CN113364501A - Power control method based on low-precision ADC (analog to digital converter) de-cellular large-scale MIMO (multiple input multiple output) system under Rice channel - Google Patents

Power control method based on low-precision ADC (analog to digital converter) de-cellular large-scale MIMO (multiple input multiple output) system under Rice channel Download PDF

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CN113364501A
CN113364501A CN202110626350.9A CN202110626350A CN113364501A CN 113364501 A CN113364501 A CN 113364501A CN 202110626350 A CN202110626350 A CN 202110626350A CN 113364501 A CN113364501 A CN 113364501A
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CN113364501B (en
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金思年
闫秋娜
岳殿武
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Dalian Maritime University
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    • 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
    • H04B7/0452—Multi-user MIMO systems
    • 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
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/24—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters
    • H04W52/241—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters taking into account channel quality metrics, e.g. SIR, SNR, CIR, Eb/lo
    • 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 provides a power control method for a large-scale MIMO system based on low-precision ADC de-cellular under a Rice channel, which comprises the following steps: s1, establishing a model for removing the cellular massive MIMO system based on the low-precision ADC under the Rice channel; s2, performing uplink pilot training based on the constructed model; s3, carrying out downlink data transmission based on the constructed model; s4, analyzing the downlink reachable rate of the user; s5, constructing an optimization problem of maximizing the total rate of the system according to the downlink reachable rate; and S6, designing a power control strategy according to the optimization problem. The technical scheme of the invention further improves the total rate of the large-scale MIMO system based on the low-precision ADC in the Rice channel on the premise of ensuring that the service quality of each user is not less than the set minimum reachable rate and the sending power of each AP is not more than the set maximum sending power.

Description

Power control method based on low-precision ADC (analog to digital converter) de-cellular large-scale MIMO (multiple input multiple output) system under Rice channel
Technical Field
The invention relates to the technical field of wireless communication, in particular to a power control method for a large-scale MIMO system based on low-precision ADC (analog-to-digital converter) de-cellular under a Rice channel.
Background
In recent years, with the rapid development of the mobile communication industry, the demand for data traffic has increased. In order to meet various diversified communication demands of people, a large-scale cellular Multiple Input Multiple Output (MIMO) system, which has made a thorough change in the architecture of a cellular network, gradually gets into the field of view of people and becomes one of core technologies that people should pay close attention to in the Beyond 5G and 6G era. The large-scale MIMO system breaks the division of cell boundaries on the basis of distributed large-scale MIMO, namely, a large number of Access Points (APs) and users are distributed in a wide area, different APs are connected with a Central Processing Unit (CPU) through backhaul links, and under the same time-frequency resource, the CPU instructions are listened to provide services for all users. Because the large-scale de-cellular MIMO system greatly reduces the distance between the user and the AP, the large-scale de-cellular MIMO system has stronger space macro diversity gain and the capability of resisting path loss, and can greatly improve the service quality of edge users.
However, the cellular massive MIMO system usually needs to deploy a large number of APs and users, which inevitably bring high hardware cost and huge energy consumption when the APs and users are configured with full-precision analog-to-digital converters (ADCs) to perform quantization processing on the received information. To cope with this problem, quantization processing by configuring ADCs of low precision at the AP and the user is undoubtedly a relatively straightforward solution. In addition, in many future communication scenarios, in order to cope with increasingly tight spectrum resources, the cellular massive MIMO system is likely to operate in the millimeter wave frequency band. Because millimeter waves have the characteristics of short wavelength and strong directivity, the line-of-sight component can occupy a dominant position in the whole channel, and therefore, the research of removing a cellular massive MIMO system based on a low-precision ADC under a Rice fading channel becomes a research hotspot of the current academic community.
For a large-scale cellular MIMO system based on a low-precision ADC in a Rice fading channel, the existing research only uses a maximum-minimum power control method to improve the reachable rate of the user with the worst performance, so as to ensure that the service quality of all users is equivalent. For modern communication systems, the total rate of the system is also a very important performance parameter, but the max-min power control method only puts the optimization center on improving the quality of service of the worst user, and is still deficient in improving the total rate of the system.
Disclosure of Invention
In light of the above-mentioned technical problems, the present invention provides a power control method for a large-scale cellular MIMO system based on a low-precision ADC in a rice channel. The invention further improves the total rate of the large-scale MIMO system based on the low-precision ADC in the Rice channel on the premise of ensuring that the service quality of each user is not less than the set minimum reachable rate and the sending power of each AP is not more than the set maximum sending power.
The technical means adopted by the invention are as follows:
a power control method for a large-scale MIMO system based on low-precision ADC de-cellular under a Rice channel comprises the following steps:
s1, establishing a model for removing the cellular massive MIMO system based on the low-precision ADC under the Rice channel;
s2, performing uplink pilot training based on the constructed model;
s3, carrying out downlink data transmission based on the constructed model;
s4, analyzing the downlink reachable rate of the user;
s5, constructing an optimization problem of maximizing the total rate of the system according to the downlink reachable rate;
and S6, designing a power control strategy according to the optimization problem.
