CN108599831A - A kind of robust beam forming design method of cloud wireless access network - Google Patents

Abstract

The invention discloses a kind of robust beam forming design methods of cloud wireless access network.There is step 1 including step:It determines model, increases by two restrictive conditions, Optimized model；Step 2：It converts two norm problems in former problem to linear problem using SDP methods；Step 3：Pass through l₀The approximate method of norm eliminates reluctant l₀Norm problem；Step 4：The probabilistic influence of signal is eliminated using Markov inequality；Step 5：It is a series of convex optimization problems convenient for solving that complicated beam forming, which is designed subproblem abbreviation, using MM algorithms；Step 6：Each subproblem is solved using ADMM algorithms.In the application, the maximum available transmission energy consumption of required communication quality and each base station of user need to only be set, it is i.e. uncertain to each user progress beam forming design in channel state information using algorithm proposed by the present invention, while so that meeting base station energy consumption constraint, most users meet Signal to Interference plus Noise Ratio constraint.

Description

A Robust Beamforming Design Method for Cloud Radio Access Network

technical field

The invention relates to a wireless communication and signal processing method, in particular to a wireless communication method suitable for an environment of uncertain channel information.

Background technique

Cloud radio access network is an emerging network architecture, which has the dual benefits of improving spectrum utilization and energy utilization at the same time. In the cloud radio access network, the base stations are connected to the central processor through digital backhaul links, so as to realize cross-site joint data processing and precoding. In order to improve energy utilization, the cloud radio access network architecture adopts the following three methods to save energy consumption: First, under the cloud radio access network architecture, most of the baseband signal processing functions in traditional base stations can be migrated to cloud computing centers , so that the high-cost and high-power base station in the traditional network architecture can be replaced by a low-cost and low-power radio remote head (RRH). Second, the existence of the central processing unit can also provide the function of joint precoding of user messages to reduce interference. Since less interference is generated, the transmit power at the base station can be reduced. Third, under normal circumstances (especially during off-peak hours), most of the network resources may be idle, and the central processor can perform joint resource allocation among base stations to realize on-demand allocation of resources, and put idle base stations into Sleep mode saves energy.

Although the cloud radio access network has a huge energy-saving advantage, due to the introduction of the central processing unit, a large amount of energy is lost on the backhaul link between the base station and the central processing unit. At present, most of the beamforming designs for cloud wireless access networks are based on ideal channels. The communication quality of users cannot be guaranteed in the changed channel environment. How to ensure the communication quality of users in the case of errors in the channel environment and at the same time significantly reduce system energy consumption has become a major problem in the development of cloud wireless access networks.

Contents of the invention

The purpose of the present invention is to solve the above problems and provide a cloud wireless access network beamforming design method suitable for realizing minimum energy consumption and stable transmission when the channel environment is uncertain, including: eliminating the channel by establishing a probabilistic channel model The impact of errors on communication quality improves the robustness of the system; the activation and sleep states of the base station are introduced to reduce energy consumption; the energy consumption of the cloud wireless transmission network in the downlink is mainly derived from the following three aspects: base station The state (activation, sleep), the transmission energy consumption of the base station and the energy loss of the backhaul link between the central processing unit and the base station, establish a suitable energy consumption model to ensure the minimum energy consumption of the network.

Specifically, the present invention adopts the following technical solutions to realize,

A robust beamforming design method for a cloud wireless access network, characterized in that the following steps are adopted:

Step 1, determine the model:

The total power consumption P of the cloud radio access network is represented as

Adding the user's quality of service and base station energy consumption constraints, adding two constraints, the model after optimization is

min P

stSINR _k ≥ γ _k

Step 2: Use the SDP method to convert the two-norm problem in the original problem into a linear problem;

Step 3: Eliminate the intractable l ₀ norm problem by approximating the l ₀ norm;

Step 4: Use Markov inequality to eliminate the influence of signal uncertainty;

Step 5: Use the MM algorithm to simplify the complex beamforming design sub-problems into a series of easy-to-solve convex optimization problems;

Step 6: Use the ADMM algorithm to solve each sub-problem.

