CN111181670A - Distributed antenna system energy efficiency optimization method, system and storage medium - Google Patents

Distributed antenna system energy efficiency optimization method, system and storage medium Download PDF

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CN111181670A
CN111181670A CN201910964139.0A CN201910964139A CN111181670A CN 111181670 A CN111181670 A CN 111181670A CN 201910964139 A CN201910964139 A CN 201910964139A CN 111181670 A CN111181670 A CN 111181670A
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何春龙
田楚
陈前
李兴泉
张勇
邓建晖
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Shenzhen University
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Abstract

The invention provides a distributed antenna system energy efficiency optimization method and a storage medium, wherein a bounded and unbounded statistical channel error model is discussed for comprehensively researching the influence of channel uncertainty on EE optimization, but interference constraint of a D2D user on CUE is described as opportunity constraint under the condition of uncertain CSI, the opportunity constraint is non-convex probability constraint and is difficult to ensure the effectiveness of the constraint, a Bernstein approximation method is introduced to convert the interference constraint into convex inequality constraint, the constraint is processed by a traditional convex optimization method, an objective function is a non-convex and non-linear optimization problem, and an optimal power distribution scheme is obtained by converting an objective function through a fractional programming theory and a D.C. optimization method. The method used by the invention can still keep better robustness under the condition of channel fluctuation, which has important significance for selecting the system performance optimization scheme in the actual model.

Description

Distributed antenna system energy efficiency optimization method, system and storage medium
Technical Field
The invention belongs to the wireless communication technology, relates to an antenna system energy efficiency optimization method, a system and a storage medium, and particularly relates to a distributed antenna system energy efficiency optimization method, a system and a storage medium based on D2D communication under uncertainty.
Background
In recent years, with the dramatic increase in usage of Cellular User Equipment (CUE), smart devices, and other wireless devices, it has become a serious challenge to reduce the energy consumption of communication devices. Distributed Antenna Systems (DAS) are considered as a potential technology for next generation wireless communication Systems, with higher capacity, more reliable links and higher coverage than Centralized Antenna Systems (CAS). Furthermore, Device to Device (D2D) technology acts as complementary network access to cellular systems, which allows the CUE to communicate directly and reuse the spectral resources of the cellular network, effectively improving Spectral Efficiency (SE).
Currently, many studies have been made to maximize Energy Efficiency (EE) in DAS. However, most studies are based on studies in which both the transmitter and the receiver have perfect Channel State Information (CSI). In fact, it is very important to explore the influence of channel uncertainty on the system performance and design a system with good robustness, and it is important to improve the anti-noise performance of the system and keep the system in a stable state. Currently, there are two methods of dealing with channel uncertainty: bernstein method for statistical channel error models and worst case analysis method for deterministic channel error models. However, the channel description of the deterministic channel model is determined as the boundary of the confidence error, the real channel is distributed in a determined elliptical domain, and the system performance can be optimized only under the worst condition of the channel by utilizing the distribution characteristics of the channel.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the distribution characteristics of actual channels, a distributed antenna system energy efficiency optimization method, a distributed antenna system energy efficiency optimization system and a storage medium based on the channel model are provided.
The aim of the invention is to maximize the EE for optimizing the DAS based on D2D communication under uncertain CSI while at the same time needing to control the aggregate interference of D2D users on the CUE and considering the limitation of the maximum transmit power of D2D users. In order to fully study the influence of channel uncertainty on EE optimization, two channel error models, a bounded statistical channel error model and an unbounded statistical channel error model, are provided. However, the interference constraint of the D2D user on the CUE is described as an opportunity constraint in the case that CSI is uncertain, which is a non-convex probability constraint, and it is difficult to guarantee the validity of the constraint. The invention introduces a Bernstein approximation method to convert a non-convex probability constraint into a convex inequality constraint, and then processes the constraint through a traditional convex optimization method. Because the objective function is a non-convex and non-linear optimization problem, the objective function can be converted and the optimal power distribution scheme can be solved through the fractional programming theory and the D.C. optimization method.
