Energy harvesting assisted UAV sensing integrated system resource allocation

Guangjun Liang; Hailiang Xu; Xilong Liu; Chuang Chen; Guangjun Liang; Hailiang Xu; Xilong Liu; Chuang Chen

doi:10.48130/wpt-0025-0020

In the context of the deep integration of wireless communication and perception technology, this paper examines the resource allocation problem of an energy harvesting-assisted unmanned aerial vehicle (UAV) communication and perception integrated systems. Firstly, an energy harvesting-assisted UAV sensing integrated system was constructed, which consists of a sensing integrated base station, sensing terminals, and ground sensing energy stations. Then, based on the separate study of energy consumption models, communication models, and perception models, an integrated energy harvesting-assisted UAV sensing system model was established. Considering the optimization objectives of communication and perception, communication metrics were transformed into constraints and the research focussed on studying the perception performance of the system. A series of convex optimization methods were used to solve the conversion optimization problem, and the optimal energy harvesting time slot allocation was solved using the binary method. The established optimization model takes into account the deep coupling between the drone beamforming vector and the position decision variable. Finally, the optimal solution was obtained through alternating iterations using semi-definite programming (SDP), the Dinkelbach method, and the successful convex approximation (SCA) method. The simulation experiment fully verifies the effectiveness of the proposed algorithm.

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Introduction

With the rapid advancement of unmanned aerial vehicle (UAV) technology and continuous innovation in wireless communication networks, unmanned aerial vehicles (UAVs) have emerged as a pioneering force in promoting the deep integration of communication and perception technologies^[1−4]. As a cutting-edge trend in network evolution, communication-perception integration (CPI) corely relies on physical infrastructure and resource sharing to significantly enhance system-wide efficiency and adaptability^[5−7]. UAVs, with their unique aerial perspective, excellent maneuverability, and rapid response capabilities, enable wide coverage of communication networks and precise acquisition of perception data, thereby opening new avenues for CPI implementation. In this context, analyzing the core role and precise positioning of UAVs in CPI systems becomes particularly urgent. Designing efficient resource allocation and scheduling strategies based on such analysis not only maximizes UAV-specific advantages but also directly influences the intelligent and flexible development of future network systems. This endeavor is crucial for harnessing the full potential of UAVs in next-generation integrated networks.

The UAV resource allocation problem mainly focuses on trajectory optimization, channel allocation, and power control^[8−12]. The trajectory optimization problem of multiple three-dimensional UAVs as aerial base stations (BS) was studied^[8]. Wireless coverage for Internet of Things (IoT) devices is considered by optimizing the trajectory and power of drones to minimize communication time for all IoT devices. Furthermore, a solution based on Hierarchical Reinforcement Learning (HRL) has been proposed. In reliability-oriented downlink wireless network assisted by drones, a deep embedding deterministic policy gradient (DDPG) algorithm was proposed, and the trajectory and transmission power allocation of unmanned aerial vehicles were jointly determined through alternately optimizing iterative schemes^[9].

The application of unmanned aerial vehicles in auxiliary hybrid non-orthogonal multiple access (NOMA) systems was studied^[10]. To improve UAV spectrum efficiency and communication connectivity, a joint optimization model for UAV positioning and user grouping that maximizes system speed was established. Finally, the paper swarm optimization algorithm and neural network method were used to iteratively solve the problem. Channel allocation and power control for uplink NOMA-assisted multi-UAV networks were researched^[11]. A mixed integer nonlinear programming model was established, and a feasible algorithm proposed to obtain the power and channel allocation scheme for the drone. A drone relay network based on NOMA was studied^[12]. A joint optimization model for NOMA user grouping, drone location, and drone transmission power were established. Similarly, an iterative algorithm was used to obtain an approximate optimal solution.

The resource allocation problem of sensory integrated systems was studied^[13−15]. In the scenario of unmanned aerial vehicle multi-cell collaborative integrated sensing and communication (ISAC), a collaborative control strategy for base station power and unmanned aerial vehicles was designed, considering the maximization of QoS (Quality of Service), and communication efficiency^[13]. To ensure the safety of ISAC-UAV systems, a joint optimization algorithm for UAV trajectory and launch power was proposed^[14], maximizing the secure communication rate under the constraints of UAV maneuverability, power, and perception. In multi UAV assisted dual function base station (BS) scenarios, a Stackelberg game model was proposed to consider the physical layer security of ISAC signals^[15].

