CN108040368A - A kind of unmanned plane distribution method of time frequency resources declined based on block coordinate - Google Patents

Abstract

The present invention provides a kind of unmanned plane distribution method of time frequency resources declined based on block coordinate, and include the following steps：Determine unmanned plane quantity, initialization system authorization channel set, the initialization system maximum power upper limit and other environmental parameters；Construct frequency spectrum allocation matrix and monkey chatter matrix introduces former problem, Utilizing question architectural characteristic simplifies the complicated max min mixed programming problems being difficult to resolve originally；A kind of low complex degree iterative algorithm declined based on block coordinate is proposed to solve the above problems；Ground control station carries out power and channel distribution according to the maximum SINR value of each unmanned plane and by being remotely controlled channel to unmanned plane, completes unmanned plane distribution method of time frequency resources design.The beneficial effects of the invention are as follows：The shown unmanned plane distribution method of time frequency resources based on the decline of block coordinate realizes the reasonable distribution of limited spectrum resources on the premise of lifting each unmanned plane and receiving reliability and the guarantee system maximum consumption power constraint of control signal.

Description

Unmanned aerial vehicle time-frequency resource allocation method based on block coordinate reduction

Technical Field

The invention belongs to the technical field of unmanned aerial vehicle communication, and particularly relates to an unmanned aerial vehicle time-frequency resource allocation method based on block coordinate descent.

Background

With the advances in sensing technology and computing power, drones are becoming a popular choice in applications such as urban searching, military reconnaissance, and agricultural surveillance. However, as the wireless service demand of the drone presents challenges such as exponential growth and spectrum resource shortage, the drone communication faces a severe challenge. Meanwhile, the cooperative operation of multiple drones also brings many challenges to be considered. One of the key technical challenges is that the safety and stability of the communication of the unmanned aerial vehicle require a certain robustness of the control signal itself, and the quality of the control signal is very sensitive to channel variation and interference; another challenge is that the available resources for communication are often limited, which can exacerbate potential mutual interference effects.

However, the existing work has not studied how to improve the spectrum resource utilization of the drone and the allocation of the limited time-frequency resources by the multi-drone system. In fact, the control signal reception of the drone is affected not only by the link quality of the communication channel, but also by the potential interference. Therefore, in the unmanned aerial vehicle communication system, in order to improve the communication capacity and ensure the communication quality, channel congestion and mutual interference are avoided, and it is indispensable to reasonably allocate time-frequency resources of the unmanned aerial vehicle.

Disclosure of Invention

The invention aims to provide an unmanned aerial vehicle time-frequency resource allocation method based on block coordinate descent aiming at the defects of the prior art.

The technical scheme of the invention is as follows: an unmanned aerial vehicle time-frequency resource allocation formula based on block coordinate descent comprises the following steps:

step 1: initializing the number M of unmanned aerial vehicles (unmanned aerial vehicles) and the maximum power upper limit p of the system_maxDistance d between unmanned aerial vehicle k and ground control station (BS)_k,BSWherein M is a positive integer, and

determining the number N of authorized channels and the reference frequency of the systemSetting system alternative channel setWherein N is a positive integer,. DELTA.f_iIndicating the carrier frequency and reference frequency of the ith channelThe interval of (a);

channel scanning is carried out by utilizing spectrum sensing technology based on power spectrum detection to obtain adjacent channel interference coefficients among different channelsWherein,representing the frequency f₁And frequency f₂Determines the LoS path loss coefficient η_LoSNLoS path loss coefficient η_NLoS(ii) a Setting transmission power of unmanned aerial vehicle k to p_kAnd the corresponding noise value is

Step 2: introducing time-frequency resource block allocation matrixFor each unmanned aerial vehicle k, establishing a time-frequency occupation matrixWherein,indicating the i channel when drone k occupies slot j,indicating no occupancy; definition vector f ═ Δ f₁,...,Δf_N]^T；

The channel frequency occupied by drone k in j time slot is denoted asWherein the column vector e_jA unit vector representing that the other elements are 0 except the jth element as 1; setting a symmetric matrix W of the adjacent channel interference coefficient, whereinThen the adjacent channel interference coefficient between the channels occupied by drone k and drone m in the jth timeslot can be expressed as:

wherein m, i and j are positive integers;

and step 3: introducing matrix X ═ X¹,x²,...,x^M]And the matrix Y ═ Y¹,y²,...,y^M]Wherein Order toWherein,indicating that unmanned plane k occupies channel i;indicating that the unmanned plane k occupies a time slot j;

the time-frequency decision problem of the unmanned aerial vehicle communication system is equivalent to the following max-min optimization problem:

wherein,

and 4, step 4: number of initialization iterations t₁0, maximum number of iterations T_1,max(ii) a Setting an initial feasible solution p⁽⁰⁾、X⁽⁰⁾And Y⁽⁰⁾Where p is a power allocation vector, p⁽⁰⁾、X⁽⁰⁾And Y⁽⁰⁾Respectively represents t₁When the power distribution vector is 0, a channel occupation matrix and a time slot occupation matrix;

and 5: fixingSolving sub-problems related to variables X and Y in a distributed mode by using a block coordinate descent algorithm, and updating to obtain

