CN108243431A - Power Allocation Algorithm for UAV Relay System Based on Energy Efficiency Optimal Criterion - Google Patents

Abstract

The invention discloses a kind of power distribution algorithms of the unmanned plane relay system based on efficiency optiaml ciriterion, first on the basis of double jump amplification forwarding relay transmission model, the Optimized model of power distribution is established, power distribution problems are converted into the optimization problem for solving maximum system efficiency.In the solution procedure of optimal power allocation, our first fixed transmission signal powers obtain Wave beam forming prioritization scheme；Then by big signal-to-noise ratio section approximation, original non-convex optimization problem is converted into convex optimization problem；Finally using KKT conditions, the closed-form solution of power allocation scheme is calculated.Emulation experiment shows the closed-form solution of algorithm acquisition disclosed in this invention close to loop iteration method, so as to reduce algorithm complexity.

Description

Power Allocation Algorithm for UAV Relay System Based on Energy Efficiency Optimal Criterion

technical field

The invention belongs to the field of unmanned aerial vehicle relay communication, relates to the energy efficiency of relay communication, power distribution, beam forming, convex optimization in the optimization method, and can be used in practical engineering fields such as unmanned aerial vehicle battlefield reconnaissance and environmental monitoring.

Background technique

In recent years, wireless relay technology has received sufficient attention and development. Compared with the traditional single-hop communication, the multi-hop communication technology of relay-assisted transmission can significantly expand the coverage of the communication network, improve the reliability of the communication system and increase the communication capacity of the system. Although communication satellites can realize relay communication functions, they are expensive, have large transmission delays, long construction periods, high maintenance costs, and communication blind spots, which prevent them from being widely used. In contrast, as a relay platform, UAV aircraft has unique advantages such as good mobility, flexible deployment and control, large coverage of high-altitude operations, and convenient update of communication equipment. It has shown broad potential in many fields such as battlefield reconnaissance and environmental monitoring. Application prospect.

Using UAV as a relay transmission platform can quickly and conveniently establish an efficient and reliable communication data transmission link. Therefore, UAV-based relay transmission technology has attracted widespread attention from scholars at home and abroad. The research on UAV-based relay transmission technology mainly includes the following aspects: study the communication model of using UAV as a communication relay node under the condition of obstacles, and achieve the optimization goal through the algorithm [1], and obtain the UAV Optimal location for relay nodes. The UAV relay transmission system under asymmetric fading channel [2] is studied, and the theoretical expressions of the main performance indicators of wireless communication systems such as system outage probability, ergodic capacity and average symbol error rate are derived. Research on the search path planning and communication performance optimization problems in the process of multi-UAV completing communication relay tasks [3]. Research on the optimal design and performance analysis of unmanned aerial vehicle relay double-hop wireless link [4] proves the advantages of multi-antenna configuration and optimal design of the UAV relay platform.

However, we see that the current research focus is mainly on the optimal layout of relays, flight path and network performance optimization, and less research on power allocation algorithms. In the era of increasingly scarce resources, reducing energy consumption has become a hot spot in the research of the communication industry. Power is an important resource in the relay communication system, and its allocation will directly affect the performance of each link, and then affect the energy efficiency of the entire communication system. At present, extensive research work has been carried out on power allocation algorithms for energy efficiency of wireless communication systems at home and abroad. The power allocation algorithms for the energy efficiency of wireless communication systems mainly include the following: based on the joint allocation method of the number of carriers in flat fading channels and user transmit power [5], based on the DF relay protocol, under the condition that the two hop rates are equal, A link adaptation algorithm [6] is proposed for relay selection and power allocation. A multi-objective algorithm [7] is proposed to implement a user selection and power allocation scheme, so as to minimize the transmit power while ensuring the maximum throughput. The problem of maximizing the total energy efficiency of the weight is studied. By solving the system carrier and the The power allocation can maximize the weight energy efficiency, and two algorithms of optimal and suboptimal are proposed [8], but this algorithm only obtains the lower boundary of maximizing the objective function through the greedy algorithm. Therefore, we can see that the current power allocation algorithms [5]-[8] are mainly based on the optimal iterative algorithm, the computational complexity is high, and the closed-form solution is difficult to obtain.

For details on UAV-based relay transmission technology research, see:

[1] Burdakov O, Doherty P, Holmberg K, et al.Optimal placement of UV-based communications relay nodes[J].Journal of Global Optimization,2010,48(4):511-531.

