CN114745754A - IRS (intelligent resilient System) assisted cloud access network uplink transmission optimization method under non-ideal channel information - Google Patents

IRS (intelligent resilient System) assisted cloud access network uplink transmission optimization method under non-ideal channel information Download PDF

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CN114745754A
CN114745754A CN202210313478.4A CN202210313478A CN114745754A CN 114745754 A CN114745754 A CN 114745754A CN 202210313478 A CN202210313478 A CN 202210313478A CN 114745754 A CN114745754 A CN 114745754A
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irs
matrix
user
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武学璐
张帆
亓洪涛
张昱
彭宏
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Zhejiang University of Technology ZJUT
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W28/00—Network traffic management; Network resource management
    • H04W28/16—Central resource management; Negotiation of resources or communication parameters, e.g. negotiating bandwidth or QoS [Quality of Service]
    • H04W28/18—Negotiating wireless communication parameters
    • H04W28/22—Negotiating communication rate
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
    • H04W16/24—Cell structures
    • H04W16/28—Cell structures using beam steering
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W24/00—Supervisory, monitoring or testing arrangements
    • H04W24/02—Arrangements for optimising operational condition
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W28/00—Network traffic management; Network resource management
    • H04W28/16—Central resource management; Negotiation of resources or communication parameters, e.g. negotiating bandwidth or QoS [Quality of Service]
    • H04W28/18—Negotiating wireless communication parameters
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention discloses an IRS-assisted cloud access network uplink transmission optimization method under non-ideal channel information, which can increase system load and bring higher energy consumption due to the fact that a BBU pool acquires ideal channel information, and can also reduce system gain brought by the IRS. Therefore, the invention considers the problem of establishing the statistical average uplink transmission and the rate maximization of the multi-antenna user in the IRS-assisted C-RAN under the constraint of the capacity of a fronthaul link, the constraint of the IRS phase shift and the constraint of the transmitting power under the condition of non-ideal channel information, and is characterized by the design of the active beam forming of a user end, the passive beam forming of the IRS and the covariance matrix of the fronthaul link compression noise. Aiming at the multi-antenna user uplink transmission system of the IRS-assisted C-RAN under the non-ideal channel information, the uplink transmission and the speed of the system are maximized by jointly optimizing the active beam forming of a user side, the passive beam forming of the IRS and the compression noise of a fronthaul link.

Description

IRS (intelligent resilient System) assisted cloud access network uplink transmission optimization method under non-ideal channel information
Technical Field
The invention relates to the technical field of wireless communication, in particular to a method for optimizing reachable uplink and rate maximization of an uplink transmission system of a multi-antenna user in an Intelligent Reflector (IRS) auxiliary cloud access network (C-RAN) under non-ideal channel information.
Background
With the commercialization of 5G, the continuous development of the internet of things, the industrial internet of things and the mobile internet, the demand of wireless communication services is exponentially increased, the requirement on the effectiveness of a communication transmission system is higher and higher, and the traditional wireless communication system faces various challenges such as system efficiency and construction economy.
A cloud access network (C-RAN) is a wireless communication system that promises to alleviate the current communication needs. The system is different from the traditional communication system, the base band processing unit is transferred from the traditional base station to a base band processing unit (BBU) pool at the cloud end, and the user signal is compressed through a Radio Remote Head (RRH) and then transmitted to the BBU pool through a fronthaul link with limited capacity. However, the communication quality between the user and the RRH is reduced due to the fact that the user in the cell is far away from the RRH or due to the obstruction of the obstacle, which affects the compression of the data by the RRH, thereby increasing the burden of the forward link. Therefore we assist the user in accessing the RRH through Intelligent Reflective Surfaces (IRS). Unlike conventional relays, IRS is a low-cost, passive reflecting plane, each of which integrates a large number of reflecting elements that can independently control the phase and amplitude of an incident electromagnetic wave. Since each reflective element is independently controllable, a passive beam suitable for transmission of the channel is generated by controlling the reflective elements. Therefore, the IRS has the characteristics of easiness in deployment, low cost, low power consumption, capability of effectively improving the performance of a wireless network and the like.
In an actual communication system, a large amount of resources of the communication system need to be consumed for acquiring complete channel information, and the energy consumption of the system is increased in order to balance the effectiveness and the economy of the system, so that the channel information known by the BBU pool is considered to be non-ideal. The method comprises the steps that an IRS assists a multi-antenna user of a C-RAN to access an RRH under non-ideal channel information, the performance of a system can be effectively improved, the RRH in the system receives signals sent by the multi-antenna user through a direct link and a reflection link, the received signals are compressed by a point-to-point (P2P) compression method, the compressed signals are transmitted to a BBU pool through a wired forward link with limited capacity, and the BBU pool recovers original signals through decompression. For the system, under the constraints of capacity of a forward link, IRS phase shift and transmission power, an uplink transmission and rate maximization optimization problem can be established. The optimization problem is characterized by active beam forming of a user side, passive beam forming of the IRS and forward link compression noise, and uplink and rate from the user to the BBU pool are further improved by jointly optimizing the active beam forming of the user side, the passive beam forming of the IRS and the forward link compression noise.
Disclosure of Invention
The invention aims to provide a method for optimizing the neutralization rate maximization of a multi-antenna user uplink transmission system of an IRS-assisted C-RAN under non-ideal channel information. I.e. under fronthaul link capacity constraints, IRS phase shift matrix constraints and transmit power constraints, the active beamforming at the user end, the passive beamforming at the IRS and the fronthaul link compression noise are iteratively optimized to maximize the uplink system transmission and rate.
