CN114389658B - Uplink power optimization method for zero-forcing reception cellular-removing large-scale MIMO system - Google Patents

Uplink power optimization method for zero-forcing reception cellular-removing large-scale MIMO system Download PDF

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CN114389658B
CN114389658B CN202111660404.XA CN202111660404A CN114389658B CN 114389658 B CN114389658 B CN 114389658B CN 202111660404 A CN202111660404 A CN 202111660404A CN 114389658 B CN114389658 B CN 114389658B
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CN114389658A (en
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杨龙祥
李欢
张尧
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Nanjing University of Posts and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/06—TPC algorithms
    • H04W52/14—Separate analysis of uplink or downlink
    • H04W52/146—Uplink power control
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/30—TPC using constraints in the total amount of available transmission power
    • H04W52/34—TPC management, i.e. sharing limited amount of power among users or channels or data types, e.g. cell loading
    • H04W52/346—TPC management, i.e. sharing limited amount of power among users or channels or data types, e.g. cell loading distributing total power among users or channels
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention discloses an uplink power optimization method of a honeycomb-removing large-scale multiple-output (MIMO) system based on zero forcing reception, which comprises the following core steps: on the premise of meeting the quality-of-service (QoS) and maximum transmitting power limit of each user, the uplink capacity of the whole system is optimized, the power of a target signal is increased, the power of part of interference signals is reduced, meanwhile, the complexity of the method is considered, and the calculation time and the consumption of calculation resources are reduced. The optimization method utilizes the relaxation variables and decoupling deformation, and utilizes partial Lagrangian functions to process constraint conditions and objective functions, so that the whole optimization problem is converted into a convex optimization problem, and the iterative closed expression of each variable is pushed, so that the solution efficiency is higher than that of the prior convex approximation mode, and meanwhile, the capacity of an uplink system can be remarkably improved. The invention can be used for improving the power utilization efficiency, improving the target signal power and reducing the partial interference signal power.

Description

Uplink power optimization method for zero-forcing reception cellular-removing large-scale MIMO system
Technical Field
The invention belongs to the technical field of mobile communication, and particularly relates to an uplink power optimization method of a zero-forcing receiving honeycomb-removing large-scale MIMO system.
Background
The de-cellular large-scale multiple-input multiple-output (MIMO) realizes distributed large-scale MIMO by taking a user as a center, and cell division in an original cellular network solves the contradiction between communication rate and coverage area in a traditional cellular communication network, avoids the problem of frequent cell switching in the cellular network, and further improves service quality and coverage area, so that the MIMO becomes one of core technologies of post 5G and 6G.
In the existing declustering MIMO system, because the user quantity is often larger than the pilot frequency quantity, the interference among users exists, and the further improvement of the system performance is limited, so that the communication power distribution of each AP (access point) needs to be optimized, and the aim of further improving the overall capacity of the system is achieved.
Disclosure of Invention
The invention aims to: aiming at the problems, the invention provides an uplink power optimization method of a zero-forcing receiving honeycomb-removing large-scale MIMO system, which utilizes power distribution optimization from an AP to each user to reduce interference among a part of users and improve the power consumption required to achieve the purpose of improving the total capacity of the system.
The technical scheme is as follows: in order to achieve the purpose of the invention, the technical scheme adopted by the invention is as follows: an uplink power optimization method of a zero-forcing receiving honeycomb-removing large-scale MIMO system specifically comprises the following steps:
step 1, constructing an uplink system model of a zero-forcing received honeycomb-removing large-scale MIMO system;
step 2, calculating a closed expression of the uplink reachable rate of the user under zero forcing reception based on an uplink system model, and establishing an optimization problem model of system power;
step 3, introducing a relaxation variable to reconstruct the optimization problem model of the system power constructed in the step 2, and improving an objective function and constraint conditions in the model;
step 4, processing the improved objective function and constraint conditions by using the Lagrangian function, and further reconstructing the improved objective function and constraint conditions into a new optimization problem model;
and step 5, decoupling deformation is carried out on the new optimization problem model, the new optimization problem model is converted into a convex optimization problem of multiple variables, and the model is solved through an iterative algorithm, so that an uplink power distribution optimization scheme of the system is obtained.