[2] Ouyang Jian, Zhuang Yi, Xue Yu, et al. UAV relay transmission scheme and performance analysis in asymmetric fading channel [J]. Acta Aeronautics Sinica, 2013, 34(1): 130-140.

[3] Fu Xiaowei, Cheng Simin, Gao Xiaoguang. Path Planning and Communication Optimization in UAV Cooperative Relay Process [J]. Systems Engineering and Electronic Technology, 2014,36(5):890-894.

[4] Lin Min, Wei Heng, Ouyang Jian, et al. Optimal design and performance analysis of unmanned aerial vehicle relay double-hop wireless link [J]. System Engineering and Electronic Technology, 2015,37(6):1391- 1398.

The power allocation algorithm algorithm for the energy efficiency of the wireless communication system is detailed in:

[5] Akbari A, Hoshyar R, Tafazolli R. Energy-efficient resource allocation in wireless OFDMA systems[C]//Personal Indoor and Mobile Radio Communications (PIMRC), 2010IEEE 21st International Symposium on.IEEE, 2010:1731-1735.

[6]Ho C Y, Huang C Y. Energy efficient subcarrier-power allocation and relay selection scheme for OFDMA-based cooperative relay networks[C]//Communications(ICC),2011IEEE International Conference on.IEEE,2011:1-6.

[7] Devarajan R, Jha S C, Phuyal U, et al. Energy-aware resource allocation for cooperative cellular network using multi-objective optimization approach [J]. IEEE Transactions on Wireless Communications, 2012, 11(5): 1797-1807.

[8] Miao G, Himayat N, Li G Y. Energy-efficient link adaptation frequency-selective channels [J]. IEEE Transactions on communications, 2010, 58(2): 545-554.

Contents of the invention

Based on the shortcomings of the above algorithms, the present invention proposes a power allocation algorithm for the UAV relay system based on the optimal energy efficiency criterion. This algorithm mainly studies the energy efficiency of the UAV relay communication system under the Amplify and Forward (AF) protocol. distribution problem. The algorithm of the present invention takes the maximization of system energy efficiency as the design goal. Under the condition that the total power of the system is fixed and the power of each hop is constrained, the power allocation problem is transformed into an optimal mathematical model under restrictive conditions, and then according to the maximum entropy theorem, the obtained Optimal beamforming scheme. On this basis, the original non-convex optimization problem is transformed into a convex optimization problem by approximating equivalence with a high signal-to-noise ratio. Finally, the closed-form solution of the power allocation scheme is obtained by using the convex optimization algorithm based on KKT conditions. The computer simulation results not only verify the correctness of the proposed algorithm, but also analyze the influence of key parameters on the energy efficiency of the system.

In order to solve the above problems, the present invention adopts the following technical scheme: the power allocation algorithm of the unmanned aerial vehicle relay system based on the optimal energy efficiency criterion, it is characterized in that, comprises the following steps:

Step 1: Establish a UAV-based relay transmission system model;

Step 2: According to the power consumption model given in the EARTH plan, the power allocation problem based on the maximum energy efficiency of the system is modeled as an optimization model;

Step 3: Optimization of the beamforming weight vector; when the transmit power P _i (i=1,2) is fixed, since the beamforming weight vector w ₁ and the beamforming weight vector w ₂ are independent of each other, they are simplified to two optimizations respectively Problem; According to the generalized Rayleigh maximum entropy theorem, the optimal beamforming weight vector is solved;

Step 4: Optimizing the transmit power; bring the optimal beamforming weight vector into the objective function, the objective function found is not a convex function, ignore the 1 in the denominator of the signal-to-noise ratio expression in the objective function, and pass the high signal-to-noise ratio Ratio approximation, transforming mathematical problems into convex optimization problems;

Step 5: Solve the convex optimization problem: use the Lagrangian algorithm and KKT conditions to finally calculate the closed-form solution of the power allocation scheme.