In order to solve the technical problems, the invention adopts the technical scheme that:
the invention provides a method, a system and a storage medium for optimizing energy efficiency of a distributed antenna system, which are characterized by comprising the following steps:
s1, establishing a D2D communication system model in a distributed antenna system, considering a downlink DAS cell, wherein N randomly distributed remote access units are arranged in the cell, DAS only provides service for a CUE, M D2D pairs in the DAS cell share the same spectrum band with the CUE, a transmitting end and a receiving end of the D2D are respectively marked as D2D-T and D2D-R, assuming that a user and the remote access unit are both provided with only one antenna, assuming that channel information of the CUE and the remote access unit is perfect and the state of the rest channel information is imperfect, establishing a channel model, and determining an optimized objective function;
s2, carrying out approximate transformation on the constraint condition with the imperfect channel information, and solving a convex approximate form of the non-convex constraint by adopting an approximate method;
s3, converting the inequality constraint obtained in the step S2 into an equivalent subtraction problem by using a score programming theory, and obtaining an optimal power distribution solution when the D2D user maximizes EE by using a D.C. programming and an interior point method;
and S4, carrying out simulation experiments.
Further, step S2 includes an opportunity constraint approximation method for the bounded case and an opportunity constraint approximation method for the unbounded case, wherein the approximation method is a Bernstein approximation method.
Further, the chance constraint approximation method of the channel under the bounded condition is expressed as:
Figure BDA0002229925360000021
wherein, therein
Figure BDA0002229925360000031
Hi,0Representing the interference channel power gain of the DTi-CUE link, assuming
Figure BDA0002229925360000032
Has a distribution area of [ ai,bi]Due to exponential distribution function
Figure BDA0002229925360000033
The lower boundary a of the distribution is 0 and the upper boundary is 0
Figure BDA0002229925360000034
Introduction of constant
Figure BDA0002229925360000035
Figure BDA0002229925360000036
For normalizing piiTo [ -1,1 ]]，Pi,iIs the power of the ith D2D transmitter. I isthRepresents the maximum polymerization interference bearable by the CUE, belongs to the interruption probability of the CUE, and viFor a safe approximation parameter, may be given at { π }iSet as a constant in the family of probability distributions, where
Figure BDA0002229925360000037
Figure BDA0002229925360000038
Satisfy the requirement of
Figure BDA0002229925360000039
νi≥0， i＝1,…,M。
Further, an opportunity constraint approximation method of a channel under an unbounded condition is expressed as:
Figure BDA00022299253600000310
wherein the content of the first and second substances,
Figure RE-GDA00024349107000000311
introduction of constant
Figure RE-GDA00024349107000000312
Wherein
Figure RE-GDA00024349107000000313
Satisfy the requirement of
Figure RE-GDA00024349107000000314
νi≥0，i＝1,…,M，
Figure RE-GDA00024349107000000315
Is 0, i.e. a is 0, let
Figure RE-GDA00024349107000000316
Is a constant, b is
Figure RE-GDA00024349107000000317
Figure RE-GDA00024349107000000318
Is composed of
Figure RE-GDA00024349107000000319
Further, a non-convex nonlinear fraction programming optimization problem is converted into an equivalent subtraction problem by using a fractional programming theory, and an objective function can be expressed as:
Figure BDA00022299253600000319
s.t.(26a)or(27)or(28)or(29),
0≤Pi,i≤Pmax,i＝1,…,M,
and converting the converted objective function into a D.C. structure, which can be expressed as:
Figure BDA00022299253600000320
s.t.(26a)or(27)or(28)or(29),
0≤Pi,i≤Pmax,i＝1,…,M,
wherein:
Figure BDA0002229925360000041
and
Figure BDA0002229925360000042
where P represents a decision vector, where φ is a scalar weight,
Figure BDA0002229925360000043
as noise power, PcIs a constant and represents the static coil power consumption.
Further, using the CCCP algorithm to scale the above equation using a first order taylor expansion, the iterative process can be expressed as:
Figure BDA0002229925360000044
where t represents the number of iteration steps,
Figure BDA0002229925360000045
to represent
Figure BDA0002229925360000046
P＝[P1,1,…,PM,M]Gradient of (A), PTIs the transpose of P.
