CN113037659B - 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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CN113037659B
CN113037659B CN202110215615.6A CN202110215615A CN113037659B CN 113037659 B CN113037659 B CN 113037659B CN 202110215615 A CN202110215615 A CN 202110215615A CN 113037659 B CN113037659 B CN 113037659B
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CN113037659A (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 IRS phase shift matrix and the forward link compression noise covariance matrix with the goal of maximizing the system uplink and rate. 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 has been developed vigorously, the demand of wireless communication services is increasing continuously, the requirement for the efficiency of communication transmission is higher and higher, and the traditional wireless communication system can not 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 baseband processing unit (BBU) pool in the cloud. The user transmits the signal to a Remote Radio Head (RRH), and the RRH transmits the signal to a BBU pool through a fronthaul link by 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 an Intelligent Reflector (IRS) to assist the users in accessing 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 relay can intelligently reconstruct a wireless network environment and can effectively improve the performance of the wireless network.
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 forward link, and the sum rate of the user 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 forward 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 system and speed, and the method comprises the following specific steps:
1.1 In a communication system based on an access link of an IRS assisted C-RAN, a user communicates with a BBU pool through an RRH, deploys a plurality of IRS between the user and the RRH, and assists the user in accessing the RRH. There are K single antenna users in the system, there are L RRHs, each RRH has N R A root receiving antenna, M IRSs disposed between the user and RRH, each IRS having N I The RRH compresses the received signal and transmits the compressed signal to the BBU pool through a wired forward link;
1.2 User K, K = 1.. K, sending a signal x to each RRH k And each RRH receives signals sent by users through a direct link and a reflection link of the IRS. RRHl, L = 1.., L, the received signal may be represented as:
Figure BDA0002953635750000021
wherein x = [ x ] 1 ,...,x k ] T x-CN (0, PI) obey 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, M =1,.., M,
Figure BDA0002953635750000024
representing the channel matrix, Θ, from IRS to RRHl m ＝diag(θ m,1 ,...,θ m,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 | θ m,n |＝1,n＝1,...,N I )，
Figure BDA0002953635750000031
Is represented by theta m A block diagonal matrix is formed. n is l ～CN(0,σ 2 I M ) Is additive Gaussian noise of the channel, G l,m Representing the channel noise, I, from the m IRS to the l RRH M Representing an identity matrix of order M, σ 2 Representing the channel additive gaussian noise factor.
1.3 RRH compresses the received signal by point-to-point compression or Wyner-Ziv coding, and then 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 is l ～CN(0,Ω l ) Quantization noise representing RRHl, which obeys a complex Gaussian distribution, Ω l Is 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
represents the direct link channel matrix of all users to all RRHs,
Figure BDA0002953635750000036
the channel matrix representing all IRS to all RRHs,
Figure BDA0002953635750000037
is represented by omega l Forming a block diagonal matrix, I is a representation form of mutual information, I represents a unit matrix, V H Representing the conjugate transpose of V.
1.4 For RRH using point-to-point compression, the fronthaul link compression ratio is less than fronthaul link capacity C l Namely, 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 smallIn forward link capacity, the need to satisfy:
Figure BDA0002953635750000039
wherein C is π(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 specific steps for designing the phase shift matrix of the IRS and the covariance matrix of the compression noise of the fronthaul link are as follows:
2.1 The optimization problem for sum rate maximization can be expressed as:
Figure BDA0002953635750000041
Figure BDA0002953635750000042
Figure BDA0002953635750000043
Figure BDA0002953635750000044
wherein V l ＝H l +G l ΘH r Representing the channel matrix for all users to RRHl.
2.2 ) re-determining the maximum number of iterations T of the joint optimization max And selecting the 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 Fix theta, omega l For W, Σ, E l By performing the update, the following results are obtained:
Figure BDA00029536357500000411
Figure BDA00029536357500000412
2.5 Re-fixing W, sigma and E l To theta, omega l Joint 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
A l ⊙B T Is shown as A l And B T The hadamard product of (a) is,
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, H L Representing the channel matrix of all users to RRHs.