Further, the method of step 1 is specifically as follows:
the de-cellular massive MIMO system comprises M APs and K single-antenna users, wherein each AP is configured with N antennas, and M multiplied by N>>K, performing K; wherein m is E [1, M]Represents the number of AP, k E [1, K ]]A number indicating the user; AP (Access Point) m Channel model g with user k mk The expression is as follows:
Figure BDA0003449401880000021
in AP m Represents the mth AP, beta mk Representing AP m Large scale fading coefficient, h, with user k mk Representing AP m The small-scale fading vector is arranged between the user k and the user k, and the elements of the small-scale fading vector are independently and uniformly distributed in complex Gaussian distribution with the mean value of 0 and the variance of 1, namely h mk CN (0, 1), g mk ～CN(0,β mk I N )，I N Is an N-dimensional identity matrix;
AP m receiving pilot signals Y sent by all users mp The method comprises the following steps:
Y mp ＝G m P 1/2 φ H +W mp (2)
wherein G is m ＝[g m1 ,g m2 ,...,g mK ]～C N×K ，C N×K Is a complex matrix of N x K, P 1/2 For the transmit power allocation matrix, phi is the pilot matrix,
Figure BDA0003449401880000022
its element->
Figure BDA0003449401880000023
The pilot assigned to user k for the system,
Figure BDA0003449401880000024
W mp is additive white Gaussian noise, W mp ～C N×τ τ is the pilot length;
based on minimum mean square error criterion, AP m Channel estimation with user k
Figure BDA0003449401880000025
The method comprises the following steps:
Figure BDA0003449401880000026
wherein ρ is p For a standardized signal-to-noise ratio of pilot transmission,
Figure BDA0003449401880000027
Figure BDA0003449401880000028
pilot allocated to user i for the system, +.>
Figure BDA0003449401880000029
The channel estimation error is
Figure BDA00034494018800000210
And->
Figure BDA00034494018800000211
Further, the calculating the closed expression of the uplink reachable rate of the user under zero forcing receiving in the step 2 specifically includes the following steps:
step 2.1, all users send data to the AP, and the data vector sent by the user k is set as s k The power satisfies E { |s k | 2 }＝1，AP m Received signal y m Expressed as:
Figure BDA0003449401880000031
wherein ρ is u G is the normalized signal to noise ratio of the signal mk Is AP m Channel model with user k, η k Is AP m For the power control coefficient of user k, 0.ltoreq.eta k ≤1，w m Is AP m Additive white gaussian noise of the channel;
the AP transmits the received signal to the CPU through the back link, the zero forcing receiver decodes the received signal, the receiving matrix of the zero forcing receiver is that
Figure BDA0003449401880000032
Wherein (1)>
Figure BDA0003449401880000033
Representation->
Figure BDA0003449401880000034
Is a transpose of (2); defining the received vector of user k as a k Specifically, it isReceiving matrix A epsilon C MN×K Is the zero-forcing received signal of user k +.>
Figure BDA0003449401880000035
The expression of (2) is:
Figure BDA0003449401880000036
in the method, in the process of the invention,
Figure BDA0003449401880000037
is inter-user interference, η, caused by channel estimation errors i Is AP m For the power control coefficient of user i, 0.ltoreq.eta i ≤1，s i Data vector sent for user i, +.>
Figure BDA0003449401880000038
For the channel estimation error of user i, the superscript H denotes the conjugate transpose of the matrix, +.>
Figure BDA0003449401880000039
Is channel noise interference;
for zero-forcing receivers, the uplink signal-to-interference-and-noise ratio of user k
Figure BDA00034494018800000310
The expression is: />
Figure BDA00034494018800000311
Wherein a is mk Representing AP m Zero forcing reception vector for user k; [ a ] mk ] n Representation a mk Is the nth element of (2);
setting up
Figure BDA00034494018800000312
Based on the Jensen inequality, a closed expression of the up-link achievable rate of user k is obtained by using an approximation method>
Figure BDA00034494018800000313
The method comprises the following steps:
Figure BDA00034494018800000314
in the method, when the system interference is maximum
Figure BDA0003449401880000041
Figure BDA0003449401880000042
Further, the optimization problem model of the system power in the step 2 is expressed as follows:
Figure BDA0003449401880000043
Figure BDA0003449401880000044
Figure BDA0003449401880000045
in the method, in the process of the invention,
Figure BDA0003449401880000046
requiring the communication rate for user k.