Further, the model constructed in step S1 is specifically represented as follows:
Figure BDA0003102212460000021
wherein, gmnRepresenting the channel coefficient between the mth access point AP and the nth user; gamma raymnRepresenting large scale fading coefficients forReflecting the influence of path loss and shadow fading on the channel coefficient; the part in parentheses represents the small scale fading coefficient, represented by the line-of-sight component
Figure BDA0003102212460000031
And a scattered component hmnCN (0,1) in whichmn～[-π，π]Represents the angle of arrival and CN (0,1) represents a circularly symmetric complex gaussian variable with a mean of 0 and a variance of 1; in addition, kmnRepresenting the Rice K-factor, representing the ratio between the line-of-sight component and the scatter component, is defined
Figure BDA0003102212460000032
And
Figure BDA0003102212460000033
wherein beta ismn＝γmn/(1+kmn) Thus, the channel coefficients are re-represented as
Figure BDA0003102212460000034
And obey
Figure BDA0003102212460000035
The statistical distribution of (c).
Further, the specific implementation process of step S2 is as follows:
s21, let the length of the correlation interval be T, and let the time occupied by the pilot training in each correlation interval be taup(τp≥N)；
S22, supposing that in the uplink pilot training phase, the nth user can send the uplink pilot sequence to all the AP
Figure BDA0003102212460000036
And that the pilot sequences transmitted between different users are mutually orthogonal, i.e.
Figure BDA0003102212460000037
The uplink pilot information received by the mth access point AP is represented as:
Figure BDA0003102212460000038
wherein p ispRepresents the normalized signal-to-noise ratio of the uplink pilot signal,
Figure BDA0003102212460000039
representing additive white gaussian noise received by the mth AP;
s23, modeling the quantization process using an additive quantization noise model, and then re-expressing the uplink pilot information received by the mth AP as:
Figure BDA00031022124600000310
wherein alpha ismIndicating the ADC accuracy at the mth access point AP and the accuracy corresponding to the number of quantization bits ρ used by the mth access point APmRelated, equivalent number of bits ρ m1,2,3,4,5, alphamIs precisely given as alpham0.6366,0.8825,0.96546,0.990503, 0.997501; when rhom>At 5 time, αmAnd rhomSatisfy
Figure BDA00031022124600000311
The approximate relationship of (a) to (b),
Figure BDA00031022124600000312
representing and receiving a signal ym,pExtraneous additive quantization noise;
s24, calculating additive quantization noise
Figure BDA0003102212460000041
Represented as:
Figure BDA0003102212460000042
s25, for the mth AP to acquireChannel state information from the nth user will be
Figure BDA0003102212460000043
And
Figure BDA0003102212460000044
multiplying to obtain:
Figure BDA0003102212460000045
s26, since the access point AP can obtain the line-of-sight component information and the large-scale fading coefficient from different users, in the channel estimation stage, the system may eliminate the influence of the line-of-sight component, that is, equation (5) may be represented again as:
Figure BDA0003102212460000046
wherein,
Figure BDA0003102212460000047
representing the quantization noise remaining after eliminating the influence of the line-of-sight component;
s27, calculating quantization noise
Figure BDA0003102212460000048
Represented as:
Figure BDA0003102212460000049
wherein,
Figure BDA00031022124600000410
s28, obtaining g by using the minimum mean square error channel estimation scheme to the formula (6)mnThe channel estimation information of (2) is as follows:
Figure BDA00031022124600000411
s29, obtaining the channel estimation scheme according to the properties of the MMSE channel estimation scheme
Figure BDA00031022124600000412
Wherein
Figure BDA00031022124600000413
Further, the specific implementation process of step S3 is as follows:
s31, after the access point AP acquires the CSI from the user, precoding the downlink transmission signal in a conjugate transpose manner, so that the transmission signal of the mth access point AP is represented as:
Figure BDA0003102212460000051
wherein x isnRepresenting data signals destined for the nth user, satisfies
Figure BDA0003102212460000052
The conditions of (a); p is a radical ofdIndicating the normalized SNR of the downlink transmission data signal; etamnRepresents a power control coefficient;
s32, adjusting power control coefficient etamnEach access point AP is satisfied
Figure BDA0003102212460000053
The power constraint of (c), namely:
Figure BDA0003102212460000054
s33, according to equation (9), after all the access points AP have sent the downlink data signal, the received signal of the nth user is represented as:
Figure BDA0003102212460000055
wherein, wnCN (0,1) represents additive white Gaussian noise received by the nth user;
s34, based on the low-precision ADC used by the user end, representing the quantized received signal of the nth user as:
Figure BDA0003102212460000056
wherein, munIndicates the ADC precision of the nth user, which is equal to the quantization bit number sigma used by the nth usernIn connection with this, the present invention is,
Figure BDA0003102212460000057
representing and receiving a signal rnUncorrelated additive quantization noise;
s35, calculating additive quantization noise
Figure BDA0003102212460000058
The covariance of (a) is calculated as follows:
Figure BDA0003102212460000059
further, the specific implementation process of step S4 is as follows:
s41, according to the formula (12), the received signal of the nth user is represented again as follows:
Figure BDA00031022124600000510
wherein,
Figure BDA0003102212460000061
Figure BDA0003102212460000062
s42, obtaining the expression of the downlink reachable speed of the nth user according to the formula (14) as follows:
Figure BDA0003102212460000063
s43, deriving the achievable rate closed expression of the nth user according to formula (15):
Figure BDA0003102212460000064
wherein q isnTo represent
Figure BDA0003102212460000065
The nth column of (1);
Figure BDA0003102212460000066
and
Figure BDA0003102212460000067
respectively represent
Figure BDA0003102212460000068
And
Figure BDA0003102212460000069
(N-1). times.N + N1A row; the corresponding elements in the matrices Q, U and V are given as [ Q [ ]]mn＝ηmn，
Figure BDA00031022124600000610
Figure BDA00031022124600000611
δ (m, n) represents a dirac δ function, i.e., when m is equal to n, δ (m, n) is equal to 1; when m ≠ n, δ (m, n) is 0.