In recent years, the energy consumption issue of UAVs has attracted increasing attention^[16−25]. The application of energy harvesting (EH) technology in unmanned aerial vehicle communication scenarios was studied^[16]. A rate-limited solution for UAV networks was proposed through UAV-assisted communication and EH channel modeling. An EH scheme based on the UAV-RIS system was proposed, enabling simultaneous signal transmission, and energy harvesting on the RIS metasurface^[17]. A robust near-end policy optimization algorithm has been developed with QoS as a constraint in dynamic wireless environments. A graph theory-based UAV energy harvesting assisted communication resource allocation algorithm was proposed^[18]. A EH optimization model based on imperfect channel state information (CSI) was established and solved to maximize network throughput.

An EH scenario based on meta reinforcement learning (RL) was studied^[19]. A joint optimization scheme for UAV trajectory and EH strategy was designed, taking QoS as the constraint condition, considering unmanned aerial vehicles with both energy collection and data transmission capabilities. An unmanned aerial vehicle RIS assisted maritime communication system in the presence of malicious interference was designed^[20]. A problem of maximizing energy efficiency (EE) in an adaptive energy harvesting system was proposed by adjusting the position and surface elements of the RIS. The UAV selection algorithm for UAV-assisted relay networks was studied^[21]. A two-stage drone selection strategy was developed. The closed-form expressions for the total interruption probability, average throughput, and average symbol error probability were derived.

A joint optimization scheme for UAV flight trajectory, user assignment, and power control was designed, with the objective of maximizing the minimum user rate^[22]. The reliability and security of unmanned aerial vehicle communication systems were studied^[23]. Taking into account the energy consumption issue of UAV ground networks, an approximate closed-form expression for the system interruption probability (OP) was provided. A drone-assisted MEC network for EH was considered^[24]. A joint optimization algorithm for user assignment, power allocation, computation offloading, and drone location was proposed with the optimization objective of improving the computational efficiency of the network. A new UAV model was constructed, which improves UAV energy efficiency via the proposed Lyapunov chain offloading algorithm^[25].

This paper proposes a joint optimization algorithm for UAV transmission beamforming and UAV position, based on optimal communication and perception performance, for the scenario of energy harvesting-assisted UAV communication-perception integration. Through a series of convex optimization processes and optimization problem transformations, the minimum perceptual performance was maximized while ensuring the communication performance of communication users. The main contributions of this paper are as follows:

(1) This study considers the energy harvesting time slots of the energy harvesting-ISAC-UAV system and solves the optimal energy harvesting time slot allocation via a binary search method.

(2) For the beamforming vector optimization of the energy harvesting-assisted ISAC-UAV system, a convex semidefinite programming approach is adopted to solve the beamforming vectors under a given UAV position.

(3) For UAV position optimization for the energy harvesting-assisted ISAC-UAV system, a continuous convex approximation method was used to solve the UAV position under the condition of beamforming vectors.

Problem solving

Convex optimization processing and time slot allocation

Optimization problem P1 is a multi-objective optimization problem, and in the actual solving process, one optimization objective can be transformed into a constraint condition, with a focus on the optimization problem of the other optimization objective. This model transforms communication metrics into constraints and instead studies the perception performance of the system.

Here we make a reasonable approximation to transform the maximum achievable rate ${R_{total}}({\boldsymbol{u}}{\mathbf{,}}\omega _n^c)$ of UAV downlink communication into any rate ${R_n}({\boldsymbol{u}}{, }\omega _n^c)$ greater than a certain threshold R_min, expressed as:

$ {R_n}({\boldsymbol{u}}{,}\omega _n^c) = \dfrac{1}{2}{\log _2}\left(1 + \dfrac{{{{\left| {{\boldsymbol{h}}_n^H\left( {{\boldsymbol{u}},{{\boldsymbol{c}}_n}} \right){\boldsymbol{\omega}} _n^c} \right|}^2}}}{{{{\left| {\displaystyle\sum\limits_{i = 1,i \ne n}^N {{\boldsymbol{h}}_n^H\left( {{\boldsymbol{u}},{{\boldsymbol{c}}_n}} \right){\boldsymbol{\omega}} _i^c} } \right|}^2} + \sigma _n^2}}\right) \geqslant {R_{\min }} $

(22)

Thus, the new optimization problem P2 can be expressed as:

$ \begin{gathered} P2: \quad\mathop {\max }\limits_{\tau ,u,\omega } {\text{ min SINR}}_n^s = \dfrac{{{{\left| {{{\boldsymbol{g}}^H}\left( {{\boldsymbol{u}},{\boldsymbol{s}}} \right){\boldsymbol{\omega}} _n^c} \right|}^2}}}{{{{\left| {\displaystyle\sum\limits_{m = 1}^M {{{\boldsymbol{g}}^H}\left( {{\boldsymbol{u}},{\boldsymbol{s}}} \right){\boldsymbol{\omega}} _m^s} } \right|}^2} + \sigma _s^2}} \\ \quad s.t.\;{\text{ C1:}}\sum _{n = 1}^N{\left\| {{\boldsymbol{\omega}} _n^c} \right\|^2} + \sum _{n' = 1}^N{\left\| {{\boldsymbol{\omega}} _{n'}^s} \right\|^2} \leq {P_{\max }} \\ \qquad\;\;\;C2:{\tau _1}+ {\tau _2} +{\tau _3} = 1 \\ \qquad\;\;\;C3:{P_{\max }}\left( {{\tau _2} + {\tau _3}} \right) = {E_{UAV}} + E_{UAV}^0 \\ \qquad\;\;\;C4:{R_n}({\boldsymbol{u}}{,}\omega _n^c) = \dfrac{1}{2}{\log _2}\left(1 + \dfrac{{{{\left| {{\boldsymbol{h}}_n^H\left( {{\boldsymbol{u}},{{\boldsymbol{c}}_n}} \right){\boldsymbol{\omega}} _n^c} \right|}^2}}}{{{{\left| {\displaystyle\sum\limits_{i = 1,i \ne n}^N {{\boldsymbol{h}}_n^H\left( {{\boldsymbol{u}},{{\boldsymbol{c}}_n}} \right){\boldsymbol{\omega}} _i^c} } \right|}^2} + \sigma _n^2}}\right) \geq {R_{\min }} \\ \end{gathered} $

(23)

Continuing to analyze optimization problem P2, according to its objective function, P2 is an MM problem. By introducing auxiliary variable A and adding a constraint condition C5, the MM problem can be transformed into a minimax problem, which can be rephrased as:

$ \begin{gathered} P3: \;\;\;\mathop {\max }\limits_{\tau ,u,\omega } {\text{ }}A \\ \quad s.t.{\text{ C1 : }}\sum _{n = 1}^N{\left\| {{\boldsymbol{\omega}} _n^c} \right\|^2} + \sum _{n' = 1}^N{\left\| {{\boldsymbol{\omega}} _{n'}^s} \right\|^2} \leq {P_{\max }} \\ \qquad\;\; C2:{\tau _1} + {\tau _2}+ {\tau _3} = 1 \\ \qquad\;\; C3:{P_{\max }}\left( {{\tau _2} + {\tau _3}} \right) = {E_{UAV}} + E_{UAV}^0 \\ \qquad\;\; C4:{R_n}({\boldsymbol{u}},\omega _n^c) = \dfrac{1}{2}{\log _2}\left(1 + \dfrac{{{{\left| {{\boldsymbol{h}}_n^H\left( {{\boldsymbol{u}},{{\boldsymbol{c}}_n}} \right){\boldsymbol{\omega}} _n^c} \right|}^2}}}{{{{\left| {\displaystyle\sum\limits_{i = 1,i \ne n}^N {{\boldsymbol{h}}_n^H\left( {{\boldsymbol{u}},{{\boldsymbol{c}}_n}} \right){\boldsymbol{\omega}} _i^c} } \right|}^2} + \sigma _n^2}}\right) \geq {R_{\min }} \\ \qquad\;\; C5:{\text{SINR}}_n^s = \dfrac{{{{\left| {{{\boldsymbol{g}}^H}\left( {{\boldsymbol{u}},{\boldsymbol{s}}} \right){\boldsymbol{\omega}} _n^c} \right|}^2}}}{{{{\left| {\displaystyle\sum\limits_{m = 1}^M {{{\boldsymbol{g}}^H}\left( {{\boldsymbol{u}},{\boldsymbol{s}}} \right){\boldsymbol{\omega}} _m^s} } \right|}^2} + \sigma _s^2}} \geq A,n \in N \\ \end{gathered} $