2.6 ) re-judgment
Figure BDA00029536357500000510
Whether the constraint conditions of the step 2.5) are met or not, and if the constraint conditions are 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 of H Is the 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
θ i Independently and uniformly distributed in [0,2 pi ]]) Second through the pair omega l Scaling 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,...,T max 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 then substituted (t-1) ，
Figure BDA00029536357500000519
The objective function brought into the step 2.5) of the current round is also obtained to obtain f (t-1) Compare, 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 R sum To 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 a permissible error range; if it is
Figure BDA0002953635750000066
Judging whether the iteration number exceeds T max If not, T is exceeded max Returning to the step 2.2) to continue iterative optimization; if T is exceeded max Then the final optimization solution is output
Figure BDA0002953635750000067
2.8 For the case of the IRS reflector phase dispersion, Θ is first obtained by 2.1) -2.7) * ,
Figure BDA0002953635750000068
Where the diagonal element theta of theta is m,n Mapping onto points of discrete phase, i.e.:
Figure BDA0002953635750000069
where phi denotes the discrete phase, tau =2 b And b =1,2 denotes a discrete level. Then to
Figure BDA00029536357500000610
Is scaled to obtain
Figure BDA00029536357500000611
So that it satisfies the constraints in step 2.1).
For the design of the Wyner-Ziv coding compression and the covariance matrix of the IRS phase shift matrix and the forward link compression noise, the specific steps 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 that:
Figure BDA00029536357500000617
the higher value of (2) is decompressed first. Re-determining maximum iteration number T of joint optimization max And selecting the initial theta satisfying the condition (0) And
Figure BDA0002953635750000071
3.3 For the optimization problem in step 3.1) can be written in the form:
Figure BDA0002953635750000072
Figure BDA0002953635750000073
Figure BDA0002953635750000074
Figure BDA0002953635750000075
wherein
Figure BDA0002953635750000076
3.4 Fix theta, omega l For the case of W, Σ,
Figure BDA0002953635750000077
by performing the update, the following results are obtained:
Figure BDA0002953635750000078
Figure BDA0002953635750000079
I K representing a K x K identity matrix.
3.5 Re-fixing W, Σ sum
Figure BDA00029536357500000710
For theta, omega l Joint 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 a column vector by a matrix
Figure BDA00029536357500000718
The composition of the diagonal line elements,
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 conditions of the step 3.5) are met or not, and if the constraint conditions are 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
Figure BDA0002953635750000086
θ i Independently and uniformly distributed in [0,2 pi ]]) Second, by pair Ω l Scaling 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,...,T max Representing the number of iterations. 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 then substituted (t-1) ，
Figure BDA0002953635750000088
The objective function brought into the step 3.5) of the current round is also obtained 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 R sum To obtain the sum rate of the iteration
Figure BDA0002953635750000089
From the last iteration
Figure BDA00029536357500000810
Make a comparison if
Figure BDA00029536357500000811
Stopping iteration and determining the optimal result
Figure BDA00029536357500000812
Output optimization solution Θ (t) ,
Figure BDA00029536357500000813
Wherein ^ represents a permissible error range; if it is
Figure BDA00029536357500000814
Then judging whether the iteration number exceeds T max If T is not exceeded max Returning to the step 3.2) to continue iterative optimization; if it exceeds T max Then the final optimization solution is output
Figure BDA00029536357500000815
3.8 For the case of discrete phases of the IRS reflectors, Θ) is first obtained by 3.1) to 3.7) * ,
Figure BDA00029536357500000816
Where the diagonal element theta of theta is m,n Mapping onto points of discrete phase, i.e.:
Figure BDA00029536357500000817
where phi denotes the discrete phase, tau =2 b And b =1,2 denotes a discrete level. Then to
Figure BDA00029536357500000818
Is scaled to obtain
Figure BDA00029536357500000819
So that it satisfies 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 forward link compression noise are subjected to joint optimization. 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 a communication system based on an access link of an IRS assisted C-RAN, a user communicates with a BBU pool through an RRH, deploys a plurality of IRS between the user and the RRH, and assists the user in accessing the RRH. There are K single antenna users in the system, there are L RRHs, each RRH has N R A root receiving antenna, M IRSs disposed between the user and RRH, each IRS having N I A reflection unit. The RRHs compress the received signals and transmit the compressed signals to the BBU pool via the wired forward link.