Further, the method of step 3 is specifically as follows:
introducing a relaxation variable ζ k Reconstructing an optimization problem model of the system power as:
Figure BDA0003449401880000047
Figure BDA0003449401880000048
Figure BDA0003449401880000049
Figure BDA00034494018800000410
wherein, when P 2 When the optimal solution is reached, the method comprises the steps of,
Figure BDA00034494018800000411
/>
further, the method of step 4 is specifically as follows:
processing the reconstructed optimization problem model by using the Lagrange function, and combining the formula (9 a) and the formula (9 b) to obtain a Lagrange function L containing partial constraint, wherein the Lagrange function L containing partial constraint is expressed as follows:
Figure BDA0003449401880000051
wherein eta, zeta and lambda respectively represent a power control factor, a relaxation variable and a Lagrange auxiliary variable; lambda (lambda) k A relaxation factor that is the kth constraint;
the optimization problem model of the system power is composed of P 2 Reconstructed as P 3 ：
Figure BDA0003449401880000052
Figure BDA0003449401880000053
Figure BDA0003449401880000054
Wherein P is 3 The method comprises two layers of optimization problems, namely an inner layer optimization problem and an outer layer optimization problem;
the inner layer optimization problem is as follows:
Figure BDA0003449401880000055
when the optimal solution is reached, ζ k Is standing point, get
Figure BDA0003449401880000056
At this time P 3 The optimal solution is taken out and the method comprises the steps of,
Figure BDA0003449401880000057
the optimization problem model of the system power is defined by P 3 Reconstruction into a new optimization problem model P 4 ：
Figure BDA0003449401880000058
Figure BDA0003449401880000059
Figure BDA00034494018800000510
Further, the decoupling deformation of the new optimization problem model in step 5 is converted into a convex optimization problem with multiple variables, and the method is as follows:
introducing the auxiliary variable y k And (3) decoupling and deforming the new optimization problem model in the step (4) to obtain:
Figure BDA0003449401880000061
when the system takes the optimal solution,
Figure BDA0003449401880000062
then for the optimal solution
Figure BDA0003449401880000063
The method comprises the following steps:
Figure BDA0003449401880000064
Figure BDA0003449401880000065
in the method, in the process of the invention,
Figure BDA0003449401880000066
at this point, the new optimization problem model is transformed into a model for the variable ζ k 、η k 、y k And obtaining all the variable iteration closed expression.
Further, in step 5, the model solution is performed by an iterative algorithm to obtain an uplink power allocation optimization scheme of the system, and the method is as follows:
step 5.1, initializing: let iteration number t=0, define convergence tolerance epsilon and maximum iteration number T, initialize feasible point eta k (t) 、ξ k (t) K=1,..k, where feasible point η k (t) And xi k (t) The feasibility of (a) may be determined by equation (12 b) and equation (12 c);
step 5.2, η is defined k (t) 、ξ k (t) Substituting formula (14) to obtain y k (t+1) ；
Step 5.3, η is defined k (t) Substituting formula (16) to obtain xi k (t+1) ；
Step 5.4, the currently obtained y k (t+1) 、ξ k (t+1) Substituting formula (15) to obtain eta k (t+1) And iteratively processing the boundary using newton-seidel, equation (12 b);
step 5.5, y is obtained k (t+1) 、ξ k (t+1) And eta k (t+1) Substituting formula (13) to obtain L (t+1) ；
Step 5.6, let t=t+1, judge T is not less than T or L (t+1) -L (t) |<Whether epsilon is true or not, if any one of epsilon and epsilon is true, obtaining an uplink power allocation optimization scheme eta of the system k (t+1) The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, returning to the step 5.2.
The beneficial effects are that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
the invention provides an uplink power optimization method of a zero-forcing receiving honeycomb-removing large-scale MIMO system, which optimizes the overall uplink capacity of the system, increases the power of a target signal, reduces the power of part of interference signals, considers the complexity of the method, and reduces the calculation time and the consumption of calculation resources on the premise of meeting the service quality requirement and the maximum transmission power limit of each user. The optimization method can obviously improve the capacity of the uplink system.
Drawings
FIG. 1 is a flow chart of an uplink power optimization method for a cellular massive MIMO system according to one embodiment;
FIG. 2 is a diagram illustrating an example of a cellular massive MIMO system architecture according to one embodiment;
fig. 3 is an uplink reception diagram of an AP under an embodiment;
FIG. 4 is a graph comparing the optimization results of the method of the present invention with those of the prior art, under an embodiment;
FIG. 5 is a graph showing the comparison of the calculated time of the method of the present invention with the prior art method, under an embodiment.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings and examples.