Further, the simulation experiment of the optimal power allocation solution algorithm for obtaining the maximized EE of the D2D user by using the d.c. programming and the interior point method in the step S3 includes the following steps:
s41, initialization, t is 0, P(0)＝Pmax，ξ>0，φ(0)＝0.01；
S42, solving an objective function which is not converted into a D.C. structure by using a CCCP algorithm;
s43, solving the convex problem in the iterative process by adopting an interior point method;
s44, introducing a logarithmic barrier function to convert the problem into an unconstrained optimization problem;
s45, obtaining a search direction by using a quasi-Newton method;
s46, obtaining the optimal step length by searching an Armijo rule through linear feedback;
s47, executing phi(t+1)＝ηEE|P(t+1)Continuing to the next step;
s48, executing t ═ t +1, and continuing the next step;
s49, judging if | h1(P(t+1),φ(t+1)))|<ξ, continue with step 410, otherwise, return to step 42;
and S410, obtaining the optimal distribution solutions P and phi.
Further, a computer program is included, which, when being invoked by a processor, is configured to carry out the steps of the above-mentioned method.
A computer-readable storage medium, having stored thereon a computer program configured to, when invoked by a processor, perform the steps of the above method.
The invention provides a distributed antenna system energy efficiency optimization method, a distributed antenna system energy efficiency optimization system and a storage medium, wherein a non-perfect channel model is adopted in a DAS based on D2D communication, energy efficiency under a bounded statistical channel model and an unbounded statistical channel model is obtained through a Bernstein approximation method, and the method used by the invention can still keep better robustness under the condition of channel fluctuation, so that the method has important significance for selecting a system performance optimization scheme in an actual model.
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The detailed structure of the invention is described in detail below with reference to the accompanying drawings
FIG. 1 is a diagram of a system model of the present invention;
FIG. 2 is a simulation diagram of EE in the bounded error channel model and the unbounded error channel model according to the present invention;
FIG. 3 is a graph of the actual outage probability of the CUE in the bounded error channel model of the present invention;
FIG. 4 is a graph illustrating the actual outage probability of the CUE in the unbounded error channel model of the present invention;
FIG. 5 is a graph of the sensitivity of EE performance in the unbounded error channel model of the present invention to δ selection when E is 0.3, 0.1 and 0.01;
FIG. 6 shows EE and interference threshold I according to the present inventionthA change in (c).
Example 1
In order to explain technical contents, structural features, and objects and effects of the present invention in detail, the following detailed description is given with reference to the accompanying drawings in conjunction with the embodiments.
Referring to fig. 1, the present embodiment provides a method for optimizing energy efficiency of a distributed antenna system, including the following steps:
s1, establishing a D2D communication system model in a distributed antenna system, considering a downlink DAS cell, wherein N randomly distributed remote access units are arranged in the cell, DAS only provides service for a CUE, M D2D pairs in the DAS cell share the same spectrum band with the CUE, a transmitting end and a receiving end of the D2D are respectively marked as D2D-T and D2D-R, assuming that a user and the remote access unit are both provided with only one antenna, assuming that channel information of the CUE and the remote access unit is perfect and the state of the rest channel information is imperfect, establishing a channel model, and determining an optimized objective function;
s2, carrying out approximate transformation on the constraint condition with the imperfect channel information, and solving a convex approximate form of the non-convex constraint by adopting an approximate method;
s3, converting the inequality constraint obtained in the step S2 into an equivalent subtraction problem by using a score programming theory, and obtaining an optimal power distribution solution when the D2D user maximizes EE by using a D.C. programming and an interior point method;
and S4, carrying out simulation experiments.
Step 2 comprises an opportunity constraint approximation method of the channel under the bounded condition and an opportunity constraint approximation method of the channel under the unbounded condition, wherein the approximation method is a Bernstein approximation method.
In this embodiment, the radius of the cell is R, and the channel links involved in the cell are:
1) the link from the RAU to the CUE is named as an RAU-CUE link;
2) the link from RAU to D2D-R is named as RAU-DR link;
3) the link from D2D-T to D2D-R is named as DT-DR link;
4) the link of D2D-T to CUE is named as DT-CUE link.
Wherein the CSI between the CUE and the RAU is assumed to be fully known. However, uncertainty occurs in other links. In practice, CSI between D2D and RAU and between D2D pairs of links is often difficult to obtain due to delayed feedback and user mobility. Furthermore, due to lack of cooperation with the cellular network, it is difficult to accurately estimate the link between D2D and the CUE, so the link CSI between D2D and the CUE is assumed to be imperfect.
