CN113037659A - Multi-intelligent-reflector-assisted uplink cloud access network access link transmission method - Google Patents

Multi-intelligent-reflector-assisted uplink cloud access network access link transmission method Download PDF

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CN113037659A
CN113037659A CN202110215615.6A CN202110215615A CN113037659A CN 113037659 A CN113037659 A CN 113037659A CN 202110215615 A CN202110215615 A CN 202110215615A CN 113037659 A CN113037659 A CN 113037659A
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CN113037659B (en
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张昱
武学璐
何宣宣
彭宏
宋秀兰
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Zhejiang University of Technology ZJUT
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/021—Estimation of channel covariance
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/024—Channel estimation channel estimation algorithms
    • H04L25/0242—Channel estimation channel estimation algorithms using matrix methods
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
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Abstract

The invention discloses a multi-intelligent-reflector-assisted uplink cloud access network access link transmission method. The system is characterized by the design of the phase shift matrix of the IRS and the covariance matrix of the fronthaul link compression noise with the aim of maximizing the system uplink and speed. Aiming at an uplink transmission system of a multi-IRS auxiliary C-RAN access link, the invention improves the total transmission rate of the communication system by carrying out joint optimization on the phase shift matrix of the IRS and the covariance matrix of the compression noise of a fronthaul link.

Description

Multi-intelligent-reflector-assisted uplink cloud access network access link transmission method
Technical Field
The invention relates to the field of wireless communication, in particular to a neutralization rate maximization optimization method in an access link transmission system based on an intelligent reflector assisted cloud wireless access network.
Background
With the development of science and technology, the wireless technology field is also developed vigorously, the demand of wireless communication services is continuously increased, the requirement on the efficiency of communication transmission is higher and higher, and the traditional wireless communication system cannot meet the requirement.
A cloud radio access network (C-RAN), which is a wireless communication system that promises to alleviate the current communication needs, is different from the conventional communication system in that it transfers baseband processing units from the conventional base station to a cloud baseband processing unit (BBU) pool. The user transmits the signal to a Radio Remote Head (RRH), and the RRH transmits the signal to a BBU pool through a fronthaul link through point-to-point compression or Wyner-Ziv coding compression. However, since the users in the cell are far away from the RRH, we here use Intelligent Reflector (IRS) to assist the users to access the RRH. The Intelligent Reflecting Surface (IRS) integrates a passive reflecting original piece on a plane, directly reflects transmitted information, and each reflecting unit is independently controllable, and enhances a reflecting signal by controlling the amplitude and the phase of the reflecting unit. Different from the traditional relay, the wireless network environment can be intelligently reconstructed, and the performance of the wireless network can be effectively improved.
Through an access link of the IRS auxiliary C-RAN, a user transmits signals to the RRH through a direct link and a reflection link, the RRH compresses and receives the signals through Wyner-Ziv coding, and the signals are transmitted to the BBU pool through a fronthaul link. The performance of the system depends on the phase shift matrix of the IRS and the compression noise of the fronthaul link, and the sum rate of users to the BBU pool is further improved by jointly optimizing the phase shift matrix of the IRS and the covariance matrix of the compression noise of the fronthaul link.
Disclosure of Invention
The invention aims to provide a method for optimizing the neutralization rate maximization in an access link transmission system based on IRS-assisted C-RAN. Namely, under the condition that the capacity of the fronthaul link is limited, the phase shift matrix of the optimal intelligent reflecting surface and the covariance matrix of the fronthaul link compression noise are optimized so as to maximize the system transmission and the speed.
The technical scheme of the invention is as follows:
a multi-intelligent reflector-assisted uplink cloud access network access link transmission method is characterized in that an IRS-assisted C-RAN access link is adopted in a system, under the condition that capacity of a forward link is limited, a phase shift matrix of the IRS and a covariance matrix of compression noise of the forward link are optimized in a combined mode with the aim of maximizing the system and the speed, and the method comprises the following specific steps:
1.1) in the communication system based on the access link of the IRS-assisted C-RAN, a user communicates with a BBU pool through RRH, a plurality of IRS are deployed between the user and RRH, and the user is assisted to access RRH. There are K single antenna users in the system, there are L RRHs, each RRH has NRA root receiving antenna, M IRSs disposed between the user and RRH, each IRS having NIThe RRH compresses the received signal and transmits the compressed signal to the BBU pool through a wired forward link;
1.2) users K, K1, K, send signals x to the individual RRHskAnd each RRH receives signals sent by users through a direct link and a reflection link of the IRS. RRHl, L1.., L, the received signal may be expressed as:
Figure BDA0002953635750000021
wherein x ═ x1,...,xk]Tx-CN (0, PI), obeying Gaussian distribution, P represents user transmission power, and I represents an identity matrix.
Figure BDA0002953635750000022
Representing the user-to-RRHl channel matrix,
Figure BDA0002953635750000023
a channel matrix representing users to IRSm, M1.., M,
Figure BDA0002953635750000024
representing the channel matrix, Θ, from IRS to RRHlm＝diag(θm,1,...,θm,n) The phase-shift matrix representing the IRS is a diagonal matrix whose diagonal elements are taken from vectors
Figure BDA0002953635750000025
(IRS adjusts only the phase, so | θm,n|＝1,n＝1,...,NI)，
Figure BDA0002953635750000031
Is represented by thetamA block diagonal matrix is formed. n isl～CN(0,σ2IM) Is additive Gaussian noise of the channel, Gl,mRepresenting the channel noise, I, from the m IRS to the l RRHMRepresenting an identity matrix of order M, σ2Representing the channel additive gaussian noise factor.