The invention relates to an uplink power optimization method of a zero-forcing receiving honeycomb-removing large-scale MIMO system, which concretely comprises the following steps with reference to FIG. 1:
(1) Constructing an uplink system model in a honeycomb-removed large-scale MIMO system received by ZF;
(2) Deducing a closed expression of the uplink rate of each user under ZF reception, and establishing a system power optimization problem model;
(3) Introducing a relaxation variable to reconstruct an objective function and constraint conditions;
(4) Deriving a partial Lagrangian function, and combining partial constraint conditions with the objective function;
(5) Decoupling deformation is carried out on the new objective function, the new objective function is converted into a convex optimization problem of multiple variables, and an iteration closed expression of each variable is solved;
(6) And solving the obtained optimization problem through iteration.
In the communication network, the system model is as follows:
in a de-cellular massive MIMO system, the entire communication system contains M APs, each AP is configured with N antennas, the system serves K single antenna users, where MN > K, and the channel model between APm and user K is:
Figure BDA0003449401880000081
wherein beta is mk For a large scale fading coefficient, h, between APm and user k mk Is a small-scale fading vector, wherein each element obeys a complex gaussian distribution with a mean value of 0 and a variance of 1, so
g mk ～CN(0,β mk I N ) (2)
Wherein I is N Is an N-dimensional identity matrix. The pilot signal received at the APm is
Y mp ＝G m P 1/2 φ H +W mp (3)
Wherein G is m ＝[g m1 ,g m2 ,...,g mK ]～C N×K ，C N×K Is a complex matrix of N x K, P 1/2 For the transmit power allocation matrix, phi is the pilot matrix,
Figure BDA0003449401880000082
its element->
Figure BDA0003449401880000083
The pilot assigned to user k for the system,
Figure BDA0003449401880000084
k∈[1,K]；W mp is additive white Gaussian noise, W mp ～C N×τ τ is the pilot length; using minimum mean square error estimation (MMSE), the channel estimate between APm and user k is:
Figure BDA0003449401880000085
/>
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003449401880000086
the estimation error is +.>
Figure BDA0003449401880000087
And have->
Figure BDA0003449401880000088
In the system model, a closed expression of the uplink user achievable rate received by the ZF is further deduced, and specifically comprises:
in the uplink data transmission process, all users send data to each AP, wherein the data vector sent by the user k is s k Its power satisfies E { |s k | 2 The signal received by apm is } =1:
Figure BDA0003449401880000089
wherein ρ is u Is the normalized signal-to-noise ratio of the signal, which is 0.ltoreq.eta k Less than or equal to 1 is the power control coefficient of APm to user k, w m Additive white gaussian noise for APm channel. Collecting all received signals in CPU through a return link, and defining the received vector of user k as a k For receiving matrix A e C MN×K Can obtain the received signal of user k as:
Figure BDA0003449401880000091
for a ZF receiver, its receiving matrix is
Figure BDA0003449401880000092
Wherein->
Figure BDA0003449401880000093
Substituting A into (6) to obtain the zero forcing receiving result of the user k as follows:
Figure BDA0003449401880000094
wherein the method comprises the steps of
Figure BDA0003449401880000095
Inter-user interference caused by channel estimation error, < >>
Figure BDA0003449401880000096
Is channel noise. Thus, for a ZF receiver, the uplink signal-to-interference-and-noise ratio for user k is available as:
Figure BDA0003449401880000097
wherein [ a ] mk ] n Representation a mk Using the Jensen inequality and considering the worst case, i.e., the maximum system interference, the uplink achievable rate expression for user k is:
Figure BDA0003449401880000098
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003449401880000099
the maximum interference condition is obtained; omega (k) is:
Figure BDA00034494018800000910
wherein the method comprises the steps of
Figure BDA00034494018800000911
/>
Therefore, on the premise of meeting the requirement of optimizing the communication rate of each user, the power optimization problem model of the total uplink rate of the system is as follows:
Figure BDA0003449401880000101
Figure BDA0003449401880000102
Figure BDA0003449401880000103
further, since (11) is a non-convex optimization problem, it is difficult to directly solve, so a relaxation variable ζ is introduced k Reconstructing the optimization problem as:
Figure BDA0003449401880000104
Figure BDA0003449401880000105
Figure BDA0003449401880000106
Figure BDA0003449401880000107
wherein (12 b) is a complementary relaxation introduction, when P 2 When the optimal solution is reached, there are:
Figure BDA0003449401880000108
for (12 c), there are two processing methods: 1) According to the nature of the relaxation variables, it can be equivalently
Figure BDA0003449401880000109
Considered as being for relaxation variable ζ k Is a constraint of (a). 2) For the original solution problem, the constraint can be regarded as a second order cone constraint, i.e
Figure BDA00034494018800001010
Wherein->
Figure BDA00034494018800001011
Is a convex constraint problem. Since the method in 1) can be regarded as a variable ζ to relaxation k The feasible domain constraint of (2) is processed by the method, and the constraint is required to be solved iteratively by using a Newton-Seidel (Gauss-Seidel) method because the constraint is solved iteratively by using a sequential iteration method.