The technical scheme of the invention is as follows:
an IRS-assisted cloud access network uplink transmission optimization method under non-ideal channel information is characterized in that IRS-assisted C-RAN multi-antenna users under the non-ideal channel information, under the conditions of capacity constraint, IRS phase shift matrix constraint and transmission power constraint of a forward link, the maximum uplink system and speed are taken as optimization problems, a pre-coding matrix of a user end, an IRS phase shift matrix and a covariance matrix of forward link compression noise are jointly optimized, and the method specifically comprises the following steps:
1.1) in the communication system of the multi-antenna user of the IRS-assisted C-RAN under the non-ideal channel information, the multi-antenna user communicates with a BBU pool through an RRH, a plurality of IRSs are deployed between the user and the RRH, and the user is assisted to access the RRH. System for controlling a power supplyThere are K multiple antenna users, each with NUA transmitting antenna having L RRHs, each RRH having NRA root receiving antenna, M IRSs disposed between the user and RRH, each IRS having NIA reflection unit. The RRH compresses the received signal through point-to-point (P2P) compression, and then transmits the compressed signal to the BBU pool through a wired fronthaul link with limited capacity, and the BBU pool recovers the original signal through decompression.
1.2) the user sends pilot frequency, and the BBU pool estimates the channel according to the signal received by the RRH. Therefore, the direct link channel matrix from user k to RRH l and the channel matrix from user k to RRH l via IRS are:
Figure BDA0003569208100000031
Figure BDA0003569208100000032
wherein
Figure BDA0003569208100000033
Representing the estimated channel matrix for users k to RRHl,
Figure BDA0003569208100000034
the channel estimation error matrix representing users k to RRHl obeys a complex normal distribution
Figure BDA0003569208100000035
Figure BDA0003569208100000036
N (N) 1,2, N, which represents the user k and IRSm (M1, 2I) The estimated channel gain of each of the reflecting elements,
Figure BDA0003569208100000037
representing the estimated channel gain of the nth reflective element of IRSm to RRHl.
Figure BDA0003569208100000038
Obeying a complex normal distribution for the user-IRS-RRH cascade channel estimation error
Figure BDA0003569208100000039
1.3) user K, K is 1,., K, the precoding information stream sent to RRHl, L is 1., L is expressed as:
xk＝Fksk
wherein
Figure BDA00035692081000000310
The data stream vector sent for the user follows Gaussian distribution, and the covariance matrix is
Figure BDA00035692081000000311
Figure BDA00035692081000000312
The power constraint is satisfied for the precoding matrix of the transmitting end, i.e. the beamforming of the user end
Figure BDA00035692081000000313
The RRH receives user signals transmitted over the direct link and the reflected link of the IRS. The received signal for RRHl can be expressed as:
Figure BDA00035692081000000314
wherein
Figure BDA0003569208100000041
An estimated channel matrix representing the direct channel from the set of users to the RRHl,
Figure BDA0003569208100000042
a set of all the users is represented,
Figure BDA0003569208100000043
representing the channel estimation error of the direct channel from the set of users to the RRHl.
Figure BDA0003569208100000044
Representing the estimated channel matrices IRSm to RRHl,
Figure BDA0003569208100000045
an estimated channel matrix representing all irs to RRH l,
Figure BDA0003569208100000046
representing the set of all IRS.
Figure BDA0003569208100000047
Representing the concatenated channel estimation error of all users arriving at the RRH via each reflecting element,
Figure BDA0003569208100000048
representing the channel estimation error of the concatenated channel of users k to RRHl.
Figure BDA0003569208100000049
The channel matrix representing user k to all IRSm,
Figure BDA00035692081000000410
a channel matrix representing user k to all irs,
Figure BDA00035692081000000411
a channel matrix representing the set of users to all irs. Phase shift matrix for IRS
Figure BDA00035692081000000412
Is a diagonal matrix whose diagonal elements are taken from vectors
Figure BDA00035692081000000413
(IRS only performs phase adjustment, so | θm,n|＝1)，
Figure BDA00035692081000000414
All the transmitting elements, theta, representing IRSmm,nThe nth reflective element of IRSm.
Figure BDA00035692081000000415
Representing the precoded information streams sent by all users to the RRH,
Figure BDA00035692081000000416
is the pre-coding matrix for all users,
Figure BDA00035692081000000417
representing the information flow sent by all users. Last nlRepresenting additive Gaussian noise, obeying a mean of 0 and a variance of σ2Complex gaussian distribution.
1.4) the RRH transmits the received signal to the BBU pool through point-to-point compression and then through a fronthaul link with limited capacity. The original signal decompressed by the BBU pool recovery can be expressed as:
Figure BDA00035692081000000418
wherein
Figure BDA00035692081000000419
Quantization noise representing RRHl, which obeys a complex Gaussian distribution, ΩlIs its covariance matrix.
1.5) user to BBU pool uplink sum rate can be expressed as:
Figure BDA0003569208100000051
wherein
Figure BDA0003569208100000052
Figure BDA0003569208100000053
Estimating trust for all users' direct connections to all RRHsThe matrix of the tracks is formed by a matrix of tracks,
Figure BDA0003569208100000054
it represents all of the set of RRHs,
Figure BDA0003569208100000055
representing the set of users to all the RRHs linear channel estimation errors.
Figure BDA0003569208100000056
The channel matrix is estimated for all irs to all RRHs,
Figure BDA0003569208100000057
representing the channel estimation error of the concatenated channel of the set of users to all the RRHs.
