CN114389658A - Uplink power optimization method of zero-forcing reception cellular large-scale MIMO (multiple input multiple output) system - Google Patents

Uplink power optimization method of zero-forcing reception cellular large-scale MIMO (multiple input multiple output) system Download PDF

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CN114389658A
CN114389658A CN202111660404.XA CN202111660404A CN114389658A CN 114389658 A CN114389658 A CN 114389658A CN 202111660404 A CN202111660404 A CN 202111660404A CN 114389658 A CN114389658 A CN 114389658A
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user
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power
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CN114389658B (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

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Abstract

The invention discloses an uplink power optimization method for a cellular large-scale multiple-input-output (MIMO) system based on zero forcing reception, which comprises the following core steps: on the premise of meeting the quality-of-service (QoS) requirement and the maximum transmission power limit of each user, the overall uplink capacity of the system is optimized, the target signal power is increased, meanwhile, the power of partial interference signals is reduced, meanwhile, the complexity of the method is considered, and the consumption of computing time and computing resources is reduced. The optimization method utilizes the relaxation variables and the decoupling deformation, processes the constraint conditions and the target function through partial Lagrange functions, converts the whole optimization problem into a convex optimization problem, and deduces the iterative closed expression of each variable, so that the solution efficiency is higher than that of the traditional convex approximation mode, and the capacity of an uplink system can be obviously improved. The invention can be used for improving the power utilization efficiency, improving the target signal power and reducing part of interference signal power.

Description

Uplink power optimization method of zero-forcing reception cellular large-scale MIMO (multiple input multiple output) 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 reception cellular massive MIMO system.
Background
The large-scale multi-input multi-output (MIMO) of the cellular realizes distributed large-scale MIMO by taking a user as a center, the cell division in the original cellular network solves the contradiction between the communication rate and the coverage area in the traditional cellular communication network, avoids the problem of frequent switching of the cells in the cellular network, and further improves the service quality and the coverage area, so the large-scale multi-input multi-output (MIMO) of the cellular network is very likely to become one of the core technologies of the next 5G and 6G.
In the existing de-cellular MIMO system, because the number of users is often greater than the number of pilots, there is interference between users, which limits further improvement of system performance, and therefore, it is necessary to optimize the communication power allocation of each AP (access point) to achieve the purpose of further improving the overall system capacity.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems, the invention provides an uplink power optimization method of a zero-forcing reception cellular massive MIMO system, which reduces the interference among a part of users and improves the required power consumption by optimizing the power distribution from an AP to each user so as to achieve the aim of improving the total capacity of the system.
The technical scheme is as follows: in order to realize the purpose of the invention, the technical scheme adopted by the invention is as follows: an uplink power optimization method for a zero forcing reception de-cellular massive MIMO system specifically comprises the following steps:
step 1, constructing an uplink system model of a zero forcing reception cellular large-scale MIMO system;
step 2, based on an uplink system model, calculating a closed expression of uplink reachable rates of users under zero forcing reception, 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 a constraint condition in the model;
step 4, the improved target function and the constraint condition are processed by utilizing the Lagrange function, and the improved target function and the constraint condition are further reconstructed into a new optimization problem model;
and 5, decoupling deformation is carried out on the new optimization problem model, the new optimization problem model is converted into a multivariable convex optimization problem, model solution is carried out through an iterative algorithm, and the uplink power distribution optimization scheme of the system is obtained.
