In this thesis, I investigate the joint optimization of sensing-communication scheduling, flight trajectory control, and hover deployment in multi-unmanned aerial vehicle (UAV) assisted integrated sensing and communication (ISAC) systems. The research is motivated by the growing demand for high-precision target detection and massive data interaction in sixth-generation mobile networks and space-air-ground integrated networks. The limited onboard energy of UAVs, combined with stringent sensing and communication performance requirements, makes it essential to jointly optimize resource allocation and trajectory planning. I first study a dynamic multi-UAV cooperative ISAC scenario and propose a multi-agent deep reinforcement learning based algorithm to minimize the total system energy consumption while satisfying sensing accuracy and communication rate constraints. Then, I investigate a static multi-objective deployment problem for multi-UAV ISAC systems, where UAV hover positions and precoding strategies are jointly optimized. I propose a hierarchical deployment and design framework that combines Voronoi-based region partitioning, an improved non-dominated sorting genetic algorithm II, and sequential quadratic programming to achieve a balanced trade-off among communication rate, sensing probability, and power consumption. Simulation results demonstrate the effectiveness and superiority of the proposed schemes over benchmark approaches.
1. Introduction and Background
The rapid development of unmanned aerial vehicles (UAVs) has transformed the way wireless networks are deployed and operated. UAVs offer high mobility, ease of deployment, and low cost, making them ideal platforms for both communications and sensing tasks. In particular, the integration of communication and sensing functions into a single UAV platform enables the construction of ISAC systems that can simultaneously provide data transmission and environmental perception. This integration improves spectral efficiency and reduces hardware redundancy compared to traditional separate communication and radar systems.
In multi-UAV ISAC systems, multiple UAVs cooperate to cover a large area and serve multiple ground users and sensing targets. However, the cooperation introduces significant challenges in resource competition, interference management, and energy efficiency. Each UAV must decide how to allocate its limited power and bandwidth between communication and sensing tasks, and how to move or hover to optimize its spatial position relative to both users and targets. The flight trajectory and hover location affect not only the channel quality for communication but also the radar sensing performance due to the dependence of path loss on the UAV-to-target distance. Moreover, the propulsion energy consumption of rotary-wing UAVs is highly sensitive to the flight speed and acceleration, making trajectory design a critical factor in overall energy efficiency.
The primary objective of this thesis is to develop algorithms that jointly optimize the communication-sensing scheduling, resource allocation, and trajectory/deployment of multiple UAVs in ISAC systems. The thesis addresses two representative scenarios: (i) a dynamic scenario where UAVs fly from start points, sense targets, and offload data to mobile edge computing (MEC) base stations, and (ii) a static scenario where UAVs hover at optimized locations to provide communication services to ground users and detect sensing targets. In both scenarios, the optimization problems are highly non-convex, involve mixed integer variables, and are computationally challenging. I therefore adopt advanced optimization techniques, including deep reinforcement learning and evolutionary multi-objective optimization.
2. System Model for Dynamic Multi-UAV ISAC
In the first scenario, I consider a multi-UAV ISAC-MEC system consisting of \(N\) UAVs, \(K\) ground sensing targets, and \(M\) base stations (BSs). Each UAV is equipped with a uniform linear array, with \(N_t\) transmit antennas and \(N_r\) receive antennas. The UAVs can sense targets and communicate with BSs for data offloading. The system time is discretized into \(T\) equal-length time slots, each of duration \(\tau\). Let \(\mathbf{q}_n(t) = [x_n(t), y_n(t), H]^T\) denote the three-dimensional position of UAV \(n\) at time slot \(t\), where \(H\) is the fixed flight altitude. The ground target \(k\) is located at \(\mathbf{q}_k^s = [x_k^s, y_k^s, 0]^T\), and BS \(m\) is located at \(\mathbf{q}_m^c = [x_m^c, y_m^c, 0]^T\).
2.1 Communication Channel Model
For the air-to-ground communication link between UAV \(n\) and BS \(m\), I adopt a probabilistic line-of-sight (LoS) model. The channel gain \(h_{n,m}(t)\) is expressed as
\[
h_{n,m}(t) = P_{n,m}^{\rm L}(t) h_{n,m}^{\rm L}(t) + \left(1 – P_{n,m}^{\rm L}(t)\right) h_{n,m}^{\rm N}(t),
\]
where \(P_{n,m}^{\rm L}(t)\) is the LoS probability, which depends on the elevation angle \(\theta_{n,m}(t)\) between the UAV and the BS:
\[
P_{n,m}^{\rm L}(t) = \frac{1}{1 + \mu \exp\left(-\omega \left(\theta_{n,m}(t) – \mu\right)\right)},
\]
\[
\theta_{n,m}(t) = \frac{180}{\pi} \arcsin\left(\frac{H}{d_{n,m}(t)}\right),
\]
\[
d_{n,m}(t) = \sqrt{(x_n(t)-x_m^c)^2 + (y_n(t)-y_m^c)^2 + H^2}.