Step 6: fixingSolving the subproblem about the variable p by using a characteristic root decomposition method, and updating to obtain the subproblem

And 7: judging whether t is satisfied₁≥T_1,max(ii) a If yes, outputtingIf not, updating the iteration times t₁＝t₁+1 and repeating steps 5-7;

and 8: based on the obtained power allocation vector p and X and Y, according toAnd calculating to obtain a time-frequency distribution matrix of each unmanned aerial vehicle, and finally realizing power distribution and channel distribution of the unmanned aerial vehicles by the ground control station to complete time-frequency decision optimization design of the unmanned aerial vehicle communication system.

Preferably, in step 5, the block coordinate descent algorithm is used for distributed solving to obtain X and Y, and the method specifically comprises the following steps:

5.1 initializing outer iteration times t₂Maximum number of iterations T, 0_2,max(ii) a Initialization of X⁽⁰⁾And Y⁽⁰⁾，p；

5.2 initializing the number of inner layer iterations k to 1, generating a randomly arranged sequence of integers from 1 to M

5.3, setting

5.4, fixingAndupdating x_m＝e_IWherein

5.5, fixingAndupdating y_m＝e_KWherein

5.6, updating the inner layer iteration number k to be k +1, and repeating the steps 5.3-5.6 until the condition k to be M is met;

5.7, updating the outer iteration times t₂＝t₂+1 and repeating steps 5.2-5.7 until condition t is satisfied₂＝T_2,max。

Preferably, the solution obtained in step 6 by using a characteristic root decomposition methodThe method specifically comprises the following steps:

6.1, setting

6.2, definition z ═ p₁,p₂…p_M,1]^TLet us orderAnd

wherein,

6.3, to C^-1B, after the characteristic root decomposition, all element symbol phases of the characteristic root vector corresponding to the characteristic value with the maximum modulus valueAnd the reciprocal of the characteristic root is the maximum value of the corresponding objective function, the corresponding characteristic root vector is normalized, the last element is 1, and the obtained vector p consisting of the first M elements is the optimal solution.

The technical scheme provided by the invention has the following beneficial effects:

the unmanned aerial vehicle time-frequency resource allocation method based on block coordinate descent constructs a frequency spectrum allocation matrix and an adjacent channel interference matrix to introduce an original problem, and simplifies the original complex and difficult-to-solve max-min hybrid planning problem by using the structural characteristics of the problem, thereby greatly reducing the design complexity;

moreover, a low-complexity iterative algorithm based on block coordinate reduction is provided to solve the problems, and finally, an unmanned aerial vehicle time-frequency resource allocation method based on block coordinate reduction is designed. .

Drawings

FIG. 1 is a system model diagram related to the unmanned aerial vehicle time-frequency resource allocation method based on block coordinate descent according to the present invention;

fig. 2 is a detailed flowchart of the unmanned aerial vehicle time-frequency resource allocation method based on block coordinate descent shown in fig. 1;

fig. 3 is a schematic diagram of an available alternative channel set for a drone and an allocated channel for the drone in an embodiment of the present invention;

fig. 4 is a convergence relationship diagram of the minimum SINR value of the unmanned aerial vehicle and the number of iterations in the embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

Unless the context clearly dictates otherwise, the elements and components of the present invention may be present in either single or in multiple forms and are not limited thereto. Although the steps in the present invention are arranged by using reference numbers, the order of the steps is not limited, and the relative order of the steps can be adjusted unless the order of the steps is explicitly stated or other steps are required for the execution of a certain step. It is to be understood that the term "and/or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.