1.3) the RRH compresses the received signal through point-to-point compression or Wyner-Ziv coding and transmits the compressed signal to the BBU pool through a wired fronthaul link. The quantized signal received at the BBU pool can be expressed as:
Figure BDA0002953635750000032
wherein q isl～CN(0,Ωl) Quantization noise representing RRHl, which obeys a complex Gaussian distribution, ΩlIs its covariance matrix. The sum rate of users to BBU pool can thus be expressed as:
Figure BDA0002953635750000033
wherein
Figure BDA0002953635750000034
Figure BDA00029536357500000310
The channel matrix representing all users to all RRHs,
Figure BDA0002953635750000035
direct link representing all users to all RRHsThe channel matrix of the way is formed,
Figure BDA0002953635750000036
the channel matrix representing all IRS to all RRHs,
Figure BDA0002953635750000037
is represented by omegalForming a block diagonal matrix, I is a representation form of mutual information, I represents an identity matrix, VHRepresenting the conjugate transpose of V.
1.4) for RRH adopting point-to-point compression, the compression ratio of the fronthaul link is less than the capacity C of the fronthaul linklNamely, it is required to satisfy:
Figure BDA0002953635750000038
1.5) for the RRH adopting Wyner-Ziv coding compression, the compression ratio of the fronthaul link is smaller than the capacity of the fronthaul link, namely, the requirements of:
Figure BDA0002953635750000039
wherein C isπ(l)Representing the fronthaul link capacity, and pi (l) represents the decompression order of the received signals at the BBU pool.
For point-to-point compression, the design of the phase shift matrix of the IRS and the covariance matrix of the compression noise of the fronthaul link comprises the following specific steps:
2.1) the optimization problem for sum rate maximization can be expressed as:
Figure BDA0002953635750000041
Figure BDA0002953635750000042
Figure BDA0002953635750000043
Figure BDA0002953635750000044
wherein Vl＝Hl+GlΘHrRepresenting the channel matrix for all users to RRHl.
2.2) re-determining the maximum iteration number T of the joint optimizationmaxAnd selecting an initial theta satisfying the constraint condition(0)And
Figure BDA0002953635750000045
2.3) the optimization problem for step 2.1) can be converted into the following form:
Figure BDA0002953635750000046
Figure BDA0002953635750000047
Figure BDA0002953635750000048
Figure BDA0002953635750000049
wherein
Figure BDA00029536357500000410
2.4) fixing theta, omegalFor W, Σ, ElBy performing the update, the following results are obtained:
Figure BDA00029536357500000411
Figure BDA00029536357500000412
2.5) re-fixing W, Σ and ElFor theta, omegalJoint optimization is performed such that the optimization problem can be expressed as:
Figure BDA00029536357500000413
Figure BDA00029536357500000414
Figure BDA00029536357500000415
Figure BDA00029536357500000416
Figure BDA00029536357500000417
Figure BDA00029536357500000418
wherein
Figure BDA0002953635750000051
Al⊙BTIs represented by AlAnd BTThe product of the Hadamard sum of (C),
Figure BDA0002953635750000052
for column vectors by matrix
Figure BDA0002953635750000053
Is made up of diagonal elements.
Figure BDA0002953635750000054
Figure BDA0002953635750000055
For column vectors by matrix
Figure BDA0002953635750000056
The composition of the diagonal line elements of (a),
Figure BDA0002953635750000057
will be relaxed by semi-positive definite (SDR)
Figure BDA0002953635750000058
Removing the constraint condition, and then performing iterative optimization on the optimization problem after the SDR is relaxed by a convex optimization tool to obtain an optimized solution:
Figure BDA0002953635750000059
represents an optimized solution of the optimization problem in this step, HLRepresenting the channel matrix of all users to the RRHs.
2.6) Re-judgment
Figure BDA00029536357500000510
Whether the constraint condition of the step 2.5) is met or not, and if the constraint condition is met, directly performing characteristic value decomposition:
Figure BDA00029536357500000511
for step 2.5) optimization of the solution to the optimization problem, where U is expressed as
Figure BDA00029536357500000512
A matrix of eigenvectors, Λ being
Figure BDA00029536357500000513
Is formed by the eigenvalues ofHIs a conjugate transpose of U;
Figure BDA00029536357500000514
the optimized column vector is represented, the column vector consisting of diagonal elements of the phase shift matrix and the column vector consisting of 1. If the constraint of step 2.5) is not satisfied, a plurality of suboptimal solutions are generated by the following method: firstly let
Figure BDA00029536357500000515
Wherein
Figure BDA00029536357500000516
Are independent random variables uniformly distributed on a unit circle of a complex plane (i.e. the unit circle is a
Figure BDA00029536357500000517
θiIndependently and uniformly distributed in [0,2 pi ]]) Second through the pair omegalScaling is carried out, the generated optimized solution meets the constraint condition of the step 2.5), and finally, one solution which enables the target function in the step 2.5) to reach the minimum value is selected as the optimal solution, and the optimal solution is obtained: phase shift matrix theta(t)Covariance matrix of sum compression noise
Figure BDA00029536357500000518
t＝1,...,TmaxThe number of iterations is indicated. Substituting the optimized solution into the objective function of the step 2.5) to obtain f(t)It means that the optimized solution is substituted into the value of the objective function, and the solution theta of the last iteration is substituted(t-1)，
Figure BDA00029536357500000519
Also brought into the objective function of step 2.5) of the current round to obtain f(t-1)Comparison is made if f(t)≤f(t-1)The optimization solution of the previous round is taken as the optimization solution of the current round.