\]
Here \(h_{n,m}^{\rm L}(t)\) and \(h_{n,m}^{\rm N}(t)\) are the LoS and non-LoS (NLoS) path losses, respectively, given by
\[
h_{n,m}^{\rm L}(t) = \eta_{\rm L} \left(\frac{4\pi d_{n,m}(t)}{\lambda_c}\right)^2, \quad
h_{n,m}^{\rm N}(t) = \eta_{\rm N} \left(\frac{4\pi d_{n,m}(t)}{\lambda_c}\right)^2,
\]
where \(\eta_{\rm L}\) and \(\eta_{\rm N}\) are the additional attenuation factors, and \(\lambda_c\) is the carrier wavelength. The UAV transmit steering vector is
\[
\mathbf{a}_{\rm tx}(\theta) = \left[1, e^{-j\pi \cos\theta}, \ldots, e^{-j\pi(N_t-1)\cos\theta}\right]^T,
\]
and the receive steering vector is
\[
\mathbf{a}_{\rm rx}(\theta) = \left[1, e^{-j\pi \cos\theta}, \ldots, e^{-j\pi(N_r-1)\cos\theta}\right]^T.
\]
Thus, the communication channel vector between UAV \(n\) and BS \(m\) is
\[
\mathbf{h}_{n,m}(t) = \frac{1}{\sqrt{h_{n,m}(t)}} \mathbf{a}_{\rm tx}(\theta_{n,m}(t)).
\]
2.2 Radar Sensing Channel Model
The sensing channel matrix between UAV \(n\) and target \(k\) is given by
\[
\mathbf{G}_{n,k}^s(t) = \frac{\sqrt{\beta_k}}{(4\pi)^{3/2} d_{n,k}(t)^2} \lambda_{\rm rad} \mathbf{a}_{\rm rx}(\theta_{n,k}(t)) \mathbf{a}_{\rm tx}^H(\theta_{n,k}(t)),
\]
where \(\lambda_{\rm rad}\) is the sensing wavelength, \(\beta_k\) is the radar cross-section coefficient of target \(k\), and \(d_{n,k}(t)\) is the distance between UAV \(n\) and target \(k\):
\[
d_{n,k}(t) = \sqrt{(x_n(t)-x_k^s)^2 + (y_n(t)-y_k^s)^2 + H^2}.
\]
2.3 Communication Rate and Radar Sensing Accuracy
The communication signal transmitted from UAV \(n\) to BS \(m\) is
\[
\mathbf{x}_{n,m}^c(t) = \mathbf{w}_{n,m}(t) s_{n,m}^c(t),
\]
where \(\mathbf{w}_{n,m}(t) \in \mathbb{C}^{N_t \times 1}\) is the communication precoding vector and \(s_{n,m}^c(t)\) is the data symbol with unit power. The received signal at BS \(m\) is
\[
y_m(t) = \mathbf{h}_{n,m}^H(t) \mathbf{x}_{n,m}^c(t) + n_m(t),
\]
with \(n_m(t) \sim \mathcal{CN}(0, \sigma^2)\). The signal-to-noise ratio (SNR) at BS \(m\) is
\[
\gamma_{n,m}^c(t) = \frac{|\mathbf{h}_{n,m}^H(t) \mathbf{w}_{n,m}(t)|^2}{\sigma^2}.
\]
The achievable communication rate is
\[
R_{n,m}(t) = B \log_2\left(1 + \gamma_{n,m}^c(t)\right),
\]
where \(B\) is the system bandwidth. For radar sensing, the sensing signal is
\[
\mathbf{x}_{n,k}^s(t) = \sqrt{P_s} \mathbf{w}_{n,k}(t) s_{n,k}^s(t),
\]
where \(P_s\) is the constant radar transmit power and \(\|\mathbf{w}_{n,k}(t)\|=1\). The received echo at UAV \(n\) is
\[
\mathbf{y}_{n,k}^s(t) = \mathbf{G}_{n,k}^s(t) \mathbf{x}_{n,k}^s(t) + \mathbf{n}_s(t),
\]
where \(\mathbf{n}_s(t) \sim \mathcal{CN}(\mathbf{0}, \sigma_s^2 \mathbf{I}_{N_r})\). After receive filtering with \(\mathbf{v}_{n,k}(t)\), the SNR for sensing target \(k\) is
\[
\gamma_{n,k}^s(t) = \frac{P_s |\mathbf{v}_{n,k}^H(t) \mathbf{G}_{n,k}^s(t) \mathbf{w}_{n,k}(t)|^2}{\sigma_s^2}.