As shown in fig. 1, the present invention considers a scenario where a ground console or Base Station (BS) remotely controls a multi-Unmanned Aerial Vehicle (UAV) to perform a task. Due to various factors, such as antenna side lobe gain, non-ideal characteristics of transmitter and receiver filters, etc., spectral leakage may occur, and adjacent channels in the remote control channel may cause mutual interference. This effect caused by adjacent channel interference is especially serious when the distance between the UAV and the BS is very different. Such as u₁And u₂Two UAVs respectively, using adjacent frequency points to receive control signals transmitted by BS, and the distances between the UAVs and the BS are respectivelyAndif it isBS sends u₁Will leak into u₂Of a channel of (c) to (u)₂Can even block u₂The control signal of (2). Therefore, the time-frequency decision of the unmanned aerial vehicle needs to be consideredThe influence of adjacent channel interference.

In addition, in the countermeasure environment, electromagnetic environment interference is also a factor to be considered when the time-frequency decision of the unmanned aerial vehicle is made. The current frequency spectrum quality is accurately obtained through sensing the electromagnetic environment. And making a dynamic spectrum decision strategy according to a spectrum sensing result so as to improve the reliability of the unmanned aerial vehicle remote control channel. Therefore, the influence of adjacent channel interference and electromagnetic environment interference on time-frequency decision of the unmanned aerial vehicle is considered in the project, an unmanned aerial vehicle time-frequency decision optimization model considering the interference is established, time-frequency resources and power resources are reasonably distributed through a design mechanism, and the system performance of the unmanned aerial vehicle is optimized and improved.

For convenience of description, assuming that the BS is located at the origin O of three-dimensional coordinates, the set of all UAVs is represented asLet the set of available channels beThe set of available slot resources isThe number of available time frequency Resource Blocks (RBs) is N x J. Assuming that the length of each slot is short enough, the position of the UAV in each slot can be considered fixed, while different slots represent communication windows of different periods. The UAV needs to periodically transmit a telemetry signal to the BS, so the BS can know the three-dimensional coordinates, flight status, and link status information of the UAV. The communication between BS and UAV can be switched between different channels, and BS is used for UAVu_kIs noted as p_k. The BS allocates time-frequency resource blocks for each UAV and adjusts the transmitting power of each remote control channel to reduce the influence of adjacent channel interference and external electromagnetic environment interference, thereby ensuring the signal quality of the remote control channels.

The signal link between the UAV and the ground BS mainly consists of a direct path (Line of Sight, LoS) and a non-direct path (None Line of Sight, NLoS), and small-scale attenuation caused by factors such as multipath is relatively small. Influenced by the flight altitude of the UAV and the ground environment, the air-ground link has LoS path and NLoS path with certain probability, and in the jth time slot, the probability that the UAV k and BS communication link is the LoS path is

In the above formula, C and B are both environment-related parameters,representing the pitch angle between UAV k and ground BS at time slot j, given the three-dimensional spatial coordinates of UAV k at time slot jThen there is

As can be seen from equation (1), the probability of LoS path occurrence depends onBecomes larger, and the probability of the occurrence of the NLoS path is

According to the Free Space (FS) propagation model, when the link between the UAV and the BS is a LoS path, the signal propagation loss can be modeled as

Wherein F represents the reference frequency and wherein,the carrier frequency of the channel occupied by UAV k in the j-th slot is shown spaced from F. In addition to this, the present invention is,denotes the distance between UAV k and BS at time slot j, η_LoSRepresenting additional loss in the LoS path. And the signal propagation loss when the link between UAV k and BS is NLoS path is

In summary, it can be derived that in the jth slot, the channel gain between UAV k and BS can be expressed as

Wherein,

in addition, due to the non-ideal characteristics of the transmitter and receiver, the signal may produce spectral leakage at adjacent frequency points. Assuming the UAV models are the same, the different UAV transmit and receive signal filter characteristics are similar. Any two UAVs u₁And u₂(frequency point of corresponding remote control channel is f₁And f₂) The remote control channels may be affected by spectral leakage. The adjacent channel interference coefficient is defined to measure the spectrum leakage effect, namely: for f₁And f₂Existence mappingWhereinExpresses the adjacent channel interference coefficient and satisfies the following characteristics

In the above formula, when | f₁-f₂When | ═ 0, it is co-channel interference; when f₁-f₂I → ∞ indicates that the intervals between the frequency points are far apart and the spectrum leakage effect is very weak. Note that these adjacent channel interference coefficients can be obtained from actual measurements.

In order not to lose generality, the situation of frequency resource shortage is considered, namely, the communication requirements of all UAVs and BSs cannot be met only through frequency allocation. However, in order to enable all UAVs to receive control signals, the number of available time-frequency resource blocks should not be less than the number of UAVs. According to the above requirement, the UAV number and the time-frequency resource block number need to satisfy the following conditions:

definition matrixTo indicate whether UAV k occupies time-frequency resource block in jth slot, if soAnd indicating that the UAV k occupies a time-frequency resource block in the time slot j, otherwise indicating that the UAV k does not occupy any time-frequency resource block in the time slot j. In the case of time-frequency resource shortage, the following constraint conditions are considered: 1) each UAV only occupies one time-frequency resource block, and 2) each time-frequency resource block is allocated to at most one UAV for use, and mathematically, the following two constraint conditions can be expressed respectively:

wherein,indicating the frequency channel occupied by the kth UAV in the jth timeslot.