Figure BDA0003569208100000058
From ΩlAnd a block diagonal matrix is formed and represents the compressed noise covariance matrix of all the RRHs. Further:
Figure BDA0003569208100000059
for convenience of presentation, definitions are provided herein
Figure BDA00035692081000000510
The achievable uplink and rate can therefore be expressed as:
Figure BDA00035692081000000511
wherein
Figure BDA00035692081000000512
1.6) each RRH adopts point-to-point compression, and the compression ratio of a fronthaul link of each RRH is smaller than the capacity C of the fronthaul linklUsing the Jensen inequality, the capacity of the fronthaul link is converted into the following form:
Figure BDA0003569208100000061
wherein
Figure BDA0003569208100000062
Thus the fronthaul capacity constraint is expressed as:
Figure BDA0003569208100000063
further, the method for optimizing the achievable uplink and rate maximization under the capacity constraint, the IRS phase shift constraint and the transmission power constraint of the fronthaul link by the IRS under the nonideal channel information is characterized in that the method for designing the precoding matrix of the user side, 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 uplink transmission and rate maximization can be expressed as:
Figure BDA0003569208100000064
Figure BDA0003569208100000065
Figure BDA0003569208100000066
Figure BDA0003569208100000067
Figure BDA0003569208100000068
2.2) determining associationsOptimized maximum number of iterations TmaxAnd selecting the initial satisfying the constraint condition
Figure BDA0003569208100000069
Θ(0)And
Figure BDA00035692081000000610
2.3) the optimization problem (P1) for step 2.1) can be converted into the following form:
Figure BDA0003569208100000071
Figure BDA0003569208100000072
Figure BDA0003569208100000073
Figure BDA0003569208100000074
Figure BDA0003569208100000075
wherein
Figure BDA0003569208100000076
2.4) iterative optimization, first fixing FkTheta and omegalAnd through
Figure BDA0003569208100000077
For W, Σ and ElAnd (6) updating.
2.5) refixing W, Sigma and ElTo FkTheta and omegalAnd (6) optimizing.
2.5.1) Here, theta and omega are fixedlTo F, forkFor optimization, the optimization problem (P2) can be written as the following sub-optimization problem (P2-1) can be expressed as:
Figure BDA0003569208100000078
Figure BDA0003569208100000079
Figure BDA00035692081000000710
solving the sub-optimization problem (P2-1) by a convex optimization tool (e.g., CVX) yields an optimal solution as:
Figure BDA00035692081000000711
(represents the solution of the neutron optimization problem (P2-1) in this step).
2.5.2) then fixing FkFor theta and omegalPerforming joint optimization, the optimization problem (P2) can be transformed into a sub-optimization problem (P2-2)
Figure BDA0003569208100000081
Figure BDA0003569208100000082
Figure BDA0003569208100000083
Figure BDA0003569208100000084
Figure BDA0003569208100000085
Wherein
Figure BDA0003569208100000086
A⊙BTDenotes A and BTThe product of the Hadamard sum of (C),
Figure BDA0003569208100000087
for column vectors by matrix
Figure BDA0003569208100000088
The composition of the diagonal line elements of (a),
Figure BDA0003569208100000089
Figure BDA00035692081000000810
is a constant term.
Figure BDA00035692081000000811
Figure BDA00035692081000000812
Figure BDA00035692081000000813
For a column vector by a matrix
Figure BDA00035692081000000814
The composition of the diagonal line elements of (a),
Figure BDA00035692081000000815
is a constant term. Ignoring constraints by semi-positive relaxation (SDR)
Figure BDA00035692081000000816
And then solving the optimization problem after the SDR is relaxed by a convex optimization tool, and obtaining an optimized solution as follows:
Figure BDA00035692081000000817
(represents an optimized solution of the neutron optimization problem (P2-2) in this step).
2.6) Re-judgment
Figure BDA00035692081000000818
Whether the constraint condition C1 of the neutron optimization problem (P2-2) in the step 2.5.2) is met or not, and if the constraint condition C1 is met, directly performing eigenvalue decomposition:
Figure BDA00035692081000000819
order to
Figure BDA00035692081000000820
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 C1 of the neutron optimization problem (P2-2) of step 2.5.2) is not satisfied, a plurality of suboptimal solutions are generated by the following method: firstly let
Figure BDA00035692081000000821
Wherein
Figure BDA00035692081000000822
Are independent random variables uniformly distributed on a unit circle of a complex plane (i.e. the unit circle is a
Figure BDA0003569208100000091
θiIndependently and uniformly distributed in [0,2 pi ]]) Second through the pair omegalAnd scaling is carried out, so that the generated optimized solution meets the constraint condition C1 of the neutron optimization problem (P2-2) in the step 2.5.2), and finally, one solution which enables the objective function of the neutron optimization problem (P2-2) in the step 2.5.2) to reach the minimum value is selected as the optimal solution. The optimal solution is finally obtained as: precoding matrix
Figure BDA0003569208100000092
Phase shift matrix theta(t)Covariance matrix of sum compression noise
Figure BDA0003569208100000093
t＝1,...,TmaxThe number of iterations is indicated. Then substituting the optimization solution into the objective function of the sub-optimization problem (P2-2) in the step 2.5.2) to obtain f(t)It means that the optimized solution is substituted into the value of the objective function, and the solution of the last iteration is substituted
Figure BDA0003569208100000094
Θ(t-1)And
Figure BDA0003569208100000095
the objective function of the sub-optimization problem (P2-2) of step 2.5.2) of the current round is also taken into account 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 uplink sum rate expression
Figure BDA0003569208100000096
Obtaining the sum rate of the iteration of the current round
Figure BDA0003569208100000097
And iterated the last round
Figure BDA0003569208100000098
Make a comparison if
Figure BDA0003569208100000099
Stopping iteration and determining the optimal result
Figure BDA00035692081000000910
Output optimization solution
Figure BDA00035692081000000911
Θ*And
Figure BDA00035692081000000912
wherein ^ represents an allowable error range; if it is
Figure BDA00035692081000000913
The number of the re-judgment iterations isWhether or not to exceed TmaxIf not, T is exceededmaxReturning to the step 2.4) to continue iterative optimization; if it exceeds TmaxThen the final optimization solution is output
Figure BDA00035692081000000914
And
Figure BDA00035692081000000915
2.8) for the case of IRS reflecting surface phase dispersion, first obtained by 2.1) to 2.7)
Figure BDA00035692081000000916
Θ*And
Figure BDA00035692081000000917
wherein will theta*Diagonal element of (a)m,nMapping onto points of discrete phase, i.e.:
Figure BDA00035692081000000918
where phi denotes the discrete phase and tau is 2bAnd b is 1,2, representing discrete levels. Then to
Figure BDA00035692081000000919
Is scaled to obtain
Figure BDA00035692081000000920
So that it meets the constraint C1 in step 2.1).