Since (12 b) is a non-convex constraint, combining (12 b) with the objective function (12 a) by a Lagrange function, the resulting partially constrained Lagrange function is:
Figure BDA0003449401880000111
thus, P 2 The method comprises the following steps of:
Figure BDA0003449401880000112
/>
Figure BDA0003449401880000113
Figure BDA0003449401880000114
wherein P is 3 Can be regarded as a two-layer optimization problem, for the inner layer optimization problem, namely
Figure BDA0003449401880000115
When the optimal solution is reached, ζ k Reaching standing point, i.e.)>
Figure BDA0003449401880000119
The method can obtain:
Figure BDA0003449401880000116
substituting (13) into (16) to obtain P 3 When the optimal solution is taken:
Figure BDA0003449401880000117
substituting (17) into P 3 The original optimization problem becomes:
Figure BDA0003449401880000118
s.t.(15b),(15c)
for (18 a), to solve the variable iteration closed expression, performing secondary decoupling treatment on the variable iteration closed expression to obtain:
Figure BDA0003449401880000121
wherein, when:
Figure BDA0003449401880000122
(19) Equivalent to the original objective function (18 a), i.e. when the system takes the optimal solution (satisfies
Figure BDA0003449401880000123
)，y k Equal to the above formula. For the overall optimal solution (ζ) k * ,η k * ,y k * ) Satisfies the condition that
Figure BDA0003449401880000124
Thus, it is possible to obtain:
Figure BDA0003449401880000125
/>
Figure BDA0003449401880000126
thus, the optimization problem can be solved iteratively, as follows:
Figure BDA0003449401880000127
Figure BDA0003449401880000131
referring to FIG. 2, an example of a system scenario employed in one embodiment is 1km 2 Within the range, 60 APs are randomly distributed and all APs serve 20 users in TDD mode, where the large scale fading model is:
Figure BDA0003449401880000132
wherein PL is mk Is the path loss intermediate AP m and user k,
Figure BDA0003449401880000133
is shadow fading, sigma sh The standard deviation is 8dB. Path loss PL mk And (5) calculating and obtaining through a three-section model. Each AP is connected to the CPU by a backhaul link for channel estimation and signal processing.
Referring to fig. 3, in the uplink transmission, each AP is equipped with 6 antennas, and the served user is a single antenna device. The default non-optimized power allocation scheme is to evenly allocate for all users, i.e. the power control coefficient is eta k ＝1，
Figure BDA0003449401880000134
The system bandwidth is set to 200MHz.
Referring to fig. 4, after power optimization, the overall uplink capacity of the system can be improved by about 23.02% compared with the equal power distribution (different results can be obtained according to various parameters such as the actual bandwidth of the system, fading, random distribution of users and the like and different tolerances); wherein the difference of the final optimization rates of the different optimization methods is related to the initial value and the tolerance, and the methods ensure convergence at the stationary point.
Referring to fig. 5, the optimization method has lower complexity in terms of operation speed, and can greatly reduce processing delay caused by power optimization and improve response speed of the communication system (operation results are different according to difference of computing capacities).

