CN106411487B - Energy efficient resource allocation method for downlink OFDMA system with fixed base station rated power - Google Patents

Abstract

The present invention relates to a kind of high energy efficiency resource allocation methods of the fixed downlink OFDMA system of base station rated power.The distribution method includes optimal Subcarrier Allocation Algorithm and optimal power allocation algorithm.When carrying out subcarrier distribution, what Base Transmitter came out does not have often a subcarrier to distribute to the strongest user of channel.In optimal power contribution algorithm, optimal total base station power is found using water-filling algorithm and dichotomy.The method of the present invention is fairly obvious to the energy saving effects of high-power ofdm signal transmitting base station, and has the characteristics that low complex degree.

Description

Energy efficient resource allocation method for downlink OFDMA system with fixed base station rated power

technical field

The invention relates to a high-energy-efficiency resource allocation method of a downlink OFDMA system with fixed base station rated power.

Background technique

As one of the important technologies of 4G communication, there is still a huge development prospect in the field of mobile communication. As the sending end of communication signals, the base station often consumes huge energy when sending signals to mobile terminals. Many problems caused by excessive energy consumption also force people to gradually pay attention to energy conservation. How to save energy at the base station while ensuring the user communication rate and quality is one of the focuses of everyone's attention.

Energy efficiency refers to the number of joules consumed to transmit one bit of data. In recent years, many people have started from the perspective of data transmission rate, hoping to find a solution to achieve high energy efficiency. However, this method often has a greater impact on the communication rate. Therefore, it has gradually become a hot spot to consider the issue of energy saving from the direction of the base station's transmitted signal power.

Contents of the invention

The purpose of the present invention is to provide a method for allocating energy-efficient resources in a downlink OFDMA system with fixed base station rated power.

To achieve the above object, the present invention adopts the following technical solutions:

An energy-efficient resource allocation method for a downlink OFDMA system with fixed base station rated power, comprising the following steps:

(1) According to the definition of energy efficiency, determine the objective function and constraints of the optimization problem (P1):

Objective function:

in, and

Restrictions:

f(P)≤P _t ;

Among them, B is the bandwidth of OFDM signals transmitted by the base station, K is the number of subcarriers transmitted, h _u,k (k=1,...,K,u=1,...,U) is the distance from the base station to the user The baseband channel coefficient of the subcarrier, ξ _s (ξ _s <1) is the efficiency of the power amplifier of the base station, P _c is the total circuit power of the base station and all users, σ ² (Watt) is the power of each receiver corresponding to each user The noise power of subcarriers, P _k is the average power of the kth subcarrier of the OFDM signal transmitted by the base station, P _t is the rated total power of the base station, P represents the power allocation set of each subcarrier, and I represents the situation that subcarriers are allocated to users;

(2) Assuming that in the constraints of the optimization problem (P1), the total power consumption of the base station is a fixed value ρ, then the optimization problem (P1) is transformed into an optimization problem (P2):

Objective function:

Restrictions: f(P)=ρ

determined by

Here G _k = max _u {G _u,k }

(3) An optimal subcarrier allocation method is determined in step (2), and the optimization problem (P2) is further transformed into an optimization problem (P3) in combination with the expression of R(I,P) in step (1). :

Objective function:

Restrictions: f(P)=ρ

Using the KKT condition in the convex optimization theory to solve the optimization problem (P3), the power allocation of the subcarriers is obtained as Among them, υ∈R is the Lagrangian multiplier introduced by the equality constraint f(P)=ρ;

(4) Combining the condition ∑ _k P _k (ρ)=ξ _s (ρ-P _c ), using the dichotomy method to find the numerical solution, we get v ^* = μ(ρ) and is a function of ρ;

(5) Using the dichotomy method to find the actual total power ρ ^* of the best energy efficiency of the base station. The specific process is as follows:

It has been proved that when ρ>P _c , is a monotonically increasing strictly concave function that satisfies thus get,

According to the above conditions, draw in the same coordinate system Graphs of η(ρ) and μ(ρ).

It is found that there is a power point ρ ₀ , when ρ increases from P _c to ρ ₀ , μ(ρ) is strictly decreasing, η(ρ) is strictly increasing, and μ(ρ)>η(ρ) (ie ) is always true.

When ρ=ρ ₀ , the two straight lines coincide, μ(ρ ₀ )=η(ρ ₀ ) (ie ) is established.

When ρ is greater than ρ ₀ and monotonically increasing, both μ(ρ) and η(ρ) are strictly decreasing, and μ(ρ)<η(ρ) (ie ) is always true.

ρ ^* = ρ ₀ is the actual total power for optimal energy efficiency of the base station.

Compared with prior art, the present invention has following advantage:

The method of the invention has a very obvious energy saving effect on the high-power OFDM signal transmitting base station, and has the characteristics of low complexity.