\]
The Cramér-Rao bound (CRB) for angle estimation of target \(k\) is modeled as
\[
\mathrm{CRB}_{n,k}(t) = \frac{3}{2 \pi^2 L \gamma_{n,k}^s(t) \sin^2(\theta_{n,k}(t)) (N_r^2-1) (\Delta_d/\lambda_{\rm rad})^2},
\]
where \(L\) is the number of snapshots and \(\Delta_d\) is the antenna element spacing. The CRB provides a quantitative measure of sensing accuracy, with a smaller CRB indicating better estimation performance.
2.4 Energy Consumption Model
The total energy consumption of UAV \(n\) at time slot \(t\) consists of four parts: communication, sensing, computation, and propulsion. I model it as
\[
E_n(t) = E_n^c(t) + E_n^s(t) + E_n^l(t) + E_n^f(t),
\]
where
\[
E_n^c(t) = \sum_{m=1}^M \mu_n \beta_{n,m}^c(t) \|\mathbf{w}_{n,m}(t)\|^2 \tau,
\]
\[
E_n^s(t) = \sum_{k=1}^K \beta_{n,k}^s(t) P_s \tau,
\]
\[
E_n^l(t) = (1-\mu_n) \kappa \tau f_n(t)^3,
\]
and \(E_n^f(t)\) is the propulsion energy, given by
\[
E_n^f(t) = \left[ P_0 \left(1 + \frac{3 v_n(t)^2}{U_{\rm tip}^2}\right) + P_i \left(\sqrt{1 + \frac{v_n(t)^4}{4 v_0^4}} – \frac{v_n(t)^2}{2 v_0^2}\right)^{1/2} + \frac{1}{2} d_0 \rho s A v_n(t)^3 \right] \tau,
\]
where \(P_0\) and \(P_i\) are the blade profile power and induced power in hover, \(U_{\rm tip}\) is the tip speed of the rotor blade, \(v_0\) is the mean rotor induced velocity in hover, \(\rho\) is the air density, \(A\) is the rotor disk area, \(d_0\) is the fuselage drag ratio, and \(s\) is the rotor solidity. When the UAV hovers, \(v_n(t)=0\), and the propulsion power reduces to \(P_0+P_i\).
2.5 Optimization Problem Formulation
I introduce binary scheduling variables: \(\beta_{n,m}^c(t)\in\{0,1\}\) indicates whether UAV \(n\) communicates with BS \(m\) at time slot \(t\), and \(\beta_{n,k}^s(t)\in\{0,1\}\) indicates whether UAV \(n\) senses target \(k\) at time slot \(t\). The binary variable \(\mu_n\in\{0,1\}\) indicates whether UAV \(n\) offloads data to BSs (\(\mu_n=1\)) or computes locally (\(\mu_n=0\)). The optimization problem is formulated to minimize the total system energy consumption while satisfying sensing accuracy, communication rate, and flight constraints:
\[
\min_{\{\beta^s, \beta^c, \mu, \mathbf{w}, \mathbf{q}\}} \sum_{t=1}^T \sum_{n=1}^N E_n(t)
\]
subject to
\[
\begin{aligned}
C1: \quad & \beta_{n,k}^s(t) \cdot \mathrm{CRB}_{n,k}(t) \leq \Gamma_{\rm th}, \quad \forall n, k, t, \\
C2: \quad & \sum_{t=1}^T \sum_{n=1}^N \beta_{n,k}^s(t) = 1, \quad \forall k, \\
C3: \quad & \sum_{t=1}^T \sum_{k=1}^K \beta_{n,k}^s(t) V_s \leq \sum_{t=1}^T \sum_{m=1}^M \mu_n \beta_{n,m}^c(t) R_{n,m}(t) \tau + \frac{(1-\mu_n) f_n(t) \tau}{C_c}, \quad \forall n, \\
C4: \quad & \beta_{n,m}^c(t) R_{n,m}(t) \geq \beta_{n,m}^c(t) R_{\rm th}, \quad \forall n, m, t, \\
C5: \quad & \sum_{m=1}^M \beta_{n,m}^c(t) \leq 1, \quad \forall n, t, \\
C6: \quad & \|\mathbf{w}_{n,m}(t)\|^2 \leq P_{\max}, \quad \forall n, m, t, \\
C7: \quad & \|\mathbf{q}_n(t+1) – \mathbf{q}_n(t)\| \leq V_{\max} \tau, \quad \forall n, t, \\
C8: \quad & \|\mathbf{q}_n(t) – \mathbf{q}_j(t)\| \geq d_{\rm safe}, \quad \forall n \neq j, t, \\
C9: \quad & \mathbf{q}_n(1) = \mathbf{q}_n(T) = \mathbf{q}_n^{\rm in}, \quad \forall n, \\
C10: \quad & \beta_{n,m}^c(t) \leq \mu_n, \quad \forall n, m, t, \\
C11: \quad & f_n(t) \leq (1-\mu_n) f_{\max}, \quad \forall n, t.