Further, the specific implementation process of step S5 is as follows:
s51, ensuring the service quality of each user not less than the set minimum reachable rate
Figure BDA00031022124600000612
And the transmission power of each AP is not more than the set maximum transmission power pdOn the premise of (2), the optimization problem of maximizing the total rate of the system is summarized into the following form:
Figure BDA0003102212460000071
s52, optimizing the problem P1The constraint (17b) in (2) is mathematically transformed to obtain:
Figure BDA0003102212460000072
wherein the constraint (17b) is equivalent to a second order cone in equation (18), i.e. equation (17b) is converted to a convex constraint in equation (18); both equations (17c) and (17d) are convex constraints;
s53, adopting a continuous convex approximation method to optimize the non-convex problem P1Approximate equivalence to optimization problem P2Form of (2), optimization problem P2The concrete form of (A) is as follows:
Figure BDA0003102212460000073
wherein l ═ l1,…,lN]And t ═ t1,…,tN]；
S54, for N ═ 1, …, N, the constraints given are as follows:
Figure BDA0003102212460000074
wherein the optimization problem P2The objective function (19a) in (1) is convex, but the constraint (20) is non-convex;
s55, converting the constraint (20) into a convex function form, and equating the constraint (20) to N of 1, …, N as follows:
Figure BDA0003102212460000081
Figure BDA0003102212460000082
s56, when N is 1, …, N, re-expressing equation (21) in the form:
Figure BDA0003102212460000083
Figure BDA0003102212460000084
wherein Q iskAnd
Figure BDA0003102212460000085
respectively represent Q and lnThe iteration values after k SCA treatments, based on which equation (20) has been successfully converted to the constraint conditions of a second order cone by equation (23), and in addition, by observing the optimization problem P2The resulting constraint (19c) is convex;
s57, according to the method of successive convex approximation, approximating the formula (22) by using a first order Taylor expansion in the formula (24);
s58, according to the method of continuous convex approximation, using inequality ln (x) equal to or more than 1-x-1Converting the constraint (19c) into a constraint having the form of a second order cone as follows:
Figure BDA0003102212460000086
s59, according to the formula (23) and the formula (25), at the k-th iteration, the problem P is optimized2Second order cone expressed in the formPlanning the problem:
Figure BDA0003102212460000091
further, the specific implementation process of step S6 is as follows:
s61, initializing and setting the performance parameters: initial iteration number K is 1, maximum iteration number K, tolerance value
Figure BDA0003102212460000092
Minimum achievable rate for user
Figure BDA0003102212460000093
Initial value Q1、l1And t1；
S62, solving the optimization problem in the formula (26) through a convex optimization solver, and enabling Q*、l*And t*Is the solution of the iteration;
s63, when
Figure BDA0003102212460000094
Or when K is equal to K, ending the process; otherwise, go to step S64;
s64, definition k ═ k +1, Qk＝Q*，lk＝l*And tk＝t*The process goes back to step S62.
Compared with the prior art, the invention has the following advantages:
1. compared with the de-cellular massive MIMO system configured with the full-precision ADC under the Rice fading channel, the power control method based on the low-precision ADC de-cellular massive MIMO system under the Rice channel provided by the invention has the advantage that the low-precision ADC configured in the invention can greatly reduce the high hardware cost and the huge energy consumption brought by the full-precision ADC.
By adopting the power control algorithm based on the SCA mode, the power control coefficient with the maximum total system rate can be iterated under the conditions of ensuring the service quality of each user and meeting the limitation of the sending power of each AP.