(24)

The new optimization problem P3 contains three decision variables. To simplify the expression, we assume τ₁ = τ and τ₂ = τ₃, and the length of the second and third time slots is (1 − τ)T/2. Upon careful observation of problem P3, the simplified time decision variable τ has no coupling relationship with the power allocation factor $\omega = \left\{ {\omega _n^c,\omega _m^s} \right\}$ and UAV horizontal coordinates u = (x, y). Therefore, we can use the binary method to first obtain τ*, and then continue to solve $\omega $ and u. Further transforming the new optimization problem P4 gives:

$ \begin{gathered} P4: \;\;\;\mathop {\max }\limits_{u,\omega } {\text{ }}A \\ \quad\; s.t.{\text{ C1:}}\sum _{n = 1}^N{\left\| {\omega _n^c} \right\|^2} + \sum _{m = 1}^M{\left\| {\omega _m^s} \right\|^2} \leq {P_{\max }} \\ \qquad\;\;\;C4:{R_n}(u{\mathbf{,}}\omega _n^c) = \dfrac{1}{2}{\log _2}\left(1 + \dfrac{{{{\left| {h_n^H\left( {u,{c_n}} \right)\omega _n^c} \right|}^2}}}{{{{\left| {\displaystyle\sum\limits_{i = 1,i \ne n}^N {h_n^H\left( {u,{c_n}} \right)\omega _i^c} } \right|}^2} + \sigma _n^2}}\right) \geq {R_{\min }} \\ \qquad\;\;\;C5:{\text{SINR}}_n^s = \dfrac{{{{\left| {{g^H}\left( {u,s} \right)\omega _n^c} \right|}^2}}}{{{{\left| {\displaystyle\sum\limits_{m = 1}^M {{g^H}\left( {u,s} \right)\omega _m^s} } \right|}^2} + \sigma _s^2}} \geq A,n \in N \\ \qquad\;\;\;C6:{P_{\max }}\left( {1 - {\tau ^*}} \right) = {E_{UAV}} + E_{UAV}^0 \\ \end{gathered} $

(25)

Optimization of the algorithm for the beamforming vector under a fixed UAV position

Given the position u of the drone, the optimization subproblem of the beamforming vector set $\mathop {\omega = \left\{ {\omega _n^c,\omega _m^s} \right\}}\nolimits_{n = 1,2,...,N,}^{m = 1,2,..,M} $ can be expressed as:

$ \begin{gathered} {\text{P5}}:\mathop {\max }\limits_\omega A \\ {\text{ s}}{\text{.t}}{\text{. C1,C4,C5,C6}} \\ \end{gathered} $

(26)

Analyzing the constraints of optimization problem P5, it can be found that constraint C1, C4−C5 contains quadratic variables $\left\{ {\omega _n^c} \right\}_{n = 1}^N$ and $\left\{ {\omega _m^s} \right\}_{m = 1}^M$. Due to the dimensionality issue of the two vectors, P5 is difficult to solve. Here, we attempt to use the convex semi definite programming (SDP) relaxation method. Defining $W_n^c \triangleq \omega _n^c{\left[ {\omega _n^c} \right]^{\text{H}}} $, $n \in N$, $W_m^s \triangleq \omega _m^s{\left[ {\omega _m^s} \right]^{\text{H}}} $, $ m \in M$, where the matrix rank one constraint is represented as:

$ \text{Rank}\left(W_n^c\right)=1,\ n\in N $

(27)