Described step 1 specifically includes the following:

In the first time slot, the transmitting end S transmits the transmitted signal x(t) through beamforming, and the signal received at the relay end R can be expressed as

P ₁ is the signal transmission power of the transmitter S, the superscript H in the formula h ^H is the conjugate transpose operator, w ₁ =[w _1,1 w _1,2 … w _1,M ] ^T is M×1 The transmit beamforming weight vector of , satisfying || || _F represents the Frobenius norm, x(t) is the transmitted signal and satisfies E(|x(t)| ² )=1, n ₁ is the mean equal to 0, and the variance equal to The additive white Gaussian noise of , h represents the channel fading vector of the SR link affected by path loss and Rician fading, which can be expressed as

In the formula: d ₁ is the distance between S and R; h ₁ =[h _1,1 h _1,2 ... h _1,M ] ^T is a random vector of M×1 (M is a positive integer), and its elements obey The independent Rician distribution can be expressed as the sum of the direct path component h _L and the scattering component h _S , namely

In the formula, k is the Rician factor, which is defined as the ratio of the energy of the direct path component of the received signal to the average energy of the scattered component;

In the second time slot, the relay terminal R first multiplies the signal y _r (t) by a fixed gain amplification factor G using the protocol, and then forwards the signal to the destination node D with power _P The signal is subjected to beamforming processing, and its output signal can be expressed as

while the gain G is given by

In formula (4), P ₂ is the signal transmission power of the relay terminal R, n ₂ is the noise vector of N×1 (N is a positive integer), obey The complex Gaussian distribution of , 0 _N is the zero vector of N×1, I _N is the unit vector of N×1, is the variance. g is the channel fading vector affected by path loss and Rician fading, which can be expressed as

In the formula: d ₂ is the distance between R and D; g ₁ =[g _1,1 g _1,2 ... g _1,N ] ^T is a random vector of N×1, and its elements obey the independent Rician distribution;

According to (4) and (5), the output signal-to-noise ratio (SNR) at the receiving end of the relay system can be expressed as

In the formula Where γ ₁ is the output signal-to-noise ratio of the relay terminal R, is the average output signal-to-noise ratio of the relay terminal R, γ ₂ is the output signal-to-noise ratio of the relay terminal R, is the average output signal-to-noise ratio of the destination node D.

Described step 2 specifically includes the following:

According to the power consumption model given in the EARTH plan, the total power consumption PT _,1 of the transmitting node and the total power consumption PT _,2 of the relay node can be expressed as

P _T,1 =a ₁ P ₁ +b ₁ (8)

P _T,2 =a ₂ P ₂ +b ₂ (9)

Then, the total system power consumption P _T can be expressed as

P _T =a ₁ P ₁ +a ₂ P ₂ +b ₁ +b ₂ (10)

The system energy efficiency EE is described as the system spectral efficiency divided by the total power consumption, which can be expressed as:

Among them, [a ₁ , b ₂ ] and [a ₂ , b ₂ ] are the power consumption model parameters of the EARTH plan. Therefore, the power allocation problem based on the maximum energy efficiency of the system can be modeled as the following optimization model:

P ₁ +P ₂ =C

P _i ≤ P _max , i=1,2 (12)

P _max is the upper limit of the maximum transmission power of each hop, P _max =KC,1/2<K<1, and C is the total power.

Described step 3 specifically includes the following:

Step 3-1: Optimization of beamforming weight vectors:

When the transmission power P _i (i=1,2) is fixed, combined with formula (7), the optimization model can be simplified as

Since the beamforming weight vectors w ₁ and w ₂ are independent of each other, the above equations can be simplified into the following two optimization problems respectively:

and

For formula (14), according to the generalized Rayleigh maximum entropy theorem, we can get

where λ _max (hh ^H ) represents the maximum eigenvalue of the matrix hh ^H ; only under the following conditions

When the maximum value is reached, take the equal sign; in the same way, the optimal solution of formula (15) can be obtained

Bringing the obtained optimal beamforming weight vector into the original formula, the optimization model can be re-expressed as

stP ₁ +P ₂ =C

P _i ≤ P _max , i=1,2 (19).

Described step 4 specifically includes the following:

The objective function referred to in formula (19) is not a convex function, ignoring the 1 in the denominator of the signal-to-noise ratio expression in the objective function, then through high signal-to-noise ratio approximation, the mathematical problem in formula (19) is transformed into the following pseudo convex optimization problem

stP ₁ +P ₂ =C

P _i ≤ P _max , i=1,2 (20).