For the uplink, considering the SINR strength of each UAV receiving BS transmitted control signals as a metric, for UAV k, the SINR of its receiving BS transmitted control signals at time slot j can be expressed as:

wherein,representing the variance of the adjacent channel interference;representing UAV u_kThe variance of the electromagnetic environment interference and noise at the receiver of (1); if it isIt means that the BS transmits the control signal to UAV k at the j-th time slot, thereforeIf it isIt means that the BS did not transmit a control signal to UAV k in the jth slot, thereforeSince UAV k only occupies one timeslot to receive the control signal, the SINR value of UAV k control signal can be expressed as:

in order to improve the reliability of each control signal as much as possible, the SINR values of all UAVs receiving the control signals should be made as large as possible. Therefore, a max-min fairness index is adopted in the research, and the frequency decision problem for the unmanned aerial vehicle is modeled into the following optimization problem:

where (C1.4) represents the maximum power limit for the BS to transmit control signals to the UAV.

Introducing time-frequency resource block allocation matrixFor each UAV k, a time-frequency occupancy matrix may be establishedWhereinRepresenting the i channel when UAV k occupies the j slot,indicating no occupancy. When in useAn all zero vector means that UAV k does not occupy any channel in the j slot. And defining vector f ═ Δ f₁,...,Δf_N]^T. Can be easily seenCan be expressed asThe channel frequency occupied by UAV k in j time slot can be expressed asWherein the column vector e_jRepresents a sheet in which the elements are 0 except the jth elementA bit vector. Setting a symmetric matrix W of the adjacent channel interference coefficient, whereinThe adjacent channel interference coefficient between the channels occupied by UAV k and UAV m in the jth time slot can be expressed as

Introducing matrix X ═ X¹,x²,...,x^M]And the matrix Y ═ Y¹,y²,...,y^M]WhereinOrder toWherein,indicating that UAV k occupies channel i, otherwise indicating not occupying;indicating UAV k occupies slot j, otherwise indicating no occupancy. According to the definition, the time-frequency decision problem of the unmanned aerial vehicle communication system is equivalent to the following max-min optimization problem:

among the constraints of the above problem, the constraints of the variables X and Y are completely independent, and can be independently optimized by using a Block Coordinate Descent (BCD) method. Also, the number of elements of X and Y is M (N + J), which is much less than the number of elements NJM in matrix A. Therefore, the model is suitable for the design of a low-complexity decision optimization algorithm and is expected to meet the time performance index requirement generated by the frequency decision strategy for the unmanned aerial vehicle.

According to the flowchart shown in fig. 2, a method for allocating time-frequency resources of an unmanned aerial vehicle based on block coordinate descent specifically includes the following steps:

step 1: initializing number M of Unmanned Aerial Vehicles (UAVs) and maximum power upper limit p of system_maxDistance between unmanned aerial vehicle k and ground control station (BS)Determining the number N of authorized channels and the reference frequency of the system at the same timeSetting system alternative channel setWherein Δ f_iIndicating the carrier frequency and reference frequency of the ith channelThe interval of (a); channel scanning is carried out by utilizing spectrum sensing technology based on power spectrum detection to obtain adjacent channel interference coefficients among different channelsWhereinRepresenting the frequency f₁And frequency f₂Determines the LoS path loss coefficient η_LoSNLoS path loss coefficient η_NLoS(ii) a Setting transmission power of unmanned aerial vehicle k to p_kAnd the corresponding noise value is

Step 2: introducing time-frequency resource block allocation matrixFor each UAV k, a time-frequency occupancy matrix may be establishedWhereinRepresenting the i channel when UAV k occupies the j slot,indicating no occupancy. When in useAn all zero vector means that UAV k does not occupy any channel in the j slot. And defining vector f ═ Δ f₁,...,Δf_N]^T. Can be easily seenCan be expressed asThe channel frequency occupied by UAV k in j time slot can be expressed asWherein the column vector e_jRepresents a unit vector of 0 except the jth element as 1. Setting a symmetric matrix W of the adjacent channel interference coefficient, whereinThe adjacent channel interference coefficient between the channels occupied by UAV k and UAV m in the jth time slot can be expressed as