\end{aligned}
\]
This is a mixed-integer nonlinear programming problem with high-dimensional non-convex constraints, which is difficult to solve optimally with traditional methods.
3. MA-DDQN-Based Joint Optimization Algorithm
To solve the above problem in a dynamic environment, I transform it into a Markov decision process (MDP) and propose a multi-agent double deep Q-network (MA-DDQN) algorithm. In the MDP, each UAV is treated as an intelligent agent that observes its local state and chooses actions to maximize the expected cumulative reward.
3.1 State Space
The global state at time slot \(t\) is the concatenation of all UAV local states:
\[
s(t) = \{s_1(t), s_2(t), \ldots, s_N(t)\}.
\]
For UAV \(n\), the local state includes its position, remaining energy, cumulative energy consumption, and channel state information:
\[
s_n(t) = \left\{ \mathbf{q}_n(t), E_n^{\rm total}(t), \mathbf{H}_n^{\rm rad}(t), \mathbf{H}_n^{\rm comm}(t) \right\},
\]
where \(E_n^{\rm total}(t)\) is the accumulated energy consumption up to time slot \(t\), and \(\mathbf{H}_n^{\rm rad}(t)\) and \(\mathbf{H}_n^{\rm comm}(t)\) denote the sensing and communication channel states, respectively.
3.2 Action Space
Each UAV chooses an action that includes a flight movement, sensing scheduling, communication scheduling, and computation mode:
\[
a_n(t) = \{ \mathbf{u}_n(t), \boldsymbol{\beta}_n^s(t), \boldsymbol{\beta}_n^c(t), \mu_n \},
\]
where \(\mathbf{u}_n(t) \in \mathcal{U}_n\) represents the three-dimensional movement action. I discretize the movement into a set of choices:
\[
\mathcal{U}_n = \left\{ [0,0]^T, [\Delta_q, 0]^T, [-\Delta_q, 0]^T, [0, \Delta_q]^T, [0, -\Delta_q]^T \right\},
\]
where \(\Delta_q = V_{\max} \tau\). The next position is updated as \(\mathbf{q}_n(t+1) = \mathbf{q}_n(t) + \mathbf{u}_n(t)\).
3.3 Reward Function
The reward function is designed to minimize energy consumption while enforcing all constraints. The immediate reward for UAV \(n\) is
\[
r_n(t) = -E_n(t) – \xi_1 \mathbb{1}\{\mathrm{CRB}_{n,k}(t) > \Gamma_{\rm th}\} – \xi_2 \mathbb{1}\{\|\mathbf{q}_n(t)-\mathbf{q}_j(t)\| < d_{\rm safe}\} – \xi_3 \mathbb{1}\{R_{n,m}(t) < R_{\rm th}\},
\]
where \(\xi_1, \xi_2, \xi_3\) are large penalty factors, and \(\mathbb{1}\{\cdot\}\) is the indicator function. With this reward, the UAV learns to avoid constraint violations and reduce energy consumption.
3.4 MA-DDQN Architecture
I adopt a centralized training and distributed execution architecture. During training, a global replay buffer stores the transition tuples \((s(t), A(t), r(t), s(t+1))\). Each UAV has its own evaluation network and target network. The DDQN target for UAV \(n\) is computed as
\[
y_n^{\rm DDQN}(t) = r_n(t) + \gamma Q_n\left(s_n(t+1), \arg\max_{a_n’} Q_n(s_n(t+1), a_n’; \theta_n); \theta_n^{-}\right),
\]
where \(\theta_n\) is the evaluation network parameters and \(\theta_n^{-}\) is the target network parameters. The loss function is
\[
L_n(\theta_n) = \mathbb{E}\left[ \left( y_n^{\rm DDQN}(t) – Q_n(s_n(t), a_n(t); \theta_n) \right)^2 \right].