2.7) substituting the optimized solution of step 2.6) into the sum-rate expression RsumTo obtain the sum rate of the iteration
Figure BDA0002953635750000061
From the last iteration
Figure BDA0002953635750000062
Make a comparison if
Figure BDA0002953635750000063
Stopping the iteration and determining the optimal result
Figure BDA0002953635750000064
Output optimization solution theta(t),
Figure BDA0002953635750000065
Wherein ^ represents an allowable error range; if it is
Figure BDA0002953635750000066
Judging whether the iteration number exceeds TmaxIf not, T is exceededmaxReturning to the step 2.2) to continue iterative optimization; if T is exceededmaxThen the final optimization solution is output
Figure BDA0002953635750000067
2.8) for the case of the IRS reflection surface phase being discrete, first theta is obtained by 2.1) to 2.7)*,
Figure BDA0002953635750000068
Where the diagonal element theta of theta ism,nMapping onto points of discrete phase, i.e.:
Figure BDA0002953635750000069
where phi denotes the discrete phase and tau is 2bAnd b is 1,2, representing discrete levels. Then to
Figure BDA00029536357500000610
Is scaled to obtain
Figure BDA00029536357500000611
So that it meets the constraints in step 2.1).
For the design of the Wyner-Ziv coding compression, the specific steps for the phase shift matrix of the IRS and the covariance matrix of the compression noise of the fronthaul link are as follows:
3.1) and the rate maximization optimization problem can be expressed as:
Figure BDA00029536357500000612
Figure BDA00029536357500000613
Figure BDA00029536357500000614
Figure BDA00029536357500000615
wherein
Figure BDA00029536357500000616
Representing a decompression order set, and pi (l) represents that RRH pi (l) is arranged at the I-th bit of the decompression order of the BBU pool.
3.2) for the sequence of the BBU decompression pools, judging:
Figure BDA00029536357500000617
the higher value of (2) is decompressed first. Re-determining maximum iteration number T of joint optimizationmaxAnd selecting the initial theta satisfying the condition(0)And
Figure BDA0002953635750000071
3.3) the optimization problem in step 3.1) can be written as follows:
Figure BDA0002953635750000072
Figure BDA0002953635750000073
Figure BDA0002953635750000074
Figure BDA0002953635750000075
wherein
Figure BDA0002953635750000076
3.4) fixing theta, omegalFor the case of W, Σ,
Figure BDA0002953635750000077
by performing the update, the following results are obtained:
Figure BDA0002953635750000078
Figure BDA0002953635750000079
IKrepresenting a K × K identity matrix.
3.5) resetting W, Sigma and
Figure BDA00029536357500000710
for theta, omegalJoint optimization is performed such that the optimization problem can be expressed as:
Figure BDA00029536357500000711
Figure BDA00029536357500000712
Figure BDA00029536357500000713
Figure BDA00029536357500000714
Figure BDA00029536357500000715
Figure BDA00029536357500000716
wherein
Figure BDA00029536357500000717
For column vectors by matrix
Figure BDA00029536357500000718
The composition of the diagonal line elements is shown,
Figure BDA00029536357500000719
and then by semi-positive relaxation (SDR)
Figure BDA00029536357500000720
Removing the constraint condition, and then performing iterative optimization on the optimization problem after the SDR is relaxed by a convex optimization tool to obtain an optimized solution:
Figure BDA00029536357500000721
the solution to the problem is optimized for this step.
3.6) Re-judgment
Figure BDA0002953635750000081
Whether the constraint condition of the step 3.5) is met or not, and if the constraint condition is met, directly performing characteristic value decomposition:
Figure BDA0002953635750000082
is an optimized solution of the optimization problem of the step 3.5),
Figure BDA0002953635750000083
the optimized column vector is represented, the column vector consisting of diagonal elements of the phase shift matrix and the column vector consisting of 1. If the constraint of step 3.5) is not satisfied, a plurality of suboptimal solutions are generated by the following method: firstly let
Figure BDA0002953635750000084
Wherein
Figure BDA0002953635750000085
Are independent random variables uniformly distributed on a unit circle of a complex plane (i.e. the unit circle is a
Figure BDA0002953635750000086
θiIndependently and uniformly distributed in [0,2 pi ]]) Second through the pair omegalScaling is carried out, the generated optimized solution meets the constraint condition of the step 3.5), and finally, one solution which enables the target function in the step 3.5) to reach the minimum value is selected as the optimal solution, and the optimal solution is obtained: phase shift matrix theta(t)Covariance matrix of sum compression noise
Figure BDA0002953635750000087
t＝1,...,TmaxThe number of iterations is indicated. Substituting the optimized solution into the objective function of the step 3.5) to obtain f(t)It means that the optimized solution is substituted into the value of the objective function, and the solution theta of the last iteration is substituted(t-1)，
Figure BDA0002953635750000088
Also taken into the objective function of step 3.5) of the current round to obtain f(t-1)Comparison is made if f(t)≤f(t-1)The optimization solution of the previous round is taken as the optimization solution of the current round.
3.7) substituting the optimized solution of step 3.6) into the sum-rate expression RsumTo obtain the sum rate of the iteration
Figure BDA0002953635750000089
From the last iteration
Figure BDA00029536357500000810
Make a comparison if
Figure BDA00029536357500000811
Stopping the iteration and determining the optimal result
Figure BDA00029536357500000812
Output optimization solution theta(t),
Figure BDA00029536357500000813
Wherein ^ represents an allowable error range; if it is
Figure BDA00029536357500000814
Judging whether the iteration number exceeds TmaxIf not, T is exceededmaxReturning to the step 3.2) to continue iterative optimization; if T is exceededmaxThen the final optimization solution is output
Figure BDA00029536357500000815
3.8) for the case of the IRS reflection surface phase being discrete, first theta is obtained by 3.1) to 3.7)*,
Figure BDA00029536357500000816
Where the diagonal element theta of theta ism,nMapping onto points of discrete phase, i.e.:
Figure BDA00029536357500000817
where phi denotes the discrete phase and tau is 2bAnd b is 1,2, representing discrete levels. Then to
Figure BDA00029536357500000818
Is scaled to obtain
Figure BDA00029536357500000819
So that it meets the constraints in step 3.1).
The invention has the advantages that for the communication system of the IRS auxiliary C-RAN access link, the system and the speed are obviously improved by optimizing the phase shift matrix of the IRS and the covariance matrix of the compression noise of the fronthaul link; in addition, the system and the speed obtained by the optimization algorithm are obviously improved compared with the system and the speed under the condition of IRS random and the condition of no IRS.