2. The power control method based on the low-precision ADC de-cellular large-scale MIMO system under the Rice channel provided by the invention designs the power control strategy based on the continuous convex approximation mode, and can iterate the power control coefficient with the maximum total rate of the system under the conditions of ensuring the service quality of each user and meeting the transmission power limit of each AP.
For the above reasons, the present invention can be widely applied to the fields of wireless communication and the like.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a model structure of a massive MIMO system based on low-precision ADC de-cellular under rice channel for which the scheme of the present invention is applicable.
Fig. 3 is a simulation diagram of the system rate performance under different iteration times according to the scheme of the invention.
Fig. 4 is a simulation diagram of a cumulative distribution function of the system rate performance using the power control method in the solution of the present invention and without using the power control algorithm.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
As shown in fig. 1, the present invention provides a power control method for a large-scale MIMO system based on low-precision ADC de-cellular under rice channel, comprising the following steps:
s1, establishing a model for removing the cellular massive MIMO system based on the low-precision ADC under the Rice channel;
s2, performing uplink pilot training based on the constructed model;
s3, carrying out downlink data transmission based on the constructed model;
s4, analyzing the downlink reachable rate of the user;
s5, constructing an optimization problem of maximizing the total rate of the system according to the downlink reachable rate;
and S6, designing a power control strategy according to the optimization problem.
In specific implementation, as a preferred embodiment of the present invention, a decellularized massive MIMO system under a leis fading channel is established as shown in fig. 2, wherein M single-antenna APs and N (M > N) single-antenna users are randomly distributed in a wide service area, and all APs are connected to a CPU through a backhaul link and provide services to all users. In addition, in order to effectively reduce the high hardware cost and the huge energy consumption brought by the full-precision ADC quantizer, in the present embodiment, it is assumed that low-precision ADC quantizers are configured at the AP and the user to quantize the received data. The model constructed in step S1 is specifically represented as follows:
Figure BDA0003102212460000111
wherein, gmnRepresenting the channel coefficient between the mth access point AP and the nth user; gamma raymnRepresenting a large-scale fading coefficient for reflecting the influence of path loss and shadow fading on a channel coefficient; the part in parentheses represents the small scale fading coefficient, represented by the line-of-sight component
Figure BDA0003102212460000112
And a scattered component hmnCN (0,1) in whichmn～[-π，π]Represents the angle of arrival and CN (0,1) represents a circularly symmetric complex gaussian variable with a mean of 0 and a variance of 1; in addition, kmnRepresenting the Rice K-factor, representing the ratio between the line-of-sight component and the scatter component, is defined
Figure BDA0003102212460000113
And
Figure BDA0003102212460000114
wherein beta ismn＝γmn/(1+kmn) Thus, the channel coefficients are re-represented as
Figure BDA0003102212460000115
And obey
Figure BDA0003102212460000116
The statistical distribution of (c).
In specific implementation, as a preferred embodiment of the present invention, the step S2 performs uplink pilot training based on the constructed model, and the specific implementation process is as follows:
s21, let the length of the correlation interval be T, and let the time occupied by the pilot training in each correlation interval be taup(τp≥N)；
S22, supposing that in the uplink pilot training phase, the nth user can send the uplink pilot sequence to all the AP
Figure BDA0003102212460000121
And that the pilot sequences transmitted between different users are mutually orthogonal, i.e.
Figure BDA0003102212460000122
The uplink pilot information received by the mth access point AP is represented as:
Figure BDA0003102212460000123
wherein p ispRepresents the normalized signal-to-noise ratio of the uplink pilot signal,
Figure BDA0003102212460000124
representing additive white gaussian noise received by the mth AP;
s23, since the AP is equipped with a low-precision ADC, its quantization error is affected by the received signal strength. In order to explore the influence of the low-precision ADC on the system performance, in this embodiment, an Additive Quantization Noise Model (AQNM) is used to model the quantization process, and then the uplink pilot information received by the mth access point AP is represented again as:
Figure BDA0003102212460000125
wherein alpha ismIndicating the ADC accuracy at the mth access point AP and the accuracy corresponding to the number of quantization bits ρ used by the mth access point APmRelated, equivalent number of bits ρm1,2,3,4,5, alphamIs precisely given as alpham0.6366,0.8825,0.96546,0.990503, 0.997501; when rhom>At 5 time, αmAnd rhomSatisfy
Figure BDA0003102212460000126
The approximate relationship of (a) to (b),
Figure BDA0003102212460000127
representing and receiving a signal ym,pExtraneous additive quantization noise;
s24, calculating additive quantization noise
Figure BDA0003102212460000128
Represented as:
Figure BDA0003102212460000129
s25, the mth AP will acquire the Channel State Information (CSI) from the nth user
Figure BDA00031022124600001210
And
Figure BDA00031022124600001211
multiplying to obtain:
Figure BDA00031022124600001212
s26, since the access point AP can obtain the line-of-sight component information and the large-scale fading coefficient from different users, in the channel estimation stage, the system may eliminate the influence of the line-of-sight component, that is, equation (5) may be represented again as:
Figure BDA0003102212460000131
wherein,
Figure BDA0003102212460000132
representing the quantization noise remaining after eliminating the influence of the line-of-sight component;
s27, calculating quantization noiseSound
Figure BDA0003102212460000133
Represented as:
Figure BDA0003102212460000134
wherein,
Figure BDA0003102212460000135
s28, obtaining g by using the minimum mean square error channel estimation scheme to the formula (6)mnThe channel estimation information of (2) is as follows:
Figure BDA0003102212460000136
s29, obtaining the channel estimation scheme according to the properties of the MMSE channel estimation scheme
Figure BDA0003102212460000137
Wherein
Figure BDA0003102212460000138
In specific implementation, as a preferred embodiment of the present invention, the step S3 performs downlink data transmission based on the constructed model, and the specific implementation process is as follows:
s31, after the access point AP acquires the CSI from the user, precoding the downlink transmission signal by using a conjugate transpose (CB) method, so that the transmission signal of the mth access point AP is represented as:
Figure BDA0003102212460000139
wherein x isnRepresenting data signals destined for the nth user, satisfies
Figure BDA00031022124600001310
The conditions of (a); p is a radical ofdIndicating the normalized SNR of the downlink transmission data signal; etamnRepresents a power control coefficient;
s32, adjusting power control coefficient etamnEach access point AP is satisfied
Figure BDA00031022124600001311
The power constraint of (c), namely:
Figure BDA0003102212460000141
s33, according to equation (9), after all the access points AP have sent the downlink data signal, the received signal of the nth user is represented as:
Figure BDA0003102212460000142
wherein, wnCN (0,1) represents additive white Gaussian noise received by the nth user;
s34, based on the low-precision ADC used by the user end, representing the quantized received signal of the nth user as:
Figure BDA0003102212460000143
wherein, munIndicates the ADC precision of the nth user, which is equal to the quantization bit number sigma used by the nth usernIn connection with, in particularnAnd σnCan refer to the ADC precision alpha of the mth APmAnd the number of quantization bits ρmThe numerical correspondence between the two is not repeated herein.
Figure BDA0003102212460000144
Representing and receiving a signal rnUncorrelated additive quantization noise;
s35, calculating additive quantizationNoise(s)
Figure BDA0003102212460000145
The covariance of (a) is calculated as follows:
Figure BDA0003102212460000146
in specific implementation, as a preferred embodiment of the present invention, the step S4 analyzes the downlink reachable rate of the user, and the specific implementation process is as follows:
s41, according to the formula (12), the received signal of the nth user is represented again as follows:
Figure BDA0003102212460000147
wherein,
Figure BDA0003102212460000148
Figure BDA0003102212460000149
s42, obtaining the expression of the downlink reachable speed of the nth user according to the formula (14) as follows:
Figure BDA0003102212460000151
s43, deriving the achievable rate closed expression of the nth user according to formula (15):
Figure BDA0003102212460000152
wherein q isnTo represent
Figure BDA0003102212460000153
The nth column of (1);
Figure BDA0003102212460000154
and
Figure BDA0003102212460000155
respectively represent
Figure BDA0003102212460000156
And
Figure BDA0003102212460000157
(N-1). times.N + N1A row; the corresponding elements in the matrices Q, U and V are given as [ Q [ ]]mn＝ηmn，
Figure BDA0003102212460000158
Figure BDA0003102212460000159
δ (m, n) represents a dirac δ function, i.e., when m is equal to n, δ (m, n) is equal to 1; when m ≠ n, δ (m, n) is 0.