1.2 User K, K = 1.. K, sending a signal x to each RRH k And each RRH receives signals sent by users through a direct link and a reflection link of the IRS. RRHl, L = 1.., L, the received signal may be represented as:
Figure BDA0002953635750000101
wherein x = [ x ] 1 ,...,x k ] T x-CN (0, PI), obeying a Gaussian distribution.
Figure BDA0002953635750000102
Representing the user-to-RRHl channel matrix,
Figure BDA0002953635750000103
representing the channel matrix of users to IRSm, M = 1.., M,
Figure BDA0002953635750000104
Figure BDA0002953635750000105
representing the channel matrix IRS to RRHl. Theta m ＝diag(θ m,1 ,...,θ m,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 | θ m,n |＝1,n＝1,...,N I )，
Figure BDA0002953635750000107
Is represented by theta m A block diagonal matrix is formed. n is a radical of an alkyl radical l ～CN(0,σ 2 I M ) Is additive gaussian noise of the channel.
1.3 RRH compresses the received signal by point-to-point compression or Wyner-Ziv coding, and then 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 is l ～CN(0,Ω l ) Quantization noise representing the RRHl, which obeys a complex Gaussian distribution, Ω l Is 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 omega l A block diagonal matrix is formed.
1.4 For RRH using point-to-point compression, the fronthaul link compression ratio is less than fronthaul link capacity C l Namely, the following needs are satisfied:
Figure BDA0002953635750000115
1.5 For the case that the RRH adopts Wyner-Ziv coding compression, the compression ratio of the fronthaul link is also smaller than the capacity of the fronthaul link, that is, it needs to satisfy:
Figure BDA0002953635750000116
wherein C is π(l) Indicating the fronthaul link capacity, and pi (l) indicating the decompression order of the received signals at the BBU pool.
2. For point-to-point compression, the transmission mode of a communication system based on an IRS auxiliary C-RAN access link and the optimization method for maximizing sum rate are characterized in that the method for designing the phase shift matrix of the IRS and the covariance matrix of the compression noise of a forward 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 V l ＝H l +G l ΘH r Representing the channel matrix of all users to RRHl.
2.2 ) re-determining the maximum number of iterations T of the joint optimization max And selecting the 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 Fix theta, omega l For W, sigma, E l By performing the update, the following results are obtained:
Figure BDA0002953635750000126
Figure BDA0002953635750000127
2.5 Re-fixing W, sigma and E l To theta, omega l Joint 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
A l ⊙B T Is shown as A l And B T The product of the Hadamard sum of (C),
Figure BDA00029536357500001215
for a column vector by a matrix
Figure BDA00029536357500001216
Is made up of diagonal elements.
Figure BDA00029536357500001217
Figure BDA00029536357500001218
For a column vector by a matrix
Figure BDA00029536357500001219
The diagonal line element of (a) is composed of,
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 conditions of the step 2.5) are met or not, and if the constraint conditions are 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, Λ 1/2 Represents 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
Figure BDA0002953635750000136
θ i Independently and uniformly distributed in [0,2 pi ]]) Second through the pair omega l Scaling 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,...,T max 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 BDA0002953635750000138
The objective function also taken into step 2.5) of the present round is taken 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 Carry the optimized solution of step 2.6) into the sum-rate expression R sum To obtain the sum rate of the 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 T max If T is not exceeded max Returning to the step 2.2) to continue iterative optimization; if T is exceeded max Then the final optimization solution is output
Figure BDA00029536357500001315
2.8 For the case of the IRS reflector phase dispersion, Θ is first obtained by 2.1) -2.7) * ,
Figure BDA00029536357500001316
Wherein the diagonal element theta of theta is divided into m,n Mapping onto points of discrete phase, i.e.:
Figure BDA00029536357500001317
where phi denotes the discrete phase, tau =2 b And b =1,2 denotes a discrete level. Then to
Figure BDA00029536357500001318
Is scaled to obtain
Figure BDA00029536357500001319
So that it meets the constraints in step 2.1).