Further, the method of step 1 specifically comprises the following steps:
the de-cellular massive MIMO system comprises M APs and K single-antenna users, wherein each AP is provided with N antennas, and M is multiplied by N>>K; wherein M is ∈ [1, M ∈]Denotes the AP number, K ∈ [1, K ∈ ]]A number representing a user; AP (Access Point)mChannel model g with user kmkThe expression is as follows:
Figure BDA0003449401880000021
in the formula, APmDenotes the m-th AP, betamkRepresenting APmLarge scale fading coefficient with user k, hmkRepresenting APmBetween the user k and the user k is a small-scale fading vector, elements of which are independently and identically distributed in a complex Gaussian distribution with the mean value of 0 and the variance of 1, namely hmkCN (0,1), then gmk～CN(0,βmkIN)，INIs an N-dimensional unit matrix;
APmthe terminal receives the pilot signal Y sent by all usersmpComprises the following steps:
Ymp＝GmP1/2φH+Wmp (2)
in the formula, Gm＝[gm1,gm2,...,gmK]～CN×K，CN×KIs a complex matrix of NxK, P1/2A matrix is allocated for the transmit power, phi is a pilot matrix,
Figure BDA0003449401880000022
elements thereof
Figure BDA0003449401880000023
The pilot assigned to user k for the system,
Figure BDA0003449401880000024
Wmpis additive white Gaussian noise, Wmp～CN×ττ is the pilot length;
based on the minimum mean square error criterion, APmChannel estimation with user k
Figure BDA0003449401880000025
Comprises the following steps:
Figure BDA0003449401880000026
in the formula, ρpFor a normalized signal-to-noise ratio for pilot transmission,
Figure BDA0003449401880000027
Figure BDA0003449401880000028
the pilot assigned to user i for the system,
Figure BDA0003449401880000029
channel estimation error is
Figure BDA00034494018800000210
And is
Figure BDA00034494018800000211
Further, the step 2 of calculating the closed expression of the uplink reachable rate of the user under zero forcing reception specifically includes the following steps:
step 2.1, all users send data to AP, and the data vector sent by user k is set as skThe power satisfies E { | sk|2}＝1，APmReceived signal ymExpressed as:
Figure BDA0003449401880000031
in the formula, ρuFor the normalized signal-to-noise ratio of the signal, gmkIs APmModel of the channel with user k, ηkIs APmFor the power control coefficient of user k, eta is more than or equal to 0k≤1，wmIs APmAdditive white gaussian noise of the channel;
the AP transmits the received signal to the CPU through a return link, and the zero forcing receiver decodes the received signal, wherein the receiving matrix of the zero forcing receiver is
Figure BDA0003449401880000032
Wherein the content of the first and second substances,
Figure BDA0003449401880000033
to represent
Figure BDA0003449401880000034
Transposing; defining the received vector of user k as akIn particular, the receiving matrix A is formed by CMN×KK column of (2), then the zero forcing received signal of user k
Figure BDA0003449401880000035
The expression of (a) is:
Figure BDA0003449401880000036
in the formula (I), the compound is shown in the specification,
Figure BDA0003449401880000037
for inter-user interference, eta, caused by channel estimation errorsiIs APmFor the power control coefficient of user i, eta is more than or equal to 0i≤1，siFor the data vector sent by user i,
Figure BDA0003449401880000038
for the channel estimation error of user i, the superscript H represents the conjugate transpose of the matrix,
Figure BDA0003449401880000039
is a letterChannel noise interference;
for zero-forcing receiver, the uplink SINR of user k
Figure BDA00034494018800000310
The expression is as follows:
Figure BDA00034494018800000311
in the formula, amkRepresenting APmA zero-forcing receive vector for user k; [ a ] Amk]nDenotes amkThe nth element of (1);
is provided with
Figure BDA00034494018800000312
Based on Jensen inequality, closed expression of uplink reachable rate of user k is obtained by using approximation method
Figure BDA00034494018800000313
Comprises the following steps:
Figure BDA00034494018800000314
where the system interference is at a maximum
Figure BDA0003449401880000041
Figure BDA0003449401880000042
Further, the optimization problem model of the system power in step 2 is represented as follows:
Figure BDA0003449401880000043
Figure BDA0003449401880000044
Figure BDA0003449401880000045
in the formula (I), the compound is shown in the specification,
Figure BDA0003449401880000046
is the communication rate requirement of user k.
