In this thesis, I investigate the energy consumption optimization problem in non-orthogonal multiple access (NOMA) based unmanned aerial vehicle (UAV) assisted mobile edge computing (MEC) systems. With the exponential growth of Internet of Things (IoT) devices and their related applications, traditional intelligent terminals with limited computing capabilities are no longer able to meet the huge traffic and complex service requirements in next-generation wireless networks. Mobile edge computing allows terminal devices to offload computation-intensive and latency-critical tasks to edge servers with stronger computing capabilities, thereby reducing computational delay and terminal energy consumption. With the continuous progress of unmanned aerial vehicle technology, more and more UAVs are being applied to scenarios such as ecological monitoring, disaster emergency response, and urban facility monitoring. In order to adapt to the high latency requirements of MEC systems, MEC servers can be deployed on UAVs, and by optimizing the position of the UAV, line-of-sight links and better communication channels can be established between the MEC server and ground devices, thereby achieving higher offloading rates. To fully utilize time-frequency resources and improve system performance, NOMA technology is introduced into UAV-assisted MEC systems to achieve efficient task offloading. Since the computing capability of a UAV is limited by its battery capacity, how to effectively reduce system energy consumption while ensuring quality of service is a key issue in NOMA-based UAV-assisted MEC systems. In addition, the broadcast nature of wireless channels makes the task offloading process vulnerable to malicious eavesdroppers in the vicinity. The offloaded computational tasks may contain private information of users, so the security of MEC systems is also crucial. In this thesis, I study the energy consumption optimization of NOMA-based UAV-assisted MEC systems from the perspectives of delay criticality and security.
1. Introduction
The proliferation of mobile smart devices and the rapid development of new services and applications have led to severe challenges in global mobile networks, including limited storage capacity, high energy consumption, low bandwidth, and high latency. The exponential growth of IoT devices and their related applications further intensifies the pressure on wireless networks. To address these challenges, mobile cloud computing (MCC) was introduced as a new computing paradigm that allows mobile devices to offload computation tasks to centralized cloud servers. However, the long physical distance between mobile devices and cloud servers results in considerable communication latency, making MCC unsuitable for latency-sensitive applications such as real-time online gaming, virtual reality, and ultra-high-definition video streaming. Mobile edge computing (MEC) addresses this issue by providing computing capabilities at the edge of the network. Compared to MCC, MEC allows devices to offload tasks to servers that are much closer to the devices, thereby achieving lower latency and higher quality of service. However, ground-deployed MEC servers are usually fixed in position, which limits the flexibility and coverage of MEC services. In scenarios requiring high flexibility and wide coverage, ground MEC may not be the best solution.
Unmanned aerial vehicles (UAVs), due to their ability to flexibly change position, can effectively reduce the influence of obstacles such as buildings on communication. In recent years, the application of UAVs in wireless communications has expanded rapidly, including disaster response, emergency rescue, traffic monitoring, and environmental sensing. By deploying MEC servers on UAVs, UAV-assisted MEC systems can exploit the flexibility of UAVs to provide effective computing services in special scenarios. Compared with fixed-location MEC systems, UAV-assisted MEC systems have two advantages: (1) because UAVs fly at high altitude, MEC servers can provide line-of-sight links to mobile devices with higher probability, further reducing the impact of obstacles; (2) because UAVs can be flexibly deployed, the distance between mobile devices and the MEC server can be shortened, increasing the communication rate and achieving lower latency and better QoS.
Although MEC alleviates the shortage of computational resources on mobile devices, the limited bandwidth resources become a bottleneck as the number of devices increases. To improve the spectrum utilization of UAV-assisted MEC systems during task offloading, NOMA is an effective solution. By adopting NOMA, multiple users can share the same time/frequency resources, improving spectrum efficiency and enhancing system performance such as lower energy consumption and lower latency. Nevertheless, the energy consumption of UAV-assisted MEC systems is a critical concern due to the limited on-board battery capacity of UAVs. Therefore, optimizing system energy consumption while satisfying task latency constraints is of great importance.
Security is another major concern. UAV-assisted wireless channels are open in nature, making the communication vulnerable to eavesdroppers. Since offloading data may contain sensitive information, secure transmission is essential. Traditional physical layer security (PLS) focuses on protecting the content of the communication, but the existence of the communication itself can still be detected, which may also cause privacy leakage. Covert communication aims to hide the communication behavior from malicious wardens by exploiting the uncertainty of the received signal at the eavesdropper. In this thesis, I apply covert communication to a NOMA-based UAV-assisted MEC system, where the UAV acts as both a MEC server and a jammer that transmits artificial noise (AN) to confuse the eavesdropper. The objective is to minimize system energy consumption under covertness constraints.