3. The optimization method for maximizing the sum rate of the transmission mode of the communication system which adopts Wyner-Ziv coding compression and is based on the IRS auxiliary C-RAN access link 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:
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 BBU decompression pools, by judging:
Figure BDA0002953635750000146
the higher value is decompressed first. Re-determining maximum iteration number T of joint optimization max And selecting the initial theta satisfying the condition (0) And
Figure BDA0002953635750000147
3.3 For 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 Fix theta, omega l For the case of W, Σ,
Figure BDA00029536357500001413
by performing the update, the following results are obtained:
Figure BDA00029536357500001415
Figure BDA00029536357500001414
3.5 Re-fixing W, sigma sum
Figure BDA0002953635750000151
For theta, omega l Joint 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 a column vector by a 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 conditions of the step 3.5) are met or not, and if the constraint conditions are met, directly performing characteristic value decomposition:
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
θ i Independently and uniformly distributed in [0,2 pi ]]) Second, by pair Ω l Scaling is carried out to enable the generated optimized solution to meet 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,...,T max 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 BDA00029536357500001520
The objective function brought into step 3.5) of the current round is also taken 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 Carry the optimized solution of step 3.6) into the sum-rate expression R sum To 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 T max If not, T is exceeded max Returning to the step 3.2) to continue iterative optimization; if T is exceeded max Then the final optimization solution is output
Figure BDA0002953635750000168
3.8 For the case of the IRS reflector phase dispersion, Θ is first obtained by 3.1) -3.7) * ,
Figure BDA0002953635750000169
Where the diagonal element theta of theta is m,n Mapping onto points of discrete phase, i.e.:
Figure BDA00029536357500001610
where phi denotes the discrete phase, tau =2 b And b =1,2 denotes a discrete level. 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 (1)

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 access link of an IRS-assisted C-RAN, a user communicates with a base band 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 N R A root receiving antenna, M IRSs disposed between the user and RRH, each IRS having N I A reflection unit; the RRH compresses the received signal and transmits the compressed signal to the BBU pool through a wired forward link;
1.2 K, K) users K, K =1, K, send signals x to the respective RRHs k Each RRH receives signals sent by users through a direct link and a reflection link of the IRS; RRHl, L = 1.., L, the received signal may be represented as:
Figure FDA0003824753780000011
wherein x = [ x ] 1 ,...,x k ] T x-CN (0, PI) obeying Gaussian distribution, P represents user transmission power, and I represents an identity matrix;
Figure FDA0003824753780000012
representing the user-to-RRHl channel matrix,
Figure FDA0003824753780000013
a channel matrix representing users to IRSm, M =1,.., M,
Figure FDA0003824753780000014
representing the channel matrix from IRS to RRHl; theta m ＝diag(θ m,1 ,...,θ m,n ) The phase-shift matrix representing the IRS is a diagonal matrix whose diagonal elements are taken from vectors
Figure FDA0003824753780000015
IRS adjusts only the phase, so | θ m,n |＝1,n＝1,...,N I ，
Figure FDA0003824753780000016
Is represented by theta m A block diagonal matrix is formed; n is l ～CN(0,σ 2 I M ) Additive gaussian noise for the channel; g l,m Representing the channel noise, I, from the m IRS to the l RRH M Representing an identity matrix of order M, σ 2 Representing the channel additive Gaussian noise factor;
1.3 RRH compresses the received signal through point-to-point compression or Wyner-Ziv coding, and then transmits the compressed signal to BBU pool through wired forward link; the quantized signal received at the BBU pool can be expressed as:
Figure FDA0003824753780000021
wherein q is l ～CN(0,Ω l ) Quantization noise representing the RRHl, which obeys a complex Gaussian distribution, Ω l Is its covariance matrix; the sum rate of users to BBU pool can thus be expressed as:
Figure FDA0003824753780000022
wherein
Figure FDA0003824753780000023
Figure FDA0003824753780000029
The channel matrix representing all users to all RRHs,
Figure FDA0003824753780000024
represents the direct link channel matrix of all users to all RRHs,
Figure FDA0003824753780000025
the channel matrix representing all IRS to all RRHs,