The step 2): make Available: Tr(·) represents the rank of the matrix. in Used to distinguish different base stations, where Indicates that the diagonal elements are the diagonal matrix. At this point, the optimization problem can be written as:

Step 3), eliminate the intractable l ₀ norm problem by approximating the l ₀ norm:

For problems with l ₀ norm, the log function approximation method is used to solve the problem. When θ→0, define Such an approximation:

After this approximation, the objective function is approximated by a discontinuous l ₀ norm function to a continuous ln function.

Described step 4): adopt Markov's inequality to eliminate the influence of signal uncertainty:

Write the SINR constraint as: P _r {SINR _k ≥γ _k }≥p _k

Among them, P _r {A} represents the probability of event A occurring, and p _k represents the proportion of the target satisfying the constraint;

Through the Markov inequality, the above probability constraints can be rewritten as:

where E[SINR _k ] is the expectation of SINR _k ;

because

in, Transform the probability constraints into:

So far, the probabilistic SINR can be transformed into the above-mentioned convex constraints.

Said step 5): use the MM algorithm to simplify the complex beamforming design sub-problems into a series of convex optimization problems that are easy to solve, specifically comprising the following steps:

(a) Solve the initial problem as the starting point of the iteration. The concave function part in the objective function is removed, and it is directly transformed into a convex optimization problem as the initial problem. The initial problem of the optimization problem is then written as:

(b) Select a Taylor expansion of the objective function as the upper limit function in the MM algorithm. In an optimization problem with J(x) as the objective function, for each iteration in the MM algorithm, its upper bound function needs to be constructed and the upper bound function should be easy to optimize. For the new upper limit objective function G _n (x) constructed in n iterations, G _n (x _n-1 )=J(x _n ) must be satisfied at the optimization point generated in the last iteration. Therefore, a Taylor expansion can meet the above construction requirements. The concave part of the objective function is constructed with a Taylor expansion to construct a new objective function. The Taylor expansion is as follows:

in, and For two constants, for the ln function in The constant term of the Taylor expansion at . Therefore, the original non-convex optimization problem can be transformed into an iterative problem composed of a series of convex problems through the MM algorithm. Among them, the nth iteration problem can be expressed as:

Described step 6), utilize ADMM algorithm to solve each subproblem, comprise the steps:

Step 6.1) In order to use the ADMM algorithm, first introduce two intermediate variables:

Γ _k,j ＝Tr(H _k W _j ),Π _l,k ＝Tr(B _l W _k )

At this point, the above optimization problem can be rewritten as:

stΓ _k,j -Tr(H _k W _j )＝0

Π _l,k -Tr(B _l W _k )＝0

in, Thus three indicator functions I _C , I _D , I _G are defined, if Γ belongs to the feasible region Then _IC = 0, otherwise _IC = +∞; if Π belongs to the feasible region Then I _D ＝0, otherwise I _D ＝+∞; if W _k belongs to the feasible domain Then I _G =0, otherwise I _G =+∞. Then its augmented Lagrange function can be written as:

in, μ _{l, k} and λ _{k, j} are Lagrangian coefficients, and ρ>0 represents the penalty coefficient of the augmented Lagrangian function.

Step 6.2) Since the above-mentioned channel variable is introduced, the problem form meets the ADMM solution process, and the original problem can be transformed into three relatively simple sub-problems through the ADMM algorithm.

(a) {Γ} update

{Γ} update can be solved by solving an optimization problem, which can be decomposed into K independent small problems:

Although this problem is a convex optimization problem, since the K variables are interrelated and subject to the same constraint, the closed-form solution cannot be obtained. The subgradient algorithm can be used to solve it. The mth update steps are as follows:

The initial value of this algorithm can be set as, Γ _k,k (m)=Γ _k,j (m)=0. Where Δ _m >0 is the subgradient step size, is the Lagrange coefficient.

(b){Π}Update

{Π}Update can also be solved by solving an optimization problem, which can be decomposed into K independent small problems:

Using the KKT condition to find the closed-form solution of the above formula is one of the following:

(c) {W _k } update

Similar to {Γ} update and {Π} update, the update of {W _k } also needs to solve an optimization problem, and the optimization problem can be decomposed into K independent small problems:

stW _k ≥ 0

The projected gradient descent method is used to solve this problem, and the results of each gradient descent method are projected into the feasible region for update iterations. The iteration formula is as follows:

Among them, Proj{·} means projection to the feasible region W _k ≥ 0, s is the step size, which is a positive real number. After the tth iteration of the objective function in gradient at .

