear Matrix Inequality (LMI) constraint (27):
Figure GDA0003003818690000089
finally, by introducing an auxiliary variable { τ }kThe } and ω can transform the problem (20) into an optimization problem (28), where
Figure GDA00030038186900000810
η＝Wmc/Wmm：
Figure GDA00030038186900000811
Figure GDA00030038186900000812
Figure GDA00030038186900000813
Figure GDA00030038186900000814
(20d)-(20g)，(21b)，(23)，(24a)，(26)，(27) (28e)
Due to log (1+ beta)k) And
Figure GDA00030038186900000815
since the objective function (28a) is a convex function, the objective function is composed of a Difference of convexity problem (DC), and the DC process is usually solved by using a Constrained concave-convex process (CCCP), so that the actual DC process is realizedIndeed, the main idea of CCCP is to solve the convex problem by converting (28a) to a convex function and then iteratively until the result converges; based on this, consider to
Figure GDA0003003818690000091
Using a first order Taylor approximation, as shown in (29), wherein
Figure GDA0003003818690000092
To represent
Figure GDA0003003818690000093
The nth iteration:
Figure GDA0003003818690000094
the objective function may then be converted to a convex function (30):
Figure GDA0003003818690000095
constraint (28d) is also a DC program, which can similarly be converted to convex constraint (31):
Figure GDA0003003818690000096
by introducing an auxiliary variable thetakAnd { lambda } andk}, (28b) may be decomposed into constraints (32):
Figure GDA0003003818690000097
Figure GDA0003003818690000098
Figure GDA0003003818690000099
according to (25), (26), (27), the non-convex constraints (32b) and (32c) can be transformed into convex constraints (33) and (34), wherein
Figure GDA00030038186900000910
Is λkThe nth iteration:
Figure GDA00030038186900000911
Figure GDA00030038186900000912
finally, the SRM problem can be translated into the following problem:
Figure GDA0003003818690000101
s.t.(20d)-(20g)，(21b)，(23)，(24a)，(26)，(27)，(28c)，(32a)，(33)，(34) (35b)
in (35), only the rank constraint (20f) is non-convex, by SDP relaxation (i.e. removing the rank-one constraint), (35) will become a convex optimization problem, which can be solved by standard convex optimization techniques, and finally, to obtain a solution (17) to the optimization problem, the solution (35) must be iteratively solved, specifically, a feasible solution is initialized first
Figure GDA0003003818690000102
The optimal solution (35) can be obtained by a classical convex optimization algorithm and then updated according to the solution obtained in the previous iteration
Figure GDA0003003818690000103
Figure GDA0003003818690000104
Until the result converges or the iteration index reaches its maximum value; in addition, due to(35) without rank constraint is a convex optimization problem, so iteratively updating all variables will increase or at least maintain the value of the objective function in (35); given a limited transmit power, the value of the objective function should be a monotonically non-decreasing sequence with an upper bound that converges to an at least locally optimal fixed solution;
step three: problem calculation and solution under constraint of transmitting power of each base station
In the foregoing, the total transmit power constraint of L base stations is considered, and although this allows more flexible allocation of power to base stations under the total transmit power constraint, each base station has a high power transmit power limit for practical purposes. Therefore, considering the transmit power constraint of each base station more realistic, the definition of B is as shown in (36):
Figure GDA0003003818690000105
the power constraint (20d) for each base station can be written in the form of (37), where
Figure GDA0003003818690000106
Represents the ith base station maximum transmission power:
Figure GDA0003003818690000107
then, under the transmit power constraint of each base station, the SRM problem is formulated (38):
Figure GDA0003003818690000111
s.t.(17b)-(17d)，(37) (38b)
finally, the convex optimization problem described above can be solved iteratively using the algorithm in step two to obtain a solution to the original problem (38).