In case of perfect CSI, the channel power gain of the nth RAU to CUE (RAUn-CUE) link, i.e. the RAUn-CUE link, is defined as:
Hn＝Ln|gn|2, (1)
wherein g isnFor small-scale fading channels, Xn＝|gn|2Is an exponential distributionRandom variable with parameters 1, Xn～E(1)。LnIs the large-scale fading channel gain, which can be expressed as:
Figure BDA0002229925360000071
wherein s isnis shadow fading, the path loss exponent α typically varies between 3.0 and 5.0, and c is constantnIndicating the distance between the CUE and the nth RAU.
For the RAU-DR link, the CSI of the DT-DR link and the DT-CUE link is imperfect, so the small-scale fading channel can be modeled as:
Figure BDA0002229925360000072
wherein
Figure BDA0002229925360000073
Refers to an estimate of g, which is constant.
Figure BDA0002229925360000074
An estimation error representing g, an
Figure BDA0002229925360000075
The process is not related to the process,
Figure BDA0002229925360000076
0<σ2<1. the coefficient ω is a constant between 0 and 1. Similar to the case of perfect CSI, the channel power gain H in the case of imperfect CSI is given by:
Figure BDA0002229925360000077
where L represents the large-scale fading channel gain. For convenience, we rewrite H to be:
Figure BDA0002229925360000078
wherein
Figure BDA0002229925360000079
Figure BDA00022299253600000710
Is a random variable subject to exponential distribution, i.e.
Figure BDA00022299253600000711
Figure BDA00022299253600000712
Represents
Figure BDA00022299253600000713
Is measured.
D2D communication may effectively improve the performance of cellular networks. However, a prerequisite for D2D communication to access the cellular network as a supplementary network in the cellular network is to ensure proper communication for cellular users. But accurate CSI of the channel between the D2D users CUE is difficult to determine due to channel estimation errors and delayed feedback. According to the channel statistical model proposed by equation (5), the interference of the D2D user to the CUE should be lower than the threshold tolerable for the CUE under channel uncertainty, and this constraint can be considered as an opportunistic constraint. The opportunity constraint may be expressed as:
Figure BDA00022299253600000714
wherein (6) indicates that the aggregate interference suffered by the CUE is less than IthThe probability in the case should be greater than 1-e, e between 0 and 1, Hi,0Representing the interference channel power gain, P, of the DTi-CUE linki,iIs the power of the ith D2D transmitter. I isthIndicating the maximum aggregate interference that the CUE can tolerate. E can be regarded as the outage probability of the CUE.
The SINR of the ith D2D user may be expressed as:
Figure BDA0002229925360000081
Pi,iis the transmit power, P, of the DTi-DRi linkn,0Is the transmit power between RAUn-CUE. The power of additive white gaussian noise can be expressed as
Figure BDA0002229925360000082
P＝[P1,1,P2,2,…,PM,M]Representing all D2D user transmit power vectors. Assuming that the system bandwidth is normalized to unity bandwidth, the sum SE of D2D users can be written as:
Figure BDA0002229925360000083
according to the existing work, the EE of the D2D user can be defined as the ratio of the sum SE and the total power consumption, which can be expressed as:
Figure BDA0002229925360000084
wherein P iscIs a constant and represents the static coil power consumption.
In a downlink DAS with a D2D communication system, the EE maximization problem for all D2D users under interference constraints of D2D users on the CUE can be expressed as:
Figure RE-GDA0002434910700000086
wherein P ismaxRepresenting the maximum transmit power of D2D.