$ \text{Rank}\left(W_m^s\right)=1,\ m\in M $

(28)

Thus, problem P5 can be transformed into:

$ \begin{gathered} {\text{P6}}:\mathop {\max }\limits_{W_n^c,W_m^s} A \\ \;\; s.t.{\text{ }} C6:{P_{\max }}\left( {1 - {\tau ^*}} \right) = {E_{UAV}} + E_{UAV}^0 \\ \qquad C7:\sum\limits_{n = 1}^N {{\text{tr}}\left( {{\boldsymbol{W}}_n^c} \right)} + \sum\limits_{m = 1}^M {{\text{tr}}\left( {{\boldsymbol{W}}_m^s} \right)} \leq {P_{\max }} \\ \qquad C8:{R_n}({\boldsymbol{u}},{\boldsymbol{W}}_n^c) = \dfrac{1}{2}{\log _2}(1 + \dfrac{{{\text{tr}}\left( {{{\boldsymbol{h}}_n}\left( {{\boldsymbol{u}},{{\boldsymbol{c}}_n}} \right){\boldsymbol{h}}_n^H\left( {{\boldsymbol{u}},{{\boldsymbol{c}}_n}} \right){\boldsymbol{W}}_n^c} \right)}}{{\displaystyle\sum\limits_{i = 1,i \ne n}^N {{\text{tr}}\left( {{{\boldsymbol{h}}_n}\left( {{\boldsymbol{u}},{{\boldsymbol{c}}_n}} \right){\boldsymbol{h}}_n^H\left( {{\boldsymbol{u}},{{\boldsymbol{c}}_n}} \right){\boldsymbol{W}}_i^c} \right)} + \sigma _n^2}}) \geq {R_{\min }} \\ \qquad C9:{\text{SINR}}_n^s = \dfrac{{{\text{tr}}\left( {{{\boldsymbol{g}}_n}\left( {{\boldsymbol{u}},{{\boldsymbol{c}}_n}} \right){\boldsymbol{g}}_n^H\left( {{\boldsymbol{u}},{{\boldsymbol{c}}_n}} \right){\boldsymbol{W}}_n^c} \right)}}{{{\text{tr}}\left( {{{\boldsymbol{g}}_n}\left( {{\boldsymbol{u}},{{\boldsymbol{c}}_n}} \right){\boldsymbol{g}}_n^H\left( {{\boldsymbol{u}},{{\boldsymbol{c}}_n}} \right){\boldsymbol{W}}_m^s} \right) + \sigma _s^2}} \geq A,n \in N \\ \qquad C10:{\text{rank}}\left( {{\boldsymbol{W}}_n^c} \right) \leq 1,n \in N \\ \qquad C11:{\text{rank}}\left( {{\boldsymbol{W}}_m^s} \right) \leq 1,m \in M \\ \end{gathered} $

(29)

After a series of convex optimization processes in this section, if we ignore the rank one constraint of the optimization problem P6, we can use common convex optimization methods, such as the CVX toolbox, or use intelligent optimization algorithms or machine learning methods for optimization. It should be noted that after using Eigen Value Decomposition (EVD), it is necessary to verify the rank one problem, that is, the feasibility of the solution.

In summary, the beamforming vector optimization algorithm under a fixed UAV position is shown in Algorithm 1 below.

Table 1. The optimization algorithm for the beamforming vector under a fixed UAV position.

1. Initialization: Set the iteration termination number $ N_P^{max} $, iteration termination accuracy $ {\varepsilon _P} $, and iteration initial values $W_n^c,\forall n$ and $\omega _m^s,\forall m$.