Further, the method of step 3 specifically includes the following steps:
introducing a relaxation variable xikAnd rebuilding the optimization problem model of the system power into:
Figure BDA0003449401880000047
Figure BDA0003449401880000048
Figure BDA0003449401880000049
Figure BDA00034494018800000410
wherein when P is2When the optimal solution is reached, the method,
Figure BDA00034494018800000411
further, the method of step 4 specifically includes the following steps:
and (3) processing the reconstructed optimization problem model by using a Lagrangian function, and combining the formula (9a) and the formula (9b) to obtain a Lagrangian function L containing partial constraint, wherein the Lagrangian function L is expressed as follows:
Figure BDA0003449401880000051
in the formula, eta, xi and lambda respectively represent a power control factor, a relaxation variable and a Lagrange auxiliary variable; lambda [ alpha ]kA relaxation factor that is the kth constraint;
optimization problem model of system power is represented by P2Is reconstructed into P3：
Figure BDA0003449401880000052
Figure BDA0003449401880000053
Figure BDA0003449401880000054
Wherein, P3The 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
xi when the optimal solution is reachedkIs a stagnation point to obtain
Figure BDA0003449401880000056
At this time P3The optimal solution is taken out, and the optimal solution is obtained,
Figure BDA0003449401880000057
the optimization problem model of the system power is represented by P3Reconstructed as a new optimization problem model P4：
Figure BDA0003449401880000058
Figure BDA0003449401880000059
Figure BDA00034494018800000510
Further, in step 5, the new optimization problem model is subjected to decoupling deformation and converted into a multivariable convex optimization problem, and the method comprises the following steps:
introducing an auxiliary variable ykDecoupling and deforming the new optimization problem model in the step 4 to obtain:
Figure BDA0003449401880000061
when the system is to take the optimal solution,
Figure BDA0003449401880000062
then for the optimal solution
Figure BDA0003449401880000063
Obtaining:
Figure BDA0003449401880000064
Figure BDA0003449401880000065
in the formula (I), the compound is shown in the specification,
Figure BDA0003449401880000066
at this point, the new optimization problem model is transformed to relate to the variable ξk、ηk、ykAnd obtaining the iteration closed expression of all the variables.
Further, in step 5, model solution is performed through an iterative algorithm to obtain an uplink power allocation optimization scheme of the system, and the method includes:
step 5.1, initialization: let the iteration number T equal to 0, and define the convergence tolerance epsilon and the maximum iteration number T, initialize the feasible point etak (t)、ξk (t)K1, K, where the feasible point ηk (t)And xik (t)The feasibility of (d) can be determined by equation (12b) and equation (12 c);
step 5.2, mixing etak (t)、ξk (t)Substituting equation (14) to obtain yk (t+1)；
Step 5.3, mixing etak (t)Substituting into formula (16) to obtain xik (t+1)；
Step 5.4, obtaining y currentlyk (t+1)、ξk (t+1)Substituting into equation (15) to obtain ηk (t+1)And processing the boundary using newton-seidel iterations, equation (12 b);
step 5.5, mixing the obtained yk (t+1)、ξk (t+1)And ηk (t+1)Substituting into equation (13) to obtain L(t+1)；
And 5.6, enabling T to be T +1, and judging that T is more than or equal to T or | L(t+1)-L(t)|<If epsilon is true, if either epsilon is true, obtaining an uplink power allocation optimization scheme eta of the systemk (t+1)(ii) a Otherwise, return to step 5.2.
Has the advantages 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 large-scale de-cellular MIMO system, which optimizes the overall uplink capacity of the system on the premise of meeting the requirement of each user on service quality and the limitation of maximum transmitting power, increases the power of a target signal, reduces the power of partial interference signals, considers the complexity of the method and reduces the consumption of calculation time and calculation resources. The optimization method can remarkably improve the capacity of an uplink system.