Example 2
The first constraint of the problem (10) is intractable because it is not a convex set and the validity of the constraint is difficult to guarantee. Moreover, even if the distribution function of H is fully known, the constraints are still computationally difficult to handle. Bernstein approximation is a useful approximation method for dealing with opportunistic constraint problems by converting opportunistic constraints into security-computationally-easy constraints. The invention utilizes a Bernstein approximation method to convert non-convex constraints into convex inequality constraints. The form in which the opportunity constraint is considered is as follows:
Figure BDA0002229925360000091
where P represents a decision + vector, { { f1(P)},…,{fM(P) } is a mapping of P. { zeta-meter1,…,ζMDenotes a random variable whose margin distribution is denoted as { π }1,…,πM}. Suppose { ζ1,…,ζMAre independent of each other, while assuming { π }1,…,πMIs between [ -1,1 }]Is bounded, which means-1 ≦ ζi1, i is equal to or less than 1, … and M. Then, the chance constraint (11) can be conservatively approximated as:
Figure BDA0002229925360000092
wherein
Figure BDA0002229925360000093
Note that equation (12) is an approximation of Bernstein for (11), which is at (t)>0, P) is convex. If Λi(y) can be efficiently computed and the opportunity constraint problem can be efficiently approximated. In general, use is made of ΛiThe upper limit of (y) can be effectively simplified in calculation, and the original formula can be expressed as:
Figure BDA0002229925360000094
wherein
Figure BDA0002229925360000095
Figure BDA0002229925360000096
Satisfy the requirement of
Figure BDA0002229925360000097
νi≥0，i＝1,…,M。
Figure BDA0002229925360000098
Figure BDA0002229925360000099
V and viIs a safe approximation parameter that can be given at { π }iSet as a constant in the family of probability distributions. Use of Λ in (13)i(. o) replacement of Λ in (12)i(. to) get a more conservative approximation:
Figure BDA0002229925360000101
suppose that
Figure BDA0002229925360000102
Has a distribution area of [ ai,bi]. Due to exponential distribution function
Figure BDA0002229925360000103
The lower boundary a of the distribution is 0 and the upper boundary is 0
Figure BDA0002229925360000104
Introduction of constant
Figure BDA0002229925360000105
For normalizing piiTo [ -1,1 ]]. Then ζiCan be expressed as:
Figure BDA0002229925360000106
order:
Figure BDA0002229925360000107
and
fi(P)＝αiPi,i,i＝1,…,M。 (17)
substitution into f0(P) and fiThe approximate inequality of the first constraint can be obtained (10) in (P) to (14)Comprises the following steps:
Figure BDA0002229925360000108
wherein
Figure BDA0002229925360000109
It is obvious that the last term of the formula (18) can be utilized2Norm and l1Relationships of a norm, i.e. | x |)2≤‖x‖1A conservative approximation of equation (18) is obtained as:
Figure BDA00022299253600001010
the present invention assumes
Figure BDA00022299253600001011
Is bounded and converts a non-convex opportunistic constraint into a convex inequality constraint using Bernstein approximation, the above equation being an opportunistic constraint approximation method for channels with bounded knowledge.
Example 3
It is not rigorous to use a bounded channel model in a real system. Because of the dynamic nature of the wireless channel, the error channel profile is always unbounded, and it is therefore more practical to consider the unbounded error channel model. Then, we introduce the unbounded support CSI channel model. Definition of
Figure BDA0002229925360000111
Figure BDA0002229925360000112
And
Figure BDA0002229925360000113
chance constraint Pr { I ≦ IthIt can be rewritten as:
Figure BDA0002229925360000114
order:
Figure BDA0002229925360000115
it can be clearly seen that the opportunity constrained case using the unbounded CSI channel model is very difficult to handle and the Bernstein approximation discussed in section 2.1 becomes unavailable. However, the formula by δ can see that the second term of (20) is much smaller than 1- δ, so we can ignore it, then (10a) can be approximated as:
Figure BDA0002229925360000116
wherein ∈ in (10a) is replaced by ∈2I.e. e2Is composed of
Figure BDA0002229925360000117
And due to
Figure BDA0002229925360000118
Figure BDA0002229925360000119
And about
Figure BDA00022299253600001110
The assumption of independence, can be easily obtained:
Figure BDA00022299253600001111
it is obvious that
Figure BDA00022299253600001112
Is 0, i.e. a is 0. Order to
Figure BDA00022299253600001113
Is a constant, then b can be expressed as:
Figure RE-GDA00024349107000001114
finally, the unbounded CSI channel model is converted into the bounded supported CSI channel model, and the unbounded distribution situation of the channel gain can be solved by adopting Bernstein approximation.