The robust beamforming design method of the above cloud wireless access network is characterized in that, with the goal of minimizing energy consumption, a total energy consumption model is established by using the transmission characteristics of the cloud wireless access network, including transmission energy consumption, backhaul link There are three parts of transmission energy consumption and base station energy consumption. The transmit energy consumption is related to the beamforming design of the base station, the energy consumption of the backhaul link is related to the target transmission rate of the user, and the energy consumption of the base station is related to the dormancy attribute of the base station.

The robust beamforming design method of the cloud wireless access network is characterized in that, the stated objective is combined with the characteristics of the actual wireless communication system to establish a total beamforming design problem. In order to reduce energy consumption, a dormant base station model is introduced. When the base station is in the idle state, it is controlled by the central processor of the cloud wireless access network to enter the dormant state; according to the actual communication system, considering that the energy consumption of the base station is limited, and then The energy consumption constraint of the base station is introduced; at the same time, the signal received by the user must meet a certain SINR requirement to ensure the reliability of the communication, thus introducing the SINR constraint of the user.

The robust beamforming design method of the cloud radio access network is characterized in that, the problem is that the channel state information is not deterministic. In wireless communication, channel state information is usually obtained through pilot signals. Due to the existence of random noise and the time-varying characteristics of wireless channels, wireless channel estimation errors are unavoidable, so the channel state information cannot be obtained completely, and only the detection channel state can be obtained. information instead of real channel state information. The beamforming design scheme uses the detected channel state information, considers the real channel state information and the detected channel state information, and uses the Markov inequality method to ensure that the user can also meet the signal-to-interference-noise ratio requirement in the wireless access network with uncertain channels The proportion of users is higher than the set proportion to ensure the robustness of the system.

The robust beamforming design method of the cloud wireless access network is characterized in that the problem is transformed into a series of relatively simple problems by using methods such as SDP, ₁₀ norm approximation, and MM algorithm. Utilize the SDP method to transform the quadratic term of the beamforming design in the problem into a first-order term; use the _l0 norm approximation to convert the discontinuous objective function caused by the _l0 norm into a continuous objective function in the described problem; The converted single optimization problem is transformed into a series of convex optimization problems which are easy to solve by using MM algorithm.

The robust beamforming design method of the cloud wireless access network is characterized in that the problem is to solve a series of complex convex optimization problems containing positive semi-definite constraints. An optimization method based on the ADMM algorithm is proposed, which simplifies the original problem into three easy-to-solve problems, and uses the subgradient descent method, KKT condition and projected gradient descent method to solve the optimization problem respectively.

The actual cloud wireless access network needs to meet the energy consumption constraints of the base station. In the case of user communication quality and considering the imperfect state of the detection channel, beamforming design is performed on it to achieve the minimum energy consumption of the entire network.

In the cloud wireless access network, in order to improve transmission efficiency, the base stations are multi-antenna base stations. Consider that when the base station has data to send, the base station is in the active state, and the base station needs to consume a lot of energy at this time; when there is no data to send on the base station, the base station enters a sleep state, and the base station needs to consume a small amount of energy to monitor user needs. , once there is data to be sent within the jurisdiction, it will immediately turn into the active state.

The energy consumption constraint of the base station means that the transmit power of the base station is limited. In a cloud wireless access network, the transmit power of each base station cannot exceed its specified upper limit of transmit power.

The communication quality requirement of each user refers to that in order for each user to realize normal communication, the received signal must meet the respective SINR requirement. In the cloud radio access network, in order to provide better communication services, a cell may contain multiple base stations, and users can simultaneously receive communication services from multiple base stations to optimize communication quality. Multiple base stations and multiple users in a cell cause unavoidable signal interference between user information. The interference of each user is no longer limited to traditional channel noise, but also includes signal interference from other users. Therefore, the user communication quality requirement in this system refers to the signal-to-interference-noise ratio after considering signal interference.