\]
The target network parameters are updated via soft update:
\[
\theta_n^{-} \leftarrow \tau_s \theta_n + (1-\tau_s) \theta_n^{-},
\]
where \(\tau_s\) is the soft update coefficient. The exploration follows an \(\epsilon\)-greedy policy to balance exploration and exploitation.
| Parameter | Value |
|---|---|
| Flight altitude \(H\) | 25 m |
| Maximum UAV speed \(V_{\max}\) | 20 m/s |
| Number of UAVs \(N\) | 4 |
| Number of targets \(K\) | 10 |
| Number of BSs \(M\) | 2 |
| System bandwidth \(B\) | 2 MHz |
| Noise power \(\sigma^2\) | -95 dBm |
| Maximum transmit power \(P_{\max}\) | 2 W |
| Sensing power \(P_s\) | 15 W |
| Radar wavelength \(\lambda_{\rm rad}\) | 2 m |
| Rotor tip speed \(U_{\rm tip}\) | 120 m/s |
| Mean induced velocity \(v_0\) | 4.03 m/s |
| Parameter | Value |
|---|---|
| Number of training episodes | 31500 |
| Experience replay buffer size | 50000 |
| Exploration rate \(\epsilon\) | 0.9 |
| Soft update coefficient \(\tau_s\) | 0.005 |
| Discount factor \(\gamma\) | 0.95 |
| Learning rate \(\alpha\) | \(5\times 10^{-5}\) |
3.5 Simulation Results
The simulation environment is a \(500\,\text{m}\times 500\,\text{m}\) area with 10 targets and 2 BSs. Figure 1 shows the flight trajectories of the UAVs obtained by the proposed MA-DDQN algorithm. The trajectories demonstrate that the UAVs effectively split the sensing tasks (3, 3, 2, 2 targets respectively), coordinate for communication offloading, and return to their initial positions. The algorithm also intelligently decides which UAVs offload to the MEC and which compute locally, based on communication costs.
Figure 1: Example of multi-UAV trajectory and resource scheduling in the ISAC-MEC system.
I evaluate the total energy consumption under different numbers of sensing targets. As shown in Figure 2 (not reproduced here), the energy consumption increases with the number of targets, but the proposed MA-DDQN algorithm consistently outperforms the baseline algorithm from the literature. The advantage is more pronounced when the communication bandwidth is larger, because larger bandwidth reduces transmission time and thus the hover time for offloading.
Figure 3 shows the relationship between total energy consumption and UAV flight altitude for different bandwidths. The energy consumption first increases slowly and then accelerates because a higher altitude improves the LoS probability but also increases the radar path loss dramatically. The proposed algorithm achieves lower energy than the baseline for all altitudes and bandwidths.
Figure 4 illustrates the energy composition breakdown under different target numbers. The flight and hover energy dominates the total energy, followed by sensing energy and communication energy. This justifies the importance of trajectory optimization. As the target number increases, all three energy components grow monotonically.
Figure 5 shows total energy versus the CRB threshold. When the CRB threshold is tight (i.e., high sensing accuracy required), energy consumption is much higher. The proposed algorithm saves more energy than the baseline under all CRB thresholds. This demonstrates the advantage of the MA-DDQN approach in handling strict sensing constraints.
4. Multi-Objective UAV Deployment and Precoding Optimization
In the second part of this thesis, I focus on a static multi-UAV ISAC scenario where UAVs hover at optimized locations to serve multiple ground users (GUs) and detect multiple sensing targets (STs). The system consists of \(N\) multi-antenna UAVs, \(M\) single-antenna GUs, and \(K\) STs. Each UAV has \(J\) antennas. I consider the joint optimization of UAV hover positions, communication precoding vectors, sensing precoding vectors, and task assignment (which UAV serves which GU and senses which ST).
4.1 Channel and Signal Models
The communication channel from UAV \(n\) to GU \(m\) is
\[
\mathbf{h}_{n,m}^c = \sqrt{\frac{\rho_0}{d_{n,m}^c}} \boldsymbol{\Psi}_{n,m}^c,
\]
where \(\rho_0\) is the reference channel gain, \(\boldsymbol{\Psi}_{n,m}^c \in \mathbb{C}^{J\times 1}\) is the small-scale fading vector, and \(d_{n,m}^c = \|\mathbf{q}_n^u – \mathbf{q}_m^c\|\). The sensing channel from UAV \(n\) to ST \(k\) is
\[
\mathbf{h}_{n,k}^s = \sqrt{\frac{\rho_0}{d_{n,k}^s}} \beta \boldsymbol{\Psi}_{n,k}^s,
\]
where \(\beta\) is a coefficient related to the radar cross-section of the target, and \(d_{n,k}^s = \|\mathbf{q}_n^u – \mathbf{q}_k^s\|\).