2. Loop body:

3. Update iteration index i = i + 1;

4. Solve the optimization problem $ F({q_i}) = \mathop {\max }\limits_{W_n^c,W_m^s} A $ and obtain $ \left\{ {W_n^{c*},W_m^{s*}} \right\} $;

5. Perform EVD decomposition on $ W_n^{c*} $ and $ W_m^{s*} $, and calculate $w_n^c,\forall n$ and $w_m^s,\forall m$ under the current iteration index;

6. End condition: $ \left| {F({q_i}) - F({q_{i - 1}})} \right| < {\varepsilon _P} $ or $ i > N_P^{max} $.

7. Output the optimal solution $ \left\{ {{q^*},W_n^{c*},W_m^{s*}} \right\} $.

Position optimization algorithm under a fixed UAV beamforming vector

After the beamforming vector $\left\{ {\omega _n^c,\forall n,\omega _m^s,\forall m} \right\}$ is determined, the optimization subproblem of drone position $u$ can be expressed as:

$ \begin{gathered} {\text{P7}}:\mathop {\max }\limits_u A \\ {\text{ s}}{\text{.t}}{\text{. C4,C5}} \\ \end{gathered} $

(30)

Adopting a trust region based continuous convex approximation optimization algorithm, the constraints C4 and C5 are first processed.

By transforming C4, we can obtain:

$ \left( {{2^{2{R_{\min }}}} - 1} \right)\left( {{{\left| {\sum\limits_{i = 1,i \ne n}^N {{\boldsymbol{h}}_n^H\left( {{\boldsymbol{u}},{{\boldsymbol{c}}_n}} \right){\boldsymbol{\omega}} _i^c} } \right|}^2} + \sigma _n^2} \right) \geq {\left| {{\boldsymbol{h}}_n^H\left( {{\boldsymbol{u}},{{\boldsymbol{c}}_n}} \right){\boldsymbol{\omega}} _n^c} \right|^2} $

(31)

Define $ {\boldsymbol{W}}_i^c = {\boldsymbol{\omega}} _n^c{\left[ {{\boldsymbol{\omega}} _n^c} \right]^{\text{H}}} $, ${\boldsymbol{W}}_j^s = {\boldsymbol{\omega}} _m^s{\left[ {{\boldsymbol{\omega}} _m^s} \right]^{\text{H}}}$. After removing the denominator, C4 can be rephrased as:

$ \left( {{2^{2{R_{\min }}}} - 1} \right)\left( {\sum\limits_{i = 1,i \ne n}^N {\left. {\left( {{\boldsymbol{W}}_i^c,d({\boldsymbol{u}},{{\boldsymbol{c}}_n})} \right.} \right)} + \sigma _n^2} \right) \geq \left. {\left( {{\boldsymbol{W}}_n^c,d({\boldsymbol{u}},{{\boldsymbol{c}}_n})} \right.} \right) $

(32)

Using the same method, C5 removes the denominator and obtains:

$ \left|\boldsymbol{g}^H\left(\boldsymbol{u},\boldsymbol{s}\right)\boldsymbol{\omega}_n^c\right|^2\ge A\left(\left|\sum\limits_{m=1}^M\boldsymbol{g}^H\left(\boldsymbol{u},\boldsymbol{s}\right)\boldsymbol{\omega}_m^s\right|^2+\sigma_s^2\right),\ n\in N $

(33)

Further transformation of C5 yields:

$ \left. {\left( {{\boldsymbol{W}}_n^c,d({\boldsymbol{u}},{{\boldsymbol{c}}_n})} \right.} \right) \geq A\left( {\sum\limits_{m = 1}^M {\left( {\left. {{\boldsymbol{W}}_m^s,d({\boldsymbol{u}},{{\boldsymbol{c}}_n})} \right)} \right.} + \sigma _s^2} \right),\; n \in N $

(34)

Based on the above processing, problem P7 can be transformed into an approximately convex problem P8:

$ \begin{gathered} {\text{P}}8:\mathop {\max }\limits_u A \\ \quad\;\;\; s.t.{\text{ C12:}}\left( {{2^{2{R_{\min }}}} - 1} \right)\left( {\sum\limits_{i = 1,i \ne n}^N {\left. {\left( {{\boldsymbol{W}}_i^c,d({\boldsymbol{u}},{{\boldsymbol{c}}_n})} \right.} \right)} + \sigma _n^2} \right) \geq \left. {\left( {{\boldsymbol{W}}_n^c,d({\boldsymbol{u}},{{\boldsymbol{c}}_n})} \right.} \right) \\ \qquad\quad C13:\left. {\left( {{\boldsymbol{W}}_n^c,d({\boldsymbol{u}},{{\boldsymbol{c}}_n})} \right.} \right) \geq A\left( {\sum\limits_{m = 1}^M {\left( {\left. {{\boldsymbol{W}}_m^s,d({\boldsymbol{u}},{{\boldsymbol{c}}_n})} \right)} \right.} + \sigma _s^2} \right), \;n \in N \\ \end{gathered} $