And step 3: introducing matrix X ═ X¹,x²,...,x^M]And the matrix Y ═ Y¹,y²,...,y^M]Wherein Order toWherein,indicating that UAV k occupies channel i, otherwise indicating not occupying;indicating UAV k occupies slot j, otherwise indicating no occupancy. According to the definition, the time-frequency decision problem of the unmanned aerial vehicle communication system is equivalent to the following max-min optimization problem:

wherein,

and 4, step 4: number of initialization iterations t₁0, maximum number of iterations T_1,max(ii) a Setting an initial feasible solution p⁽⁰⁾、X⁽⁰⁾And Y⁽⁰⁾；

And 5: fixingSolving sub-problems related to variables X and Y in a distributed mode by using a block coordinate descent algorithm, and updating to obtain

Step 6: fixingSolving the subproblem about the variable p by using a characteristic root decomposition method, and updating to obtain the subproblem

And 7: judging whether t is satisfied₁≥T_1,maxt₁0; if yes, outputtingOtherwise updating the iteration times t₁＝t₁+1 and repeating steps 5-7;

and 8: the resulting power allocation vector p and X and Y are based onAnd calculating to obtain a time-frequency distribution matrix of each unmanned aerial vehicle, and finally realizing power distribution and channel distribution of the unmanned aerial vehicles by the ground control station to complete time-frequency decision optimization design of the unmanned aerial vehicle communication system.

Further, in the step 5, the block coordinate descent algorithm is used for distributed solving to obtain X and Y, and the method specifically comprises the following steps:

5.1 initializing outer iteration times t₂Maximum number of iterations T, 0_2,max(ii) a Initialization of X⁽⁰⁾And Y⁽⁰⁾，p；

5.2 initializing the number of inner layer iterations k to 1, generating a randomly arranged sequence of integers from 1 to M

5.3, setting

5.4, fixingAndupdating x_m＝e_IWherein

5.5, fixingAndupdating y_m＝e_KWherein

5.6, updating the inner layer iteration number k to be k +1, and repeating the steps 5.3-5.6 until the condition k to be M is met;

5.7, updating the outer iteration times t₂＝t₂+1 and repeating steps 5.2-5.7 until condition t is satisfied₂＝T_2,max。

Further, the solution obtained in the step 6 by using a characteristic root decomposition methodThe method specifically comprises the following steps:

6.1, setting

6.2, definition z ═ p₁,p₂…p_M,1]^TLet us orderAnd

wherein,

6.3, to C^-1And B, after the characteristic root decomposition, all element signs of the characteristic root vector corresponding to the characteristic value with the maximum modulus are the same, the reciprocal of the characteristic root is the maximum value of the corresponding target function, the corresponding characteristic root vector is normalized, the last element is 1, and the obtained vector p consisting of the first M elements is the optimal solution.

Fig. 3-4 are simulation verifications of the designed solution by Matlab of the present invention. The parameters are specifically set as: the number of the unmanned aerial vehicles M is 6, N is 5, and J is 5; upper limit of power consumption P of system_max30 dBm; base band carrier frequencyChannel frequency spacing Δ f_i＝i×5MHz，And orderSetting sigma²LoS path loss coefficient η at-90 dBm_LoS3dB, NLoS path loss coefficient η_NLoS23 dB; the environmental parameter B is 0.136 and C is 11.95.

Fig. 3 shows the set of available alternative channels for drones and the allocated channels for drones in this embodiment. Fig. 3 shows a shaded portion on the left of the channel set of available alternative channels for each drone in the embodiment of the present invention; fig. 3 shows the situation of the channel allocated to the drone after the method of the present invention is applied.

Fig. 4 shows a convergence relationship diagram of the minimum SINR value of the drone and the number of iterations after the method of the present invention is applied. The block coordinate-based descent algorithm proposed by the method of the invention can always monotonically converge to a stable value after a very few iterations of updating, which means that the method of the invention can achieve fast convergence.

It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.

Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (3)

1. An unmanned aerial vehicle time-frequency resource allocation method based on block coordinate descent is characterized in that: the method comprises the following steps:

step 1: initializing the number M of unmanned aerial vehicles (unmanned aerial vehicles) and the maximum power upper limit p of the system_maxDistance d between unmanned aerial vehicle k and ground control station (BS)_k,BSWherein M is a positive integer, and

determining a system authorized channel number N, a referenceFrequency ofSetting system alternative channel setWherein N is a positive integer,. DELTA.f_iIndicating the carrier frequency and reference frequency of the ith channelThe interval of (a);

channel scanning is carried out by utilizing spectrum sensing technology based on power spectrum detection to obtain adjacent channel interference coefficients among different channelsWherein,representing the frequency f₁And frequency f₂Determines the LoS path loss coefficient η_LoSNLoS path loss coefficient η_NLoS(ii) a Setting transmission power of unmanned aerial vehicle k to p_kAnd the corresponding noise value is

Step 2: introducing time-frequency resource block allocation matrixFor each unmanned aerial vehicle k, establishing a time-frequency occupation matrixWherein, indicating the i channel when drone k occupies slot j,indicating no occupancy; definition vector f ═ Δ f₁,...,Δf_N]^T；

The channel frequency occupied by drone k in j time slot is denoted asWherein the column vector e_jA unit vector representing that the other elements are 0 except the jth element as 1; setting a symmetric matrix W of the adjacent channel interference coefficient, whereinThen the adjacent channel interference coefficient between the channels occupied by drone k and drone m in the jth timeslot can be expressed as:

<mrow> <msub> <mi>&amp;mu;</mi> <mrow> <msubsup> <mi>f</mi> <mi>k</mi> <mi>j</mi> </msubsup> <mo>,</mo> <msubsup> <mi>f</mi> <mi>m</mi> <mi>j</mi> </msubsup> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>a</mi> <mi>j</mi> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <msubsup> <mi>Wa</mi> <mi>j</mi> <mi>m</mi> </msubsup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mi>k</mi> </msub> <msub> <mi>e</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mi>T</mi> </msup> <msub> <mi>WA</mi> <mi>m</mi> </msub> <msub> <mi>e</mi> <mi>j</mi> </msub> <mo>,</mo> </mrow>

wherein m, i and j are positive integers;

and step 3: introducing matrix X ═ X¹,x²,...,x^MAnd matrix Y ═ Y¹,y²,...,y^M]Wherein Order toWherein,indicating that unmanned plane k occupies channel i;indicating that the unmanned plane k occupies a time slot j;

the time-frequency decision problem of the unmanned aerial vehicle communication system is equivalent to the following max-min optimization problem:

<mrow> <mtable> <mtr> <mtd> <mtable> <mtr> <mtd> <munder> <mi>max</mi> <mrow> <mo>{</mo> <mrow> <msup> <mi>x</mi> <mi>k</mi> </msup> <mo>,</mo> <msup> <mi>y</mi> <mi>k</mi> </msup> <mo>,</mo> <msub> <mi>p</mi> <mi>k</mi> </msub> </mrow> <mo>}</mo> </mrow> </munder> </mtd> <mtd> <mrow> <munder> <mi>min</mi> <mi>k</mi> </munder> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>J</mi> </munderover> <mfrac> <mrow> <msub> <mi>p</mi> <mi>k</mi> </msub> <msubsup> <mi>C</mi> <mi>k</mi> <mi>j</mi> </msubsup> <msubsup> <mi>e</mi> <mi>j</mi> <mi>T</mi> </msubsup> <msup> <mi>y</mi> <mi>k</mi> </msup> <msup> <mrow> <mo>(</mo> <mrow> <mi>F</mi> <mo>+</mo> <msup> <mi>f</mi> <mi>T</mi> </msup> <msup> <mi>x</mi> <mi>k</mi> </msup> <msubsup> <mi>e</mi> <mi>j</mi> <mi>T</mi> </msubsup> <msup> <mi>y</mi> <mi>k</mi> </msup> </mrow> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>m</mi> <mo>&amp;NotEqual;</mo> <mi>k</mi> </mrow> <mi>M</mi> </munderover> <msub> <mi>p</mi> <mi>m</mi> </msub> <msubsup> <mi>C</mi> <mi>k</mi> <mi>j</mi> </msubsup> <msubsup> <mi>e</mi> <mi>j</mi> <mi>T</mi> </msubsup> <msup> <mi>y</mi> <mi>m</mi> </msup> <msup> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mi>m</mi> </msup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <msup> <mi>Wx</mi> <mi>k</mi> </msup> <msubsup> <mi>e</mi> <mi>j</mi> <mi>T</mi> </msubsup> <msup> <mi>y</mi> <mi>k</mi> </msup> <msup> <mrow> <mo>(</mo> <mrow> <mi>F</mi> <mo>+</mo> <msup> <mi>f</mi> <mi>T</mi> </msup> <msup> <mi>x</mi> <mi>m</mi> </msup> <msubsup> <mi>e</mi> <mi>j</mi> <mi>T</mi> </msubsup> <msup> <mi>y</mi> <mi>m</mi> </msup> </mrow> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msubsup> <mi>&amp;sigma;</mi> <mi>k</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>s</mi> <mi>u</mi> <mi>b</mi> <mi>j</mi> <mi>e</mi> <mi>c</mi> <mi>t</mi> <mi> </mi> <mi>t</mi> <mi>o</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mo>(</mo> <mrow> <mi>C</mi> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>:</mo> <msup> <mn>1</mn> <mi>T</mi> </msup> <msup> <mi>x</mi> <mi>k</mi> </msup> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>&amp;ForAll;</mo> <mi>k</mi> <mo>&amp;Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>M</mi> </mrow> <mo>}</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mo>(</mo> <mrow> <mi>C</mi> <mn>2</mn> </mrow> <mo>)</mo> </mrow> <mo>:</mo> <msup> <mn>1</mn> <mi>T</mi> </msup> <msup> <mi>y</mi> <mi>k</mi> </msup> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>&amp;ForAll;</mo> <mi>k</mi> <mo>&amp;Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>M</mi> </mrow> <mo>}</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mo>(</mo> <mrow> <mi>C</mi> <mn>3</mn> </mrow> <mo>)</mo> </mrow> <mo>:</mo> <msubsup> <mi>x</mi> <mi>i</mi> <mi>k</mi> </msubsup> <mo>&amp;Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> <mo>}</mo> </mrow> <mo>,</mo> <mo>&amp;ForAll;</mo> <mi>i</mi> <mo>&amp;Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>N</mi> </mrow> <mo>}</mo> </mrow> <mo>,</mo> <mo>&amp;ForAll;</mo> <mi>j</mi> <mo>&amp;Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>J</mi> </mrow> <mo>}</mo> </mrow> <mo>,</mo> <mo>&amp;ForAll;</mo> <mi>k</mi> <mo>&amp;Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>M</mi> </mrow> <mo>}</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mo>(</mo> <mrow> <mi>C</mi> <mn>4</mn> </mrow> <mo>)</mo> </mrow> <mo>:</mo> <msubsup> <mi>y</mi> <mi>j</mi> <mi>k</mi> </msubsup> <mo>&amp;Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>0</mn> <mo>,</mo> <mn>1</mn> </mrow> <mo>}</mo> </mrow> <mo>,</mo> <mo>&amp;ForAll;</mo> <mi>j</mi> <mo>&amp;Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>J</mi> </mrow> <mo>}</mo> </mrow> <mo>,</mo> <mo>&amp;ForAll;</mo> <mi>k</mi> <mo>&amp;Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>M</mi> </mrow> <mo>}</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mo>(</mo> <mrow> <mi>C</mi> <mn>5</mn> </mrow> <mo>)</mo> </mrow> <mo>:</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>p</mi> <mi>k</mi> </msub> <mo>&amp;le;</mo> <msub> <mi>P</mi> <mi>max</mi> </msub> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mo>(</mo> <mrow> <mi>C</mi> <mn>6</mn> </mrow> <mo>)</mo> </mrow> <mo>:</mo> <mn>0</mn> <mo>&amp;le;</mo> <msub> <mi>p</mi> <mi>k</mi> </msub> <mo>,</mo> <mo>&amp;ForAll;</mo> <mi>k</mi> <mo>&amp;Element;</mo> <mrow> <mo>{</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>M</mi> </mrow> <mo>}</mo> </mrow> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> <mo>,</mo> </mrow>

wherein,

<mrow> <msubsup> <mi>C</mi> <mi>k</mi> <mi>j</mi> </msubsup> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>32.4</mn> <mo>-</mo> <msub> <mi>&amp;eta;</mi> <mrow> <mi>L</mi> <mi>o</mi> <mi>S</mi> </mrow> </msub> </mrow> </msup> <mo>&amp;times;</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>d</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>B</mi> <mi>S</mi> </mrow> <mi>j</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>L</mi> <mi>o</mi> <mi>S</mi> <mi> </mi> <mi>l</mi> <mi>i</mi> <mi>n</mi> <mi>k</mi> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>32.4</mn> <mo>-</mo> <msub> <mi>&amp;eta;</mi> <mrow> <mi>N</mi> <mi>L</mi> <mi>o</mi> <mi>S</mi> </mrow> </msub> </mrow> </msup> <mo>&amp;times;</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>d</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>B</mi> <mi>S</mi> </mrow> <mi>j</mi> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>N</mi> <mi>L</mi> <mi>o</mi> <mi>S</mi> <mi> </mi> <mi>l</mi> <mi>i</mi> <mi>n</mi> <mi>k</mi> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>

and 4, step 4: number of initialization iterations t₁0, maximum number of iterations T_1,max(ii) a Setting an initial feasible solution p⁽⁰⁾、X⁽⁰⁾And Y⁽⁰⁾Where p is a power allocation vector, p⁽⁰⁾、X⁽⁰⁾And Y⁽⁰⁾Respectively represents t₁When the power distribution vector is 0, a channel occupation matrix and a time slot occupation matrix;

and 5: fixingSolving sub-problems related to variables X and Y in a distributed mode by using a block coordinate descent algorithm, and updating to obtain