Described step 5 specifically includes the following:

Use the Lagrangian optimization algorithm to optimize the solution; the Lagrangian function can be expressed as

According to the KKT condition of convex optimization theory, we can know that:

P _i -P _max ≤0,i=1,2 (23)

λ _i (P _i -P _max )=0,i=1,2 (25)

λ _i ≥ 0, i = 1,2 (26)

From formula (22) can get

Since the Lagrangian multipliers λ ₁ ≥ 0, λ ₂ ≥ 0, discuss and solve according to the situation;

1) When λ ₁ =λ ₂ =0,

From equations (27) and (28), we can get

According to formula (23), the following situations are divided into the following cases to verify the KKT condition:

(1) When P ₁ ＝P _max , P ₂ ＝P _max , P ₁ +P ₂ >C, which is inconsistent with formula (24), so it is discarded;

(2) When P ₁ =P _max , P ₂ <P _max ,

At this time, P ₂ =CP _max , which is consistent with the KKT condition;

(3) When P ₁ <P _max , P ₂ <P _max , it can be obtained from formula (30)

Solutions have to Compatible with KKT conditions;

(4) When P ₁ <P _max , P ₂ =P _max ,

At this time, P ₁ =CP _max , which is consistent with the KKT condition;

From the above analysis, it is concluded that

Beneficial effects: the present invention proposes a power allocation algorithm for the UAV relay system based on the optimal energy efficiency criterion, and uses KKT optimization conditions to obtain a closed-form solution to the power allocation scheme, thereby reducing the complexity of the algorithm. Compared with the average power allocation algorithm, the algorithm of the invention can obtain greater system energy efficiency, thereby improving the performance of the communication system.

Description of drawings

Fig. 1 is a detailed flow chart of the present invention;

Fig. 2 is the relay transmission system model based on UAV;

Figure 3 is a schematic diagram of the comparison results between the optimization algorithm and the exhaustive search method;

Fig. 4 is a schematic diagram of comparison results between the power optimization scheme and the average power scheme.

Detailed ways

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

As shown in Fig. 1, the present invention provides a kind of power distribution algorithm of the unmanned aerial vehicle relay system based on the optimal criterion of energy efficiency, comprising the following steps:

Step 1: Establish a UAV-based relay transmission system model;

In the first time slot, the transmitting end S transmits the transmitted signal x(t) through beamforming, and the signal received at the relay end R can be expressed as

P ₁ is the signal transmission power of the transmitter S, the superscript H in the formula h ^H is the conjugate transpose operator, w ₁ =[w _1,1 w _1,2 … w _1,M ] ^T is M×1 The transmit beamforming weight vector of , satisfying || || _F represents the Frobenius norm, x(t) is the transmitted signal and satisfies E(|x(t)| ² )=1, n ₁ is the mean equal to 0, and the variance equal to The additive white Gaussian noise of , h represents the channel fading vector of the SR link affected by path loss and Rician fading, which can be expressed as

In the formula: d ₁ is the distance between S and R; h ₁ =[h _1,1 h _1,2 ... h _1,M ] ^T is a random vector of M×1 (M is a positive integer), and its elements obey The independent Rician distribution can be expressed as the sum of the direct path component h _L and the scattering component h _S , namely

In the formula, k is the Rician factor, which is defined as the ratio of the energy of the direct path component of the received signal to the average energy of the scattered component;

In the second time slot, the relay terminal R first multiplies the signal y _r (t) by a fixed gain amplification factor G using the protocol, and then forwards the signal to the destination node D with power P ₂ , and the node D is sensitive to the received The signal is subjected to beamforming processing, and its output signal can be expressed as

while the gain G is given by

In formula (4), P ₂ is the signal transmission power of the relay terminal R, n ₂ is the noise vector of N×1 (N is a positive integer), obey The complex Gaussian distribution of , 0 _N is the zero vector of N×1, I _N is the unit vector of N×1, is the variance. g is the channel fading vector affected by path loss and Rician fading, which can be expressed as

In the formula: d ₂ is the distance between R and D; g ₁ =[g _1,1 g _1,2 ... g _1,N ] ^T is a random vector of N×1, and its elements obey the independent Rician distribution;

According to (4) and (5), the output signal-to-noise ratio (SNR) at the receiving end of the relay system can be expressed as

In the formula Where γ ₁ is the output signal-to-noise ratio of the relay terminal R, is the average output signal-to-noise ratio of the relay terminal R, γ ₂ is the output signal-to-noise ratio of the relay terminal R, is the average output signal-to-noise ratio of the destination node D.