The invention has the beneficial effects that: firstly, the method comprises the following steps: a C-RAN based on base station cooperative transmission in the microwave multicast forward direction is provided, wherein adjacent base stations form a cooperative cluster and serve users together by means of millimeter wave carriers, and the base stations receive forward data from a CP through microwave multicast. Secondly, the method comprises the following steps: a safe millimeter wave cloud wireless access network downlink safe BF design method based on microwave multicast forwarding is researched, and an advanced analog BF design scheme is provided. Thirdly, the method comprises the following steps: the multicast BF, the digital BF and the artificial noise covariance are jointly optimized, and the information transmission secret rate is maximized under the constraint of the total base station and the transmitting power of each base station. Fourthly: the ideal CSI of the Eve connection is replaced by the imperfect CSI, and the SRM problem under the worst condition is considered, so that the method is more practical and meaningful.
Drawings
FIG. 1 is a diagram of a model of a system contemplated by the present invention;
FIG. 2 is a flow chart of an analog beam design algorithm for L cooperative base stations of the present invention;
FIG. 3 is a flow chart of an iterative algorithm proposed using the present invention;
FIG. 4 is a graph of the effectiveness of the privacy ratio versus the number of iterations obtained using the present invention;
FIG. 5 is a graph of the effect of secret keeping rate versus total allowed transmit power for L base stations obtained using the present invention;
FIG. 6 is a graph of the effect of secret ratio versus allowable transmit power of a CP obtained using the present invention;
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1: as shown in fig. 1-6, the design of the present invention is under a C-RAN downlink system depending on a central CP, the system diagram is as shown in fig. 1, the system is composed of L cooperative base stations to form a base station cluster, wherein all the base stations provide services for K single-antenna users together through cooperative millimeter wave BF, and we assume that Eve with Z single antennas may eavesdrop the user's message. The CP equipped with N antennas first transmits the user-required information to base stations, each equipped with a single RA and M TAs, over a microwave multicast forward link. Assume that one RF serves M TAs through a set of phase shifters. The method comprises the following specific steps:
the first step is as follows: system model building
In the microwave multicast forward link, the forward link channel vector from the CP to the l base station is recorded as
Figure GDA0003003818690000121
The multicast BF vector sent from CP to base station cluster is recorded as
Figure GDA0003003818690000122
x0Is E { | x0|2The multicast signal of 1, the signal received by the l base station is shown as (1), nlIs satisfied with CN (0, N)0) Independently equally distributed Additive White Gaussian Noise (AWGN),
Figure GDA0003003818690000123
let the downlink microwave bandwidth be WmcThen the forward rate available to the ith base station is:
Figure GDA0003003818690000124
since the forward multicast rate is limited by the base station under the worst channel conditions, the CP provides the forward rate as:
Figure GDA0003003818690000125
wherein L ═ { 1.., L } represents a set of base stations;
in the millimeter wave access link, the received signal of the kth user is:
Figure GDA0003003818690000126
wherein
Figure GDA0003003818690000127
Representing the channel vectors from the L base stations to the k user,
Figure GDA0003003818690000128
representing the channel vectors from the l base station to the k user,
Figure GDA0003003818690000131
representing artificial noise vectors sent by a base station cluster, assuming that q is equal to CN (0, Λ), and Λ represents an artificial noise covariance matrix to be optimized,
Figure GDA0003003818690000132
and xiRespectively representing the digital BF vector and the signal required by the k-th user, nkIs an AWGN that satisfies the independent same distribution,
Figure GDA0003003818690000133
is a simulated BF, in a specific form as shown in (5), wherein
Figure GDA0003003818690000134
Represents an analog BF vector designed by the l-th base station, and flAll elements of (a) have the same amplitude but different phases, i.e.
Figure GDA0003003818690000135
M ═ { 1.. M } is the set of antennas for each base station, fl(m) represents flThe mth element of (1);
Figure GDA0003003818690000136
the achievable rate for the kth user is:
Figure GDA0003003818690000137
Wmmrepresents a millimeter wave bandwidth;
on the other hand, Eve tries to eavesdrop on the information of the kth user, and the signal received by the z-th Eve is:
Figure GDA0003003818690000138
wherein
Figure GDA0003003818690000139
Showing the channel vectors from the lth base station to the z-th Eve,
Figure GDA00030038186900001310
representing the channel vectors from the l base station to the z-th Eve;
the interception capacity of the kth user intercepted by the z-th Eve is as follows:
Figure GDA0003003818690000141
finally, the privacy rate that the kth user can achieve is:
Figure GDA0003003818690000142
wherein
Figure GDA00030038186900001412
Representing an Eve set.