Step 6: fixingSolving the subproblem about the variable p by using a characteristic root decomposition method, and updating to obtain the subproblem

And 7: judging whether t is satisfied₁≥T_1,max(ii) a If yes, outputtingAndif not, updating the iteration times t₁＝t₁+1 and repeating steps 5-7;

and 8: based on the obtained power allocation vector p and X and Y, according toAnd calculating to obtain a time-frequency distribution matrix of each unmanned aerial vehicle, and finally realizing power distribution and channel distribution of the unmanned aerial vehicles by the ground control station to complete time-frequency decision optimization design of the unmanned aerial vehicle communication system.

2. The unmanned aerial vehicle time-frequency resource allocation method based on block coordinate descent according to claim 1, wherein in step 5, X and Y are obtained by distributed solution using a block coordinate descent algorithm, and the method specifically comprises the following steps:

5.1 initializing outer iteration times t₂Maximum number of iterations T, 0_2,max(ii) a Initialization of X⁽⁰⁾And Y⁽⁰⁾，p；

5.2 initializing the number of inner layer iterations k to 1, generating a randomly arranged sequence of integers from 1 to M

5.3, setting

5.4, fixingAndupdating x_m＝e_IWherein

5.5, fixingAndupdating y_m＝e_KWherein

5.6, updating the inner layer iteration number k to be k +1, and repeating the steps 5.3-5.6 until the condition k to be M is met;

5.7, updating the outer iteration times t₂＝t₂+1 and repeating steps 5.2-5.7 until condition t is satisfied₂＝T_2,max。

3. The unmanned aerial vehicle time-frequency resource allocation method based on block coordinate descent according to claim 1, wherein the solution obtained in step 6 by using a characteristic root decomposition methodThe method specifically comprises the following steps:

6.1, setting

6.2, definition z ═ p₁,p₂…p_M,1]^TLet us orderAnd

<mrow> <mi>C</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>I</mi> <mrow> <mi>M</mi> <mo>&amp;times;</mo> <mi>M</mi> </mrow> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mi>M</mi> <mo>&amp;times;</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>1</mn> <mrow> <mn>1</mn> <mo>&amp;times;</mo> <mi>M</mi> </mrow> </msub> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>P</mi> <mi>max</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>B</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>R</mi> <mrow> <mi>M</mi> <mo>&amp;times;</mo> <mi>M</mi> </mrow> </msub> </mtd> <mtd> <mi>h</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>1</mn> <mo>&amp;times;</mo> <mi>M</mi> </mrow> </msub> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow>

wherein,

<mrow> <mi>R</mi> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <msubsup> <mi>b</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>m</mi> </mrow> <mi>j</mi> </msubsup> <msubsup> <mi>b</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>k</mi> </mrow> <mi>j</mi> </msubsup> </mfrac> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>k</mi> <mo>&amp;NotEqual;</mo> <mi>m</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>k</mi> <mo>=</mo> <mi>m</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>h</mi> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mfrac> <msubsup> <mi>&amp;sigma;</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msubsup> <mi>b</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> <mi>j</mi> </msubsup> </mfrac> <mo>,</mo> <mfrac> <msubsup> <mi>&amp;sigma;</mi> <mn>2</mn> <mn>2</mn> </msubsup> <msubsup> <mi>b</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>2</mn> </mrow> <mi>j</mi> </msubsup> </mfrac> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mfrac> <msubsup> <mi>&amp;sigma;</mi> <mi>M</mi> <mn>2</mn> </msubsup> <msubsup> <mi>b</mi> <mrow> <mi>M</mi> <mo>,</mo> <mi>M</mi> </mrow> <mi>j</mi> </msubsup> </mfrac> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>;</mo> </mrow>

6.3, to C^-1And B, after the characteristic root decomposition, all element signs of the characteristic root vector corresponding to the characteristic value with the maximum modulus are the same, the reciprocal of the characteristic root is the maximum value of the corresponding target function, the corresponding characteristic root vector is normalized, the last element is 1, and the obtained vector p consisting of the first M elements is the optimal solution.