Claims (1)

1. The uplink power optimization method of the zero-forcing receiving honeycomb-removing large-scale MIMO system is characterized by comprising the following steps:
step 1, constructing an uplink system model of a zero-forcing received honeycomb-removing large-scale MIMO system;
step 2, calculating a closed expression of the uplink reachable rate of the user under zero forcing reception based on an uplink system model, and establishing an optimization problem model of system power;
step 3, introducing a relaxation variable to reconstruct the optimization problem model of the system power constructed in the step 2, and improving an objective function and constraint conditions in the model;
step 4, processing the improved objective function and constraint conditions by using the Lagrangian function, and further reconstructing the improved objective function and constraint conditions into a new optimization problem model;
step 5, decoupling deformation is carried out on the new optimization problem model, the new optimization problem model is converted into a convex optimization problem of multiple variables, and model solving is carried out through an iterative algorithm, so that an uplink power allocation optimization scheme of the system is obtained;
the method of the step 1 comprises the following specific steps:
the de-cellular massive MIMO system comprises M APs and K single-antenna users, wherein each AP is configured with N antennas, and M multiplied by N > K; wherein m is E [1, M]Represents the number of AP, k E [1, K ]]A number indicating the user; AP (Access Point) m Channel model g with user k mk The expression is as follows:
Figure FDA0004178602130000011
in AP m Represents the mth AP, beta mk Representing AP m Large scale fading coefficient, h, with user k mk Representing AP m The element of the small-scale fading vector between the user k and the small-scale fading vector is independently and uniformly distributed in complex Gaussian distribution with mean value of 0 and variance of 1, namely h mk CN (0, 1), g mk ～CN(0,β mk I N )，I N Is an N-dimensional identity matrix;
AP m receiving pilot signals Y sent by all users mp The method comprises the following steps:
Y mp ＝G m P 1/2 φ H +W mp (2)
wherein G is m ＝[g m1 ,g m2 ,...,g mK ]～C N×K ，C N×K Complex matrix of N x K，P 1/2 For the transmit power allocation matrix, phi is the pilot matrix,
Figure FDA0004178602130000012
its element->
Figure FDA0004178602130000013
Pilot allocated to user k for the system, +.>
Figure FDA0004178602130000014
k∈[1,K]；W mp Is additive white Gaussian noise, W mp ～C N×τ τ is the pilot length;
based on minimum mean square error criterion, AP m Channel estimation with user k
Figure FDA0004178602130000015
The method comprises the following steps:
Figure FDA0004178602130000021
wherein ρ is p For a standardized signal-to-noise ratio of pilot transmission,
Figure FDA0004178602130000022
Figure FDA0004178602130000023
pilot allocated to user i for the system, +.>
Figure FDA0004178602130000024
The channel estimation error is g mk ＝g mk -g mk And (2) and
Figure FDA0004178602130000025
and step 2, calculating a closed expression of the uplink reachable rate of the user under zero forcing receiving, which specifically comprises the following steps:
step 2.1, all users send data to the AP, and the data vector sent by the user k is set as s k The power satisfies E { |s k | 2 }＝1，AP m Received signal y m Expressed as:
Figure FDA0004178602130000026
wherein ρ is u G is the normalized signal to noise ratio of the signal mk Is AP m Channel model with user k, η k Is AP m For the power control coefficient of user k, 0.ltoreq.eta k ≤1，w m Is AP m Additive white gaussian noise of the channel;
the AP transmits the received signal to the CPU through the back link, the zero forcing receiver decodes the received signal, the receiving matrix of the zero forcing receiver is that
Figure FDA0004178602130000027
Wherein (1)>
Figure FDA0004178602130000028
Figure FDA0004178602130000029
Representation->
Figure FDA00041786021300000210
Is a transpose of (2); defining the received vector of user k as a k Specifically, the receiving matrix A epsilon C MN×K Is the zero-forcing received signal of user k +.>
Figure FDA00041786021300000211
The expression of (2) is:
Figure FDA00041786021300000212
in the method, in the process of the invention,
Figure FDA00041786021300000213
is inter-user interference, η, caused by channel estimation errors i Is AP m For the power control coefficient of user i, 0.ltoreq.eta i ≤1，s i Data vector g sent for user i i For the channel estimation error of user i, the superscript H denotes the conjugate transpose of the matrix, +.>
Figure FDA00041786021300000214
Is channel noise interference;
for zero-forcing receivers, the uplink signal-to-interference-and-noise ratio of user k
Figure FDA00041786021300000215
The expression is:
Figure FDA0004178602130000031