The invention has the following beneficial effects: the invention obviously improves the uplink transmission and the rate of the system by optimizing the pre-coding matrix of the user side, the phase shift matrix of the IRS and the covariance matrix of the compression noise of the fronthaul link for the communication system accessed by the multi-antenna user in the IRS-assisted C-RAN under the non-ideal channel information.
Drawings
Fig. 1 is a schematic diagram of a multi-antenna user system in an intelligent reflector assisted cloud access network under non-ideal channel information;
fig. 2 is an average uplink sum rate of an uplink transmission system of a multi-antenna user in an intelligent reflector assisted cloud access network under non-ideal channel information after the joint optimization method of the present invention is adopted; the graph shows the relation between the average ascending speed and the speed of the system and the number of the reflecting units of a single intelligent reflecting surface; fig. 2 shows the continuous phase, 2bit discrete phase, 1bit discrete phase, random phase and average up-going and rate without intelligent reflecting surface under the condition of point-to-point compression, respectively.
Detailed Description
The IRS assists the transmission process of the communication system accessed by the multi-antenna user in the C-RAN under the non-ideal channel information, and the system model is shown in figure 1. The transmission process comprises the following steps: the RRH receives signals sent by the user through a direct link and a reflection link, compresses the received signals through a point-to-point compression method, and transmits the signals to the BBU pool through a wired fronthaul link with limited capacity. The system and the rate are improved by performing joint optimization on a pre-coding matrix of a user side, a phase shift matrix of an IRS (inter-range radio Access System) and a covariance matrix of forward link compression noise.
The IRS-assisted cloud access network uplink transmission optimization method under the non-ideal channel information comprises the following specific optimization processes:
1.1) in the communication system of the multi-antenna user of the IRS-assisted C-RAN under the non-ideal channel information, the multi-antenna user communicates with a BBU pool through an RRH, a plurality of IRSs are deployed between the user and the RRH, and the user is assisted to access the RRH. In the system, there are K multi-antenna users, each of which has NUA transmitting antenna having L RRHs, each RRH having NRA root receiving antenna, M IRSs disposed between the user and RRH, each IRS having NIA reflection unit. The RRH compresses the received signal through point-to-point (P2P) compression, and then transmits the compressed signal to the BBU pool through a wired fronthaul link with limited capacity, and the BBU pool recovers the original signal through decompression.
1.2) the user sends pilot frequency, and the BBU pool estimates the channel according to the signal received by the RRH. Therefore, the direct link channel matrix from user k to RRH l and the channel matrix from user k to RRH l via IRS are:
Figure BDA0003569208100000111
Figure BDA0003569208100000112
wherein
Figure BDA0003569208100000113
Representing the estimated channel matrix for users k to RRHl,
Figure BDA0003569208100000114
the channel estimation error matrix representing users k to RRHl obeys a complex normal distribution
Figure BDA0003569208100000115
Figure BDA0003569208100000116
N (N) 1,2, N, which represents the user k and IRSm (M1, 2I) The estimated channel gain of each of the reflecting elements,
Figure BDA0003569208100000117
representing the estimated channel gain of the nth reflective element of IRSm to RRHl.
Figure BDA0003569208100000118
Obeying a complex normal distribution for the user-IRS-RRH cascade channel estimation error
Figure BDA0003569208100000119
1.3) user K, K is 1,., K, the precoding information stream sent to RRHl, L is 1., L is expressed as:
xk＝Fksk
wherein
Figure BDA00035692081000001110
For the userThe transmitted data stream vector follows Gaussian distribution, and the covariance matrix is
Figure BDA00035692081000001111
Figure BDA00035692081000001112
The power constraint is satisfied for the precoding matrix of the transmitting end, i.e. the beamforming of the user end
Figure BDA00035692081000001113
The RRH receives user signals transmitted over the direct link and the reflected link of the IRS. The received signal for RRHl can be expressed as:
Figure BDA00035692081000001114
wherein
Figure BDA0003569208100000121
An estimated channel matrix representing the direct channel from the set of users to the RRHl,
Figure BDA0003569208100000122
a set of all the users is represented,
Figure BDA0003569208100000123
representing the channel estimation error of the direct channel from the set of users to the RRHl.
Figure BDA0003569208100000124
Representing the estimated channel matrices IRSm to RRHl,
Figure BDA0003569208100000125
an estimated channel matrix representing all irs to RRH l,
Figure BDA0003569208100000126
representing the set of all IRS.
Figure BDA0003569208100000127
Representing the concatenated channel estimation errors of all users arriving at the RRH via each reflecting element,
Figure BDA0003569208100000128
representing the channel estimation error of the concatenated channel of users k to RRHl.