Drawings
Fig. 1 is a schematic diagram of an access link system of an auxiliary cloud access network based on an intelligent reflector according to the present invention;
fig. 2 is a schematic speed diagram of an access link system of an auxiliary cloud access network based on an intelligent reflector according to the present invention after the joint optimization method of the present invention is adopted;
FIG. 2 shows the relationship between the system and speed and the number of intelligent reflecting surfaces, and FIG. 2 shows the continuous phase of the optimal decompression sequence, the continuous phase of the suboptimal decompression sequence, the 2-bit discrete phase of the suboptimal decompression sequence, the 1-bit discrete phase of the suboptimal decompression sequence, the sum speed of the suboptimal decompression sequence when no intelligent reflecting surface exists in the stochastic phase and the suboptimal decompression sequence, and the sum speed of the continuous phase, the 2-bit discrete phase, the 1-bit discrete phase, the random phase and the situation when no intelligent reflecting surface exists in the point-to-point compression.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The communication system transmission process based on the IRS assisted C-RAN access link is shown in fig. 1. Before transmission begins, channel information in the system is collected, and then a phase shift matrix of the IRS and a covariance matrix of the compression noise of a fronthaul link are jointly optimized. The transmission process comprises the following steps: the user communicates with the BBU pool through the RRH, the user sends signals to transmit the signals to the RRH through direct and reflected paths, and the RRH compresses the received signals through point-to-point or Wyner-Ziv coding and transmits the signals to the BBU pool through a fronthaul link. The method comprises the following steps of performing joint optimization on a phase shift matrix of the IRS and a covariance matrix of compression noise of a fronthaul link to improve the system and the speed, wherein the specific optimization process is as follows:
1.1) in the communication system based on the access link of the IRS-assisted C-RAN, a user communicates with a BBU pool through RRH, a plurality of IRS are deployed between the user and RRH, and the user is assisted to access RRH. There are K single antenna users in the system, there are L RRHs, each RRH has NRA root receiving antenna, M IRSs disposed between the user and RRH, each IRS having NIA reflection unit. The RRH compresses the received signal and transmits the compressed signal to the BBU pool through a wired forward link.
1.2) users K, K1, K, send signals x to the individual RRHskAnd each RRH receives signals sent by users through a direct link and a reflection link of the IRS. RRHl, L1.., L, the received signal may be expressed as:
Figure BDA0002953635750000101
wherein x ═ x1,...,xk]Tx-CN (0, PI), obeying a Gaussian distribution.
Figure BDA0002953635750000102
Representing the user-to-RRHl channel matrix,
Figure BDA0002953635750000103
a channel matrix representing users to IRSm, M1.., M,
Figure BDA0002953635750000104
Figure BDA0002953635750000105
representing the channel matrix IRS to RRHl. Thetam＝diag(θm,1,...,θm,n) The phase-shift matrix representing the IRS is a diagonal matrix whose diagonal elements are taken from vectors
Figure BDA0002953635750000106
(IRS adjusts only the phase, so | θm,n|＝1,n＝1,...,NI)，
Figure BDA0002953635750000107
Is represented by thetamA block diagonal matrix is formed. n isl～CN(0,σ2IM) Is additive gaussian noise of the channel.
1.3) the RRH compresses the received signal through point-to-point compression or Wyner-Ziv coding and transmits the compressed signal to the BBU pool through a wired fronthaul link. The quantized signal received at the BBU pool can be expressed as:
Figure BDA0002953635750000108
wherein q isl～CN(0,Ωl) Quantization noise representing RRHl, which obeys a complex Gaussian distribution, ΩlIs its covariance matrix. The sum rate of users to BBU pool can thus be expressed as:
Figure BDA0002953635750000109
wherein
Figure BDA0002953635750000111
The channel matrix representing all users to all RRHs,
Figure BDA0002953635750000112
represents the direct link channel matrix of all users to all RRHs,
Figure BDA0002953635750000113
the channel matrix representing all IRS to all RRHs,
Figure BDA0002953635750000114
is represented by omegalA block diagonal matrix is formed.
1.4) for RRH adopting point-to-point compression, the compression ratio of the fronthaul link is less than the capacity C of the fronthaul linklNamely, it is required to satisfy:
Figure BDA0002953635750000115
1.5) for the RRH adopting Wyner-Ziv coding compression, the compression ratio of the fronthaul link is smaller than the capacity of the fronthaul link, namely, the requirements of:
Figure BDA0002953635750000116
wherein C isπ(l)Representing the fronthaul link capacity, and pi (l) represents the decompression order of the received signals at the BBU pool.
2. For point-to-point compression, the optimization method for maximizing the sum rate according to the transmission mode of the communication system based on the IRS assisted C-RAN access link in claim 1 is characterized in that the design of the phase shift matrix of the IRS and the covariance matrix of the compression noise of the fronthaul link comprises the following specific steps:
2.1) the optimization problem for sum rate maximization can be expressed as:
Figure BDA0002953635750000117
Figure BDA0002953635750000118
Figure BDA0002953635750000119
Figure BDA00029536357500001110
wherein Vl＝Hl+GlΘHrRepresenting the channel matrix for all users to RRHl.
2.2) re-determining the maximum iteration number T of the joint optimizationmaxAnd selecting an initial theta satisfying the constraint condition(0)And
Figure BDA00029536357500001111
2.3) the optimization problem for step 2.1) can be converted into the following form:
Figure BDA0002953635750000121
Figure BDA0002953635750000122
Figure BDA0002953635750000123
Figure BDA0002953635750000124
wherein
Figure BDA0002953635750000125
2.4) fixing theta, omegalFor W, Σ, ElBy performing the update, the following results are obtained:
Figure BDA0002953635750000126
Figure BDA0002953635750000127
2.5) re-fixing W, Σ and ElFor theta, omegalJoint optimization is performed such that the optimization problem can be expressed as:
Figure BDA0002953635750000128
Figure BDA0002953635750000129
Figure BDA00029536357500001210
Figure BDA00029536357500001211
Figure BDA00029536357500001212
Figure BDA00029536357500001213
wherein
Figure BDA00029536357500001214
Al⊙BTIs represented by AlAnd BTThe product of the Hadamard sum of (C),
Figure BDA00029536357500001215
for column vectors by matrix
Figure BDA00029536357500001216
Is made up of diagonal elements.
