A multi-unmanned aerial vehicle assisted trajectory planning and resource allocation method integrating sensing

Abstract

The present application relates to a kind of multi-unmanned aerial vehicle assisted trajectory planning and resource allocation method of integrated sensing, comprising the following steps: build integrated sensing system including multiple unmanned aerial vehicles, multiple ground nodes and multiple mobile terminals, wherein the integrated sensing signal launched by unmanned aerial vehicle is received and reflected by mobile terminal, and the reflected integrated sensing signal is received and handled by ground node;According to the path loss of the integrated sensing signal, the Cramer-Rao bound model of mobile terminal at its target position is constructed;With the maximum Cramer-Rao bound of all the mobile terminal at its target position as the target, a joint optimization problem is established based on the set constraint condition;Solve the joint optimization problem to obtain the moving trajectory and transmission power of unmanned aerial vehicle and corresponding ground node.The present application realizes the optimization of sensing performance under the constraint of communication performance, and reduces the communication and calculation burden of data fusion under the premise of ensuring the sensing performance.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of integrated sensing and communication, and in particular to a multi-unmanned aerial vehicle (UAV) assisted integrated sensing and communication trajectory planning and resource allocation method. BACKGROUND

[0002] Unmanned aerial vehicles (UAVs) have the characteristics of strong maneuverability, intelligence, and flexibility. By taking advantage of the high viewing angle and wide coverage of UAVs, UAV-assisted communication can provide greater coverage and better channel quality. In addition, UAV-assisted sensing can also be used in applications such as measurement, photography, mapping, and positioning. In order to improve the efficiency of electromagnetic spectrum use, integrated sensing and communication (ISAC) technology, which aims to integrate communication and radar sensing in waveform and hardware, has received widespread attention from the industry and academia. Compared with single-function UAVs, UAV-assisted ISAC technology can achieve lighter load, and the communication and sensing functions on the UAV can achieve mutual benefits.

[0003] However, there are still some challenges in current UAV-assisted ISAC technology. First, a trajectory planning method suitable for UAV-assisted ISAC systems needs to be designed. Since the communication channel gain is affected by the distance between the UAV and the user, and the sensing performance is also affected by the geometry of the UAV and the channel gain, a trajectory planning method that takes into account both communication performance and sensing performance is needed. Second, UAV-assisted ISAC systems need to use appropriate resource allocation methods. Since multi-station radars aim to improve sensing performance through cooperation, and multi-station communication needs to avoid interference to improve communication performance, there is a trade-off between communication and sensing resource allocation, and appropriate resource allocation schemes need to be designed to maximize sensing performance and manage communication interference. Finally, for networked UAV-assisted ISAC systems, data fusion between multiple nodes increases the communication and computing burden between nodes while introducing performance gains. In order to ensure performance, appropriate node selection methods also need to be considered. Most importantly, trajectory optimization, power control, and node selection problems are often coupled, so joint optimization of these parameters is challenging.

[0004] In addition, most existing joint optimization strategies only consider static target scenarios and do not consider multi-mobile target scenarios, and the target positioning information is pre-known in the optimization algorithm. These assumptions may not be applicable to actual scenarios and waste multi-UAV sensing resources. SUMMARY

[0005] The technical problem solved by the present application is to provide a multi-unmanned aerial vehicle assisted integrated sensing and communication trajectory planning and resource allocation method, which can optimize sensing performance under communication performance constraints and reduce communication and computing burden of data fusion while ensuring sensing performance.