In this context, a millimeter wave channel model with C scattering clusters is employed, wherein each scattering cluster comprises a propagation path, and thus, a millimeter wave channel
Figure GDA0003003818690000143
Can be expressed as:
Figure GDA0003003818690000144
wherein
Figure GDA0003003818690000145
The complex gain of the c-th path is shown,
Figure GDA0003003818690000146
is the azimuth of arrival of the c-th path,
Figure GDA0003003818690000147
the antenna array steering vector is represented, the concrete form is shown as (11), d and lambda respectively represent the distance between antennas and the signal wavelength; further, the channel model expression of Eve is similar to (10).
Figure GDA0003003818690000148
The second step is that: analog beam design
In practice only quantized phase can be achieved, so we assume that a B-bit quantization phase shifter is used and that the non-zero elements of F should belong to
Figure GDA0003003818690000149
According to (5), analog BF must be designed for L base stations, respectively, and for the k-th user,
Figure GDA00030038186900001410
therefore we can again maximize the array by appropriately selecting the best quantization phase from (12)
Figure GDA00030038186900001411
For example, the simulated BF of the l-th base stationQuantity flIs shown as (13), where & (·) represents the angle:
Figure GDA0003003818690000151
thus, f can be obtainedl(m) As shown in (14):
Figure GDA0003003818690000152
the specific design scheme of the analog BF is shown in fig. 2, in order to ensure fairness of users, the BF designed for L base stations should not only maximize array gain of a single user, but also allocate at least one base station to each user to maximize array gain thereof;
the third step: secret rate transmission problem
Firstly, a Secret Rate Maximization (SRM) problem is formulated under the constraint of total base station transmitting power and CP transmitting power, then a convex approximation technology and Semi-definite programming (SDP) relaxation are adopted to convert the problem, an iterative algorithm is adopted to carry out joint optimization, and an original solution and a dual optimal solution of the SDP relaxation problem are utilized to construct a solution of the original problem. Finally, considering the transmission power constraint of each base station, an effective iterative SRM algorithm is designed, and the specific steps are as follows:
the method comprises the following steps: problem planning under total base station transmit power constraint
After designing the analog BF, the equivalent channel of the kth user can be obtained
Figure GDA0003003818690000153
The z-th Eve equivalent channel is
Figure GDA0003003818690000154
Assuming that the multicast forward transmission time frame includes K time slots, and each time slot is used for transmitting a message of a single user from the CP to L cooperative base stations, assuming a frame length and a K-th timeGap lengths of 1 and t, respectivelyk，
Figure GDA0003003818690000155
Then, according to certain constraints, the achievable capacity of the kth user must be smaller than the forwarding capacity provided by the CP for the kth user, and therefore (15) is available,
Figure GDA0003003818690000156
representing a set of users:
Figure GDA0003003818690000157
from (15), a constraint (16) can be derived:
Figure GDA0003003818690000161
finally, the design problem of combining BF and artificial noise variance of the maximized secret keeping rate is provided;
Figure GDA0003003818690000162
Figure GDA0003003818690000163
Figure GDA0003003818690000164
Figure GDA0003003818690000165
wherein (17b) represents the fronthaul capacity constraint, (17c) is the total transmit power constraint of the L cooperative base stations, and (17d) represents the CP transmit power constraint, but the direct solution (17) is difficult due to the non-convexity of the objective function (17a) and the constraint (17 b);
step two: transformation and solution of problem (17)
First, the objective function (17a) is converted into the form (18):
Figure GDA0003003818690000166
wherein, { beta ]kAnd
Figure GDA0003003818690000167
is an introduced auxiliary variable, the form of which is shown in (19):
Figure GDA0003003818690000168
Figure GDA0003003818690000169
then define BF matrix
Figure GDA00030038186900001610
And
Figure GDA00030038186900001611
restating the problem (17) as a problem (20), wherein
Figure GDA00030038186900001612
||Fvk||2＝Tr(FHFVk)＝Tr(Vk)；
Figure GDA00030038186900001613
Figure GDA0003003818690000171
Figure GDA0003003818690000172
Figure GDA0003003818690000173
Figure GDA0003003818690000174
Figure GDA0003003818690000175
Figure GDA0003003818690000176
Figure GDA0003003818690000177