Description of drawings

Fig. 1 is a downlink OFDMA system model of the present invention.

Fig. 2 is when the present invention carries out the maximum energy efficiency power distribution, the total power ρ of the base station and the energy efficiency function η (ρ), the data transmission rate function of the optimal energy efficiency and the function image of the Lagrangian variable μ(ρ) with optimal energy efficiency.

Fig. 3 is a flow chart of the method of the present invention.

Detailed ways

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

As shown in FIG. 1 , the base station of a cell transmits OFDM signals to U users of the cell. The total power rating of the base station is _Pt . The total bandwidth of the signal is B Hz, and there are K subcarriers, and each subcarrier is allocated to only one user. The baseband channel coefficient of subcarrier k from the base station to user u is h _u,k (k=1,...,K,u=1,...,U). The efficiency of the power amplifier of the base station is ξ _s (ξ _s <1). The total circuit power of the base station and all users is P _c (not including the power of the base station power amplifier). The noise power of each subcarrier corresponding to each user receiver is σ ² (Watt).

At the same time, the variable P _k ≥ 0 is defined to represent the average power transmitted from the base station to subcarrier k symbols. And the variable t _ku ∈{0,1}, when t _ku =1, subcarrier k is allocated to user u, and when t _ku =0, subcarrier k is not allocated to user u. It can be seen that the optimization variable of energy-efficient resource allocation in the downlink OFDMA system is Where P represents the power allocation set of each sub-carrier, and I represents the situation that the sub-carrier is allocated to the user.

The measure of system energy efficiency is the number of bits transmitted per joule of energy consumed, so it is necessary to find the total power and data transmission rate when the base station transmits signals.

The total power includes circuit power P _c and transmit power P _T , and its specific expression is as follows:

According to the Shannon formula, the data transmission rate from the base station to all users is:

in then in the known In the case of , an algorithm can be executed to find the optimal resource allocation that achieves the maximum energy efficiency when the total power of the base station is fixed.

It is assumed that the total power consumption of the base station is limited below a specified effective value P _t (P _t >P _c ). The resource allocation problem for maximum energy efficiency can be formulated as an optimization problem (P1):

The constraints are:

f(P)≤P _t ;

This embodiment is divided into two parts to solve the above energy efficiency optimization problem. Step 1 performs the optimal allocation of subcarriers, and Step 2 performs the optimal allocation of the power of the transmitted signal of the base station.

The optimal subcarrier allocation method in step 1 is as follows.

Assuming that the total power consumption of the system is a fixed value ρ, then the optimization problem (P1) can be transformed into a spectrally efficient resource allocation problem (P2):

The constraints are:

Formula (3), (4), (5), f(P)=ρ;

but determined by

Here, G _k =max _u {G _u,k }.

The practical meaning of formula (6) is that each subcarrier transmitted by the base station is allocated to the user with the strongest channel, which specifies an optimal subcarrier allocation method. The allocation method should be determined according to the specific environment of the community.

After the optimal allocation of subcarriers is achieved, the next problem is to find a power allocation method that can maximize the energy efficiency of the base station. When the total power consumption is ρ, the maximum energy efficiency expression is:

here,

At this point, finding the optimal resource allocation for problem (P1) is equivalent to first finding

Then I ^* and P ^* (ρ ^* ) are the optimal solution of (P1).

In step 2, the method of optimally allocating the power of the base station's transmitted signal is as follows.

Combining problems (P1), (P2) and formula (8), the optimization problem (P3) for solving P ^* (ρ) is obtained:

The constraints are:

Formula (5), f(P)=ρ

Step 201: The problem (P3) can be solved using the KKT condition of a convex problem.

The Lagrangian multiplier λ∈R ⁿ is introduced into the inequality constraint (5), and a multiplier υ∈R is introduced into the equality constraint condition f(P)=ρ, and the Lagrangian function of the optimization problem (P3) is obtained as :

Then the KKT condition is used to solve the optimization problem. P _k ^* , (λ ^* , v ^* ) are the optimal solutions that satisfy the original function and the dual problem respectively, and at the same time, satisfy the following KKT conditions:

Analytical solution to get:

It can be expressed as:

Step 202: It can be seen from formula (13) that P _k cannot be expressed with a definite analytical formula, but it can be determined that it is a decreasing function about υ, and satisfies ∑ _k P _k (ρ)=ξ _s (ρ -P _c ). Therefore, when the total power ρ of the base station is given a value by using the idea of dichotomy, the specific value of υ corresponding to it is obtained, and then obtained Numerical solution of η(ρ). Step 203: Both η(ρ) and the value of the optimal Lagrangian variable υ ^* are related to ρ. Next, the properties of these three functions and their interrelationships will be analyzed, and then the actual power ρ ^* of the base station transmitting signal will be found when the energy efficiency function η(ρ) reaches the maximum.