Example 4
How to find the optimal power allocation when the D2D user maximizes EE is discussed. While real-time channel gain and instantaneous SINR are not available, it is reasonable to see the D2D user as a similarly stationary user, so long-term SINR can be used instead of instantaneous SINR over a very small period of time. However, the long-term SINR has the same trend as the statistical average of the SINR. To simplify the system model and make it mathematically tractable, we use the statistical expectation of the channel gain to calculate the SINR, which can be written as:
Figure BDA0002229925360000122
in the problem (10)
Figure BDA0002229925360000123
Has a distribution domain of [ a, b]，a＝0，
Figure BDA0002229925360000124
Utilizing the first constraint of (10) by l2The approximation problem can be expressed as:
Figure RE-GDA0002434910700000124
since | x |2≤‖x‖1(26) the first constraint may be replaced by (27):
Figure BDA0002229925360000126
because of the channel distribution
Figure BDA0002229925360000127
Is unbounded and is used in section 2.2The method handles constraints by2And l1Approximating the first constraint of (26) by the equations (28) and (29):
Figure BDA0002229925360000131
and
Figure BDA0002229925360000132
wherein
Figure BDA0002229925360000133
βiand alphai' where a is 0 and
Figure BDA0002229925360000134
time is a constant.
Non-convex interference constraints can be converted to convex inequality constraints using the Bernstein approximation method. However, the objective function is still a non-convex nonlinear fractional programming optimization problem, and cannot be solved by using the traditional convex optimization method. However, this problem can be converted into an equivalent subtraction problem using fractional programming theory:
Figure BDA0002229925360000135
where phi is one is a scalar weight. According to the fractional programming theory, the following theorem proves:
theorem1 order
Figure RE-GDA0002434910700000135
And
Figure RE-GDA0002434910700000136
if and only if F (phi)*)＝0， f(φ*)＝P*When (30) is the solution P of the optimal power allocation*Is also the optimal solution of equation (26).
The original problem has been converted to an equivalent subtraction problem, but the objective function (30) is still a non-convex and non-linear problem. (30) Can be converted to a d.c. structure, i.e.:
Figure BDA0002229925360000138
wherein
Figure BDA0002229925360000139
And
Figure BDA0002229925360000141
Figure BDA0002229925360000142
for the case where P is strictly concave, the concave shape is,
Figure BDA0002229925360000143
is strictly convex for P. This and above problems can be solved using the concave-convex process (CCCP) algorithm. In each step, a first-order Taylor expansion is used for conversion
Figure BDA0002229925360000144
The iterative process can be expressed as:
Figure BDA0002229925360000145
where t represents the number of iteration steps,
Figure BDA0002229925360000146
to represent
Figure BDA0002229925360000147
P＝[P1,1,…,PM,M]Gradient of (A), PTIs the transpose of P. The CCCP algorithm converts the non-convex nonlinear optimization problem into a standard convex optimization problem, and then obtains an optimal power distribution solution through an interior point method.
The method converts the original problem into an equivalent subtraction problem by introducing a fractional programming theory, and then obtains an optimal power distribution solution by using a D.C. programming and an interior point method.
Example 5
The simulation experiment for designing the optimal power distribution solution algorithm for obtaining the D2D user maximum EE by using the D.C. programming and the interior point method comprises the following steps:
s41, initialization, t is 0, P(0)＝Pmax，ξ>0，φ(0)＝0.01；
S42, solving an objective function which is not converted into a D.C. structure by using a CCCP algorithm;
s43, solving the convex problem in the iterative process by adopting an interior point method;
s44, introducing a logarithmic barrier function to convert the problem into an unconstrained optimization problem;
s45, obtaining a search direction by using a quasi-Newton method;
s46, obtaining the optimal step length by searching an Armijo rule through linear feedback;
s47, executing phi(t+1)＝ηEE|P(t+1)Continuing to the next step;
s48, executing t ═ t +1, and continuing the next step;
s49, judging if | h1(P(t+1),φ(t+1)))|<ξ, continue with step 410, otherwise, return to step 42;
and S410, obtaining the optimal distribution solutions P and phi.
The specific simulation parameters in this embodiment are that the radius R of the cell is 500m, and the noise power δ0 2Is-104 dbm, and static power consumption Pst1.5W, number of D2D pairs 4, maximum transmission power of the sender in D2D pair
Figure BDA0002229925360000151
10dbm, and 4 for the path loss exponent α fig. 2 shows the variation of EE with e, and as can be seen from fig. 2, EE increases with increasing eAnd then becomes loose. In addition, due to l1Approximate ratio l2The approximation is more stringent, which leads to l1EE is less than l under similar conditions2Approximately the following EE. Meanwhile, as can be seen from fig. 2, the EE of the unbounded error channel model is lower than that of the bounded error channel model. This means that the channel fluctuation range for the unbounded case is wider than for the bounded case. However, in the perfect CSI case, the value of EE does not change with e, since the opportunity constraint is a deterministic constraint that is independent of e. From fig. 2, we can conclude that channel uncertainty affects system performance, and perfect CSI has a significant impact on system performance.