The indeterminate channel state information refers to the channel through which the signal is transmitted, and the state information of which is not definite. In wireless communication, due to the existence of random noise and the time-varying characteristics of the wireless channel, wireless channel estimation errors are unavoidable, so the channel state information cannot be completely obtained, and the channel error can only be detected through the pilot signal, and the detection channel state Information is uncertain.

Beneficial effects of the present invention:

(1) The present invention utilizes the characteristics of the Cloud RAN system (cloud radio access network system) and adopts a multi-antenna and multi-base station cooperative communication mode to establish a reasonable cloud radio access network energy consumption model. For actual cloud radio access The energy consumption of the network has good theoretical guidance.

(2) The present invention utilizes relevant knowledge of probability theory to establish a communication model of channel error. The probabilistic channel model of the present invention and its method for eliminating random channel errors are not only applicable to the elimination of channel errors in the Cloud RAN system, but also have practical significance for the uncertain channel state problems faced by other wireless systems in practical applications.

(3) The present invention cleverly transforms the original non-convex problem into a series of relatively simple problems by adopting methods such as SDP (Semi-Definite Programming), _l0 norm approximation and MM algorithm (Majorization-Minimization). These conversion methods have a good reference for the conversion and solution of other similar problems.

(4) Introduce the activation and dormancy states of the base station. When the base station has data to send, the base station is in the active state. At this time, the base station needs to consume a large amount of energy; when there is no data to be sent on the base station, the base station enters the sleep state. At this time The base station needs to consume a small amount of energy to monitor user needs. Once there is data to be sent within the jurisdiction, it will immediately switch to the active state. The energy loss of the system can be significantly improved.

(5) seven sub-methods for solving problems are disclosed in the solution method of the present invention:

1) Transform the quadratic optimization problem of the vector into a positive semi-definite relaxation method of the primary optimization problem of the matrix;

2) To solve the channel uncertainty, through the Markov inequality, ensure that the channel that meets the communication requirements is higher than a certain ratio.

3) Solve the ₁₀ approximation problem introduced by the base station due to the different standby energy caused by different working states.

4) An iterative optimization algorithm for beamforming design that systematically reduces energy loss step by step.

5) A beamforming design scheme based on the ADMM algorithm, which converts complex problems into simpler sub-problems.

6) A subgradient descent algorithm for solving mixed optimization parameters.

7) The projection gradient algorithm based on the gradient algorithm can use the projection method to apply the gradient descent method to solve constrained optimization problems.

The present invention can ensure the communication quality of the user and the energy consumption limit of the base station under the condition of uncertain channel state information, and can obtain the beamforming design scheme with the minimum comprehensive energy consumption. It is very suitable for scenarios that require high energy efficiency and user communication quality. In the future, further research can also apply this system to the future 5G wireless access network.

Description of drawings

Fig. 1 is a schematic diagram of the basic framework of the cloud wireless access network system in the method of the present invention

Fig. 2 is the schematic flow sheet of solution in the method of the present invention

Figure 3 is a flow chart of beamforming design based on ADMM algorithm

Detailed ways

The present invention conducts theoretical modeling on the basis of researching non-ideal channels, and performs joint beamforming design on different cloud wireless access networks from the perspective of energy saving, and analyzes the optimization problem at the same time, and the design is suitable The optimization algorithm is used to solve the optimal beamforming design scheme, so that the proposed optimization scheme not only has high energy consumption efficiency, but also has strong anti-interference characteristics and improves the robustness of the system.

The present invention will be further described below in conjunction with the accompanying drawings.

Figure 1 shows the basic architecture of the cloud radio access network system

Assume that in a cloud radio access network system, there are L base stations providing data services for K users. Each base station has N _t antennas, while the user has only one antenna. All base stations are linked to the same CP (central processing unit) through backhaul links, and each user receives an independent data stream from the base station. It is assumed that the information required by the user comes from the CP, and is delivered to each base station after joint processing by the CP. We assume that the CP can obtain channel information through the pilot signal. The obtained channel information is very close to the actual channel information, but it is not the real channel information. At this time, we can model the channel information as:

Among them, h _k is the actual channel state information, is the channel state information detected by the base station, Δh _k is the channel state information error vector, which is used to represent the uncertainty of the channel information, in the actual communication system, Δh _k is a random channel error satisfying the Gaussian distribution, and its distribution satisfies At in means that the mean is 0 and the variance is The normal distribution of , I is the identity matrix.