Figure BDA00029536357500001217
Figure BDA00029536357500001218
For column vectors by matrix
Figure BDA00029536357500001219
The composition of the diagonal line elements of (a),
Figure BDA00029536357500001220
will be relaxed by semi-positive definite (SDR)
Figure BDA00029536357500001221
Removing the constraint condition, and then performing iterative optimization on the optimization problem after the SDR is relaxed by a convex optimization tool to obtain an optimized solution:
Figure BDA00029536357500001222
represents the optimal solution of the optimization problem in this step. 2.6) Re-judgment
Figure BDA0002953635750000131
Whether the constraint condition of the step 2.5) is met or not, and if the constraint condition is met, directly performing characteristic value decomposition:
Figure BDA0002953635750000132
is an optimized solution of the optimization problem of the step 2.5),
Figure BDA0002953635750000133
represents the optimized column vector, the column vector consisting of the diagonal elements of the phase shift matrix and the column vector consisting of 1, Λ1/2Represents the square of the lambda. If the constraint of step 2.5) is not satisfied, a plurality of suboptimal solutions are generated by the following method: firstly let
Figure BDA0002953635750000134
Wherein
Figure BDA0002953635750000135
Are independent random variables uniformly distributed on a unit circle of a complex plane (i.e. the unit circle is a
Figure BDA0002953635750000136
θiIndependently and uniformly distributed in [0,2 pi ]]) Second through the pair omegalScaling is carried out, the generated optimized solution meets the constraint condition of the step 2.5), and finally, one solution which enables the target function in the step 2.5) to reach the minimum value is selected as the optimal solution, and the optimal solution is obtained: phase shift matrix theta(t)Covariance matrix of sum compression noise
Figure BDA0002953635750000137
t＝1,...,TmaxThe number of iterations is indicated. Substituting the optimized solution into the objective function of the step 2.5) to obtain f(t)It means that the optimized solution is substituted into the value of the objective function, and the solution theta of the last iteration is substituted(t-1)，
Figure BDA0002953635750000138
Also brought into the objective function of step 2.5) of the current round to obtain f(t-1)Comparison is made if f(t)≤f(t-1)The optimization solution of the previous round is taken as the optimization solution of the current round.
2.7) substituting the optimized solution of step 2.6) into the sum-rate expression RsumTo obtainThe sum rate of the current iteration
Figure BDA0002953635750000139
From the last iteration
Figure BDA00029536357500001310
Make a comparison if
Figure BDA00029536357500001311
Stopping the iteration and determining the optimal result
Figure BDA00029536357500001312
Output optimization solution theta(t),
Figure BDA00029536357500001313
Wherein ^ represents an allowable error range; if it is
Figure BDA00029536357500001314
Judging whether the iteration number exceeds TmaxIf not, T is exceededmaxReturning to the step 2.2) to continue iterative optimization; if T is exceededmaxThen the final optimization solution is output
Figure BDA00029536357500001315
2.8) for the case of the IRS reflection surface phase being discrete, first theta is obtained by 2.1) to 2.7)*,
Figure BDA00029536357500001316
Where the diagonal element theta of theta ism,nMapping onto points of discrete phase, i.e.:
Figure BDA00029536357500001317
where phi denotes the discrete phase and tau is 2bAnd b is 1,2, representing discrete levels. Then to
Figure BDA00029536357500001318
Is scaled to obtain
Figure BDA00029536357500001319
So that it meets the constraints in step 2.1).
3. For the optimization method of adopting Wyner-Ziv coding compression, according to the transmission mode of communication system based on IRS auxiliary C-RAN access link in claim 1, the optimization method of maximum sum rate is characterized by that the design of the described IRS phase-shift matrix and covariance matrix of forward link compression noise includes the following concrete steps:
3.1) and the rate maximization optimization problem can be expressed as:
Figure BDA0002953635750000141
Figure BDA0002953635750000142
Figure BDA0002953635750000143
Figure BDA0002953635750000144
wherein
Figure BDA0002953635750000145
Representing a decompression order set, and pi (l) represents that RRH pi (l) is arranged at the I-th bit of the decompression order of the BBU pool.
3.2) for the sequence of the BBU decompression pools, judging:
Figure BDA0002953635750000146
the higher value of (2) is decompressed first. Re-determining maximum iteration number T of joint optimizationmaxAnd selecting the initial theta satisfying the condition(0)And
Figure BDA0002953635750000147
3.3) the optimization problem in step 3.1) can be written as follows:
Figure BDA0002953635750000148
Figure BDA0002953635750000149
Figure BDA00029536357500001410
Figure BDA00029536357500001411
wherein
Figure BDA00029536357500001412
3.4) fixing theta, omegalFor the case of W, Σ,
Figure BDA00029536357500001413
by performing the update, the following results are obtained:
Figure BDA00029536357500001415
Figure BDA00029536357500001414
3.5) resetting W, Sigma and
Figure BDA0002953635750000151
for theta, omegalJoint optimization is performed such that the optimization problem can be expressed as:
Figure BDA0002953635750000152
Figure BDA0002953635750000153
Figure BDA0002953635750000154
Figure BDA0002953635750000155
Figure BDA0002953635750000156
Figure BDA0002953635750000157
wherein
Figure BDA0002953635750000158
For column vectors by matrix
Figure BDA0002953635750000159
The composition of the diagonal line elements is shown,
Figure BDA00029536357500001510
and then by semi-positive relaxation (SDR)
Figure BDA00029536357500001511
Removing the constraint condition, and then performing iterative optimization on the optimization problem after the SDR is relaxed by a convex optimization tool to obtain an optimized solution:
Figure BDA00029536357500001512
the solution to the problem is optimized for this step.