[0006] The technical solution adopted by the present application to solve its technical problem is to provide a multi-unmanned aerial vehicle assisted integrated sensing and communication trajectory planning and resource allocation method, comprising the following steps:

[0007] An integrated sensing and communication system including multiple unmanned aerial vehicles, multiple ground nodes and multiple mobile terminals is built, wherein the integrated sensing and communication signals transmitted by the unmanned aerial vehicles are received and reflected by the mobile terminals, and the reflected integrated sensing and communication signals are received and processed by the ground nodes;

[0008] According to the path loss of the integrated sensing and communication signals from the unmanned aerial vehicles to the mobile terminals and then to the ground nodes, a Cramer-Rao bound model of the mobile terminal at its target position is constructed, and the target position is the position of the mobile terminal in the next time slot;

[0009] A joint optimization problem of ground node selection, unmanned aerial vehicle trajectory planning and resource allocation is established based on the set constraints, with the goal of minimizing the maximum Cramer-Rao bound of all mobile terminals at their target positions;

[0010] The joint optimization problem is solved to obtain the movement trajectory and transmission power of each unmanned aerial vehicle and the corresponding ground node selection.

[0011] Further, the set constraints include total communication spectral efficiency constraints, minimum maximum sensing performance constraints, unmanned aerial vehicle position constraints, unmanned aerial vehicle speed constraints, unmanned aerial vehicle collision avoidance constraints, unmanned aerial vehicle motion constraints, transmission power constraints, and ground node selection vector constraints.

[0012] Further, the solving of the joint optimization problem to obtain the movement trajectory and transmission power of each unmanned aerial vehicle and the corresponding ground node selection is realized by dividing the optimization parameters of the joint optimization problem into a ground node selection vector, a transmission power vector and an unmanned aerial vehicle trajectory vector and performing alternating optimization.

[0013] Further, the alternating optimization of the ground node selection vector, the transmission power vector and the unmanned aerial vehicle trajectory vector is performed by the following method:

[0014] The objective function is converted into a convex problem for the ground node selection vector, a convex problem for the transmission power vector, and a convex problem for the unmanned aerial vehicle trajectory vector using the Schur complement theorem;

[0015] The three convex problems obtained in the previous step are solved iteratively using a convex optimization algorithm to obtain the receiving ground node, transmission power, and movement trajectory of each UAV in the next time slot.

[0016] Furthermore, the integrated sensing signal includes an integrated sensing phase signal transmitted by multiple UAVs in a time-division mode and a communication-only phase signal transmitted simultaneously by multiple UAVs.

[0017] Furthermore, the step of constructing a Cramer-Rao bound model of the mobile terminal at its target location based on the path loss of the integrated sensing signal from the drone to the mobile terminal and then to the ground node includes:

[0018] Predict the target location;

[0019] Based on the model of the integrated sensing signal transmitted by the UAV and its path loss from the UAV to the mobile terminal and then to the ground node, a pilot signal model of the integrated sensing signal received and processed by the ground node is constructed.

[0020] Based on the pilot signal model, a likelihood function is derived with the path loss and the target position as the parameters to be estimated. Then, the inverse of the Fisher information matrix of the likelihood function is obtained to obtain the Cramer-Rao bound model of the mobile terminal at its target position.

[0021] Furthermore, the target position is predicted based on a uniform motion model.

[0022] Furthermore, the joint optimization problem is expressed as:

[0023]

[0024] Where η is the objective function, Let R be the set of mobile terminals that receive communication signals in the nth time slot. k (n) is the downlink spectral efficiency of the k-th mobile terminal, R min It is the minimum total spectral efficiency. and These are the mobile terminal locations x k (n) and y k The Craméro boundary of (n), and It is the nth t The location of the drone, X min and X max They are The minimum and maximum values ​​of Y min and Y max They are The minimum and maximum values ​​of V max drone speed The maximum value, dmin is the minimum inter-UAV distance, ΔT is the frame length of the CINT signal, P P max is the transmit power of the UAV , b(n) is the selection vector of the ground nodes is equal to 1 if and only if the nth r ground node is selected, N r is the number of ground nodes.

[0025] Further, the downlink spectral efficiency R k (n) is expressed as

[0026]

[0027] where, is the channel gain of the nth t UAV and the kth mobile terminal in the nth time slot, is the transmit power of the nth t UAV in the nth time slot, σ 2 is the noise variance.