In the cloud wireless transmission network, the total energy consumption of the system depends on the energy consumption of the base station itself and the energy consumption of the backhaul link. It depends on how much data the base station transmits to the base station through the central processing unit. Next, we will consider the total energy consumption of the system from the following two aspects.

1) Base station energy consumption model: in the present invention, the base station that is in non-working state is set to sleep state, and now the base station only consumes a small amount of energy for monitoring; and for the base station that is in working state, the total energy consumed by the base station should include The energy consumed by the base station itself and the transmission power used by the base station to transmit signals, so the total energy consumption of the base station can be written as:

Among them, P _l,tx is the energy consumption of base station transmission, and η ₁ >0 is a constant indicating the proportion of transmission power, P _l,active is the energy consumed by the base station in the active state, P _l,sleep is the energy consumed by the base station in the sleep state power. Generally speaking, P _l,active >P _l,sleep , so for the central processing unit, putting as many base stations as possible in the sleep state is beneficial to save energy.

2) Energy loss of the backhaul link: The loss of the backhaul link is related to the transmission rate of the central processor to the base station, and the transmission rate is related to the beamforming design and the working mode of the cloud wireless transmission network. Therefore, the backhaul link can be loss Expressed as:

Among them, ρ _l is a constant, which is related to the channel capacity of the backhaul link, is the transmission rate of the backhaul link.

3) Total energy consumption of the signal: Based on the above analysis, the total energy consumption of the system can be expressed as the energy consumption of each base station plus the energy consumption of the backhaul link, which can be written as the following expression:

Among them, ||P _l,tx || ₀ represents the l ₀ norm of P _l,tx , which represents the number of base stations in the active state; P _l , _Δ =P _l,active -P _l,sleep represents the activation state and Power consumption in sleep state is poor.

In the cloud wireless transmission network, in addition to the signal required by itself and Gaussian white noise, the signal received by the receiving end may also have interference between different user signals. For example, user k may receive the signal required by user j. For user As far as k is concerned, the signal of user j is a kind of interference, so in the cloud wireless transmission network, the received signal y _k of user k can be expressed as:

Among them, h _k is a matrix of N _t ×N _t , expressed as a real transmission channel matrix, ω _k is a vector of N _t *L ×1, indicating the beamforming vector sent by the base station; η _k ~CN(0, σ ² ) represents the Gaussian white noise superimposed in the signal transmission process, and σ ² is the noise variance. _sk represents the symbol vector sent. In this paper, we assume that the symbol energy is 1. So the transmit power P _l,tx of the lth base station can be written as:

At this point, it can be seen that the SINR _k of user k is:

At the same time, it can be obtained that the target receiving rate r _k of user k is:

Wherein, Γ _m is a constant, and the parameters are generally set according to actual application scenarios.

Because there are a total of K users in the cloud wireless transmission network, the total transmission rate on the backhaul link from the central processing unit to the base station is equal to the total reception rate. Therefore, the backhaul link transmission rate can be written as:

in, Indicates whether the user is receiving data. If all transmit beams are 0, the user is not receiving data. If not all 0, it indicates that the user is receiving data.

According to the above analysis, the total power consumption P of the cloud wireless access network can be written as:

In the actual wireless access network, not only the minimum energy consumption is required, but also the quality of service of the user and the energy consumption constraints of the base station need to be considered. Therefore, the above problem can be described as an optimization problem, its objective function is the energy consumption function, and there are two constraints that can be written as:

min P

stSINR _k ≥ γ _k

Among them, γ _k is the SINR requirement of user k; P _l is the maximum transmission power of the lth base station. From this, the entire beamforming design problem has been characterized.

The flow chart shown in Figure 2, in the above discussion, the beamforming design problem has been summarized into the form of an optimization problem, it can be seen that the above optimization problem is a non-convex problem, which cannot be solved directly, so we use the 5 A step submethod transforms it into a solvable problem.