In specific implementation, as a preferred embodiment of the present invention, the step S5 constructs an optimization problem that maximizes the total system rate according to the downlink reachable rate, and the specific implementation process is as follows:
s51, aiming at the modern communication system, the total rate of the system and the reachable rate of each user are important performance indexes for evaluating the quality of a communication system. Therefore, the service quality of each user is ensured not to be less than the set minimum achievable rate
Figure BDA00031022124600001510
And the transmission power of each AP is not more than the set maximum transmission power pdOn the premise of (2), the optimization problem of maximizing the total rate of the system is summarized into the following form:
Figure BDA0003102212460000161
s52, optimizing the problem P1The constraint (17b) in (2) is mathematically transformed to obtain:
Figure BDA0003102212460000162
wherein the constraint (17b) is equivalent to a second order cone in equation (18), i.e. equation (17b) is converted to a convex constraint in equation (18); both equations (17c) and (17d) are convex constraints;
s53, optimization problem P1The objective function in (1) is non-convex, so the optimization problem cannot directly obtain a global optimal solution through a convex optimization solver. Therefore, in order to solve the above optimization problem, in this embodiment, a continuous convex approximation method is adopted to solve the non-convex optimization problem P1Approximate equivalence to optimization problem P2If the optimization problem P can be solved smoothly2Then a solution to the optimization problem P can be obtained1And this suboptimal solution is close to the global optimal solution. In this embodiment, an optimization problem P is given2The concrete form of (A) is as follows:
Figure BDA0003102212460000163
wherein l ═ l1,…,lN]And t ═ t1,…,tN]；
S54, for N ═ 1, …, N, the constraints given are as follows:
Figure BDA0003102212460000164
wherein the optimization problem P2The objective function (19a) in (1) is convex, but the constraint (20) is non-convex;
s55, converting the constraint (20) into a convex function form, and equating the constraint (20) to N of 1, …, N as follows:
Figure BDA0003102212460000171
Figure BDA0003102212460000172
s56, when N is 1, …, N, re-expressing equation (21) in the form:
Figure BDA0003102212460000173
Figure BDA0003102212460000174
wherein Q iskAnd
Figure BDA0003102212460000175
respectively represent Q and lnThe iteration values after k SCA treatments, based on which equation (20) has been successfully converted to the constraint conditions of a second order cone by equation (23), and in addition, by observing the optimization problem P2The resulting constraint (19c) is convex;
s57, according to the method of successive convex approximation, approximating the formula (22) by using a first order Taylor expansion in the formula (24);
s58, according to the method of continuous convex approximation, using inequality ln (x) equal to or more than 1-x-1Converting the constraint (19c) into a constraint having the form of a second order cone as follows:
Figure BDA0003102212460000176
s59, according to the formula (23) and the formula (25), at the k-th iteration, the problem P is optimized2The second order cone programming problem (convexity optimization problem) is expressed as follows:
Figure BDA0003102212460000181
in specific implementation, as a preferred embodiment of the present invention, the step S6 designs a power control strategy according to the optimization problem, and the specific implementation process is as follows:
s61, initializing and setting the performance parameters: initial iteration number K is 1, maximum iteration number K, tolerance value
Figure BDA0003102212460000189
Minimum achievable rate of user to be guaranteed
Figure BDA0003102212460000182
Initial value Q1、l1And t1；
S62, solving the optimization problem in the formula (26) through a convex optimization solver, and enabling Q*、l*And t*Is the solution of the iteration;
s63, when
Figure BDA0003102212460000183
Or when K is equal to K, ending the process; otherwise, go to step S64;
s64, definition k ═ k +1, Qk＝Q*，lk＝l*And tk＝t*The process goes back to step S62.
Examples
In order to verify the validity of the scheme of the invention, the following simulation experiment is carried out:
setting a scene: all users and access points AP are assumed to be uniformly and randomly distributed in a square area of 1 x 1km, and the distance between the mth access point AP and the nth user is defined as dmn. The large-scale fading coefficients describe path loss and shadow fading and are given by: gamma raymn＝-30.18-26log10(dmn)+Fmn(dB) in which
Figure BDA0003102212460000184
Indicating a shadow fade. Coefficient of performance
Figure BDA0003102212460000185
And
Figure BDA0003102212460000186
are independent of each other and are given bysf0.5 and σ sf8. The Rice K-factor describes the ratio between the line-of-sight component and the scatter component, given as
Figure BDA0003102212460000187
Other parameter values required in the simulation by the inventive solution are set as in table 1.
TABLE 1 parameter settings
Figure BDA0003102212460000188
Figure BDA0003102212460000191
As shown in fig. 3, the simulation results of the total rate of the system varying with the number of iterations when using the inventive scheme for power control are given. As can be seen from fig. 2, as the number of iterations increases, the overall rate performance of the system increases continuously, and after the number of iterations exceeds 8, the system gradually approaches a fixed value, which indicates that the method in the present invention will gradually converge after 8 iterations.
As shown in fig. 4, the cumulative distribution function of the total rate of the system when the power control algorithm in the solution of the present invention is used and when the power control algorithm is not used is shown when the number of iterations K is 10. By observation, it can be seen that without the system using a power control algorithm, the total rate of the system is more than 31.8bits/s/Hz with a 95% probability; however, in the case of a system using the scheme of the present invention for power control, the total rate of the system is more than 42.9bits/s/Hz with a 95% probability, which is 1.35 times that of the system without the power control algorithm. The simulation result verifies the effectiveness of the scheme of the invention in improving the overall rate performance of the system.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (7)

1. A power control method for a large-scale MIMO system based on low-precision ADC de-cellular under a Rice channel is characterized by comprising the following steps:
s1, establishing a model for removing the cellular massive MIMO system based on the low-precision ADC under the Rice channel;
s2, performing uplink pilot training based on the constructed model;
s3, carrying out downlink data transmission based on the constructed model;
s4, analyzing the downlink reachable rate of the user;
s5, constructing an optimization problem of maximizing the total rate of the system according to the downlink reachable rate;
and S6, designing a power control strategy according to the optimization problem.