Step 2: Relay transmission power allocation model based on energy efficiency

The power consumption of a relay communication system mainly includes transmission power, circuit consumption, conversion efficiency consumption, and cooling consumption. According to the power consumption model given in the EARTH plan, the total power consumption PT _,1 of the transmitting node and the total power consumption PT _,2 of the relay node can be expressed as

P _T,1 =a ₁ P ₁ +b ₁ (45)

P _T,2 =a ₂ P ₂ +b ₂ (46)

Then, the total system power consumption P _T can be expressed as

P _T =a ₁ P ₁ +a ₂ P ₂ +b ₁ +b ₂ (47)

The system energy efficiency EE is described as the system spectral efficiency divided by the total power consumption, which can be expressed as:

Among them, [a ₁ , b ₂ ] and [a ₂ , b ₂ ] are the power consumption model parameters of the EARTH plan. Therefore, the power allocation problem based on the maximum energy efficiency of the system can be modeled as the following optimization model:

P ₁ +P ₂ =C

P _i ≤ P _max , i=1,2 (49)

P _max is the upper limit of the maximum transmission power of each hop, P _max =KC,1/2<K<1, and C is the total power.

Algorithm Description

System energy efficiency is related to beamforming weight vector and transmit power. To obtain maximum system energy efficiency, the above two parameters must be optimized. Therefore, the optimization idea proposed by the present invention is to optimize the beamforming weight vector under the premise of a fixed transmission power. Then, the optimal beamforming weight vector is substituted into the optimization model to optimize the power parameters to obtain the maximum energy efficiency.

Step 3: Optimization of beamforming weight vectors

When the transmission power P _i (i=1,2) is fixed, combined with formula (7), the optimization model can be simplified as

Since the beamforming weight vectors w ₁ and w ₂ are independent of each other, the above equations can be simplified into the following two optimization problems respectively:

and

For formula (14), according to the generalized Rayleigh maximum entropy theorem, we can get

where λ _max (hh ^H ) represents the maximum eigenvalue of the matrix hh ^H ; only under the following conditions

When the maximum value is reached, take the equal sign; in the same way, the optimal solution of formula (15) can be obtained

Bringing the obtained optimal beamforming weight vector into the original formula, the optimization model can be re-expressed as

stP ₁ +P ₂ =C

P _i ≤ P _max , i=1,2 (56).

Step 4: Optimization of transmit power

The objective function referred to in formula (19) is not a convex function, ignoring the 1 in the denominator of the signal-to-noise ratio expression in the objective function, then through high signal-to-noise ratio approximation, the mathematical problem in formula (19) is transformed into the following pseudo convex optimization problem

stP ₁ +P ₂ =C

P _i ≤ P _max , i=1,2 (57).

Step 5: Solve the convex optimization problem. Through the Lagrangian algorithm, using the KKT condition, the discussion is carried out according to the situation, and finally the closed form solution of the power allocation scheme is calculated.

Therefore, we can use the Lagrangian optimization algorithm to optimize the solution; the Lagrangian function can be expressed as

According to the KKT condition of convex optimization theory, we can know that:

P _i -P _max ≤0,i=1,2 (60)

λ _i (P _i -P _max )=0,i=1,2 (62)

λ _i ≥ 0, i = 1,2 (63)

From formula (22) can get

Since the Lagrangian multipliers λ ₁ ≥ 0, λ ₂ ≥ 0, discuss and solve according to the situation;

1) When λ ₁ =λ ₂ =0,

From equations (27) and (28), we can get

According to formula (23), the following situations are divided into the following cases to verify the KKT condition:

(1) When P ₁ ＝P _max , P ₂ ＝P _max , P ₁ +P ₂ >C, which is inconsistent with formula (24), so it is discarded;

(2) When P ₁ =P _max , P ₂ <P _max ,

At this time, P ₂ =CP _max , which is consistent with the KKT condition;

(3) When P ₁ <P _max , P ₂ <P _max , it can be obtained from formula (30)

Solutions have to Compatible with KKT conditions;

(4) When P ₁ <P _max , P ₂ =P _max ,

At this time, P ₁ =CP _max , which is consistent with the KKT condition;

From the above analysis, it is concluded that

Description of simulation results

According to the power consumption model parameters of the EARTH program and the actual application of the UAV relay, the simulation parameters [a ₁ , b ₁ ] are set to [3.14,69], and [a ₂ ,b ₂ ] are set to [7.25,469]. Assuming that the relay nodes are distributed on the connection line from the source node to the receiving node, the present invention normalizes the distance from the source node to the destination node to 1, that is, d ₁ +d ₂ =1.