The process is detailed as follows:

Step 1): Use the SDP method to transform the two-norm problem in the original problem into a linear problem.

1) SDP: let W _k =ω _k ω _k ^H , as long as W _k with rank 1 can be obtained, it must be decomposed into W _k =ω _k ω _k ^H , so as to obtain ω _k . If W _k ＝ω _k ω _k ^H , we can get: Tr(·) represents the rank of the matrix. in Used to distinguish different base stations, where Indicates that the diagonal elements are The diagonal matrix. At this point, the optimization problem can be written as:

Analyzing the above two equations, the optimization problem is not a convex optimization problem, the main reason comes from two aspects: 1) The objective function contains l ₀ norm function; 2) Δh _k is an uncertain value. So next, we will consider these two aspects to solve this problem.

Step 2): Eliminate the intractable l ₀ norm problem by approximating the l ₀ norm.

2) l ₀ norm approximation. For problems with l ₀ norm, the log function approximation method is generally used to solve the problem. When θ→0, define An approximation can be made like this:

After this approximation, the objective function is approximated by a discontinuous l ₀ norm function to a continuous ln function, which is more meaningful for the subsequent solution.

Step 3): Use Markov inequality to eliminate the influence of signal uncertainty.

3) Markov Inequality

In the optimization problem, due to the uncertain Δh _k , the solution becomes very difficult. By analyzing the actual requirements of the present invention, it can be known that the present invention requires most of the base stations to meet the user’s minimum SINR requirements, so the signal The interference-to-noise ratio constraint can be written as:

P _r {SINR _k ≥γ _k }≥p _k

Among them, P _r {A} represents the probability of event A occurring, and p _k represents the proportion of the target satisfying the constraint. It can be seen that through the above constraints, we can ensure that users with a proportion above p _k can meet the minimum SINR requirement.

Via the Markov inequality, the above probability constraints can be rewritten as:

Among them, E[SINR _k ] is the expectation of SINR _k . Note that the above problem is not completely equivalent to the probabilistic SINR constraint, and the above constraint is more stringent. because,

in, Thus, the probability constraint can be transformed into:

So far, the probabilistic SINR can be transformed into the above-mentioned convex constraints.

Step 4): Use the MM algorithm to simplify the complex beamforming design sub-problems into a series of easy-to-solve convex optimization problems.

4) So far, except that the objective function contains the log function, other optimization problems satisfy the convex optimization problem. To solve the problem that the objective function is a concave function and the constraint condition is a convex function, we often use the MM algorithm for iterative optimization.

(a) Solve the initial problem as the starting point of the iteration. In the present invention, the concave function part in the objective function is removed, and it is directly transformed into a convex optimization problem as the initial problem. Then the initial problem of the optimization problem can be written as:

(b) Select a Taylor expansion of the objective function as the upper limit function in the MM algorithm. In an optimization problem with J(x) as the objective function, for each iteration in the MM algorithm, an upper bound function needs to be constructed and the upper bound function should be easy to optimize. For the new upper limit objective function G _n (x) constructed in n iterations, G _n (x _n-1 )=J(x _n ) must be satisfied at the optimization point generated in the last iteration. Therefore, a Taylor expansion can meet the above construction requirements. The concave part of the objective function is constructed with a Taylor expansion to construct a new objective function. The Taylor expansion is as follows:

in, and are two constants, and are the constant terms of the Taylor expansion of the ln function at W _k ⁽ⁿ⁾ . Therefore, the original non-convex optimization problem can be transformed into an iterative problem composed of a series of convex problems through the MM algorithm. Among them, the nth iteration problem can be expressed as:

Step 5): Use the ADMM algorithm to solve each sub-problem.

5) In this algorithm, a beamforming design method based on the ADMM algorithm is proposed to transform the above-mentioned converted complex convex optimization problems into three simpler optimization problems.