The sensing signal transmitted by UAV \(n\) to ST \(k\) is
\[
\mathbf{x}_{n,k}^s = \alpha_{n,k}^s \mathbf{w}_{n,k}^s s_{n,k}^s,
\]
where \(\alpha_{n,k}^s\in\{0,1\}\) is the sensing scheduling variable, \(\mathbf{w}_{n,k}^s\) is the sensing precoding vector, and \(s_{n,k}^s\) is the radar symbol with unit power. The target detection is formulated as a binary hypothesis test. The received echo at UAV \(n\) is
\[
\mathbf{y}_{n,k}^s = \begin{cases}
\mathbf{h}_{n,k}^s \mathbf{w}_{n,k}^s s_{n,k}^s + \mathbf{n}_{n,k}, & \mathcal{H}_1, \\
\mathbf{n}_{n,k}, & \mathcal{H}_0,
\end{cases}
\]
where \(\mathbf{n}_{n,k} \sim \mathcal{CN}(0, \sigma_{n,k}^2 \mathbf{I})\) is the noise vector. The detection probability is
\[
P_{n,k}^d = Q\left(\sqrt{2 \gamma_{n,k}^s})\right) – Q\left(\sqrt{2 \gamma_{n,k}^s} + \sqrt{-2\ln P_f}\right),
\]
where \(P_f\) is the false alarm probability and \(\gamma_{n,k}^s\) is the sensing SNR:
\[
\gamma_{n,k}^s = \frac{|\mathbf{h}_{n,k}^H \mathbf{w}_{n,k}^s|^2}{\sigma_{n,k}^2}.
\]
The communication received signal at GU \(m\) is
\[
y_m = \sum_{n=1}^N \alpha_{n,m}^c \mathbf{h}_{n,m}^{c,H} \mathbf{w}_{n,m}^c s_m + \sum_{n=1}^N \sum_{j\neq m} \alpha_{n,j}^c \mathbf{h}_{n,m}^{c,H} \mathbf{w}_{n,j}^c s_j + n_m,
\]
where \(\alpha_{n,m}^c\in\{0,1\}\) is the communication scheduling variable. The signal-to-interference-plus-noise ratio (SINR) is
\[
\gamma_{n,m}^c = \frac{\alpha_{n,m}^c |\mathbf{h}_{n,m}^{c,H} \mathbf{w}_{n,m}^c|^2}{1 + \sum_{j\neq m} |\mathbf{h}_{n,m}^{c,H} \mathbf{w}_{n,j}^c|^2}.
\]
The achievable rate is \(R_{n,m}=B\log_2(1+\gamma_{n,m}^c)\).
4.2 Multi-Objective Optimization Problem
I define three objective functions: the average detection probability, the total communication rate, and the total power consumption. They are given by
\[
f_1(\mathbf{Q}, \mathbf{w}, \boldsymbol{\alpha}) = \frac{1}{K} \sum_{n=1}^N \sum_{k=1}^K \alpha_{n,k}^s P_{n,k}^d,
\]
\[
f_2(\mathbf{Q}, \mathbf{w}, \boldsymbol{\alpha}) = \sum_{n=1}^N \sum_{m=1}^M \alpha_{n,m}^c R_{n,m},
\]
\[
f_3(\mathbf{Q}, \mathbf{w}, \boldsymbol{\alpha}) = P = \sum_{n=1}^N (P_n^c + P_n^s),
\]
where \(P_n^c = \sum_{m=1}^M \alpha_{n,m}^c \mathrm{Tr}(\mathbf{w}_{n,m}^c \mathbf{w}_{n,m}^{c,H})\) and \(P_n^s = \sum_{k=1}^K \alpha_{n,k}^s \mathrm{Tr}(\mathbf{w}_{n,k}^s \mathbf{w}_{n,k}^{s,H})\). The multi-objective optimization problem is
\[
\max_{\mathbf{Q}, \mathbf{w}, \boldsymbol{\alpha}} \left[ f_1, f_2, -f_3 \right]^T
\]
subject to
\[
\begin{aligned}
C1: &\quad \sum_{n=1}^N \alpha_{n,m}^c = 1, \quad \forall m, \\
C2: &\quad \sum_{n=1}^N \alpha_{n,k}^s = 1, \quad \forall k, \\
C3: &\quad \sum_{m=1}^M \mathrm{Tr}(\mathbf{w}_{n,m}^c \mathbf{w}_{n,m}^{c,H}) + \sum_{k=1}^K \mathrm{Tr}(\mathbf{w}_{n,k}^s \mathbf{w}_{n,k}^{s,H}) \leq P_{\max}, \quad \forall n, \\
C4: &\quad R_{n,m} \geq R_{\min}, \quad \forall n, m, \\
C5: &\quad P_{n,k}^d \geq P_{\min}^d, \quad \forall n, k, \\
C6: &\quad \|\mathbf{q}_n – \mathbf{q}_j\| \geq d_s, \quad \forall n \neq j.