However, the problem (20) is difficult to solve due to the non-convexity of (20a), (20b), (20c), (20f) and (20h), and to solve this problem, the transform (20b) is first transformed into a convex constraint by introducing an auxiliary variable { ε }kThe following transformations can be obtained:
Figure GDA0003003818690000178
Figure GDA0003003818690000179
βkεkas shown in (22) is the upper bound of,
Figure GDA00030038186900001710
and
Figure GDA00030038186900001711
is represented by betakAnd εkThe nth iteration:
Figure GDA00030038186900001712
it is thus possible to convert (21a) into a convex constraint (23):
Figure GDA00030038186900001713
next, an auxiliary variable is introduced
Figure GDA00030038186900001714
And
Figure GDA00030038186900001715
and decomposing (20c) into constraints (24):
Figure GDA0003003818690000181
Figure GDA0003003818690000182
Figure GDA0003003818690000183
it can be seen that (24a) is a convex constraint, for (24b), the quadratic term is developed by a first order Taylor series
Figure GDA0003003818690000184
May be (25):
Figure GDA0003003818690000185
thus (24b) can be converted into a convex constraint (26),
Figure GDA0003003818690000186
to represent
Figure GDA0003003818690000187
The nth iteration:
Figure GDA0003003818690000188
the nonlinear constraint (24c) may be converted to a convex Linear Matrix Inequality (LMI) constraint (27):
Figure GDA0003003818690000189
finally, by introducing an auxiliary variable { τ }kThe } and ω can transform the problem (20) into an optimization problem (28), where
Figure GDA00030038186900001810
η＝Wmc/Wmm：
Figure GDA00030038186900001811
Figure GDA00030038186900001812
Figure GDA00030038186900001813
Figure GDA00030038186900001814
(20d)-(20g)，(21b)，(23)，(24a)，(26)，(27) (28e)
Due to log (1+ beta)k) And
Figure GDA00030038186900001815
is a convex function, so the objective function (28a) consists of a Difference of convexity problem (DC), the DC process is usually solved using a Constrained concave-convex process (CCCP), in fact, the main idea of CCCP is to solve the convex problem by converting (28a) into a convex function and then iteratively until the result converges; based on this, consider to
Figure GDA0003003818690000191
Using a first order Taylor approximation, as shown in (29), wherein
Figure GDA0003003818690000192
To represent
Figure GDA0003003818690000193
The nth iteration:
Figure GDA0003003818690000194
the objective function may then be converted to a convex function (30):
Figure GDA0003003818690000195
constraint (28d) is also a DC program, which can similarly be converted to convex constraint (31):
Figure GDA0003003818690000196
by introducing an auxiliary variable thetakAnd { lambda } andk}, (28b) may be decomposed into constraints (32):
Figure GDA0003003818690000197
Figure GDA0003003818690000198
Figure GDA0003003818690000199
according to (25), (26), (27), the non-convex constraints (32b) and (32c) can be transformed into convex constraints (33) and (34), wherein
Figure GDA00030038186900001910
Is λkThe nth iteration:
Figure GDA00030038186900001911
Figure GDA00030038186900001912
finally, the SRM problem can be translated into the following problem:
Figure GDA0003003818690000201
s.t.(20d)-(20g)，(21b)，(23)，(24a)，(26)，(27)，(28c)，(32a)，(33)，(34) (35b)
in (35), only the rank constraint (20f) is non-convex, by SDP relaxation (i.e. removing the rank-one constraint), (35) will become a convex optimization problem, which can be solved by standard convex optimization techniques, and finally, to obtain a solution (17) to the optimization problem, the solution (35) must be iteratively solved, specifically, a feasible solution is initialized first
Figure GDA0003003818690000202
The optimal solution (35) can be obtained by a classical convex optimization algorithm and then updated according to the solution obtained in the previous iteration
Figure GDA0003003818690000203
Figure GDA0003003818690000204
Until the result converges or the iteration index reaches its maximum value; in addition, since (35) without rank constraint is a convex optimization problem, iteratively updating all variables will increase or at least maintain the value of the objective function in (35); given a finite transmit power, the value of the objective function should be a monotonically non-decreasing sequence with an upper bound that converges to an at least locally optimal fixed solution, and the specific iteration flow is shown in fig. 3;
step three: problem calculation and solution under constraint of transmitting power of each base station
In the foregoing, the total transmit power constraint of L base stations is considered, and although this allows more flexible allocation of power to base stations under the total transmit power constraint, each base station has a high power transmit power limit for practical purposes. Therefore, considering the transmit power constraint of each base station more realistic, the definition of B is as shown in (36):
Figure GDA0003003818690000205