Drawings
FIG. 1 is a flowchart of an uplink power optimization method for a cellular massive MIMO system according to an embodiment;
FIG. 2 is a diagram of an exemplary cellular massive MIMO system architecture under an embodiment;
fig. 3 is a diagram of uplink reception by an AP according to an embodiment;
FIG. 4 is a graph comparing the optimization results of the method of the present invention with those of the prior art in one embodiment;
FIG. 5 is a graph comparing the calculated time of the method of the present invention with that of the prior art under one embodiment.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Referring to fig. 1, the uplink power optimization method for a zero forcing reception cellular massive MIMO system specifically includes the following steps:
(1) constructing an uplink system model in a de-cellular large-scale MIMO system received by ZF;
(2) deducing a closed expression of the uplink rate of each user under ZF receiving, and establishing a system power optimization problem model;
(3) introducing a relaxation variable to reconstruct a target function and a constraint condition;
(4) deducing a part of Lagrange functions, and combining part of constraint conditions with the target function;
(5) decoupling deformation is carried out on the new objective function, the new objective function is converted into a multivariable convex optimization problem, and an iterative closed expression of each variable is solved;
(6) the resulting optimization problem is solved by 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 a channel model between APm and user K is:
Figure BDA0003449401880000081
wherein, betamkIs a large scale fading coefficient between APm and user k, hmkIs a small scale fading vector in which each element follows a complex gaussian distribution with a mean of 0 and a variance of 1, so
gmk～CN(0,βmkIN) (2)
Wherein, INIs an N-dimensional identity matrix. The pilot signal received at the APm terminal is
Ymp＝GmP1/2φH+Wmp (3)
In the formula, Gm＝[gm1,gm2,...,gmK]～CN×K，CN×KIs a complex matrix of NxK, P1/2A matrix is allocated for the transmit power, phi is a pilot matrix,
Figure BDA0003449401880000082
elements thereof
Figure BDA0003449401880000083
The pilot assigned to user k for the system,
Figure BDA0003449401880000084
k∈[1,K]；Wmpis additive white Gaussian noise, Wmp～CN×ττ is the pilot length; using minimum mean square error estimation (MMSE), the channel estimate between APm and user k is:
Figure BDA0003449401880000085
wherein the content of the first and second substances,
Figure BDA0003449401880000086
estimate error of
Figure BDA0003449401880000087
And is provided with
Figure BDA0003449401880000088
In the system model, a closed expression of the uplink user reachable rate received by ZF is further derived, and the closed expression specifically includes:
in the uplink data transmission process, all users send data to each AP, wherein the data vector sent by user k is skThe power of the power satisfies E { | sk|21, the signal received by APm is:
Figure BDA0003449401880000089
where ρ isuIs the normalized signal-to-noise ratio of the signal, 0 ≦ ηk1 is the power control coefficient of APm to user k, wmIs additive white gaussian noise for the APm channel. Summarizing all received signals in a CPU through a return link, and defining the receiving vector of a user k as akFor the receiving matrix A ∈ CMN×KIn the kth column, the received signal of user k is obtained as:
Figure BDA0003449401880000091
for a ZF receiver, the receive matrix is
Figure BDA0003449401880000092
Wherein
Figure BDA0003449401880000093
Substituting a into (6) can obtain the zero-forcing reception result of user k as:
Figure BDA0003449401880000094
wherein
Figure BDA0003449401880000095
For inter-user interference caused by channel estimation errors,
Figure BDA0003449401880000096
is the channel noise. Therefore, for the ZF receiver, the uplink signal-to-interference-and-noise ratio of user k is:
Figure BDA0003449401880000097
wherein [ a ]mk]nDenotes amkThe nth element of (a) takes the Jensen inequality into consideration, that is, when the system interference is the maximum, the uplink reachable rate expression of the user k is as follows:
Figure BDA0003449401880000098
wherein the content of the first and second substances,
Figure BDA0003449401880000099
namely, acquiring the maximum interference condition; Ω (k) is:
Figure BDA00034494018800000910
wherein
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 and is difficult to directly solve, a relaxation variable ξ is introducedkThe optimization problem is reconstructed as:
Figure BDA0003449401880000104
Figure BDA0003449401880000105
Figure BDA0003449401880000106
Figure BDA0003449401880000107
wherein (12b) is a complementary relaxation introduction when P is2When the optimal solution is reached, the following are provided:
Figure BDA0003449401880000108
for (12c), there are two processing methods: 1) according to the nature of the relaxation variables, can be equated to
Figure BDA0003449401880000109
Viewed as a function of the relaxation variable ξkOf (3) is performed. 2) For the original solution problem, the constraint can be regarded as a second order cone constraint, i.e. the constraint is
Figure BDA00034494018800001010
Wherein
Figure BDA00034494018800001011
Is a convex constraint problem. Since the method in 1) can be regarded as the method for the relaxation variableξkThe feasible domain constraint of (2) cannot guarantee that the constraint converges to (13) for any user k in the feasible domain, so that the equivalence with the original problem cannot be guaranteed, the method adopts the method 2) for processing, and due to the use of sequential iterative solution, the constraint needs to be iteratively solved by using a Newton-Seidel (Gauss-Seidel) method.