Figure FDA00038247537800000210
is represented by omega l A block diagonal matrix of components; i is the representation form of mutual information, I represents an identity matrix, V H Represents the conjugate transpose of V;
1.4 For RRH using point-to-point compression, the fronthaul link compression ratio is less than fronthaul link capacity C l Namely, it is required to satisfy:
Figure FDA0003824753780000026
1.5 For the case that the RRH adopts Wyner-Ziv encoding compression, the compression rate of the fronthaul link is also smaller than the capacity of the fronthaul link, that is, it needs to satisfy:
Figure FDA0003824753780000027
wherein C π(l) Representing the fronthaul link capacity, pi (l) represents the decompression sequence of the received signals in the BBU pool,
Figure FDA0003824753780000028
a decompression sequence set representing the first l-1 received signals;
for the design of the 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 FDA0003824753780000031
Figure FDA0003824753780000032
Figure FDA00038247537800000318
Figure FDA0003824753780000033
wherein V l ＝H l +G l ΘH r Representing the channel matrix from all users to the RRHl;
2.2 ) re-determining the maximum number of iterations T of the joint optimization max And selecting the initial theta satisfying the constraint condition (0) And
Figure FDA0003824753780000034
2.3 The optimization problem for step 2.1) can be converted into the following form:
Figure FDA0003824753780000035
Figure FDA0003824753780000036
Figure FDA0003824753780000037
Figure FDA0003824753780000038
wherein
Figure FDA0003824753780000039
W is the receive matrix, sigma denotes the covariance matrix of the data symbols estimated by the a posteriori criterion, E l An auxiliary variable matrix;
2.4 Fix theta, omega l For W, Σ, E l By performing the update, the following results are obtained:
Figure FDA00038247537800000310
Figure FDA00038247537800000311
2.5 Re-fixing W, sigma and E l To theta, omega l Joint optimization is performed such that the optimization problem can be expressed as:
Figure FDA00038247537800000312
Figure FDA00038247537800000313
Figure FDA00038247537800000314
Figure FDA00038247537800000315
Figure FDA00038247537800000316
Figure FDA00038247537800000317
wherein
Figure FDA0003824753780000041
A l ⊙B T Is shown as A l And B T The product of the Hadamard sum of (C),
Figure FDA0003824753780000042
is the column vector moment of inertiaMatrix of
Figure FDA0003824753780000043
Diagonal element composition of (a);
Figure FDA0003824753780000044
Figure FDA0003824753780000045
for column vectors by matrix
Figure FDA0003824753780000046
The diagonal line element of (a) is composed of,
Figure FDA0003824753780000047
relaxing SDR by semi-positive fixation
Figure FDA0003824753780000048
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 FDA0003824753780000049
representing an optimization solution to the optimization problem in this step; h L A channel matrix representing all users to RRHs;
2.6 ) re-judgment
Figure FDA00038247537800000410
Whether the constraint conditions of the step 2.5) are met or not, and if the constraint conditions are met, directly performing characteristic value decomposition:
Figure FDA00038247537800000411
for the optimized solution of the optimization problem of step 2.5), U is expressed as
Figure FDA00038247537800000412
A matrix of eigenvectors, Λ being
Figure FDA00038247537800000413
Is formed by the eigenvalues of H Is a conjugate transpose of U;
Figure FDA00038247537800000414
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 FDA00038247537800000415
Wherein
Figure FDA00038247537800000416
Unit circles uniformly distributed in the complex plane as independent random variables, followed by a pair of Ω l Scaling 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 FDA00038247537800000417
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 FDA00038247537800000418
The objective function also taken into step 2.5) of the present round is taken 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 R sum To obtain the sum rate of the iteration
Figure FDA0003824753780000051
From the last iteration
Figure FDA0003824753780000052
Make a comparison if
Figure FDA0003824753780000053
Stopping the iteration and determining the optimal result
Figure FDA0003824753780000054
Output optimization solution Θ * ,
Figure FDA00038247537800000518
Wherein ^ represents an allowable error range; if it is
Figure FDA0003824753780000055
Judging whether the iteration number exceeds T max If not, T is exceeded max Returning to the step 2.2) to continue iterative optimization; if T is exceeded max Then the final optimization solution is output
Figure FDA0003824753780000056
2.8 For the case of discrete phases of the IRS reflecting surfaces, this is achieved firstly by 2.1) to 2.7)
Figure FDA0003824753780000057