wherein a is mk Representing AP m Zero forcing reception vector for user k; [ a ] mk ] n Representation a mk Is the nth element of (2);
setting up
Figure FDA0004178602130000032
Based on Jensen inequality, a closed expression R of the uplink reachable rate of the user k is obtained by using an approximation method k ZF The method comprises the following steps:
Figure FDA0004178602130000033
in the method, when the system interference is maximum
Figure FDA0004178602130000034
Figure FDA0004178602130000035
m∈[1,M]；
The optimization problem model of the system power in the step 2 is expressed as follows:
P 1 :
Figure FDA0004178602130000036
Figure FDA0004178602130000037
Figure FDA0004178602130000038
in the method, in the process of the invention,
Figure FDA0004178602130000039
a communication rate requirement for user k;
the method of the step 3 comprises the following specific steps:
introducing a relaxation variable ζ k Reconstructing an optimization problem model of the system power as:
P 2 :
Figure FDA00041786021300000310
Figure FDA0004178602130000041
Figure FDA0004178602130000042
Figure FDA0004178602130000043
wherein, when P 2 When the optimal solution is reached, the method comprises the steps of,
Figure FDA0004178602130000044
the method of the step 4 comprises the following specific steps:
processing the reconstructed optimization problem model by using a Lagrange function, and combining the formula (9 a) and the formula (9 b) to obtain a Lagrange function containing partial constraint, wherein the Lagrange function containing partial constraint is expressed as follows:
Figure FDA0004178602130000045
wherein L () represents a lagrangian function, and η, ζ, λ represent a power control factor, a relaxation variable, and a lagrangian auxiliary variable, respectively; lambda (lambda) k A relaxation factor that is the kth constraint;
the optimization problem model of the system power is composed of P 2 Reconstructed as P 3 ：
P 3 :
Figure FDA0004178602130000046
Figure FDA0004178602130000047
Figure FDA0004178602130000048
Wherein P is 3 The method comprises two layers of optimization problems, namely an inner layer optimization problem and an outer layer optimization problem;
the inner layer optimization problem is as follows:
Figure FDA0004178602130000049
when the optimal solution is reached, ζ k Is standing point, get
Figure FDA0004178602130000051
At this time P 3 The optimal solution is taken out and the method comprises the steps of,
Figure FDA0004178602130000052
the optimization problem model of the system power is defined by P 3 Reconstruction into a new optimization problem model P 4 ：
P 4 :
Figure FDA0004178602130000053
Figure FDA0004178602130000054
Figure FDA0004178602130000055
And 5, decoupling deformation is carried out on the new optimization problem model, and the new optimization problem model is converted into a convex optimization problem with multiple variables, wherein the method comprises the following steps:
introducing the auxiliary variable y k And (3) decoupling and deforming the new optimization problem model in the step (4) to obtain:
Figure FDA0004178602130000056
when the system takes the optimal solution,
Figure FDA0004178602130000057
then for the optimal solution (ζ k *,η k *,y k * ) The method comprises the following steps of:
Figure FDA0004178602130000058
Figure FDA0004178602130000059
in the method, in the process of the invention,
Figure FDA0004178602130000061
at this point, the new optimization problem model is transformed into a model for the variable ζ k 、η k 、y k Convex optimization problem of the above-mentioned all variables are obtained;
and 5, carrying out model solving through an iterative algorithm to obtain an uplink power allocation optimization scheme of the system, wherein the method comprises the following steps of:
step 5.1, initializing: let iteration number t=0, define convergence tolerance epsilon and maximum iteration number T, initialize feasible point eta k (t) 、ξ k (t) K=1,..k, where feasible point η k (t) And xi k (t) The feasibility of (a) may be determined by equation (12 b) and equation (12 c);
step 5.2, η is defined k (t) 、ξ k (t) Substituting formula (14) to obtain y k (t+1) ；
Step 5.3, η is defined k (t) Substituting formula (16) to obtain xi k (t+1) ；
Step 5.4, the currently obtained y k (t+1) 、ξ k (t+1) Substituting formula (15) to obtain eta k (t+1) And iteratively processing the boundary using newton-seidel, equation (12 b);
step 5.5, y is obtained k (t+1) 、ξ k (t+1) And eta k (t+1) Substituting formula (13) to obtain L (t+1) ；
Step 5.6, let t=t+1, judge T is not less than T or L (t+1) -L (t) Whether < epsilonIf any one of the two is true, an uplink power allocation optimization scheme eta of the system is obtained k (t+1) The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, returning to the step 5.2.
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