2. Background and Related Work
2.1 MEC Technology
MEC is an emerging architecture that brings cloud computing capabilities to the edge of the radio access network. According to the European Telecommunications Standards Institute (ETSI), MEC provides IT service environments and cloud-computing capabilities at the mobile network edge, allowing mobile users to directly connect to the nearest cloud-enabled edge node. MEC servers can be deployed at cellular base stations, WiFi access points, or even on mobile objects such as UAVs and buses. The key idea is to transfer cloud resources (compute, network, and storage) to the network edge to meet latency-sensitive and high-bandwidth application requirements.
The three-layer architecture of MEC consists of the cloud center, MEC servers, and edge mobile devices. Edge devices offload computation tasks to MEC servers through wireless links, which not only reduces transmission energy and latency but also relieves the core network pressure. Key technologies in MEC include cloud computing, network function virtualization (NFV), and software-defined networking (SDN). MEC is widely used in intelligent transportation, smart cities, industrial IoT, augmented reality (AR)/virtual reality (VR), and video surveillance.
2.2 NOMA
NOMA is one of the most promising radio access technologies for next-generation cellular communications. Unlike orthogonal multiple access (OMA), NOMA allows multiple users to share the same resource block by allocating different power levels or codebooks, thus improving spectral efficiency. Power-domain NOMA employs superposition coding (SC) at the transmitter and successive interference cancellation (SIC) at the receiver. In downlink NOMA, the base station transmits a superimposed signal to multiple users; users with better channel gains perform SIC to decode their own signals. In uplink NOMA, multiple users transmit simultaneously to the base station, and the base station uses SIC to separate users in the order of decreasing channel gains. The achievable rate of user $i$ in uplink NOMA is given by
$$ R_i = B \log_2\left(1 + \frac{p_i h_i}{\sum_{j \in \Omega, j \neq i} p_j h_j + B\sigma^2}\right), $$
where $p_i$ is the transmit power of user $i$, $h_i$ is the channel gain, $B$ is the bandwidth, and $\sigma^2$ is the noise power spectral density.
2.3 UAV-assisted MEC
UAVs can act as aerial MEC servers to provide computing services to ground devices, especially in emergency and rural scenarios. The advantages of UAV-assisted MEC include stable line-of-sight links, wide coverage, and on-demand deployment. However, the limited battery capacity of UAVs imposes strict energy constraints. Therefore, optimizing system energy consumption in UAV-assisted MEC systems has attracted significant attention. Moreover, NOMA can be integrated into UAV-assisted MEC to further improve spectrum efficiency and reduce task latency.
2.4 Covert Communication
Covert communication, also known as low probability detection (LPD) communication, aims to hide the existence of transmission from a warden. The classic model is the prisoner problem: Alice wants to communicate with Bob without being detected by Willie. Willie observes the received signal and decides whether Alice is transmitting or not. The detection error probability is the sum of the false alarm probability and the miss detection probability. In covert communication, the transmitter or an assistant jammer can manipulate the warden’s detection uncertainty to guarantee that the total error probability is above a desired threshold. In UAV-assisted systems, the UAV can intentionally transmit AN to increase the uncertainty at the eavesdropper, thereby enabling covert offloading from ground devices to the UAV.
3. Optimal SIC Order Design and Energy Consumption Optimization in NOMA-based UAV-assisted MEC
3.1 System Model
Consider a NOMA-based UAV-assisted MEC system as depicted in the following figure. The system consists of $K$ ground devices and one UAV equipped with a MEC server. The ground devices are randomly distributed in a rectangular area. The UAV flies at a fixed altitude $H$ and serves the ground devices over $N$ time slots. In each time slot, a subset of $M$ devices offload their computation tasks to the UAV using NOMA. The UAV has a predetermined initial position $\mathbf{q}_0$ and final position $\mathbf{q}_F$. The trajectory of the UAV is subject to a maximum displacement constraint between consecutive time slots.
Let $\mathbf{w}_k = [x_k, y_k, 0]^T$ denote the position of the $k$-th ground device, and $\mathbf{q}[n] = [X[n], Y[n], H]^T$ denote the UAV position in time slot $n$. The channel gain between ground device $k$ and the UAV in slot $n$ follows the free-space path loss model:
$$ h_{k,u}[n] = \frac{\beta_0}{H^2 + \|\mathbf{q}[n] – \mathbf{w}_k\|^2}, $$
where $\beta_0$ is the path loss at reference distance 1 m.