Figure BDA0003569208100000129
The channel matrix representing user k to all IRSm,
Figure BDA00035692081000001210
a channel matrix representing user k to all irs,
Figure BDA00035692081000001211
a channel matrix representing the set of users to all irs. Phase shift matrix for IRS
Figure BDA00035692081000001212
Is a diagonal matrix whose diagonal elements are taken from vectors
Figure BDA00035692081000001213
(IRS only performs phase adjustment, so | θm,n|＝1)，
Figure BDA00035692081000001214
All the transmitting elements, theta, representing IRSmm,nThe nth reflective element of IRSm.
Figure BDA00035692081000001215
Representing the precoded information streams sent by all users to the RRH,
Figure BDA00035692081000001216
is the pre-coding matrix for all users,
Figure BDA00035692081000001217
representing the information flow sent by all users. Last nlMeans plusGaussian noise, obedience mean 0, variance σ2Complex gaussian distribution.
1.4) the RRH transmits the received signal to the BBU pool through point-to-point compression and then through a fronthaul link with limited capacity. The original signal decompressed by the BBU pool recovery can be expressed as:
Figure BDA00035692081000001218
wherein
Figure BDA00035692081000001219
Quantization noise representing RRHl, which obeys a complex Gaussian distribution, ΩlIs its covariance matrix.
1.5) user to BBU pool uplink sum rate can be expressed as:
Figure BDA0003569208100000131
wherein
Figure BDA0003569208100000132
Figure BDA0003569208100000133
The channel matrix is estimated for all users' direct connections to all RRHs,
Figure BDA0003569208100000134
it represents all of the set of RRHs,
Figure BDA0003569208100000135
representing the set of users to all the RRHs linear channel estimation errors.
Figure BDA0003569208100000136
The channel matrix is estimated for all irs to all RRHs,
Figure BDA0003569208100000137
to representChannel estimation errors for the concatenated channel of the set of users to all the RRHs.
Figure BDA0003569208100000138
From ΩlAnd a block diagonal matrix is formed and represents the compressed noise covariance matrix of all the RRHs. Further:
Figure BDA0003569208100000139
for convenience of presentation, definitions are provided herein
Figure BDA00035692081000001310
The achievable uplink and rate can therefore be expressed as:
Figure BDA00035692081000001311
wherein
Figure BDA00035692081000001312
1.6) each RRH adopts point-to-point compression, and the compression ratio of a fronthaul link of each RRH is smaller than the fronthaul link capacity ClUsing the Jensen inequality, the capacity of the fronthaul link is converted into the following form:
Figure BDA0003569208100000141
wherein
Figure BDA0003569208100000142
Thus the fronthaul capacity constraint is expressed as:
Figure BDA0003569208100000143
2. according to the transmission mode of the uplink communication system of the IRS-assisted C-RAN multi-antenna user under the non-ideal channel information in claim 1, the method for optimizing the achievable uplink sum rate maximization under the constraints of the capacity of the fronthaul link, the phase shift constraint of the IRS, and the transmit power is characterized in that the method for designing the precoding matrix of the user side, the phase shift matrix of the IRS, and the covariance matrix of the compressed noise of the fronthaul link comprises the following specific steps:
2.1) the optimization problem for uplink transmission and rate maximization can be expressed as:
Figure BDA0003569208100000144
Figure BDA0003569208100000145
Figure BDA0003569208100000146
Figure BDA0003569208100000147
Figure BDA0003569208100000148
2.2) determining the maximum iteration number T of the joint optimizationmaxAnd selecting the initial satisfying the constraint condition
Figure BDA0003569208100000149
Θ(0)And
Figure BDA00035692081000001410
2.3) the optimization problem (P1) for step 2.1) can be converted into the following form:
Figure BDA0003569208100000151
Figure BDA0003569208100000152
Figure BDA0003569208100000153
Figure BDA0003569208100000154
Figure BDA0003569208100000155
wherein
Figure BDA0003569208100000156
2.4) iterative optimization, first fixing FkTheta and omegalAnd pass through
Figure BDA0003569208100000157
For W, Σ and ElAnd (6) updating.
2.5) re-fixing W, Σ and ElTo FkTheta and omegalAnd (6) optimizing.
2.5.1) Here first theta, omega is fixedlTo FkTo optimize, the optimization problem (P2) can be written as the following sub-optimization problem (P2-1) can be expressed as:
Figure BDA0003569208100000158
Figure BDA0003569208100000159
Figure BDA00035692081000001510
solving the sub-optimization problem (P2-1) by a convex optimization tool (e.g., CVX) yields an optimal solution:
Figure BDA00035692081000001511
(represents the solution of the neutron optimization problem (P2-1) in this step).
2.5.2) then fixing FkFor theta and omegalPerforming joint optimization, the optimization problem (P2) can be transformed into a sub-optimization problem (P2-2)
Figure BDA0003569208100000161
Figure BDA0003569208100000162
Figure BDA0003569208100000163
Figure BDA0003569208100000164
Figure BDA0003569208100000165
Wherein
Figure BDA0003569208100000166
A⊙BTDenotes A and BTThe product of the Hadamard sum of (C),
Figure BDA0003569208100000167
for column vectors by matrix
Figure BDA0003569208100000168
The composition of the diagonal line elements of (a),
Figure BDA0003569208100000169
Figure BDA00035692081000001610
is a constant term.
Figure BDA00035692081000001611
Figure BDA00035692081000001612
Figure BDA00035692081000001613
For column vectors by matrix
Figure BDA00035692081000001614
The composition of the diagonal line elements of (a),
Figure BDA00035692081000001615
is a constant term. Ignoring constraints by semi-positive relaxation (SDR)
Figure BDA00035692081000001616
And then solving the optimization problem after the SDR is relaxed by a convex optimization tool, and obtaining an optimized solution as follows:
Figure BDA00035692081000001617
(represents an optimized solution of the neutron optimization problem (P2-2) in this step).