Since (12b) is a non-convex constraint, combining (12b) with the objective function (12a) by a lagrangian function, the resulting partially constrained lagrangian function is:
Figure BDA0003449401880000111
thus, P2Conversion to:
Figure BDA0003449401880000112
Figure BDA0003449401880000113
Figure BDA0003449401880000114
wherein, P3Can be viewed as a two-layer optimization problem, for the inner layer optimization problem, i.e.
Figure BDA0003449401880000115
Xi when the optimal solution is reachedkTo a stagnation point, i.e.
Figure BDA0003449401880000119
The following can be obtained:
Figure BDA0003449401880000116
substitution of (13) into (16) gives P3When the optimal solution is obtained:
Figure BDA0003449401880000117
substituting (17) into P3The original optimization problem becomes:
Figure BDA0003449401880000118
s.t.(15b),(15c)
for (18a), in order to solve the variable iteration closed expression, the second decoupling processing is performed on the variable iteration closed expression, and then:
Figure BDA0003449401880000121
wherein, when:
Figure BDA0003449401880000122
(19) equivalent to the original objective function (18a), i.e. when the system takes the optimal solution (satisfies)
Figure BDA0003449401880000123
)，ykEqual to the above formula. For the global optimum solution ([ xi ])k *,ηk *,yk *) Satisfies the conditions
Figure BDA0003449401880000124
Thus, it is possible to obtain:
Figure BDA0003449401880000125
Figure BDA0003449401880000126
thus, the optimization problem can be solved by iteration, as follows:
Figure BDA0003449401880000127
Figure BDA0003449401880000131
referring to FIG. 2, an example of a system scenario employed under one embodiment is 1km2Within the range, 60 APs are randomly distributed and operate in TDD mode, and all APs serve 20 users, wherein the large scale fading model is:
Figure BDA0003449401880000132
wherein PLmkIs the path loss between AP m and user k,
Figure BDA0003449401880000133
for shadow fading, σshIs the standard deviation, and the value is 8 dB. Path loss PLmkAnd calculating by a three-section model. Each AP is connected to the CPU via a backhaul link for channel estimation and signal processing.
Referring to fig. 3, in the uplink transmission process, each AP is equipped with 6 antennas, and the served users are single-antenna devices. The default non-optimized power allocation scheme is equally allocated to all users, namely the power control coefficient is etak＝1，
Figure BDA0003449401880000134
The system bandwidth is set to 200 MHz.
Referring to fig. 4, after power optimization is performed, the uplink total capacity of the system can be improved by about 23.02% compared with equal power allocation by the method proposed in the present patent (different results may be obtained according to various parameters and tolerances, such as the actual bandwidth of the system, fading, and the random distribution of users); where the difference in final optimization rates for the different optimization methods is related to the initial value and the tolerance, the methods all guarantee convergence at the stationary point.
Referring to fig. 5, the optimization method has low complexity in terms of operation speed, and can greatly reduce processing delay caused by power optimization and improve the response rate of the communication system (operation results may be different according to differences in computing power).

Claims (8)

1. An uplink power optimization method for a zero forcing reception de-cellular massive MIMO system is characterized by comprising the following steps:
step 1, constructing an uplink system model of a zero forcing reception cellular large-scale MIMO system;
step 2, based on an uplink system model, calculating a closed expression of uplink reachable rates of users under zero forcing reception, 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 a constraint condition in the model;
step 4, the improved target function and the constraint condition are processed by utilizing the Lagrange function, and the improved target function and the constraint condition are further reconstructed into a new optimization problem model;
and 5, decoupling deformation is carried out on the new optimization problem model, the new optimization problem model is converted into a multivariable convex optimization problem, model solution is carried out through an iterative algorithm, and the uplink power distribution optimization scheme of the system is obtained.