the power constraint (20d) for each base station can be written in the form of (37), where
Figure GDA0003003818690000206
Represents the ith base station maximum transmission power:
Figure GDA0003003818690000207
then, under the transmit power constraint of each base station, the SRM problem is formulated (38):
Figure GDA0003003818690000211
s.t.(17b)-(17d)，(37) (38b)
finally, the convex optimization problem described above can be solved iteratively using the algorithm in step two to obtain a solution to the original problem (38).
As shown in fig. 4, is provided
Figure GDA0003003818690000212
And
Figure GDA0003003818690000213
the privacy rate under the total base station transmit power constraint is slightly lower than the privacy rate under the individual base station transmit power constraint. This is because the tolerable transmit power of each base station is fixed and limited under each base station transmit power constraint. However, the present invention can flexibly allocate power among base stations according to CSI, thereby improving the privacy ratio under the constraint of the total base station transmission power.
As shown in fig. 5, is provided
Figure GDA0003003818690000214
The privacy rate increases with increasing total base station transmit power, but the rate provided by the fronthaul link is limited due to the limited transmit power of the CP. Thus, even though the access link could potentially provide higher rates, the privacy rate would be limited by the fronthaul link. Furthermore, when the transmission power is low, the secret ratio under the constraint of the total base station transmission power is higher than that under the constraint of the transmission power of each base station, and when the total base station allowed transmission power is high, they are almost the same.
As shown in fig. 6, is provided
Figure GDA0003003818690000215
For all schemes, the secret ratio increases with increasing CP transmit power, and moreover, the secret ratio is the same under the constraints of total and individual base station transmit power. This is because when
Figure GDA0003003818690000216
And
Figure GDA0003003818690000217
the rate provided by the fronthaul link is still lower than the rate of the access link.
Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that modifications may be made to the embodiments or portions thereof without departing from the spirit and scope of the invention.

Claims (2)

1. A millimeter wave cloud wireless access network beam design method based on secure transmission is characterized in that: the method comprises the following steps:
the first step is as follows: system model building
In the microwave multicast forward link, the forward link channel vector from the central processor CP to the l base station is recorded as
Figure FDA0003033916330000011
N represents the number of CP antennas, the multicast beam forming sent from CP to base station cluster, BF vector is recorded
Figure FDA0003033916330000012
x0Is E { | x0|2The multicast signal of 1, the signal received by the l base station is shown as (1), nlIs satisfied with CN (0, N)0) Independently identically distributed additive white Gaussian noise, CN (0, N)0) Mean 0 and variance N0Gaussian distribution of (a):
Figure FDA0003033916330000013
let the downlink microwave bandwidth be WmcThen the first base stationThe forward rates that can be achieved are:
Figure FDA0003033916330000014
since the forward multicast rate is limited by the base station under the worst channel conditions, the CP provides the forward rate as:
Figure FDA0003033916330000015
wherein L ═ { 1.., L } represents a set of base stations;
in the millimeter wave access link, the received signal of the kth user is:
Figure FDA0003033916330000016
wherein
Figure FDA0003033916330000017
Representing the channel vectors from the lth base station to the kth user,
Figure FDA0003033916330000018
representing the channel vectors from the l base station to the k user,
Figure FDA0003033916330000019
representing AN artificial noise vector AN sent by a base station cluster, assuming that q is equal to CN (0, Λ), and Λ represents AN artificial noise covariance matrix to be optimized,
Figure FDA0003033916330000021
and xkRespectively representing the digital BF vector from the lth base station to the kth user and the signal required by the kth user,
Figure FDA0003033916330000022
and xiRespectively representing the digital BF vector sum signals from other base stations except the target base station L to the k-th user, nkIs an AWGN that satisfies the independent same distribution,
Figure FDA0003033916330000023
is a simulated BF, in a specific form as shown in (5), wherein
Figure FDA0003033916330000024
Represents an analog BF vector designed by the l-th base station, and flAll elements of (a) have the same amplitude but different phases, i.e.