2.6) Re-judgment
Figure BDA00035692081000001618
Whether the constraint condition C1 of the neutron optimization problem (P2-2) in the step 2.5.2) is met or not, and if the constraint condition C1 is met, directly performing eigenvalue decomposition:
Figure BDA00035692081000001619
order to
Figure BDA00035692081000001620
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 C1 of the neutron optimization problem (P2-2) of step 2.5.2) is not satisfied, a plurality of suboptimal solutions are generated by the following method: firstly let
Figure BDA00035692081000001621
Wherein
Figure BDA00035692081000001622
Are independent random variables uniformly distributed on a unit circle of a complex plane (i.e. the unit circle is a
Figure BDA0003569208100000171
θiIndependently and uniformly distributed in [0,2 pi ]]) Second through the pair omegalScaling is carried out, so that the generated optimized solution meets the constraint condition C1 of the neutron optimization problem (P2-2) in the step 2.5.2), and finally, the solution which enables the objective function of the neutron optimization problem (P2-2) in the step 2.5.2) to reach the minimum value is selected as the optimal solution. The optimal solution is finally obtained as: precoding matrix
Figure BDA0003569208100000172
Phase shift matrix theta(t)Covariance matrix of sum compression noise
Figure BDA0003569208100000173
t＝1,...,TmaxThe number of iterations is indicated. Then substituting the optimization solution into the objective function of the sub-optimization problem (P2-2) in the step 2.5.2) to obtain f(t)It means that the optimized solution is substituted into the value of the objective function, and the solution of the last iteration is substituted
Figure BDA0003569208100000174
Θ(t-1)And
Figure BDA0003569208100000175
the objective function of the sub-optimization problem (P2-2) of step 2.5.2) of the current round is also taken into account to obtain f(t-1)Comparison is made if f(t)≤f(t-1)Will be the previous roundThe optimization solution is used as the optimization solution of the current round.
2.7) substituting the optimized solution of step 2.6) into the uplink sum rate expression
Figure BDA0003569208100000176
Obtaining the sum rate of the iteration of the current round
Figure BDA0003569208100000177
And iterated over the previous round
Figure BDA0003569208100000178
Make a comparison if
Figure BDA0003569208100000179
Stopping the iteration and determining the optimal result
Figure BDA00035692081000001710
Output optimization solution
Figure BDA00035692081000001711
Θ*And
Figure BDA00035692081000001712
wherein ^ represents an allowable error range; if it is
Figure BDA00035692081000001713
Judging whether the iteration number exceeds TmaxIf not, T is exceededmaxReturning to the step 2.4) to continue iterative optimization; if T is exceededmaxThen the final optimization solution is output
Figure BDA00035692081000001714
And
Figure BDA00035692081000001715
2.8) for the case of IRS reflecting surface phase dispersion, first obtained by 2.1) to 2.7)
Figure BDA00035692081000001716
Θ*And
Figure BDA00035692081000001717
wherein theta will be*Diagonal element of (a)m,nMapping onto points of discrete phase, i.e.:
Figure BDA00035692081000001718
where phi denotes the discrete phase and tau is 2bAnd b is 1,2, representing discrete levels. Then to
Figure BDA00035692081000001719
Is scaled to obtain
Figure BDA00035692081000001720
So that it meets the constraint C1 in step 2.1).
Computer simulation shows that the system uplink transmission and rate of the communication system of the IRS assisted multi-antenna user uplink transmission in the C-RAN under the non-ideal channel information are obviously higher than those of the traditional C-RAN after the joint optimization method of the patent is adopted.

Claims (2)

1. The IRS assisted cloud access network uplink transmission optimization method under the non-ideal channel information is characterized by comprising the following steps: the IRS assists the uplink communication of a multi-antenna user of the C-RAN under irrational channel information, and the active beam forming of the user, the passive beam forming of the IRS and the forward link compression noise are jointly optimized by taking the purpose of maximizing the uplink transmission and the speed of a system, and the method comprises the following steps:
1.1) in a communication system of an IRS-assisted C-RAN multi-antenna user under non-ideal channel information, the multi-antenna user communicates with a baseband processing unit (BBU) pool through a Remote Radio Head (RRH), a plurality of intelligent reflecting surfaces IRS are deployed between the user and the Remote Radio Head (RRH), and the user is assisted to access the Remote Radio Head (RRH); in the system, there are K multi-antenna users, each of which has NUA transmitting antenna having L RRHs, each RRH having NRA root receiving antenna, M IRSs disposed between the user and RRH, each IRS having NIAn inverseA shooting unit; the RRH compresses the received signals through point-to-point compression, and transmits the compressed signals to the BBU pool through a wired fronthaul link with limited capacity, and the BBU pool recovers the original signals through decompression;
1.2) the user sends pilot frequency, and the BBU pool estimates a channel according to the signal received by the RRH; therefore, the direct link channel matrix from user k to RRH l and the channel matrix from user k to RRH l via IRS are:
Figure FDA0003569208090000011
Figure FDA0003569208090000012
wherein
Figure FDA0003569208090000013
Representing the estimated channel matrix for users k to RRHl,
Figure FDA0003569208090000014
the channel estimation error matrix representing users k to RRHl obeys a complex normal distribution
Figure FDA0003569208090000015
Figure FDA0003569208090000016
Indicating channel estimation error