3.6) Re-judgment
Figure BDA00029536357500001513
Whether the constraint condition of the step 3.5) is met or not, and if the constraint condition is metAnd (3) directly carrying out eigenvalue decomposition on the constraint conditions:
Figure BDA00029536357500001514
is an optimized solution of the optimization problem of the step 3.5),
Figure BDA00029536357500001515
the optimized column vector is represented, the column vector consisting of diagonal elements of the phase shift matrix and the column vector consisting of 1. If the constraint of step 3.5) is not satisfied, a plurality of suboptimal solutions are generated by the following method: firstly let
Figure BDA00029536357500001516
Wherein
Figure BDA00029536357500001517
Are independent random variables uniformly distributed on a unit circle of a complex plane (i.e. the unit circle is a
Figure BDA00029536357500001518
θiIndependently and uniformly distributed in [0,2 pi ]]) Second through the pair omegalScaling is carried out, the generated optimized solution meets the constraint condition of the step 3.5), and finally, one solution which enables the target function in the step 3.5) to reach the minimum value is selected as the optimal solution, and the optimal solution is obtained: phase shift matrix theta(t)Covariance matrix of sum compression noise
Figure BDA00029536357500001519
t＝1,...,TmaxThe number of iterations is indicated. Substituting the optimized solution into the objective function of the step 3.5) to obtain f(t)It means that the optimized solution is substituted into the value of the objective function, and the solution theta of the last iteration is substituted(t-1)，
Figure BDA00029536357500001520
Also taken into the objective function of step 3.5) of the current round to obtain f(t-1)Comparison is made if f(t)≤f(t-1)The optimization solution of the previous round is taken as the optimization solution of the current round.
3.7) step 3.6)Optimized solution entry-and-speed expression RsumTo obtain the sum rate of the iteration
Figure BDA0002953635750000161
From the last iteration
Figure BDA0002953635750000162
Make a comparison if
Figure BDA0002953635750000163
Stopping the iteration and determining the optimal result
Figure BDA0002953635750000164
Output optimization solution theta(t),
Figure BDA0002953635750000165
Wherein
Figure BDA0002953635750000166
Indicating an allowable error range; if it is
Figure BDA0002953635750000167
Judging whether the iteration number exceeds TmaxIf not, T is exceededmaxReturning to the step 3.2) to continue iterative optimization; if T is exceededmaxThen the final optimization solution is output
Figure BDA0002953635750000168
3.8) for the case of the IRS reflection surface phase being discrete, first theta is obtained by 3.1) to 3.7)*,
Figure BDA0002953635750000169
Where the diagonal element theta of theta ism,nMapping onto points of discrete phase, i.e.:
Figure BDA00029536357500001610
where phi denotes the discrete phase and tau is 2bAnd b is 1,2, representing discrete levels. Then to
Figure BDA00029536357500001611
Is scaled to obtain
Figure BDA00029536357500001612
So that it meets the constraints in step 3.1).
Computer simulation shows that the system and the speed of the communication system based on the IRS auxiliary C-RAN access link are obviously higher than those of the traditional C-RAN after the joint optimization method is adopted.

Claims (3)

1. A multi-intelligent reflector-assisted uplink cloud access network access link transmission method is characterized in that a cloud radio access network C-RAN access link performs joint optimization on a phase shift matrix of an Intelligent Reflector (IRS) and a covariance of a forward link compression noise through the assistance of an Intelligent Reflector (IRS) and with the aim of maximizing a system and a speed, and is characterized in that: the method specifically comprises the following steps:
1.1) in a communication system based on an IRS-assisted C-RAN access link, a user communicates with a baseband processing unit (BBU) pool through a Radio Remote Head (RRH), a plurality of IRSs are deployed between the user and the RRH, and the user is assisted to access the RRH; there are K single antenna users in the system, there are L RRHs, each RRH has NRA root receiving antenna, M IRSs disposed between the user and RRH, each IRS having NIA reflection unit; the RRH compresses the received signal and transmits the compressed signal to the BBU pool through a wired forward link;
1.2) users K, K1, K, send signals x to the individual RRHskEach RRH receives signals sent by users through a direct link and a reflection link of the IRS; RRHl, L1.., L, the received signal may be expressed as:
Figure FDA0002953635740000011
wherein x ═ x1,...,xk]Tx-CN (0, PI) obeying Gaussian distribution, wherein P represents user transmission power, and I represents an identity matrix;
Figure FDA0002953635740000012
representing the user-to-RRHl channel matrix,
Figure FDA0002953635740000013
a channel matrix representing users to IRSm, M1.., M,
Figure FDA0002953635740000014
Figure FDA0002953635740000015
representing the channel matrix from IRS to RRHl; thetam＝diag(θm,1,...,θm,n) The phase-shift matrix representing the IRS is a diagonal matrix whose diagonal elements are taken from vectors
Figure FDA0002953635740000016
IRS adjusts only the phase, so | θm,n|＝1,n＝1,...,NI，
Figure FDA0002953635740000017
Is represented by thetamA block diagonal matrix of components; n isl～CN(0,σ2IM) Additive gaussian noise for the channel; gl,mRepresenting the channel noise, I, from the m IRS to the l RRHMRepresenting an identity matrix of order M, σ2Representing the channel additive Gaussian noise factor;
1.3) the RRH compresses the received signal through point-to-point compression or Wyner-Ziv coding and transmits the compressed signal to the BBU pool through a wired fronthaul link; the quantized signal received at the BBU pool can be expressed as:
Figure FDA0002953635740000021
wherein q isl～CN(0,Ωl) Quantization noise representing RRHl, which obeys a complex Gaussian distribution, ΩlIs its covariance matrix(ii) a The sum rate of users to BBU pool can thus be expressed as:
Figure FDA0002953635740000022
wherein
Figure FDA0002953635740000023
Figure FDA0002953635740000024
The channel matrix representing all users to all RRHs,
Figure FDA0002953635740000025
represents the direct link channel matrix of all users to all RRHs,
Figure FDA0002953635740000026
the channel matrix representing all IRS to all RRHs,
Figure FDA0002953635740000027
is represented by omegalA block diagonal matrix of components; i is the representation form of mutual information, I represents an identity matrix, VHRepresents the conjugate transpose of V;
1.4) for RRH adopting point-to-point compression, the compression ratio of the fronthaul link is less than the capacity C of the fronthaul linklNamely, it is required to satisfy:
Figure FDA0002953635740000028
1.5) for the RRH adopting Wyner-Ziv coding compression, the compression ratio of the fronthaul link is smaller than the capacity of the fronthaul link, namely, the requirements of:
Figure FDA0002953635740000029
wherein C isπ(l)Representing the capacity of the forwarding link, pi (l) representing the decompression order of the received signals in the BBU pool,
Figure FDA00029536357400000210
representing the decompressed sequential set of the first l-1 received signals.