Figure 3 shows the maximum value of system energy efficiency obtained by using the exhaustive search method and the optimization scheme of the present invention when the total power C is changed from 5w to 40w when the Rician factor k=6, d ₁ =d ₂ =0.5 The obtained comparison curve of system energy efficiency. In the case where two and four antennas are configured at the transmitting end and the receiving end of the relay system, it can be seen that the two curves basically coincide, thus proving the correctness of the present invention.

Fig. 4 has provided M=N=2 and under the situation of M=N=4, the power distribution optimization scheme of the present invention and the system energy efficiency contrast curve of source-unmanned aerial vehicle relay average power distribution scheme, wherein Rician factor k= 6, d ₁ =d ₂ =0.5. It can be seen from the figure that when the total power changes from 5w to 40w, the energy efficiency performance obtained by the power distribution optimization scheme of the present invention has been greatly improved compared with the energy efficiency performance obtained by the source-UAV relay average power scheme, and with With the increase of the total power, the energy efficiency performance is improved more obviously.

For those skilled in the art, other advantages and variants can easily be ascertained from the above-mentioned implementation types. Therefore, the present invention is not limited to the above example, which is merely used as an example to describe in detail and exemplary one form of the present invention. Within the scope of not departing from the gist of the present invention, technical solutions obtained by those skilled in the art through various equivalent replacements based on the above specific examples shall be included in the claims of the present invention and their equivalent scope.

Claims (6)

1. the power distribution algorithm of the unmanned plane relay system based on efficiency optiaml ciriterion, which is characterized in that include the following steps：

Step 1：Establish the relay transmission system model based on unmanned plane；

Step 2：The power consumption models provided in the works according to EARTH, by the power distribution based on system energy efficiency maximum Problem is modeled as Optimized model；

Step 3：The optimization of Wave beam forming weight vector；In transmission power P_iIn the case of (i=1,2) is fixed, since Wave beam forming is weighed Vectorial w₁With Wave beam forming weight vector w₂Independently of each other, it is reduced to two optimization problems respectively；According to Generalized Rayleigh maximum entropy Theorem solves optimal beam forming weight vector；

Step 4：The optimization of transmission power；Optimal beam forming weight vector will be solved to be brought into object function, the target of discovery Function is not convex function, ignores 1 in object function in signal-to-noise ratio expression formula denominator, and by high s/n ratio approximation, mathematics is asked Topic is converted to convex optimization problem；

Step 5：Solve convex optimization problem：By Lagrangian Arithmetic, using KKT conditions, power allocation scheme is finally calculated Closed-form solution.

2. the power distribution algorithm of the unmanned plane relay system according to claim 1 based on efficiency optiaml ciriterion, special Sign is that the step 1 specifically includes the following contents：

In first time slot, the signal x (t) of transmission is carried out Wave beam forming and launched by transmitting terminal S, and in relay, R is received Signal can be expressed as

P₁For the signal transmission power of transmitting terminal S, formula h^HIn subscript H for conjugate transposition operator, w₁=[w_1,1 w_1,2 … w_1,M]^TLaunching beam for M × 1 forms weight vector, meets|| ||_FRepresent Frobenius norms, x (t) is transmitting Signal and meet E (| x (t) |²)=1, n₁It is equal to 0 for mean value, variance is equal toAdditive white Gaussian noise, h represent S-R links By the channel fading of path loss and Rician influence of fading vector, can be expressed as

In formula：d₁For the distance between S and R；h₁=[h_1,1 h_1,2 … h_1,M]^TFor the random vector (M is positive integer) of M × 1, Its element obeys mutually independent Rician distributions, is represented by line of sight component h_LWith scattering component h_SThe sum of, i.e.,

K is the Rician factors in formula, is defined as receiving the ratio between signal line of sight component energy and scattering component average energy；

In second time slot, relay R is first using agreement first to signal y_r(t) the amplification factor G of a fixed gain is multiplied by, Then with power P₂Signal is forwarded to destination node D, node D carries out received signal in Wave beam forming processing, output letter It number is represented by

And gain G is given by

In formula (4), P₂For the signal transmission power of relay R, n₂For the noise vector (N is positive integer) of N × 1, obeyMultiple Gauss distribution, 0_NFor the null vector of N × 1, I_NFor the unit vector of N × 1,For variance.G be by Path loss and the channel fading vector with Rician influence of fading, can be expressed as

In formula：d₂For the distance between R and D；g₁=[g_1,1 g_1,2 … g_1,N]^TFor the random vector of N × 1, element obeys phase Mutually independent Rician distributions；

The output signal-to-noise ratio SNR expression formulas that relay system receiving terminal is obtained according to (4) and (5) are

In formulaWherein γ₁For the defeated of relay R Go out signal-to-noise ratio,For the average output SNR of relay R, γ₂For the output signal-to-noise ratio of relay R,For purpose node D's Average output SNR.