In order to use the ADMM algorithm, first introduce two intermediate variables:

Γ _k,j ＝Tr(H _k W _j ),Π _l,k ＝T _r (B _l W _k )

At this point, the above optimization problem can be rewritten as:

stΓ _k,j -Tr(H _k W _j )＝0

Π _l,k -Tr(B _l W _k )＝0

in, Thus three indicator functions I _C , I _D , I _G are defined, if Γ belongs to the feasible region Then _IC = 0, otherwise _IC = +∞; if Π belongs to the feasible region Then I _D ＝0, otherwise I _D ＝+∞; if W _k belongs to the feasible domain Then I _G =0, otherwise I _G =+∞. Then its augmented Lagrange function can be written as:

in, μ _{l, k} and λ _{k, j} are Lagrangian coefficients, and ρ>0 represents the penalty coefficient of the augmented Lagrangian function.

Figure 3 shows the beamforming algorithm diagram based on the ADMM algorithm. Since the channel variable is introduced above, the problem form has met the ADMM solution process. The original problem can be transformed into three relatively simple sub-problems through the ADMM algorithm.

(a) {Γ} update

It can be seen from Figure 3 that {Γ} update can be solved by solving an optimization problem, which can be decomposed into K independent small problems:

Although this problem is a convex optimization problem, since the K variables are interrelated and subject to the same constraint, the closed-form solution cannot be obtained. The subgradient algorithm can be used to solve it. The mth update steps are as follows:

The initial value of this algorithm can be set as, Γ _k,k (m)=Γ _k,j (m)=0. Where Δ _m >0 is the subgradient step size, is the Lagrange coefficient.

(b){Π}Update

It can be seen from Figure 3 that {Π} update can also be solved by solving an optimization problem, which can be decomposed into K independent small problems:

Using the KKT condition to find the closed-form solution of the above formula is one of the following:

(c) {W _k } update

Similar to {Γ} update and {Π} update, the update of {W _k } also needs to solve an optimization problem, and the optimization problem can be decomposed into K independent small problems:

In the present invention, the projected gradient descent method is used to solve this problem, and the results of each gradient descent method are projected into the feasible domain for update iteration. The iteration formula is as follows:

Among them, Proj{·} means projection to the feasible region W _k ≥ 0, s is the step size, which is a positive real number. After the tth iteration of the objective function in gradient at .

So far, the robust beamforming design derivation and technical details of the cloud wireless access network based on the ADMM algorithm have been published.

The basic principles, main features and advantages of the present invention have been shown and described above. Those skilled in the industry should understand that the present invention is not limited by the above-mentioned embodiments. What are described in the above-mentioned embodiments and the description only illustrate the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will also have Variations and improvements all fall within the scope of the claimed invention. The protection scope of the present invention is defined by the appended claims and their equivalents.

Claims (6)