[0028] Further, the Cramér-Rao bound model is expressed as

[0029]

[0030] The function terms A k,11 , A k,22 and A k,12 are defined as

[0031]

[0032] where the parameter β is defined as l = 1, 2, …, L is the pilot sequence number, L is the number of pilots, k l is the wave number, is the processed noise variance, is the channel gain of the nth t UAV and the kth mobile terminal in the nth time slot, is the transmit power of the nth t UAV in the nth time slot, and are the propagation distances of the CINT signal from the UAV to the mobile terminal and from the mobile terminal to the ground node, respectively, and are the positions of the nth r ground node, and are the predicted target positions of the mobile terminal, Nt and N r are the number of UAVs and ground nodes, respectively.

[0033] Advantages

[0034] Compared with the prior art, the present application has the following advantages and positive effects: the present application builds a multi-UAV assisted multi-user integrated sensing and communication (ISAC) system, in which the UAVs provide communication services for mobile terminals (ISAC users) and act as transmitters of the MIMO radar system, while the ground nodes (GNs) receive reflected signals and fuse data to locate the ISAC users, fully utilizing the mobility, flexibility and intelligence of the UAVs, while the introduction of GNs avoids complex full-duplex design and reduces communication and computing burden; the present application further proposes a real-time joint trajectory planning and resource allocation scheme based on the foregoing system, predicts the target position of the next time slot according to the positioning result of the previous time slot, and constructs a joint GN selection, transmit power control and trajectory design problem based on the Pareto criterion, which aims to jointly optimize the GN selection, transmit power of the UAV and trajectory planning under the constraint of minimizing the total spectral efficiency, achieving optimization of the sensing performance under the constraint of communication performance, while the selection of GN reduces the communication and computing burden of data fusion under the premise of ensuring the sensing performance; the present application also approximates and simplifies the CRB expression, then alternately optimizes the variables based on the block coordinate descent method (BCD technique), and rewrites the optimization problem by introducing equivalent transformation, penalty function and continuous convex approximation SCA technique, finally realizes the solution of the foregoing joint optimization problem. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 is a flowchart of an embodiment of the present application;

[0036] Figure 2 is a system schematic diagram of an embodiment of the present application. DETAILED DESCRIPTION

[0037] The present application will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present application and not to limit the scope of the present application. Furthermore, it should be understood that those skilled in the art can make various modifications or changes to the present application after reading the content taught by the present application, and these equivalent forms also fall within the scope defined by the appended claims of the present application.

[0038] An embodiment of the present application relates to a multi-UAV assisted integrated sensing and communication trajectory planning and resource allocation method, as shown in Figure 1 comprising the following steps:

[0039] S0 constructs an integrated sensing and communication (ISAC) system that includes multiple unmanned aerial vehicles (UAVs), multiple ground nodes (GNs), and multiple mobile terminals (UEs, i.e., ISAC users). The integrated sensing and communication signals transmitted by the UAVs are received and reflected by the mobile terminals, and the reflected signals are received and processed by the ground nodes.

[0040] S1 constructs a Cramer-Rao bound model of the mobile terminal at its target location based on the path loss of the integrated sensor signal from the drone to the mobile terminal and then to the ground node.

[0041] S2 aims to minimize the maximum Cramer-Rao bound of all mobile terminals at their target locations, and establishes a joint optimization problem of ground node selection, UAV trajectory planning, and resource allocation based on set constraints.

[0042] S3 solves this joint optimization problem to obtain the UAV's movement trajectory, transmission power, and corresponding ground node selection.

[0043] The following description, in conjunction with the ISAC system, further illustrates this implementation method.

[0044] (1) ISAC system model and ISAC signal frame structure launched by UAV.