2. The uplink power optimization method for the zero-forcing reception de-cellular massive MIMO system according to claim 1, wherein the method of step 1 specifically comprises the following steps:
the de-cellular massive MIMO system comprises M APs and K single-antenna users, wherein each AP is provided with N antennas, and M is multiplied by N>>K; wherein M is ∈ [1, M ∈]Denotes the AP number, K ∈ [1, K ∈ ]]A number representing a user; AP (Access Point)mChannel model g with user kmkThe expression is as follows:
Figure FDA0003449401870000011
in the formula, APmDenotes the m-th AP, betamkRepresenting APmLarge scale fading coefficient with user k, hmkRepresenting APmThe small-scale fading vector between the user k and the user k has elements which are independently and identically distributed in a complex Gaussian distribution with the mean value of 0 and the variance of 1, namely hmkCN (0,1), then gmk～CN(0,βmkIN)，INIs an N-dimensional unit matrix;
APmthe terminal receives the pilot signal Y sent by all usersmpComprises the following steps:
Ymp＝GmP1/2φH+Wmp (2)
in the formula, Gm＝[gm1,gm2,...,gmK]～CN×K，CN×KIs a complex matrix of NxK, P1/2A matrix is allocated for the transmit power, phi is a pilot matrix,
Figure FDA0003449401870000012
elements thereof
Figure FDA0003449401870000013
The pilot assigned to user k for the system,
Figure FDA0003449401870000014
k∈[1,K]；Wmpis additive white Gaussian noise, Wmp～CN×ττ is the pilot length;
based on the minimum mean square error criterion, APmChannel estimation with user k
Figure FDA0003449401870000015
Comprises the following steps:
Figure FDA0003449401870000021
in the formula, ρpFor a normalized signal-to-noise ratio for pilot transmission,
Figure FDA0003449401870000022
Figure FDA0003449401870000023
the pilot assigned to user i for the system,
Figure FDA0003449401870000024
channel estimation error is
Figure FDA0003449401870000025
And is
Figure FDA0003449401870000026
3. The uplink power optimization method of the zero forcing reception de-cellular massive MIMO system according to claim 1, wherein the step 2 of calculating the closed expression of the uplink achievable rate of the user under zero forcing reception specifically includes the following steps:
step 2.1, all users send data to AP, and the data vector sent by user k is set as skThe power satisfies E { | sk|2}＝1，APmReceived signal ymExpressed as:
Figure FDA0003449401870000027
in the formula, ρuFor the normalized signal-to-noise ratio of the signal, gmkIs APmModel of the channel with user k, ηkIs APmFor the power control coefficient of user k, eta is more than or equal to 0k≤1，wmIs APmAdditive white gaussian noise of the channel;
the AP transmits the received signal to the CPU through a return link, and the zero forcing receiver decodes the received signal, wherein the receiving matrix of the zero forcing receiver is
Figure FDA0003449401870000028
Wherein the content of the first and second substances,
Figure FDA0003449401870000029
Figure FDA00034494018700000210
to represent
Figure FDA00034494018700000211
Transposing; defining the received vector of user k as akIn particular, the receiving matrix A is formed by CMN×KK column of (2), then the zero forcing received signal of user k
Figure FDA00034494018700000212
The expression of (a) is:
Figure FDA00034494018700000213
in the formula (I), the compound is shown in the specification,
Figure FDA00034494018700000214
for inter-user interference, eta, caused by channel estimation errorsiIs APmFor the power control coefficient of user i, eta is more than or equal to 0i≤1，siFor the data vector sent by user i,
Figure FDA00034494018700000215
for the channel estimation error of user i, the superscript H represents the conjugate transpose of the matrix,
Figure FDA00034494018700000216
is channel noise interference;
for zero-forcing receiver, the uplink SINR of user k
Figure FDA0003449401870000031
The expression is as follows:
Figure FDA0003449401870000032
in the formula, amkRepresenting APmA zero-forcing receive vector for user k; [ a ] Amk]nDenotes amkThe nth element of (1);
is provided with
Figure FDA0003449401870000033
Based on Jensen inequality, closed expression of uplink reachable rate of user k is obtained by using approximation method
Figure FDA0003449401870000034
Comprises the following steps:
Figure FDA0003449401870000035
where the system interference is at a maximum
Figure FDA0003449401870000036
Figure FDA0003449401870000037
4. The uplink power optimization method of claim 3, wherein the optimization problem model of the system power in step 2 is represented as follows:
P1:
Figure FDA0003449401870000038
Figure FDA0003449401870000039
Figure FDA00034494018700000310
in the formula (I), the compound is shown in the specification,
Figure FDA00034494018700000311
is the communication rate requirement of user k.