Figure FDA0003569208090000017
The covariance of (a);
Figure FDA0003569208090000018
representing users k and IRSmN (N) of (M1, 2,.., M) is 1, 2.., NI) The estimated channel gain of each of the reflecting elements,
Figure FDA0003569208090000019
represents the estimated channel gain of the nth reflective element of IRSm to RRHl;
Figure FDA00035692080900000110
for cascade channel estimation error of user-IRS-RRH, obeying complex normal distribution
Figure FDA00035692080900000111
1.3) the precoding information stream sent to user K, K1, K, RRHl, L1, L is expressed as: x is the number ofk＝Fksk
Wherein
Figure FDA0003569208090000021
The data stream vector sent for the user follows Gaussian distribution, and the covariance matrix is
Figure FDA0003569208090000022
Figure FDA0003569208090000023
The power constraint is satisfied for the precoding matrix of the transmitting end, i.e. the beamforming of the user end
Figure FDA0003569208090000024
Tr denotes the trace of the matrix, PkRepresents the transmit power of user k;
the RRH receives user signals transmitted through a direct link and a reflection link of the IRS; the received signal for RRHl can be expressed as:
Figure FDA0003569208090000025
wherein
Figure FDA0003569208090000026
An estimated channel matrix representing the direct channel from the set of users to the RRHl,
Figure FDA0003569208090000027
a set of all the users is represented,
Figure FDA0003569208090000028
representing the channel estimation error of the direct channel from the user set to the RRHl;
Figure FDA0003569208090000029
representing the estimated channel matrices IRSm to RRHl,
Figure FDA00035692080900000210
an estimated channel matrix representing all irs to RRH l,
Figure FDA00035692080900000211
represents the set of all IRSs;
Figure FDA00035692080900000212
representing the concatenated channel estimation errors of all users arriving at the RRH via each reflecting element,
Figure FDA00035692080900000213
representing the channel estimation error of the cascade channel from the user k to the RRHl;
Figure FDA00035692080900000214
the channel matrix representing user k to all IRSm,
Figure FDA00035692080900000215
a channel matrix representing user k to all irs,
Figure FDA00035692080900000216
a channel matrix representing a set of users to all IRSs; phase shift matrix for IRS
Figure FDA0003569208090000031
Is a diagonal matrix whose diagonal elements are taken from vectors
Figure FDA0003569208090000032
IRS only performs phase adjustment, therefore | θm,n|＝1，
Figure FDA0003569208090000033
Representation of IRSmAll the transmitting elements of (a) (-)m,nIndicating IRSmTo (1) anA reflective element, m represents a set of fingers
Figure FDA0003569208090000034
Wherein m is also an integer NIThe nth of the plurality of reflective elements;
Figure FDA0003569208090000035
representing the precoded information streams sent by all users to the RRH,
Figure FDA0003569208090000036
is the pre-coding matrix for all users,
Figure FDA0003569208090000037
representing the information flow sent by all users; last nlRepresenting additive Gaussian noise, obeying a mean of 0 and a variance of σ2Complex gaussian distribution of (a);
1.4) the RRH compresses the received signal point to point and transmits the compressed signal to a BBU pool through a fronthaul link with limited capacity; the original signal decompressed by the BBU pool recovery can be expressed as:
Figure FDA0003569208090000038
wherein
Figure FDA0003569208090000039
Representing the quantization noise of RRHl, which obeys a complex gaussian distribution, with Ω 1 being its covariance matrix;
1.5) user to BBU pool uplink sum rate is expressed as:
Figure FDA00035692080900000310
wherein
Figure FDA00035692080900000311
It represents all of the set of RRHs,
Figure FDA00035692080900000312
Figure FDA00035692080900000313
the channel matrix is estimated for all users directly connected to all RRHs,
Figure FDA00035692080900000314
representing the set of users to all RRHs linear channel estimation errors.
Figure FDA0003569208090000041
The channel matrix is estimated for all irs to all RRHs,
Figure FDA0003569208090000042
representing the channel estimation error of the concatenated channel of the user set to all RRHs.
Figure FDA0003569208090000043
From ΩlA block diagonal matrix of components, a covariance matrix representing the compression noise of all the RRHs,
Figure FDA0003569208090000044
is the mathematics periodA hoped representation form, representing the expectation of the matrix;
further:
Figure FDA0003569208090000045
for convenience of presentation, definitions are provided herein
Figure FDA0003569208090000046
The achievable uplink and rate can therefore be expressed as:
Figure FDA0003569208090000047
wherein
Figure FDA0003569208090000048
1.6) each RRH adopts point-to-point compression, and the compression ratio of a fronthaul link of each RRH is smaller than the fronthaul link capacity ClUsing the Jensen inequality, the capacity of the fronthaul link is converted into the following form:
Figure FDA0003569208090000049
wherein
Figure FDA00035692080900000410
Thus the fronthaul capacity constraint is expressed as:
Figure FDA00035692080900000411
2. the method for optimizing uplink transmission of the IRS-assisted cloud access network according to the non-ideal channel information in claim 1, wherein the specific steps for designing the precoding matrix of the ue, the phase shift matrix of the IRS, and the covariance matrix of the compression noise are as follows:
2.1) the optimization problem for uplink transmission and rate maximization can be expressed as:
P1:
Figure FDA0003569208090000051
s.t.C1:
Figure FDA0003569208090000052
C2:
Figure FDA0003569208090000053
C3:
Figure FDA0003569208090000054
C4:
Figure FDA0003569208090000055
2.2) determining the maximum iteration number T of the joint optimizationmaxAnd selecting the initial satisfying the constraint condition
Figure FDA0003569208090000056