2. The method for transmitting the access link of the multi-intelligent-reflector-assisted uplink cloud access network according to claim 1, wherein for the design of point-to-point compression, the phase shift matrix of the IRS and the covariance matrix of the compression noise of the fronthaul link, the specific steps are as follows:
2.1) the optimization problem for sum rate maximization can be expressed as:
Figure FDA0002953635740000031
Figure FDA0002953635740000032
Figure FDA0002953635740000033
Figure FDA0002953635740000034
wherein Vl＝Hl+GlΘHrRepresenting the channel matrix from all users to the RRHl;
2.2) re-determining the maximum iteration number T of the joint optimizationmaxAnd selecting an initial theta satisfying the constraint condition(0)And
Figure FDA00029536357400000312
2.3) the optimization problem for step 2.1) can be converted into the following form:
Figure FDA0002953635740000035
Figure FDA0002953635740000036
Figure FDA0002953635740000037
Figure FDA0002953635740000038
wherein
Figure FDA0002953635740000039
W is the receive matrix, sigma denotes the a posteriori criterion estimate the covariance matrix of the data symbols, ElAn auxiliary variable matrix;
2.4) fixing theta, omegalFor W, Σ, ElBy performing the update, the following results are obtained:
Figure FDA00029536357400000310
Figure FDA00029536357400000311
2.5) re-fixing W, Σ and ElFor theta, omegalJoint optimization is performed such that the optimization problem can be expressed as:
Figure FDA0002953635740000041
Figure FDA0002953635740000042
Figure FDA0002953635740000043
Figure FDA0002953635740000044
Figure FDA0002953635740000045
Figure FDA0002953635740000046
wherein
Figure FDA0002953635740000047
Al⊙BTIs represented by AlAnd BTThe product of the Hadamard sum of (C),
Figure FDA0002953635740000048
for column vectors by matrix
Figure FDA0002953635740000049
Diagonal element composition of (a);
Figure FDA00029536357400000410
Figure FDA00029536357400000411
for column vectors by matrix
Figure FDA00029536357400000412
The composition of the diagonal line elements of (a),
Figure FDA00029536357400000413
by semi-positive relaxationSDR will
Figure FDA00029536357400000414
Removing the constraint condition, and then performing iterative optimization on the optimization problem after the SDR is relaxed by a convex optimization tool to obtain an optimized solution:
Figure FDA00029536357400000415
Figure FDA00029536357400000416
representing an optimization solution to the optimization problem in this step; hLA channel matrix representing all users to RRHs;
2.6) Re-judgment
Figure FDA00029536357400000417
Whether the constraint condition of the step 2.5) is met or not, and if the constraint condition is met, directly performing characteristic value decomposition:
Figure FDA00029536357400000418
for the optimized solution of the optimization problem of step 2.5), U is expressed as
Figure FDA00029536357400000419
A matrix of eigenvectors, Λ being
Figure FDA00029536357400000420
Is formed by the eigenvalues ofHIs a conjugate transpose of U;
Figure FDA00029536357400000421
representing the optimized column vector, the column vector consisting of diagonal elements of the phase shift matrix and the column vector consisting of 1; if the constraint of step 2.5) is not satisfied, a plurality of suboptimal solutions are generated by the following method: firstly let
Figure FDA00029536357400000422
Wherein
Figure FDA00029536357400000423
Unit circles uniformly distributed in the complex plane as independent random variables, followed by a pair of ΩlScaling is carried out, the generated optimized solution meets the constraint condition of the step 2.5), and finally, one solution which enables the target function in the step 2.5) to reach the minimum value is selected as the optimal solution, and the optimal solution is obtained: phase shift matrix theta(t)Covariance matrix of sum compression noise
Figure FDA0002953635740000051
The number of iterations is indicated. Substituting the optimized solution into the objective function of the step 2.5) to obtain f(t)It means that the optimized solution is substituted into the value of the objective function, and the solution theta of the last iteration is substituted(t-1)，
Figure FDA0002953635740000052
Also brought into the objective function of step 2.5) of the current round to obtain f(t-1)Comparison is made if f(t)≤f(t-1)Taking the optimization solution of the previous round as the optimization solution of the current round;
2.7) substituting the optimized solution of step 2.6) into the sum-rate expression RsumTo obtain the sum rate of the iteration
Figure FDA0002953635740000053
From the last iteration
Figure FDA0002953635740000054
Make a comparison if
Figure FDA0002953635740000055
Stopping the iteration and determining the optimal result
Figure FDA0002953635740000056
Output optimization solution theta*,
Figure FDA0002953635740000057
Wherein
Figure FDA0002953635740000058
Indicating an allowable error range; if it is
Figure FDA0002953635740000059
Judging whether the iteration number exceeds TmaxIf not, T is exceededmaxReturning to the step 2.2) to continue iterative optimization; if T is exceededmaxThen the final optimization solution is output
Figure FDA00029536357400000515
2.8) for the case of the IRS reflection surface phase being discrete, first theta is obtained by 2.1) to 2.7)*,
Figure FDA00029536357400000511
Where the diagonal element theta of theta ism,nMapping onto points of discrete phase, i.e.:
Figure FDA00029536357400000512
where phi denotes the discrete phase and tau is 2bAnd b is 1,2. represents discrete levels; then to
Figure FDA00029536357400000513
Is scaled to obtain
Figure FDA00029536357400000514
So that it meets the constraints in step 2.1).