Each device has a computation task of size $D$ bits and a task completion deadline constraint $T_k$. The devices are divided into $N$ groups, each group containing $M$ devices (assuming $K = NM$). In time slot $n$, the $M$ devices in the group simultaneously offload their tasks to the UAV using NOMA. The UAV also computes the received tasks in the same slot. Let $\mathbf{r}[n] = [r_1(n), r_2(n), \ldots, r_M(n)]$ denote the ordered decoding sequence of the devices in slot $n$, where $r_i(n)$ is the device index with the $i$-th decoding order. The achievable offloading rate of device $r_i(n)$ is given by
$$ R_{r_i(n)}[n] = B \log_2\left(1 + \frac{p_{r_i(n)} g_{r_i(n)}[n]}{ I_{r_i(n)} + B\sigma^2} \right), $$
where $I_{r_i(n)} = \sum_{j > i} p_{r_j(n)} g_{r_j(n)}[n]$ is the interference from devices decoded later.
3.2 Energy Consumption Model
The total system energy consumption consists of three parts: offloading energy, computation energy, and UAV flight energy.
Offloading energy: The offloading time for device $r_i(n)$ is
$$ T_{r_i(n)}^{\text{off}} = \frac{D}{R_{r_i(n)}[n]}. $$
The total offloading energy is
$$ E^{\text{off}} = \sum_{n=1}^{N} \sum_{i=1}^{M} p_{r_i(n)} T_{r_i(n)}^{\text{off}}. $$
Computation energy: The UAV allocates its computing capability equally to the $M$ devices, so the computation time for each device is
$$ T^{\text{comp}} = \frac{C D}{f_{CPU}^{U}/M}, $$
where $f_{CPU}^{U}$ is the UAV’s CPU frequency and $C$ is the number of CPU cycles required per bit. The computation energy is
$$ E^{\text{comp}} = \sum_{n=1}^{N} \sum_{i=1}^{M} \kappa_U (f_{CPU}^{U}/M)^3 T^{\text{comp}}. $$
UAV flight energy: The UAV flies along the trajectory with constant speed $v$, and the flight energy is
$$ E^{\text{fly}} = \sum_{n=1}^{N} \frac{W}{2 v} \|\mathbf{q}[n+1] – \mathbf{q}[n]\|^2, $$
where $W$ is the UAV mass.
Thus, the total energy consumption is
$$ E = E^{\text{off}} + E^{\text{comp}} + E^{\text{fly}}. $$
The time slot length $T_n$ must be no smaller than the maximum of the offloading and computation times for all devices in that slot, i.e.,
$$ T_n \ge \max_i \{T_{r_i(n)}^{\text{off}}, T^{\text{comp}}\}, $$
and must also satisfy the task deadlines: $T_n \le \min_i \{T_{r_i(n)}\}$.
3.3 Problem Formulation
Let $\mathbf{A}$ be the device grouping matrix, where $a_{k,n}=1$ if device $k$ offloads in slot $n$. Let $\mathbf{P} = \{p_k\}$ be the device transmit powers, and $\mathbf{Q} = \{\mathbf{q}[n]\}$ be the UAV trajectory. The optimization problem is to minimize the total system energy:
$$ \min_{\mathbf{A}, \mathbf{P}, \mathbf{Q}} E $$
subject to:
\begin{align}
& a_{k,n} \in \{0,1\}, \quad \forall k \in \mathcal{K}, n \in \mathcal{N}, \\
& \sum_{n=1}^{N} a_{k,n} = 1, \quad \forall k \in \mathcal{K}, \\
& \sum_{k=1}^{K} a_{k,n} = M, \quad \forall n \in \mathcal{N}, \\
& \mathbf{q}[1] = \mathbf{q}_0, \quad \mathbf{q}[N+1] = \mathbf{q}_F, \\
& \|\mathbf{q}[n+1] – \mathbf{q}[n]\| \le d, \quad n \in \{1,\ldots,N-1\}, \\
& T_n \le \min_{i} \{T_{r_i(n)}\}, \quad \forall i, n, \\
& 0 \le p_k \le p_{\text{th}}, \quad \forall k.
\end{align}
This is a mixed-integer nonlinear programming problem, which is generally NP-hard. I solve it by first determining the optimal SIC order, then applying alternating optimization to optimize power and trajectory, and finally using matching theory for device grouping.