1. A robust beamforming design method for cloud wireless access network, characterized in that, the following steps are adopted: Step 1, determine the model: The total power consumption P of the cloud radio access network is represented as Adding the user's quality of service and base station energy consumption constraints, adding two constraints, the model after optimization is min P st SINR _k ≥ γ _k Step 2: Use the SDP method to convert the two-norm problem in the original problem into a linear problem; Step 3: Eliminate the intractable l ₀ norm problem by approximating the l ₀ norm; Step 4: Use Markov inequality to eliminate the influence of signal uncertainty; Step 5: Use the MM algorithm to simplify the complex beamforming design sub-problems into a series of easy-to-solve convex optimization problems; Step 6: Use the ADMM algorithm to solve each sub-problem. 2. The robust beamforming design method of a kind of cloud radio access network as claimed in claim 1, is characterized in that, described step 2): Let W _k ＝ω _k ω _k ^H , we can get: Tr(·) represents the rank of the matrix. in Used to distinguish different base stations, where Indicates that the diagonal elements are the diagonal matrix. At this point, the optimization problem can be written as: W _k >= 0. 3. The robust beamforming design method of a cloud wireless access network as claimed in claim 1, wherein said step 3) eliminates the intractable _l0 norm by approximating the _l0 norm question: For problems with l ₀ norm, the log function approximation method is used to solve the problem. When θ→0, define Such an approximation: After this approximation, the objective function is approximated by a discontinuous l ₀ norm function to a continuous ln function. 4. the robust beamforming design method of a kind of cloud wireless access network as claimed in claim 1, it is characterized in that, described step 4): adopt Markov's inequality to eliminate the influence of signal uncertainty: Write the SINR constraint as: P _r {SINR _k ≥γ _k }≥p _k Among them, P _r {A} represents the probability of event A occurring, and p _k represents the proportion of the target satisfying the constraint; Through the Markov inequality, the above probability constraints can be rewritten as: where E[SINR _k ] is the expectation of SINR _k ; because in, Transform the probability constraints into: So far, the probabilistic SINR can be transformed into the above-mentioned convex constraints. 5. The robust beamforming design method of a cloud wireless access network as claimed in claim 1, characterized in that, said step 5): using the MM algorithm to simplify the complex beamforming design sub-problems into a series of A convex optimization problem that is easy to solve, specifically includes the following steps: (a) Solve the initial problem as the starting point of the iteration. The concave function part in the objective function is removed, and it is directly transformed into a convex optimization problem as the initial problem. The initial problem of the optimization problem is then written as: W _k ＞=0 (b) Select a Taylor expansion of the objective function as the upper limit function in the MM algorithm. In an optimization problem with J(x) as the objective function, for each iteration in the MM algorithm, an upper bound function needs to be constructed and the upper bound function should be easy to optimize. For the new upper limit objective function G _n (x) constructed in n iterations, G _n (x _n-1 )=J(x _n ) must be satisfied at the optimization point generated in the last iteration. Therefore, a Taylor expansion can meet the above construction requirements. The concave part of the objective function is constructed with a Taylor expansion to construct a new objective function. The Taylor expansion is as follows: in, and For two constants, for the ln function in The constant term of the Taylor expansion at . Therefore, the original non-convex optimization problem can be transformed into an iterative problem composed of a series of convex problems through the MM algorithm. Among them, the nth iteration problem can be expressed as: W _k >= 0. 6. the robust beamforming design method of a kind of cloud wireless access network as claimed in claim 1, is characterized in that, described step 6), utilizes ADMM algorithm to solve each subproblem, comprises the steps: Step 6.1) In order to use the ADMM algorithm, first introduce two intermediate variables: Γ _k,j ＝Tr(H _k W _j ),Π _l,k ＝Tr(B _l W _k ) At this point, the above optimization problem can be rewritten as: stΓ _k,j -Tr(H _k W _j )＝0 Π _l,k -Tr(B _l W _k )＝0 W _k ＞=0 in, Thus three indicator functions I _C , I _D , I _G are defined, if Γ belongs to the feasible region Then _IC = 0, otherwise _IC = +∞; if Π belongs to the feasible region Then I _D =0, otherwise I _D =+∞; if W _k belongs to the feasible region W _k >=0, then I _G =0, otherwise I _G =+∞. Then its augmented Lagrange function can be written as: in, μ _{l, k} and λ _{k, j} are Lagrangian coefficients, and ρ>0 represents the penalty coefficient of the augmented Lagrangian function. Step 6.2) Since the above-mentioned channel variable is introduced, the problem form has satisfied the ADMM solution process, and the original problem can be transformed into three relatively simple sub-problems through the ADMM algorithm. (a) {Γ} update {Γ} update can be solved by solving an optimization problem, which can be decomposed into K independent small problems: Although this problem is a convex optimization problem, since the K variables are interrelated and subject to the same constraint, the closed-form solution cannot be obtained. The subgradient algorithm can be used to solve it. The mth update steps are as follows: The initial value of this algorithm can be set as, Γ _k,k (m)=Γ _k,j (m)=0. Where Δ _m >0 is the subgradient step size, is the Lagrange coefficient. (b){Π}Update {Π}Update can also be solved by solving an optimization problem, which can be decomposed into K independent small problems: Using the KKT condition to find the closed-form solution of the above formula is one of the following: (c) {W _k } update Similar to {Γ} update and {Π} update, the update of {W _k } also needs to solve an optimization problem, and the optimization problem can be decomposed into K independent small problems: st W _k ≥ 0 The projected gradient descent method is used to solve this problem, and the results of each gradient descent method are projected into the feasible region for update iterations. The iteration formula is as follows: Among them, Proj{·} means projection to the feasible region W _k ≥ 0, s is the step size, which is a positive real number. After the tth iteration of the objective function in gradient at .