Figure FDA0003033916330000025
Where M ∈ M, M ═ { 1.. M } is the set of antennas for each base station, fl(m) represents flThe mth element of (1);
Figure FDA0003033916330000026
the insecure rate for the kth user is:
Figure FDA0003033916330000027
Wmmrepresents a millimeter wave bandwidth;
a millimeter wave channel model is used having C scattering clusters, each of which includes a propagation path, so that a millimeter wave channel
Figure FDA0003033916330000028
Can be expressed as:
Figure FDA0003033916330000029
wherein
Figure FDA00030339163300000210
The complex gain of the c-th path is shown,
Figure FDA00030339163300000211
is the azimuth of arrival of the c-th path,
Figure FDA00030339163300000212
the antenna array steering vector is represented, the concrete form is shown as (11), d and lambda respectively represent the distance between antennas and the signal wavelength;
Figure FDA00030339163300000213
the second step is that: analog beam design
In practice only quantized phases can be achieved, so it is assumed that a B-bit quantization phase shifter is used and that the non-zero elements of F should belong to
Figure FDA0003033916330000031
Where φ represents a phase; according to (5), analog BF must be designed for L base stations, respectively, and for the k-th user,
Figure FDA0003033916330000032
the array can thus be re-maximized by appropriate selection of the best quantization phase from (12)
Figure FDA0003033916330000033
Analog BF vector f of the l base stationlIs shown as (13), where & (·) represents the angle:
Figure FDA0003033916330000034
thus, we can get fl(m) As shown in (14):
Figure FDA0003033916330000035
the third step: secret rate transmission problem
Firstly, formulating a privacy ratio maximization problem SRM under the constraint of total base station transmitting power and CP transmitting power, then adopting a convex approximation technology and semi-definite programming relaxation to convert the problem, adopting an iterative algorithm to carry out joint optimization, and constructing a solution of an original problem by utilizing an original and dual optimal solution of a semi-definite programming SDP relaxation problem;
in the third step of secret rate transmission, the involved iterative SRM algorithm comprises the following specific steps:
the method comprises the following steps: problem planning under total base station transmit power constraint
After designing the analog BF, the equivalent channel of the kth user can be obtained
Figure FDA0003033916330000036
The equivalent channel of the z-th eavesdropper Eve is
Figure FDA0003033916330000037
Figure FDA0003033916330000038
Representing the channel gain from the K-th user to Eve, assuming that the multicast forward transmission time frame includes K slots, and each slot is used for transmitting a message of a single user from the CP to the L cooperative base stations, assuming that the frame length and the K-th slot length are 1 and t, respectivelyk，
Figure FDA0003033916330000039
Then, according to certain constraints, the achievable capacity of the kth user must be smaller than the forwarding capacity provided by the CP for the kth user, and thus (15), R, is obtainedFHRepresenting the forward rate provided by the CP under worst-case channel conditions,
Figure FDA0003033916330000041
representing a set of users:
Figure FDA0003033916330000042
from (15), constraints (16) can be derived, wherein
Figure FDA0003033916330000043
Represents the forward rate available to the ith base station:
Figure FDA0003033916330000044
finally, the design problem of combining BF and artificial noise variance of the maximized secret keeping rate is provided;
Figure FDA0003033916330000045
Figure FDA0003033916330000046
Figure FDA0003033916330000047
Figure FDA0003033916330000048
wherein
Figure FDA0003033916330000049
Indicates that there is moreMaximum eavesdropping rate for user k at an eavesdropper, s.t. represents a constraint, (17b) represents a fronthaul capacity constraint, (17c) is a total transmit power constraint for the L cooperative base stations,
Figure FDA00030339163300000410
represents the base station maximum transmit power, (17d) represents the CP transmit power constraint,
Figure FDA00030339163300000411
represents the CP maximum transmit power;