[0045] like Figure 2 As shown, in the nth time slot, the system consists of N t Located in n t =1,…,N t The drones, of which H T It is the drone's altitude, N r,tot Located in n r =1,…,N r,tot Composed of ground nodes, the UAV directs to K nodes located at x k (n)=(x k (n),y k (n),0) T Communication services are provided to mobile ISAC users (k = 1, ..., K), and the location of these ISAC users is also monitored. This location information can be used for target tracking, UAV trajectory optimization, and resource scheduling. The UAV transmits Orthogonal Frequency Division Modulation (OFDM) signals as ISAC signals, and the GN receives the reflected signals from the ISAC users. The introduction of the GN avoids complex full-duplex designs. To reduce the communication and computational burden of data fusion, only N is selected here. r One GN is used as an ISAC receiving station.

[0046] Figure 2The structure of the ISAC frame is also demonstrated. The ISAC frame consists of two parts: a sensing-integrated phase and a communication-only phase. This structure is adopted because the sensing duration does not need to be long (a few milliseconds) and this structure reduces data redundancy. To maximize sensing performance, the UAV transmits signals in a time-division multiplexing mode during the sensing-integrated phase. During the communication phase, multiple UAVs transmit signals simultaneously. In our proposed real-time trajectory planning and resource allocation scheme, based on the positioning results of the previous moment, the system predicts the UE's position at the next ISAC frame transmission time, selects a certain number of GNs to receive and process the reflected ISAC signals, determines the UAV's transmit power for interference management during the communication phase, and optimizes the target location's CRB (Continuous Reference Scale). The system plans the UAV's trajectory to further optimize the CRB. The UAV then moves along the predetermined trajectory and transmits downlink signals, while the selected GNs receive and preprocess the reflected signals. The fusion center collects and processes the signals to locate the ISAC user. The system repeats the above steps to provide communication services and continuously manage location information.

[0047] (2) Sensing signal model

[0048] nth t The signal transmitted by a drone in the nth time slot can be represented as:

[0049]

[0050] Where i is the OFDM symbol index. It is the nth t The transmit power of the UAV in the nth ISAC time slot, f c Here, m is the carrier frequency, m is the subcarrier index, M is the number of subcarriers, Δf is the subcarrier spacing, and T is the carrier frequency. s Let be the duration of a single OFDM symbol, and rect(t) be a rectangular window function that has a non-zero value of 1 only in t∈[0,1]. Then, in the nth time slot, the nth... r The nth GN receives data from the nth GN. t The signal of a drone can be represented as:

[0051]

[0052] Where k is the ISAC user sequence number. Indicates starting from the nth t From the first drone to the kth UE and then to the nth UE r The signal strength change caused by path loss of 1 GN This indicates the propagation delay in the above path. It is to satisfy Complex Gaussian white noise.

[0053] According to the radar equation Satisfy: where Γ0is the reference channel gain at 1 m, defined as

[0054] After sampling and OFDM demodulation at the receiver, the signal can be converted from time domain to frequency domain, and located using pilots. The received pilot subcarrier signal is multiplied by the conjugate of the corresponding pilot symbol, and the pilot signals of the I OFDM symbols are averaged. The processed signal can be modeled as

[0055]

[0056] where l = 1, 2, …, L is the pilot sequence number, L is the number of pilots, f l is the pilot subcarrier frequency of the lth, k l is the wave number satisfying k l = 2pif l / c, is the signal propagation distance, is the incident signal propagation distance and the reflected signal propagation distance, respectively. is the processed noise, which can be proved to be complex Gaussian white noise, and the variance is reduced to To simplify the expression, define

[0057] (3) Communication channel model

[0058] Assuming that the communication channel is dominated by the line-of-sight (LoS) component, according to the free space path loss model, the channel gain between the nth t unmanned aerial vehicle and the kth user in the nth time slot can be written as

[0059]

[0060] Let represent the unmanned aerial vehicle sequence number related to the kth UE, and the downlink SE of the kth UE can be modeled as

[0061]

[0062] (4) Cramer-Rao lower bound derivation

[0063] According to the properties of Gaussian white noise, the parameter to be estimated can be defined as where The expression of the likelihood function of the received signal can be derived as

[0064]

[0065] Where C is a constant that can be ignored in subsequent steps, and s(d) is defined as s(d) = [exp(-jk1d), exp(-jk2d), ..., exp(-jk... L d)] T .