\end{aligned}
\]
This problem is a non-convex mixed-integer multi-objective optimization problem. To solve it, I propose a hierarchical deployment and design framework (HDDF).
4.3 Voronoi-Based Region Partitioning
The first step of HDDF is to partition the system area into \(N\) disjoint sub-regions using a Voronoi diagram. The generation points of the Voronoi diagram are the initial UAV positions. For load balancing, I define the load of generation point \(n\) as
\[
Q_n^r = \sum_{k=1}^K \beta_s \chi_{n,k}^s \|\mathbf{q}_k^s – \mathbf{q}_n\| + \sum_{m=1}^M \beta_c \chi_{n,m}^c \|\mathbf{q}_m^c – \mathbf{q}_n\|,
\]
where \(\chi_{n,k}^s=1\) if ST \(k\) is assigned to UAV \(n\), and \(\chi_{n,m}^c=1\) if GU \(m\) is assigned to UAV \(n\). The load balancing condition is
\[
Q_{\max} – Q_{\min} \leq \varepsilon.
\]
I update the generation points by a force-driven mechanism. The force on point \(n\) exerted by point \(n’\) is
\[
F_{n’,n} = \mathrm{sign}(Q_{n’} – Q_n) \frac{|Q_{n’} – Q_n|^a}{r_{n’,n}^b} \hat{\mathbf{r}}_{n’,n},
\]
and the total force is \(F_n = \sum_{n’\neq n} F_{n’,n}\). The position is updated by
\[
\mathbf{q}_n^{(j+1)} = \mathbf{q}_n^{(j)} + \mu F_n^{(j)}.
\]
This process repeats until the load balancing threshold is met.
| Parameter | Value |
|---|---|
| Area size | 1000 m \(\times\) 1000 m |
| Number of UAVs \(N\) | 4 |
| Number of GUs \(M\) | 15 |
| Number of STs \(K\) | 10 |
| UAV altitude \(H\) | 100 m |
| Safety distance \(d_s\) | 50 m |
| Carrier frequency | 2.4 GHz |
| Bandwidth \(B\) | 20 MHz |
| Noise power spectral density | -85 dBm/Hz |
| Path loss exponent | 2 |
| Maximum transmit power \(P_{\max}\) | 40 W |
| False alarm probability \(P_f\) | \(10^{-6}\) |
4.4 UA V Deployment Subproblem: Improved NSGA-II
With the precoding vectors fixed, the original problem becomes a UAV location optimization subproblem. I use an improved NSGA-II algorithm to search for the global Pareto front. The improvements include a SQP-driven local mutation strategy and an entropy-based crowding selection mechanism.
The crowding distance of individual \(i\) is
\[
d_i = \sum_{h=1}^{3} \frac{f_{h,i+1} – f_{h,i-1}}{f_h^{\max} – f_h^{\min}}.
\]
For each Pareto front \(F_b\), I convert the crowding distances into probabilities:
\[
p_i = \frac{d_i}{\sum_{j\in F_b} d_j}.
\]
The crowding entropy of frontier \(F_b\) is then computed using Shannon’s entropy:
\[
H(F_b) = -\sum_{i=1}^{|F_b|} p_i \log_2 p_i.
\]
In the binary tournament selection, if two individuals belong to the same non-dominated front, I compare the crowding entropy with a threshold \(H_T(F_b)\). If \(H(F_b) > H_T(F_b)\), I select the individual with a larger weighted utility function \(\Psi\); otherwise, I select the individual with a larger crowding distance.
The SQP-driven local mutation works as follows: for each offspring generated by crossover, with probability \(p_m\), an SQP algorithm is applied starting from this offspring to optimize a single-objective utility function that aggregates the three normalized objectives. The converged solution becomes the mutated individual. This significantly improves the local search capability of the evolutionary algorithm.