step two: transformation and solution of problem (17)
First, the objective function (17a) is converted into the form (18):
Figure FDA00030339163300000412
wherein, { beta ]kAnd
Figure FDA00030339163300000413
is an introduced auxiliary variable, the form of which is shown in (19):
Figure FDA0003033916330000051
Figure FDA0003033916330000052
then define BF matrix
Figure FDA0003033916330000053
And
Figure FDA0003033916330000054
restating the problem (17) as a problem (20), the problem (17) comprising an objective function (17a) and constraint conditions (17b) (17c) (17d), passingThe simplification translates to a problem (20), the problem (20) including an objective function (20a) and constraint conditions (20b) - (20h), wherein
Figure FDA0003033916330000055
||Fvk||2＝Tr(FHFVk)＝Tr(Vk)；
Figure FDA0003033916330000056
Figure FDA0003033916330000057
Figure FDA0003033916330000058
Figure FDA0003033916330000059
Figure FDA00030339163300000510
Figure FDA00030339163300000511
Figure FDA00030339163300000512
Figure FDA00030339163300000513
However, since (20a)The non-convexity of (20b), (20c), (20f) and (20h), the problem (20) is difficult to solve, the transformation (20b) is first transformed into a convex constraint, by introducing an auxiliary variable { epsilon ∈kThe following transformations can be obtained:
Figure FDA0003033916330000061
Figure FDA0003033916330000062
βkεkas shown in (22) is the upper bound of,
Figure FDA0003033916330000063
and
Figure FDA0003033916330000064
is represented by betakAnd εkThe nth iteration:
Figure FDA0003033916330000065
it is thus possible to convert (21a) into a convex constraint (23):
Figure FDA0003033916330000066
next, an auxiliary variable is introduced
Figure FDA0003033916330000067
And
Figure FDA0003033916330000068
and decomposing (20c) into constraints (24):
Figure FDA0003033916330000069
Figure FDA00030339163300000610
Figure FDA00030339163300000611
it can be seen that (24a) is a convex constraint, for (24b), the quadratic term is developed by a first order Taylor series
Figure FDA00030339163300000612
Can be expressed as:
Figure FDA00030339163300000613
thus (24b) can be converted into a convex constraint (26) in which
Figure FDA00030339163300000614
To represent
Figure FDA00030339163300000615
Of the nth iteration z [ n ]]Represents the nth iteration of z:
Figure FDA00030339163300000616
the nonlinear constraint (24c) may be converted to a convex linear matrix inequality constraint (27):
Figure FDA00030339163300000617
finally, by introducing an auxiliary variable { τ }k} and ω may beThe problem (20) is transformed into an optimization problem (28), wherein
Figure FDA0003033916330000071
η＝Wmc/Wmm，glRepresenting the forward link channel vector, W, from the CP to the ith base stationmcAnd the bandwidth of a downlink microwave link channel is represented as follows:
Figure FDA0003033916330000072
Figure FDA0003033916330000073
Figure FDA0003033916330000074
Figure FDA0003033916330000075
(20d)-(20g),(21b),(23),(24a),(26),(27) (28e)
since the constraints of the problem are excessive, and most of the conditions have been explained previously, the constraints (20d) - (20g), (21b), (23), (24a), (26), (27), log (1+ β) are denoted by (28e) for the sake of simplifying the expressionk) And
Figure FDA0003033916330000076
is a convex function, so the objective function (28a) consists of a convex difference problem DC, the DC process is usually solved using a constrained concave-convex process CCCP, in practice, the main idea of CCCP is to solve the convex problem by converting (28a) into a convex function and then iterating until the result converges; based on this principle, consider the pair
Figure FDA0003033916330000077
Using a first order Taylor approximation, as shown in (29), wherein
Figure FDA0003033916330000078
To represent
Figure FDA0003033916330000079
The nth iteration:
Figure FDA00030339163300000710
the objective function may then be converted to a convex function (30):
Figure FDA00030339163300000711
constraint (28d) is also a DC program, which can similarly be converted to convex constraint (31):
Figure FDA00030339163300000712
wherein
Figure FDA00030339163300000713
Representing auxiliary variables τkThe nth iteration of (1); by introducing an auxiliary variable thetakAnd { lambda } andk}, (28b) may be decomposed into constraints (32):