[0066] To model the GN selection problem, we define the GN selection vector. Where only when n is selected r The element equals 1 only when the GNth element is reached. The likelihood function can be rewritten in a form related to b(n).

[0067]

[0068] It is worth noting that, without loss of generality and for the sake of simplicity of expression, we will use 1, 2, ..., N after selecting GN. r For the selected N r Each GN is renumbered.

[0069] CRB can be obtained from the inverse of Fisher's information matrix F, i.e.

[0070]

[0071] MSEu i )≥CRB(u i )=[F -1 ] ii .

[0072] Since the CRB is related to the true value of the estimated parameter u(n), it is impossible to obtain an accurate CRB before sensing. Therefore, we use the expected value of the predicted target position and path loss to calculate the CRB. The prediction of the target position adopts the simplest uniform motion model, i.e.

[0073] Assuming the targets are far apart and their mutual influence can be ignored, after a series of derivations, the CRB of the k-th target can be approximated as...

[0074]

[0075]

[0076] Where A k,11 A k,22 and A k,12 Defined as

[0077]

[0078] Wherein, parameter β is defined as

[0079] (5) Construction and solution of optimization problem

[0080] The joint optimization problem is constructed according to the Pareto criterion:

[0081]

[0082] where is the set of UEs receiving the communication signal in the nth time slot, and the transmit power vector p(n) is defined as The objective function η is the maximum target location CRB, V max , d min is the maximum speed of the UAV and the minimum inter-UAV distance. The constraints of the optimization problem are respectively the communication and rate constraints, the minimum maximum sensing performance constraint, the UAV location constraint, the maximum speed of the UAV constraint, the UAV collision avoidance constraint, the UAV motion constraint, the transmit power constraint, and the GN selection vector constraint.

[0083] The BCD technique is adopted to divide the optimization parameters into three groups, i.e., the GN selection vector, the transmit power vector, and the UAV trajectory, which are alternately optimized.

[0084] In the GN selection vector optimization problem, the CRB constraint is rewritten by using the Schur complement theorem, and the constraint can be written as a convex positive definite constraint. At the same time, the 0-1 constraint of the GN selection vector is solved by using the penalty function method, and an auxiliary variable is introduced and guaranteed The penalty function is defined as

[0085]

[0086] where ∈ is a penalty coefficient, which decreases with the increase of the iteration round number. The GN selection vector optimization problem is thus rewritten as the problem of alternately optimizing b(n), and p(n). The optimization problem of can directly write a closed-form expression:

[0087]

[0088] When is given, the optimization problem of b(n) can be written as the following convex problem

[0089]

[0090] where N r,tot is a vector, and the nth r element of is defined as

[0091]

[0092]

[0093] Similarly, for the transmit power control problem, the constraints related to CRB can be rewritten using Schur's complement theorem. For communication constraints, the SCA technique can be used to rewrite them as a convex lower bound. The transmit power optimization problem can be written as:

[0094]

[0095] Where N t dimensional vector The nth t Each element is defined as

[0096]

[0097] Defined as

[0098]

[0099] For trajectory planning problems, auxiliary parameters are introduced. And satisfy constraints Using auxiliary parameters The communication constraints were rewritten, and SCA technology was used to integrate the communication constraints, CRB constraints, and collision avoidance constraints. Rewritten in convex form, the trajectory planning problem can be rewritten as:

[0100]

[0101] in, Defined as

[0102]

[0103] Defined as

[0104]

[0105] They represent the parameters x respectively k ,y k Approximate CRBs and their corresponding Taylor expansions.