Θ(0)And
Figure FDA0003569208090000057
2.3) the optimization problem P1 for step 2.1) is transformed into the following form:
P2:
Figure FDA0003569208090000058
s.t.C1:
Figure FDA0003569208090000059
C2:
Figure FDA00035692080900000510
C3:
Figure FDA00035692080900000511
C4:
Figure FDA00035692080900000512
wherein
Figure FDA00035692080900000513
W is the receive matrix, sigma is the covariance matrix of the data symbols estimated by the a posteriori criterion, ElIs an auxiliary variable;
2.4) iterative optimization, first fixing FkTheta and omegalAnd through
Figure FDA00035692080900000514
For W, Sigma and EelUpdating is carried out;
2.5) re-fixing W, Σ and ElTo FkTheta and omegalOptimizing;
2.5.1) Here first theta, omega is fixedlTo FkTo optimize, optimization problem P2 can be written as the following sub-optimization problem P2-1, expressed as:
P2-1:
Figure FDA0003569208090000061
s.t.C1:
Figure FDA0003569208090000062
C2:
Figure FDA0003569208090000063
solving the sub-optimization problem P2-1 by a convex optimization tool to obtain the optimal solution as follows:
Figure FDA0003569208090000064
represents the solution of the neutron optimization problem P2-1 in the step, and Re represents the real number part;
2.5.2) then fixing FkFor theta and omegalPerforming joint optimization, the optimization problem P2 can be transformed into the following sub-optimization problem P2-2
P2-2:
Figure FDA0003569208090000065
s.t.C1:
Figure FDA0003569208090000066
C2:
Figure FDA0003569208090000067
C3:
Figure FDA0003569208090000068
C4:
Figure FDA0003569208090000069
Wherein
Figure FDA00035692080900000610
A⊙BTDenotes A and BTThe product of the Hadamard sum of (C),
Figure FDA00035692080900000611
for column vectors by matrix
Figure FDA00035692080900000612
The composition of the diagonal line elements of (a),
Figure FDA00035692080900000613
Figure FDA00035692080900000614
is a constant term;
Figure FDA00035692080900000615
Figure FDA00035692080900000616
Figure FDA00035692080900000617
for column vectors by matrix
Figure FDA0003569208090000071
The diagonal line element of (a) is composed of,
Figure FDA0003569208090000072
is a constant term. Ignoring constraints by semi-positive relaxation (SDR)
Figure FDA0003569208090000073
And then solving the optimization problem after the SDR is relaxed by a convex optimization tool, and obtaining an optimized solution as follows:
Figure FDA0003569208090000074
represents the optimized solution of the neutron optimization problem P2-2 in the step;
2.6) Re-judgment
Figure FDA0003569208090000075
Whether the constraint condition C1 of the neutron optimization problem P2-2 in the step 2.5.2) is met or not, and if the constraint condition C1 is met, directly performing characteristic value decomposition:
Figure FDA0003569208090000076
order to
Figure FDA0003569208090000077
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 condition C1 of the neutron optimization problem P2-2 in the step 2.5.2) is not met, a plurality of suboptimal solutions are generated by the following method: firstly let
Figure FDA0003569208090000078
Wherein
Figure FDA0003569208090000079
Are independent random variables uniformly distributed on a unit circle of a complex plane (i.e. the unit circle is a
Figure FDA00035692080900000710
θiIndependently and uniformly distributed in [0,2 pi ]]) Second through the pair omegalScaling is carried out, so that the generated optimized solution meets the constraint condition C1 of the neutron optimization problem P2-2 in the step 2.5.2), and finally, the solution which enables the objective function of the neutron optimization problem P2-2 in the step 2.5.2) to reach the minimum value is selected as the optimal solution. Finally, the optimal solution is obtained as follows: precoding matrix
Figure FDA00035692080900000711
Phase shift matrix theta(t)Covariance matrix of sum compression noise
Figure FDA00035692080900000712
t＝1,...,TmaxRepresenting the number of iterations; then substituting the optimization solution into the objective function of the sub-optimization problem P2-2 of the step 2.5.2) to obtain f(t)The optimized solution is substituted into the value of the objective function, and the solution of the last iteration is substituted
Figure FDA00035692080900000713
Θ(t-1)And
Figure FDA00035692080900000714
the objective function of the sub-optimization problem P2-2 of step 2.5.2) of the current round is also taken into account 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 uplink sum rate expression
Figure FDA00035692080900000715
Obtaining the sum rate of the iteration of the current round
Figure FDA00035692080900000716
And iterated the last round
Figure FDA00035692080900000717
Make a comparison if
Figure FDA00035692080900000718
Stopping the iteration and determining the optimal result
Figure FDA00035692080900000719
Output optimization solution
Figure FDA00035692080900000720
Θ*And
Figure FDA00035692080900000721
wherein
Figure FDA00035692080900000722
Indicating an allowable error range; if it is
Figure FDA00035692080900000723
Judging whether the iteration number exceeds TmaxIf not, T is exceededmaxReturning to the step 2.4) to continue iterative optimization; if T is exceededmaxThen the final optimization solution is output
Figure FDA0003569208090000081
Figure FDA0003569208090000088
And
Figure FDA0003569208090000082
2.8) for the case of IRS reflecting surface phase dispersion, first obtained by 2.1) to 2.7)
Figure FDA0003569208090000083
Θ*And
Figure FDA0003569208090000084
wherein will theta*Diagonal element of (a)m,nMapping onto points of discrete phase, i.e.:
Figure FDA0003569208090000085
where phi denotes the discrete phase and tau is 2bAnd b is 1,2. represents discrete levels; then to
Figure FDA0003569208090000086
Is scaled to obtain
Figure FDA0003569208090000087
So that it satisfies the constraint C1 in step 2.1).
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