Assuming v=μ(ρ), according to the convex optimization theory, we can get:

It can also be proved is a strictly concave function with respect to the increase of ρ. according to The properties of can be approximated to draw a curve that varies with ρ, as shown in Figure 2. The thick solid line in the figure indicates: hour, Image. Then the meaning of the η(ρ) function image (dotted line) is the origin and The connection line between, the meaning of μ(ρ) function image (dotted line) is exist tangent.

Find the derivative with respect to ρ for η(ρ):

Combining with the analysis of Figure 2, it can be seen that when ρ increases from _Pc to ρ ₀ , η(ρ) is strictly increasing, and μ(ρ)>η(ρ) always holds true. When ρ=ρ ₀ , two straight lines coincide, and μ(ρ ₀ )=η(ρ ₀ ) holds. When ρ is greater than ρ ₀ , η(ρ) is strictly decreasing, and μ(ρ)<η(ρ) is always established.

We find that ρ ^* = ρ ₀ , so that ρ ₀ is the distribution point of the best total power. The dichotomy method can be used to find ρ ^* . This process is actually a process of comparing the relationship between μ(ρ) and η(ρ). When the two are equal or approximately equal, it is the power with optimal energy efficiency.

As shown in FIG. 3 , a flow chart of an energy-efficient resource allocation algorithm for the entire downlink OFDMA system is given. The core part of this algorithm is to prove the relationship between μ(ρ) and η(ρ) through observation, and use the dichotomy method to find an energy-efficient power allocation method. In the worst case, its algorithmic complexity is

Claims (1)

1. A method for allocating energy-efficient resources of a downlink OFDMA system with a fixed base station rated power is characterized by comprising the following steps:

(1) according to the definition of energy efficiency, an objective function and a constraint condition of an optimization problem (P1) are determined:

an objective function:

wherein,and is

Constraint conditions are as follows:

f(P)≤P_t；

wherein, B is the bandwidth of the base station to transmit OFDM signals, K is the number of transmitted sub-carriers, h_u,k(K1., K, U1., U) is the baseband channel coefficient of the sub-carrier from the base station to the user, U denotes the total number of users in the cell, ξ_s(ξ_s< 1) efficiency of the power amplifier of the base station, P_cTotal circuit power, σ, for the base station and all users²Noise power, P, for each sub-carrier corresponding to each user receiver_kTransmitting the average power, P, of the k sub-carrier of an OFDM signal to a base station_tIs the nominal total power of the base station,p represents a power allocation set of each subcarrier, and I represents the condition that the subcarriers are allocated to users; when t is_kuWhen 1, subcarrier k is allocated to user u, when t_kuWhen 0, subcarrier k is not allocated to user u;

(2) assuming that the total power consumption of the base stations is a fixed value P in the constraints of the optimization problem (P1), the optimization problem (P1) is transformed into an optimization problem (P2):

an objective function:

constraint conditions are as follows:f(P)＝ρ

is determined by the following formula

Where G is_k＝max_u{G_u,k}

(3) Determining an optimal subcarrier allocation mode in the step (2), and further converting the optimization problem (P2) into an optimization problem (P3) by combining the expression of R (I, P) in the step (1):

an objective function:

constraint conditions are as follows:f(P)＝ρ

solving an optimization problem (P3) by utilizing a KKT condition in a convex optimization theory to obtain the power distribution of subcarriers asWherein υ e R is a lagrangian multiplier introduced by an equivalent constraint condition f (p) ═ ρ;

(4) combining conditions sigma_kP_k(ρ)＝ξ_s(ρ-P_c) Using a dichotomy to obtain a numberMethod of value solution to obtainv^*Mu (ρ) andis a function of p; i is^*And P^*(ρ^*) The optimal solution is (P1); p_k ^*,(λ^*,v^*) Respectively, the optimal solutions satisfying the primitive function and the dual problem;

(5) actual total power rho for finding optimal energy efficiency of base station by utilizing dichotomy^*The specific process is as follows:

proved that P is more than P_cWhen the temperature of the water is higher than the set temperature,is a monotonically increasing function of the exact concavity while satisfyingSo as to obtain the compound with the characteristics of,

according to the above conditions, drawing in the same coordinate systemη (p) and μ (p), it was found that there was a power point ρ₀ρ from P_cIncrease to p₀When μ (ρ) is strictly decreasing, η (ρ) is strictly increasing, and μ (ρ) > η (ρ), i.e.Always being true; when rho is rho₀When the two lines coincide, μ (ρ)₀)＝η(ρ₀) I.e. byIf true; when rho is greater than rho₀Increasing all the time, mu (rho) and η (rho) are strictly decreasing, and mu (rho) < η (rho), namelyAlways being true; rho^*＝ρ₀The base station energy efficiency is the optimal actual total power.