4.5 Precoding Subproblem: SQP
With the UAV hover positions fixed, the problem reduces to a precoding optimization problem. I first convert the three objectives into a single weighted utility function:
\[
\Psi(w, \alpha) = w_s \tilde{f}_1 + w_c \tilde{f}_2 – w_e \tilde{f}_3,
\]
where \(\tilde{f}_i\) are normalized objective functions, and \(w_s, w_c, w_e\) are weighting coefficients. Then the precoding optimization problem is
\[
\max_{\mathbf{w}, \boldsymbol{\alpha}} \Psi
\]
subject to the same constraints. I convert complex precoding vectors into real vectors by separating real and imaginary parts. The constraints are convexified or expressed as inequalities. At each iteration, I construct a quadratic programming subproblem using a second-order Taylor expansion of the Lagrangian and solve it to find a search direction. The iteration update uses the BFGS approximation of the Hessian matrix and an Armijo line search to determine the step size.
4.6 HDDF Algorithm Flow
The overall HDDF algorithm works as follows:
- Run the Voronoi-based region partitioning algorithm to assign GU/ST sets to each UAV and obtain an initial deployment \(\mathbf{Q}_0\).
- Initialize a population of UAV deployment solutions using \(\mathbf{Q}_0\) and Gaussian perturbations.
- For each individual, solve the precoding subproblem using SQP and evaluate the three objectives.
- Perform non-dominated sorting and compute the crowding entropy.
- Generate offspring via binary tournament selection, simulated binary crossover, and SQP-driven local mutation.
- Merge parent and offspring populations, perform non-dominated sorting, and select the next generation using the crowding-entropy-based rule.
- Repeat until the maximum number of generations is reached. Output the Pareto-optimal set and the final deployment.
4.7 Simulation Results
I evaluate the HDDF framework via simulations. The Voronoi partitioning result shows that each UAV receives a non-overlapping sub-region, and the deployment is balanced. The obtained Pareto front is shown in a two-dimensional projection, indicating a clear trade-off between communication rate, detection probability, and power consumption. As the performance objectives increase, the required power also increases.
I compare HDDF with the benchmark algorithm AWOA-lite from the literature. Figure 4 (not shown) presents the comprehensive objective versus system bandwidth under different noise powers. The comprehensive objective increases with bandwidth and decreases with noise power. HDDF achieves a higher comprehensive objective than the benchmark for all bandwidth values, demonstrating the benefit of jointly optimizing communication and sensing.
Similarly, Figure 5 (not shown) shows the comprehensive objective versus the total number of tasks. The objective increases with the number of tasks but with diminishing returns due to resource saturation. HDDF outperforms the benchmark under all task counts.
Figure 6 (not shown) examines the effect of UAV altitude. Higher altitudes reduce the comprehensive objective because of increased path loss. Lower noise power improves the overall performance. Again, HDDF is superior to the benchmark, confirming its effectiveness in balancing communication, sensing, and energy efficiency.
5. Conclusions and Future Work
In this thesis, I have studied the joint resource scheduling and trajectory/deployment optimization in multi-UAV integrated sensing and communication systems. In the first part, I formulated a total energy minimization problem for a dynamic multi-UAV ISAC-MEC scenario and proposed a multi-agent double deep Q-network algorithm. The algorithm effectively learns to allocate communication and sensing resources, coordinate trajectories, and adaptively choose between local computation and edge offloading. Simulation results confirmed that the proposed algorithm reduces system energy consumption compared to a benchmark deep reinforcement learning algorithm while satisfying sensing and communication constraints.
In the second part, I investigated a multi-objective deployment and precoding problem for a static multi-UAV ISAC system. I proposed a hierarchical deployment and design framework that combines a Voronoi-based load-balancing partition, an improved NSGA-II with SQP-driven local mutation and entropy-based selection, and an SQP-based precoding solver. The simulation results showed that the framework achieves a well-distributed Pareto front and outperforms a baseline evolutionary algorithm in terms of overall communication-sensing-energy trade-off.
There are several directions for future research. First, robust design under imperfect channel state information and cluttered sensing environments is important for practical deployment. Second, the integration of edge computing and real-time task dependencies between sensing, communication, and computation deserves further investigation. Third, heterogeneous UAV fleets with different types of platforms and battery capacities should be considered. Fourth, the extension to tracking high-mobility targets and the use of semantic communication to compress sensing data are also promising. Finally, the development of continuous action-space multi-agent reinforcement learning algorithms that account for the true UAV dynamics would further improve the practical applicability of trajectory optimization.