(35)

Considering the accuracy and efficiency of UAV position optimization, we set the iteration accuracy. As long as the iteration accuracy is set small enough, the convergence of the optimization algorithm can always be ensured. The specific optimization algorithm is shown in Algorithm 2, which gives the optimal UAV position under a fixed beamforming vector.

Table 2. UAV position optimization algorithm under a fixed beamforming vector.

1. Initialization: Set the iteration termination number $ N_u^{max} $, iteration termination accuracy $ {\varepsilon _u} $, and iteration initial values u.

2. Loop body:

3. Update iteration index i = i + 1;

4. Solve the optimization problem F(q_i) = $ \mathop {\max }\limits_u A $ and obtain u*;

5. Analyze the position information of u* and calculate the UAV position
(x, y, h⁰) under the current iteration index;

6. End condition: | F(q_i) − F(q_i−1) | < ${\varepsilon _u} $ or i > $N_u^{max} $.

7. Output the optimal solution {q*, u*}.

Joint optimization algorithm for beamforming and position based on UAV energy harvesting

In the earlier sections, Algorithm 1 solved the optimal beamforming vector $ \left\{ {W_n^{c*},W_m^{s*}} \right\} $ under a fixed UAV position, while Algorithm 2 solved the optimal UAV position u* under a fixed UAV beamforming vector. Below is a joint resource allocation algorithm for an energy harvesting-assisted UAV sensing integrated system based on iterative thinking, as shown in Algorithm 3. First, the initial value and loop termination conditions are set. Then, the energy efficiency problem is solved based on the Dinkelbach method. Finally, the SDP method is used to obtain the optimal UAV ISAC resource allocation solution.

Table 3. UAV position optimization algorithm under a fixed beamforming vector.

1. Initialization: Set the termination times $ N_{outer}^{max} $ and $ N_{inner}^{max} $ for the outer loop and inner loop, as well as the termination precision $ {\varepsilon _{outer}} $ and $ {\varepsilon _{inner}} $

2. External circulation body :

3. Set the initial values q₀ = 0 and n = 0 for the outer loop;

4. Using binary method to solve the optimal energy harvesting time slot allocation factor τ;

5. Internal circulation body 1:

6. Set the iteration termination number $ N_P^{max} $, iteration termination accuracy $ {\varepsilon _P} $, and iteration initial values $W_n^c,\forall n$ and $\omega _m^s,\forall m$;

7. Run Algorithm 1 to solve the optimization problem and run F(q_i) = $ \mathop {\max }\limits_{W_n^c,W_m^s} A $.

8. Output the optimal solution $ \left\{ {{q^*},W_n^{c*},W_m^{s*}} \right\} $;

9. End condition of inner loop 1: | F(q_i − F(q_i−1) | < $ {\varepsilon _P} $ or i > $ N_P^{max} $

10. Internal circulation body 2:

11. Set the iteration termination number $ N_u^{max} $, iteration termination accuracy $ {\varepsilon _u} $, and iteration initial value u;

12. Run Algorithm 2 to solve the optimization problem F(q_i) = $ \mathop {\max }\limits_u A $;

13. Output the optimal solution {q*, u*};

14. End condition for inner loop 2: | F(q_i) − F(q_i−1) | < $ {\varepsilon _u} $ or i > $ N_u^{max} $.

15. Calculate F(q) = $ \mathop {\max }\limits_{\tau ,u,\omega } A $ and update q;

16. End condition of outer loop: | q_n − q_n−1) | < $ {\varepsilon _{outer}} $ or n > $ N_{outer}^{max} $.

17. Output the optimal solution {q*, τ*, u*, $ \omega ^* $} and obtain the joint resource allocation scheme for the energy harvesting assisted UAV sensing integration system.

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Energy harvesting assisted UAV sensing integrated system resource allocation

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