Wherein the diagonal element theta of theta is divided into m,n Mapping onto points of discrete phase, i.e.:
Figure FDA0003824753780000058
where phi denotes the discrete phase, tau =2 b B =1,2 denotes a discrete level; then to
Figure FDA0003824753780000059
Is scaled to obtain
Figure FDA00038247537800000510
Making it meet the constraint conditions in step 2.1);
for the design of the Wyner-Ziv coding compression, the phase shift matrix of the IRS and the covariance matrix of the compression noise of the fronthaul link are specifically designed as follows:
3.1 And the rate maximization optimization problem can be expressed as:
Figure FDA00038247537800000511
Figure FDA00038247537800000512
Figure FDA00038247537800000513
Figure FDA00038247537800000514
wherein
Figure FDA00038247537800000517
Representing a decompression sequence set, wherein pi (l) represents the I bit of the decompression sequence of the RRH pi (l) arranged in the BBU pool;
3.2 For the sequence of BBU decompression pools, by judging:
Figure FDA00038247537800000516
decompressing the larger value of (1); then determining the maximum iteration number T of the joint optimization max And selecting the initial theta satisfying the condition (0) And
Figure FDA0003824753780000061
3.3 For the optimization problem in step 3.1) can be written in the form:
Figure FDA0003824753780000062
Figure FDA0003824753780000063
Figure FDA0003824753780000064
Figure FDA0003824753780000065
wherein
Figure FDA0003824753780000066
3.4 Fix theta, omega l For is to
Figure FDA00038247537800000623
By performing the update, the following results are obtained:
Figure FDA0003824753780000067
Figure FDA0003824753780000068
I K an identity matrix representing K;
3.5 Re-fixing W, Σ sum
Figure FDA0003824753780000069
To theta, omega l Joint optimization is performed such that the optimization problem can be expressed as:
Figure FDA00038247537800000610
Figure FDA00038247537800000611
Figure FDA00038247537800000612
Figure FDA00038247537800000613
Figure FDA00038247537800000614
Figure FDA00038247537800000615
wherein
Figure FDA00038247537800000616
Figure FDA00038247537800000617
For column vectors by matrix
Figure FDA00038247537800000618
The composition of the diagonal line elements is shown,
Figure FDA00038247537800000619
then relaxing SDR through semipositive definite
Figure FDA00038247537800000620
Removing the constraint condition, and performing iterative optimization on the optimization problem after the SDR is relaxed by a convex optimization toolThe optimal solution can be obtained as follows:
Figure FDA00038247537800000621
optimizing the solution of the problem in the step;
3.6 ) re-judgment
Figure FDA00038247537800000622
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 FDA0003824753780000071
is an optimized solution of the optimization problem in the step 3.5),
Figure FDA0003824753780000072
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 FDA0003824753780000073
Wherein
Figure FDA0003824753780000074
Are independent random variables, are uniformly distributed on a unit circle of a complex plane, and then are subjected to omega pair l Scaling 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 FDA0003824753780000075
t＝1,...,T max 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 then substituted (t-1) ，
Figure FDA0003824753780000076
The objective function brought into step 3.5) of the current round is also taken to obtain f (t-1) Compare, if f (t) ≤f (t-1) Taking the optimization solution of the previous round as the optimization solution of the current round;
3.7 Carry the optimized solution of step 3.6) into the sum-rate expression R sum To obtain the sum rate of the iteration
Figure FDA0003824753780000077
From the last iteration
Figure FDA0003824753780000078
Make a comparison if
Figure FDA0003824753780000079
Stopping iteration and determining the optimal result
Figure FDA00038247537800000710
Output optimization solution theta (t) ,
Figure FDA00038247537800000711
Wherein
Figure FDA00038247537800000712
Indicating an allowable error range; if it is
Figure FDA00038247537800000713
Then judging whether the iteration number exceeds T max If not, T is exceeded max Returning to the step 3.2) to continue iterative optimization; if it exceeds T max Then the final optimization solution is output
Figure FDA00038247537800000714
3.8 For the case of the IRS reflector phase dispersion, Θ is first obtained by 3.1) -3.7) * ,
Figure FDA00038247537800000715
Where the diagonal element theta of theta is m,n Mapping onto points of discrete phase, i.e.:
Figure FDA00038247537800000716
where phi denotes the discrete phase, tau =2 b And b =1,2 denotes a discrete level. Then to
Figure FDA00038247537800000717
Is scaled to obtain
Figure FDA00038247537800000718
So that it satisfies the constraints in step 3.1).
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