Fig. 3 and 4 show the actual outage probability of the CUE under the bounded error channel model and the unbounded error channel model, respectively. First generate 104Random channels of exponentially distributed CUEs. As can be seen from fig. 3, the actual percentage of interruptions in the bounded error channel model is well below the theoretical value. The reason is that robust EE optimization based on opportunity constraint can effectively control the transmission power of D2D users, thereby always satisfying the communication requirements of the CUE. At the same time,/2The approximate actual interruption percentage is higher than l1. This is mainly because of l1Approximate ratio l2More strictly, this makes interference controlled1Approximate ratio l2The approximation is more efficient. From fig. 4, we can not only draw the same conclusion as fig. 3, but also see that under the unbounded error channel model,/1And l2The approximate actual interruption percentage is close to 0, which means that the unbounded error channel model is closer to the actual channel fluctuation model, and the power control of the D2D user is more efficient than the bounded error channel model.
FIG. 5 shows the sensitivity of EE performance in the unbounded error channel model to δ selection for ∈ 0.3, ∈ 0.1, and ∈ 0.01. We can see that the EE performance is not sensitive to delta changes when e is 0.01 or e is 0.1. The reason is that when ∈ is equal to 0.01, ∈ is2Always equal to 1 and the values of a and b tend to be stable. The same is true for e 0.1. However, when ∈ equals 0.3, the network topology becomes less stable, and therefore less robust than ∈ equals 1Or 0.01. It follows that we need to carefully choose e and δ to design a stable system.
FIG. 6 shows EE and interference threshold IthAs can be seen from fig. 6, with the interference threshold IthEE gradually increased. This is because the greater the interference that the CUE can withstand, the greater the EE that the D2D user can obtain. Furthermore, the more stringent the constraint approximation, the stronger the interference control of the D2D user, the smaller the EE that can be obtained for the D2D user. Thus, using l under unbounded error channel gain model1The EE obtained by the approximate method is minimum.
In summary, according to the energy efficiency optimization method and the storage medium for the distributed antenna system provided by the invention, the imperfect channel model is adopted in the DAS based on D2D communication, and the energy efficiency under the bounded statistical channel model and the unbounded statistical channel model is obtained by the Bernstein approximation method.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes, which are made by the contents of the present specification and the accompanying drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (9)

1. A distributed antenna system energy efficiency optimization method is characterized by comprising the following steps:
s1, establishing a system model of D2D communication in a distributed antenna system, considering a downlink single-cell DAS cell, wherein N randomly distributed remote access units are arranged in the cell, the DAS only provides service for a CUE, M D2D pairs are also arranged in the DAS cell, the DAS cell shares the same spectrum band with the CUE, a transmitting end and a receiving end of the D2D are respectively marked as D2D-T and D2D-R, assuming that a user and the remote access unit are both provided with only one antenna, assuming that channel information of the CUE and the remote access unit is perfect, and the rest channel information state is imperfect, establishing a channel model, and determining an optimization objective function;
s2, carrying out approximate transformation on the constraint condition with the imperfect channel information, and solving a convex approximate form of the non-convex constraint by adopting an approximate method;
s3, converting the inequality constraint obtained in the step S2 into an equivalent subtraction problem by using a score programming theory, and obtaining an optimal power distribution solution when the D2D user maximizes EE by using a D.C. programming and an interior point method;
and S4, carrying out simulation experiments.
2. The method for energy efficiency optimization of a distributed antenna system according to claim 1, wherein the step S2 includes an opportunity constraint approximation method for a bounded channel and an opportunity constraint approximation method for an unbounded channel, and the opportunity constraint approximation method is a Bernstein approximation method.