3. the power distribution algorithm of the unmanned plane relay system according to claim 1 based on efficiency optiaml ciriterion, special Sign is that the step 2 specifically includes the following contents：

The power consumption models provided in the works according to EARTH, the total power consumption P of transmitting node_T,1With the total work of relay node Rate consumes P_T,2It can be expressed as

P_T,1=a₁P₁+b₁ (8)

P_T,2=a₂P₂+b₂ (9)

So, system total power consumption P_TIt can be expressed as

P_T=a₁P₁+a₂P₂+b₁+b₂ (10)

System energy efficiency EE is described as system spectral efficiency divided by total power consumption, can be expressed as：

Wherein, [a₁,b₂] and [a₂,b₂] it is the power consumption models parameter that EARTH plans.Therefore, based on system energy efficiency most Big power distribution problems can be modeled as following Optimized model：

P₁+P₂=C

P_i≤P_max, i=1,2 (12)

P_maxFor every jump maximum transmission power upper limit, P_max=KC, 1/2<K<1, C is general power.

4. the power distribution algorithm of the unmanned plane relay system according to claim 2 based on efficiency optiaml ciriterion, special Sign is that the step 3 specifically includes the following contents：

Step 3-1：The optimization of Wave beam forming weight vector：

In transmission power P_iIn the case of (i=1,2) is fixed, with reference to formula (7), Optimized model can be reduced to

Due to Wave beam forming weight vector w₁And w₂Independently of each other, above formula can be reduced to following two optimization problems respectively：

With

For formula (14), according to Generalized Rayleigh maximum entropy theorem, can obtain

λ in formula_max(hh^H) representing matrix hh^HMaximum eigenvalue；Only under the following conditions

Reach maximum value and take equal sign；Can similarly obtain can obtain the optimal solution of formula (15)

Bring obtained optimal beam forming weight vector into former formula, Optimized model can be expressed as again

s.t.P₁+P₂=C

P_i≤P_max, i=1,2 (19).

5. the power distribution algorithm of the unmanned plane relay system according to claim 4 based on efficiency optiaml ciriterion, special Sign is that the step 4 specifically includes the following contents：

The object function that formula (19) meaning is stated is not convex function, ignores 1 in object function in signal-to-noise ratio expression formula denominator, that By high s/n ratio approximation, the mathematical problem in formula (19) is converted to following pseudo-convex optimization problem

s.t.P₁+P₂=C

P_i≤P_max, i=1,2 (20).

6. the power distribution algorithm of the unmanned plane relay system according to claim 5 based on efficiency optiaml ciriterion, special Sign is that the step 5 specifically includes the following contents：

Optimization is carried out using lagrangian optimization algorithm；Lagrangian can be expressed as

From the KKT conditions of convex optimum theory:

P_i-P_max≤ 0, i=1,2 (23)

λ_i(P_i-P_max)=0, i=1,2 (25)

λ_i>=0, i=1,2 (26)

It can be obtained by formula (22)

Due to Lagrange multiplier λ₁≥0,λ₂>=0, so carrying out point situation discussion and a solution；

1) work as λ₁=λ₂When=0,

By formula (27) and (28), can obtain

It is divided into situations below below according to formula (23) to verify KKT conditions：

(1)P₁=P_max,P₂=P_maxWhen, P₁+P₂>C is not inconsistent with formula (24), therefore casts out；

(2)P₁=P_max,P₂<P_maxWhen,

P at this time₂=C-P_max, it is consistent with KKT conditions；

(3)P₁<P_max,P₂<P_maxWhen, it is obtained by formula (30)

It solvesIt is consistent with KKT conditions；

(4)P₁<P_max,P₂=P_maxWhen,

P at this time₁=C-P_max, it is consistent with KKT conditions；

It is obtained by upper analysis and summary