2. The power control method for the massive MIMO system based on the low-precision ADC de-cellular under rice channel according to claim 1, wherein the model constructed in the step S1 is specifically expressed as follows:
Figure FDA0003102212450000011
wherein, gmnRepresenting the channel coefficient between the mth access point AP and the nth user; gamma raymnRepresenting the large-scale fading coefficients of the signal,reflecting the influence of path loss and shadow fading on the channel coefficient; the part in parentheses represents the small scale fading coefficient, represented by the line-of-sight component
Figure FDA0003102212450000012
And a scattered component hmnCN (0,1) in whichmn～[-π，π]Represents the angle of arrival and CN (0,1) represents a circularly symmetric complex gaussian variable with a mean of 0 and a variance of 1; in addition, kmnRepresenting the Rice K-factor, representing the ratio between the line-of-sight component and the scatter component, is defined
Figure FDA0003102212450000013
And
Figure FDA0003102212450000014
wherein beta ismn＝γmn/(1+kmn) Thus, the channel coefficients are re-represented as
Figure FDA0003102212450000015
And obey
Figure FDA0003102212450000016
The statistical distribution of (c).
3. The power control method for the massive MIMO system based on the low-precision ADC de-cellular under rice channel as claimed in claim 1, wherein the step S2 is implemented as follows:
s21, let the length of the correlation interval be T, and let the time occupied by the pilot training in each correlation interval be taup(τp≥N)；
S22, supposing that in the uplink pilot training phase, the nth user can send the uplink pilot sequence to all the AP
Figure FDA0003102212450000021
And assumes that the pilot sequences sent between different users are relative to each otherOrthogonal, i.e.
Figure FDA0003102212450000022
The uplink pilot information received by the mth access point AP is represented as:
Figure FDA0003102212450000023
wherein p ispRepresents the normalized signal-to-noise ratio of the uplink pilot signal,
Figure FDA0003102212450000024
representing additive white gaussian noise received by the mth AP;
s23, modeling the quantization process using an additive quantization noise model, and then re-expressing the uplink pilot information received by the mth AP as:
Figure FDA0003102212450000025
wherein alpha ismIndicating the ADC accuracy at the mth access point AP and the accuracy corresponding to the number of quantization bits ρ used by the mth access point APmRelated, equivalent number of bits ρm1,2,3,4,5, alphamIs precisely given as alpham0.6366,0.8825,0.96546,0.990503, 0.997501; when rhom>At 5 time, αmAnd rhomSatisfy
Figure FDA0003102212450000026
The approximate relationship of (a) to (b),
Figure FDA0003102212450000027
representing and receiving a signal ym,pExtraneous additive quantization noise;
s24, calculating additive quantization noise
Figure FDA0003102212450000028
Represented as:
Figure FDA0003102212450000029
s25, the mth AP will acquire the channel state information from the nth user
Figure FDA00031022124500000210
And
Figure FDA00031022124500000211
multiplying to obtain:
Figure FDA00031022124500000212
s26, since the access point AP can obtain the line-of-sight component information and the large-scale fading coefficient from different users, in the channel estimation stage, the system may eliminate the influence of the line-of-sight component, that is, equation (5) may be represented again as:
Figure FDA0003102212450000031
wherein,
Figure FDA0003102212450000032
representing the quantization noise remaining after eliminating the influence of the line-of-sight component;
s27, calculating quantization noise
Figure FDA0003102212450000033
Represented as:
Figure FDA0003102212450000034
wherein,
Figure FDA0003102212450000035
s28, obtaining g by using the minimum mean square error channel estimation scheme to the formula (6)mnThe channel estimation information of (2) is as follows:
Figure FDA0003102212450000036
s29, obtaining the channel estimation scheme according to the properties of the MMSE channel estimation scheme
Figure FDA0003102212450000037
Wherein
Figure FDA0003102212450000038
4. The power control method for the massive MIMO system based on the low-precision ADC de-cellular under rice channel as claimed in claim 1, wherein the step S3 is implemented as follows:
s31, after the access point AP acquires the CSI from the user, precoding the downlink transmission signal in a conjugate transpose manner, so that the transmission signal of the mth access point AP is represented as:
Figure FDA0003102212450000039
wherein x isnRepresenting a data signal addressed to an nth user, satisfies E { | xn|2Condition of 1; p is a radical ofdIndicating the normalized SNR of the downlink transmission data signal; etamnRepresents a power control coefficient;
s32, adjusting power control coefficient etamnMake each access point AP satisfy E { | sm|2}≤pdWork ofRate constraints, namely:
Figure FDA00031022124500000310
s33, according to equation (9), after all the access points AP have sent the downlink data signal, the received signal of the nth user is represented as:
Figure FDA0003102212450000041
wherein, wnCN (0,1) represents additive white Gaussian noise received by the nth user;