3. The method for transmitting the access link of the multi-intelligent-reflector-surface-assisted uplink cloud access network according to claim 1, wherein for the design of the Wyner-Ziv coding compression adopted, the phase shift matrix of the IRS and the covariance matrix of the compression noise of the fronthaul link are specifically as follows:
3.1) and the rate maximization optimization problem can be expressed as:
Figure FDA0002953635740000061
Figure FDA0002953635740000062
Figure FDA0002953635740000063
Figure FDA0002953635740000064
wherein
Figure FDA0002953635740000065
Figure FDA0002953635740000066
Representing a decompression sequence set, and pi (l) represents that RRH pi (l) is arranged at the ith position of a BBU pool decompression sequence;
3.2) for the sequence of the BBU decompression pools, judging:
Figure FDA0002953635740000067
decompressing the larger value of (1); re-determining maximum iteration number T of joint optimizationmaxAnd selecting the initial theta satisfying the condition(0)And
Figure FDA0002953635740000068
3.3) the optimization problem in step 3.1) can be written as follows:
Figure FDA0002953635740000069
Figure FDA00029536357400000610
Figure FDA00029536357400000611
Figure FDA00029536357400000612
wherein
Figure FDA00029536357400000613
3.4) fixing theta, omegalFor the case of W, Σ,
Figure FDA00029536357400000614
by performing the update, the following results are obtained:
Figure FDA00029536357400000615
Figure FDA00029536357400000616
IKan identity matrix representing K;
3.5) resetting W, Sigma and
Figure FDA00029536357400000617
for theta, omegalJoint optimization is performed such that the optimization problem can be expressed as:
Figure FDA0002953635740000071
Figure FDA0002953635740000072
Figure FDA0002953635740000073
Figure FDA0002953635740000074
Figure FDA0002953635740000075
Figure FDA0002953635740000076
wherein
Figure FDA0002953635740000077
For column vectors by matrix
Figure FDA0002953635740000078
The composition of the diagonal line elements is shown,
Figure FDA0002953635740000079
then relaxing SDR through semipositive definite
Figure FDA00029536357400000710
Removing the constraint condition, and then performing iterative optimization on the optimization problem after the SDR is relaxed by a convex optimization tool to obtain an optimized solution:
Figure FDA00029536357400000711
optimizing the solution of the problem in the step;
3.6) Re-judgment
Figure FDA00029536357400000712
Whether the constraint condition of the step 3.5) is met or not, and if the constraint condition is met, directly performing characteristic value decomposition:
Figure FDA00029536357400000713
is an optimized solution of the optimization problem of the step 3.5),
Figure FDA00029536357400000714
the optimized column vector is represented, the column vector consisting of diagonal elements of the phase shift matrix and the column vector consisting of 1. If the constraint of step 3.5) is not satisfied, a plurality of suboptimal solutions are generated by the following method: firstly let
Figure FDA00029536357400000715
Wherein
Figure FDA00029536357400000716
Are independent random variables, are uniformly distributed on a unit circle of a complex plane, and then are subjected to omega pairlScaling is carried out, the generated optimized solution meets the constraint condition of the step 3.5), and finally, one solution which enables the target function in the step 3.5) to reach the minimum value is selected as the optimal solution, and the optimal solution is obtained: phase shift matrix theta(t)Covariance matrix of sum compression noise
Figure FDA00029536357400000717
The number of iterations is indicated. Substituting the optimized solution into the objective function of the step 3.5) to obtain f(t)It means that the optimized solution is substituted into the value of the objective function, and the solution theta of the last iteration is substituted(t-1)，
Figure FDA00029536357400000718
Also taken into the objective function of step 3.5) of the current round to obtain f(t-1)Comparison is made if f(t)≤f(t-1)Taking the optimization solution of the previous round as the optimization solution of the current round;
3.7) optimal solution entry and rate of step 3.6)Expression RsumTo obtain the sum rate of the iteration
Figure FDA0002953635740000081
From the last iteration
Figure FDA0002953635740000082
Make a comparison if
Figure FDA0002953635740000083
Stopping the iteration and determining the optimal result
Figure FDA0002953635740000084
Output optimization solution theta(t),
Figure FDA0002953635740000085
Wherein
Figure FDA0002953635740000086
Indicating an allowable error range; if it is
Figure FDA0002953635740000087
Judging whether the iteration number exceeds TmaxIf not, T is exceededmaxReturning to the step 3.2) to continue iterative optimization; if T is exceededmaxThen the final optimization solution is output
Figure FDA0002953635740000088
3.8) for the case of the IRS reflection surface phase being discrete, first theta is obtained by 3.1) to 3.7)*,
Figure FDA0002953635740000089
Where the diagonal element theta of theta ism,nMapping onto points of discrete phase, i.e.:
Figure FDA00029536357400000810
wherein phi is shownShowing a discrete phase, τ ═ 2bAnd b is 1,2, representing discrete levels. Then to
Figure FDA00029536357400000812
Is scaled to obtain
Figure FDA00029536357400000811
So that it meets the constraints in step 3.1).
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