5. The uplink power optimization method of the zero-forcing reception de-cellular massive MIMO system according to claim 4, wherein the method of step 3 specifically comprises the following steps:
introducing a relaxation variable xikAnd rebuilding the optimization problem model of the system power into:
P2:
Figure FDA0003449401870000041
Figure FDA0003449401870000042
Figure FDA0003449401870000043
Figure FDA0003449401870000044
wherein when P is2When the optimal solution is reached, the method,
Figure FDA0003449401870000045
6. the uplink power optimization method for the zero-forcing reception de-cellular massive MIMO system according to claim 5, wherein the method of step 4 specifically comprises the following steps:
and (3) processing the reconstructed optimization problem model by using a Lagrangian function, and combining the formula (9a) and the formula (9b) to obtain a Lagrangian function containing partial constraint, wherein the Lagrangian function is expressed as follows:
Figure FDA0003449401870000046
in the formula, L () represents a Lagrange function, and eta, xi and lambda respectively represent a power control factor, a relaxation variable and a Lagrange auxiliary variable; lambda [ alpha ]kA relaxation factor that is the kth constraint;
optimization problem model of system power is represented by P2Is reconstructed into P3：
P3:
Figure FDA0003449401870000047
Figure FDA0003449401870000048
Figure FDA0003449401870000049
Wherein, P3The 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 FDA0003449401870000051
xi when the optimal solution is reachedkIs a stagnation point to obtain
Figure FDA0003449401870000052
At this time P3The optimal solution is taken out, and the optimal solution is obtained,
Figure FDA0003449401870000053
the optimization problem model of the system power is represented by P3Reconstructed as a new optimization problem model P4：
P4:
Figure FDA0003449401870000054
Figure FDA0003449401870000055
Figure FDA0003449401870000056
7. The uplink power optimization method of the zero-forcing reception de-cellular massive MIMO system according to claim 6, wherein the step 5 of decoupling and transforming the new optimization problem model into a multivariate convex optimization problem comprises the following steps:
introducing an auxiliary variable ykDecoupling and deforming the new optimization problem model in the step 4 to obtain:
Figure FDA0003449401870000057
when the system is to take the optimal solution,
Figure FDA0003449401870000058
then for the optimal solution (ξ)k*,ηk*,ykA), obtaining:
Figure FDA0003449401870000061
Figure FDA0003449401870000062
in the formula (I), the compound is shown in the specification,
Figure FDA0003449401870000063
at this point, the new optimization problem model is transformed to relate to the variable ξk、ηk、ykAnd obtaining the iteration closed expression of all the variables.
8. The uplink power optimization method of the zero-forcing reception de-cellular massive MIMO system according to claim 7, wherein the model solution is performed by an iterative algorithm in step 5 to obtain an uplink power allocation optimization scheme of the system, and the method is as follows:
step 5.1, initialization: let the iteration number T equal to 0, and define the convergence tolerance epsilon and the maximum iteration number T, initialize the feasible point etak (t)、ξk (t)K1, K, where the feasible point ηk (t)And xik (t)The feasibility of (d) can be determined by equation (12b) and equation (12 c);
step 5.2, mixing etak (t)、ξk (t)Substituting equation (14) to obtain yk (t+1)；
Step 5.3, mixing etak (t)Substituting into formula (16) to obtain xik (t+1)；
Step 5.4, obtaining y currentlyk (t+1)、ξk (t+1)Substituting into equation (15) to obtain ηk (t+1)And processing the boundary using newton-seidel iterations, equation (12 b);
step 5.5, mixing the obtained yk (t+1)、ξk (t+1)And ηk (t+1)Substituting into equation (13) to obtain L(t+1)；
And 5.6, enabling T to be T +1, and judging that T is more than or equal to T or | L(t+1)-L(t)|<If epsilon is true, if either epsilon is true, obtaining an uplink power allocation optimization scheme eta of the systemk (t+1)(ii) a Otherwise, return to step 5.2.
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