s34, based on the low-precision ADC used by the user end, representing the quantized received signal of the nth user as:
Figure FDA0003102212450000042
wherein, munIndicates the ADC precision of the nth user, which is equal to the quantization bit number sigma used by the nth usernIn connection with this, the present invention is,
Figure FDA0003102212450000043
representing and receiving a signal rnUncorrelated additive quantization noise;
s35, calculating additive quantization noise
Figure FDA0003102212450000044
The covariance of (a) is calculated as follows:
Figure FDA0003102212450000045
5. the power control method for the massive MIMO system based on the low-precision ADC de-cellular under rice channel as claimed in claim 1, wherein the step S4 is implemented as follows:
s41, according to the formula (12), the received signal of the nth user is represented again as follows:
Figure FDA0003102212450000046
wherein,
Figure FDA0003102212450000047
Figure FDA0003102212450000048
s42, obtaining the expression of the downlink reachable speed of the nth user according to the formula (14) as follows:
Figure FDA0003102212450000049
s43, deriving the achievable rate closed expression of the nth user according to formula (15):
Figure FDA0003102212450000051
wherein q isnTo represent
Figure FDA0003102212450000052
The nth column of (1);
Figure FDA0003102212450000053
and
Figure FDA0003102212450000054
respectively represent
Figure FDA0003102212450000055
And
Figure FDA0003102212450000056
(N-1). times.N + N1A row; the corresponding elements in the matrices Q, U and V are given as [ Q [ ]]mn＝ηmn，
Figure FDA0003102212450000057
Figure FDA0003102212450000058
δ (m, n) represents a dirac δ function, i.e., when m is equal to n, δ (m, n) is equal to 1; when m ≠ n, δ (m, n) is 0.
6. The power control method for the massive MIMO system based on the low-precision ADC de-cellular under rice channel as claimed in claim 1, wherein the step S5 is implemented as follows:
s51, ensuring the service quality of each user not less than the set minimum reachable rate
Figure FDA00031022124500000510
And the transmission power of each AP is not more than the set maximum transmission power pdOn the premise of (2), the optimization problem of maximizing the total rate of the system is summarized into the following form:
Figure FDA0003102212450000059
s52, optimizing the problem P1The constraint (17b) in (2) is mathematically transformed to obtain:
Figure FDA0003102212450000061
wherein the constraint (17b) is equivalent to a second order cone in equation (18), i.e. equation (17b) is converted to a convex constraint in equation (18); equations (17c) and (17d) are also both convex constraints;
s53, adopting a continuous convex approximation method to optimize the non-convex problem P1Approximate equivalence to optimization problem P2Form of (2), optimization problem P2The concrete form of (A) is as follows:
Figure FDA0003102212450000062
wherein l ═ l1,…,lN]And t ═ t1,…,tN]；
S54, for N ═ 1, …, N, the constraints given are as follows:
Figure FDA0003102212450000063
wherein the optimization problem P2The objective function (19a) in (1) is convex, but the constraint (20) is non-convex;
s55, converting the constraint (20) into a convex function form, and equating the constraint (20) to N of 1, …, N as follows:
Figure FDA0003102212450000064
Figure FDA0003102212450000071
s56, when N is 1, …, N, re-expressing equation (21) in the form:
Figure FDA0003102212450000072
Figure FDA0003102212450000073
wherein Q iskAnd
Figure FDA0003102212450000074
respectively represent Q and lnThe iteration values after k SCA treatments, based on which equation (20) has been successfully converted to the constraint conditions of a second order cone by equation (23), and in addition, by observing the optimization problem P2The resulting constraint (19c) is convex;
s57, according to the method of successive convex approximation, approximating the formula (22) by using a first order Taylor expansion in the formula (24);
s58, according to the method of continuous convex approximation, using inequality ln (x) equal to or more than 1-x-1Converting the constraint (19c) into a constraint having the form of a second order cone as follows:
Figure FDA0003102212450000075
s59, according to the formula (23) and the formula (25), at the k-th iteration, the problem P is optimized2A second order cone programming problem expressed in the form:
Figure FDA0003102212450000076
7. the power control method for the massive MIMO system based on the low-precision ADC de-cellular under rice channel as claimed in claim 1, wherein the step S6 is implemented as follows:
s61, initializing and setting the performance parameters: the initial iteration number K is 1, the maximum iteration number K, the tolerance value theta is 0.01, and the minimum reachable rate of the user
Figure FDA0003102212450000081
Initial value Q1、l1And t1；
S62, solving the optimization problem in the formula (26) through a convex optimization solver, and enabling Q*、l*And t*Is the solution of the iteration;
s63, when
Figure FDA0003102212450000082
Or when K is equal to K, ending the process; otherwise, go to step S64;
s64, definition k ═ k +1, Qk＝Q*，lk＝l*And tk＝t*The process goes back to step S62.
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