3. The method for energy efficiency optimization of a distributed antenna system according to claim 2, wherein the chance constraint approximation method of the channel under the bounded condition is represented as:
Figure FDA0002229925350000011
wherein the content of the first and second substances,
Figure FDA0002229925350000012
said Hi,0For the interference channel power gain of DTi-CUE link, assume
Figure FDA0002229925350000013
Has a distribution area of [ ai,bi]From an exponential distribution function
Figure FDA0002229925350000014
The lower boundary a of the distribution is 0 and the upper boundary is 0
Figure FDA0002229925350000015
Introduction of constant
Figure FDA0002229925350000016
Figure FDA0002229925350000017
For normalizing piiTo [ -1,1 ]]，Pi,iIs the power of the ith D2D transmitter. I isthMaximum polymerization interference bearable by CUE, interruption probability of CUE, viFor a safe approximation parameter, may be given at { π }iSet as a constant in the family of probability distributions, where
Figure FDA0002229925350000018
Satisfy the requirement of
Figure FDA0002229925350000019
νi≥0，i＝1,…,M。
4. The distributed antenna system energy efficiency optimization method and storage medium of claim 3, wherein the chance constraint approximation method for a channel under unbounded conditions is expressed as:
Figure RE-FDA0002434910690000021
wherein the content of the first and second substances,
Figure RE-FDA0002434910690000022
introduction of constant
Figure RE-FDA0002434910690000023
Wherein
Figure RE-FDA0002434910690000024
Satisfy the requirement of
Figure RE-FDA0002434910690000025
Figure RE-FDA0002434910690000026
Is 0, i.e. a is 0, let
Figure RE-FDA0002434910690000027
Is a constant, b is
Figure RE-FDA0002434910690000028
∈2Is composed of
Figure RE-FDA0002434910690000029
5. The distributed antenna system energy efficiency optimization method of claim 3, wherein a non-convex non-linear fractional programming optimization problem is transformed into an equivalent subtraction problem using fractional programming theory, and the objective function is expressed as:
Figure FDA00022299253500000210
s.t.(26a)or(27)or(28)or(29),
0≤Pi,i≤Pmax,i＝1,…,M,
and converting the converted objective function into a D.C. structure, which is expressed as:
Figure FDA00022299253500000211
s.t.(26a)or(27)or(28)or(29),
0≤Pi,i≤Pmax,i＝1,…,M,
wherein:
Figure FDA00022299253500000212
and
Figure FDA00022299253500000213
where P represents a decision vector, where φ is a scalar weight,
Figure FDA0002229925350000031
as noise power, PcIs a constant and represents the static coil power consumption.
6. The method and storage medium for energy efficiency optimization of distributed antenna systems according to claim 5, wherein the CCCP algorithm is used to perform first order Taylor expansion scaling
Figure FDA0002229925350000032
The iterative process can be expressed as:
Figure FDA0002229925350000033
where t represents the number of iteration steps,
Figure FDA0002229925350000034
to represent
Figure FDA0002229925350000035
P＝[P1,1,…,PM,M]Gradient of (A), PTIs the transpose of P.
7. The method and the storage medium for energy efficiency optimization of distributed antenna system according to claim 1, wherein the simulation experiment of the algorithm for obtaining the optimal power distribution solution when the D2D user maximizes EE in step S3 by using d.c. programming and interior point method comprises the following steps:
s41, initialization, t is 0, P(0)＝Pmax，ξ>0，φ(0)＝0.01；
S42, solving an objective function which is not converted into a D.C. structure by using a CCCP algorithm;
s43, solving the convex problem in the iterative process by adopting an interior point method;
s44, introducing a logarithmic barrier function to convert the problem into an unconstrained optimization problem;
s45, obtaining a search direction by using a quasi-Newton method;
s46, obtaining the optimal step length by searching an Armijo rule through linear feedback;
s47, executing phi(t+1)＝ηEE|P(t+1)Continuing to the next step;
s48, executing t ═ t +1, and continuing the next step;
s49, judging if | h1(P(t+1),φ(t+1)))|<ξ, continue with step S410, otherwise, return to step S42;
s410, obtaining an optimal distribution solution P*And phi*。
8. A distributed antenna system energy efficiency optimization system, comprising: computer program configured to perform the steps of the method according to any of claims 1-7 when invoked by a processor.
9. A computer-readable storage medium, characterized in that the computer-readable storage medium stores a computer program configured to, when invoked by a processor, perform the steps of the method according to any one of claims 1-7.
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