Figure FDA0003033916330000081
Figure FDA0003033916330000082
Figure FDA0003033916330000083
according to (25), (26), (27), the non-convex constraints (32b) and (32c) can be transformed into convex constraints (33) and (34), wherein
Figure FDA0003033916330000084
Is λkThe nth iteration:
Figure FDA0003033916330000085
Figure FDA0003033916330000086
finally, the SRM problem can be translated into the following problem:
Figure FDA0003033916330000087
s.t.(20d)-(20g),(21b),(23),(24a),(26),(27),(28c),(32a),(33),(34) (35b)
since the constraints are excessive and most of the conditions have been explained before, for the sake of simplifying the expression, the problem (35) is an optimization problem consisting of an objective function (35a) and constraint conditions (35b), the constraints (20d) - (20g), (21b), (23), (24a), (26), (27), (28c), (32a), (33), (34) are denoted by (35b), in (35) only the rank constraint (20f) is non-convex, by semi-deterministic programming SDP relaxation, (35) will become a convex optimization problem, which can be solved by standard convex optimization techniques, and finally, to obtain a solution to the optimization problem (17), the solution (35) must be iteratively solved, in particular, a feasible solution is initialized first
Figure FDA0003033916330000088
The optimal solution (35) can be obtained by a classical convex optimization algorithm and then updated according to the solution obtained in the previous iteration
Figure FDA0003033916330000089
Figure FDA00030339163300000810
Until the result converges or the iteration index reaches its maximum value; in addition, since (35) without rank constraint is a convex optimization problem, iteratively updating all variables will increase or at least maintain the value of the objective function in (35); given a limited transmit power, the value of the objective function should be a monotonically non-decreasing sequence with an upper bound that converges to an at least locally optimal fixed solution;
step three: problem calculation and solution under constraint of transmitting power of each base station
The transmit power constraint for each base station is more realistic, and B is defined as shown in (36):
Figure FDA0003033916330000091
the power constraint (20d) for each base station can be written in the form of (37), where
Figure FDA0003033916330000092
Represents the ith base station maximum transmission power:
Figure FDA0003033916330000093
then, under the transmit power constraint of each base station, the SRM problem is formulated (38):
Figure FDA0003033916330000094
s.t.(17b)-(17d),(37) (38b)
since the constraints of the problem are excessive and most of the conditions have been explained in the foregoing, for the sake of simplifying the expression, the constraints (17b) - (17d), (37) are denoted by (38b), and finally, the above-mentioned convex optimization problem, i.e., the solution of the problem (38) obtained by the convex optimization algorithm, can be iteratively solved using the algorithm in step two, and the problem (38) refers to the optimization problem composed of the objective function (38a) and the constraints (38 b).
2. The method for designing beams of the millimeter wave cloud wireless access network based on the secure transmission according to claim 1, wherein the method comprises the following steps: in the first step of system model establishment, an eavesdropper Eve tries to eavesdrop the information of the kth user, and the signal received by the z th Eve is as follows:
Figure FDA0003033916330000095
wherein
Figure FDA0003033916330000096
Showing the channel vectors from the lth base station to the z-th Eve,
Figure FDA0003033916330000097
representing the channel vectors from the l base station to the z-th Eve;
the interception rate of the kth user intercepted by the z-th Eve is as follows:
Figure FDA0003033916330000101
finally, the privacy rate that the kth user can achieve is:
Figure FDA0003033916330000102
wherein the content of the first and second substances,
Figure FDA0003033916330000103
representing the speed of non-secrecy of the k-th userThe ratio of the total weight of the particles,
Figure FDA0003033916330000104
representing an Eve set.
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