[0106] For the three sets of problems above, mature convex optimization tools can be used to solve them. The convergent suboptimal solution can be obtained by iterative solution.

Claims

1. A method for trajectory planning and resource allocation of multi-UAV assisted integrated sensing, characterized in that, The method comprises the following steps: constructing a Cramer-Rao bound model of the mobile terminal at its target position according to path loss of the C3I signal from the UAV to the mobile terminal and then to the ground node, the target position being the position of the mobile terminal in the next time slot; solving the joint optimization problem by alternately optimizing the ground node selection vector, the transmission power vector, and the UAV trajectory vector, to obtain the moving trajectory and transmission power of each UAV and the corresponding ground node selection; the alternately optimizing the ground node selection vector, the transmission power vector, and the UAV trajectory vector is performed by the following method: translating the objective function into a convex problem for the ground node selection vector, a convex problem for the transmission power vector, and a convex problem for the UAV trajectory vector by using the Shur complement theorem; in, It is the objective function. In the first A set of mobile terminals that receive communication signals in a time slot. It is the first Downlink spectrum efficiency of a mobile terminal It is the minimum total spectral efficiency. and These are the mobile terminal locations. and The boundary of Clamero, and It is the first The location of the drone. and They are The minimum and maximum values, and They are The minimum and maximum values, drone speed The maximum value, It is the minimum distance between drones. It is the frame length of the integrated sensing signal and the transmit power vector. , It is the drone's launch power. The maximum value, Ground node selection vector If and only if the first option is selected When there are multiple ground nodes, Only equals 1. This is the number of ground nodes; iteratively solving the three convex problems obtained in the previous step by using a convex optimization algorithm to obtain the receiving ground node, transmission power, and moving trajectory of each UAV in the next time slot. The set constraints include a total communication spectrum efficiency constraint, a minimum maximum sensing performance constraint, a UAV position constraint, a UAV speed constraint, a UAV collision avoidance constraint, a UAV motion constraint, a transmission power constraint, and a ground node selection vector constraint. The C3I signal comprises a C3I phase signal transmitted by multiple UAVs in a time division mode and a communication-only phase signal transmitted by multiple UAVs simultaneously.

2. The method of claim 1, wherein, The Cramer-Rao bound model of the mobile terminal at its target position is constructed according to path loss of the C3I signal from the UAV to the mobile terminal and then to the ground node, the target position being the position of the mobile terminal in the next time slot, and comprises the following steps:

3. The method of claim 1, wherein, predicting the target position; 4. The method of claim 1, wherein, constructing a pilot signal model of the C3I signal received and processed by the ground node according to a model of the C3I signal transmitted by the UAV and path loss of the C3I signal from the UAV to the mobile terminal and then to the ground node; deriving a likelihood function with the path loss and the target position as to-be-estimated parameters according to the pilot signal model, and then inverting a Fisher information matrix of the likelihood function to obtain the Cramer-Rao bound model of the mobile terminal at its target position. The target position is predicted based on a uniform motion model. The Cramer-Rao bound model is represented as 5. The method of claim 1, wherein, ​ 6. The method of claim 1, wherein, The downlink spectral efficiency is represented as wherein, is the channel gain of the first drone and the first mobile terminal at the first time slot, is the transmit power of the first drone at the first time slot, is the noise variance.

7. The method of claim 1, wherein, ​ function term and is defined as wherein the parameters are defined as , is a pilot sequence number, is a pilot number, is a wave number, is a processed noise variance, is a channel gain between the th unmanned aerial vehicle and the th mobile terminal in the th time slot, is a transmission power of the th unmanned aerial vehicle in the th time slot, and are propagation distances of the integrated sensing and communication signal from the unmanned aerial vehicle to the mobile terminal and from the mobile terminal to the ground node, respectively, and are positions of the th ground node, and are predicted target positions of the mobile terminal, and are numbers of unmanned aerial vehicles and ground nodes, respectively.

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