3.4 Optimal SIC Order
In a conventional uplink NOMA system, the SIC decoding order is usually based on decreasing channel gains to maximize rates or minimize transmit power. However, when devices have heterogeneous task deadlines, the conventional order may not be energy-efficient. I propose the following theorem.
Theorem 1: In time slot $n$, the optimal SIC decoding order for the $M$ devices is to decode the devices in descending order of $\frac{g_k[n]}{T_k}$, where $g_k[n]$ is the channel gain between device $k$ and the UAV, and $T_k$ is the task completion deadline of device $k$.
Proof sketch: Consider two adjacent decoding devices $i$ and $j$ in the same slot. There are two possible decoding orders. Let $I$ be the interference from later-decoded devices. For the order that decodes $i$ first, the minimum power constraints are:
$$ \frac{p_i g_i[n]}{p_j g_j[n] + I + B\sigma^2} \ge \eta_i,\qquad \frac{p_j g_j[n]}{I + B\sigma^2} \ge \eta_j, $$
where $\eta_i = 2^{D/(B T_i^{\text{off}})} – 1$, and $T_i^{\text{off}}$ is the maximum allowed offloading time for device $i$. For the opposite order, the constraints are similar. Under the NOMA constraint that the earlier decoded device must have transmit power no smaller than that of the later decoded device, I compare the total offloading energies for both cases. By analyzing the pairwise deviations and using the fact that $\eta_i$ is monotonically related to the deadline, it can be shown that the order with higher $\frac{g_i}{T_i}$ decoded earlier yields smaller or equal energy consumption. Following this pairwise exchange argument, the global optimal order is obtained by sorting $\frac{g_k[n]}{T_k}$ in descending order. ∎
Thus, for a given slot and a fixed device group, the SIC order is completely determined by this metric.
3.5 Power and Trajectory Optimization
With the optimal SIC order, the achievable rate of device $i$ can be rewritten as
$$ R_i[n] = B \log_2\left(1 + \frac{p_i g_i[n]}{ \sum_{j: \frac{g_j[n]}{T_j} < \frac{g_i[n]}{T_i} } p_j g_j[n] + B\sigma^2} \right). $$
When the device grouping is fixed, the original problem reduces to a joint power and trajectory optimization problem. Since the objective function contains a fractional form, I use quadratic transform to convert it into a convex problem. Specifically, the offloading energy can be equivalently expressed as
$$ f_{\text{off}}(p) = \sum_{i=1}^{M} \left[ 2 \sqrt{p_i} y_i – y_i^2 R_i[n] \right], $$
where $y_i$ is a Lagrangian multiplier updated iteratively. After another quadratic transform for the logarithmic rate expression, the subproblem for power allocation becomes convex and can be solved efficiently by CVX. Algorithm 1 summarizes the iterative power allocation algorithm.
| Step | Procedure |
|---|---|
| 1 | Initialize power vector $\mathbf{p}^*$, convergence tolerance $\xi$, maximum iterations $T_{\max}$ |
| 2 | For each slot $n=1,\ldots,N$ |
| 3 | Set $t=0$, $f_{\text{off}}^{(0)} = +\infty$ |
| 4 | While $t < T_{\max}$ do |
| 5 | Update multipliers $y_i, z_i$ based on current power |
| 6 | Solve the convex problem P3 and obtain $f_{\text{off}}(\mathbf{p})$ |
| 7 | If $|f_{\text{off}} – f_{\text{off}}^{(t-1)}| < \xi$, break; otherwise update $\mathbf{p}^*$ |
| 8 | End while |
| 9 | End for |
For trajectory optimization, I fix the transmit power and apply the same quadratic transform to convert the offloading energy into a form involving the channel gains. The channel gain term is non-convex, but it can be approximated by its first-order Taylor expansion at the previous trajectory point:
$$ g_i[n] \approx g_i^*[n] – \frac{\|\mathbf{q}[n]-\mathbf{w}_i\|^2 – \|\mathbf{q}^*[n]-\mathbf{w}_i\|^2}{2 \|\mathbf{q}^*[n]-\mathbf{w}_i\|^2}, $$
where $\mathbf{q}^*[n]$ and $g_i^*[n]$ are the trajectory and channel gain from the previous iteration. This approximation renders the problem convex, and successive convex approximation (SCA) can be applied. Algorithm 2 gives the trajectory optimization procedure.
| Step | Procedure |
|---|---|
| 1 | Initialize UAV trajectory $\mathbf{Q}^*$, convergence tolerance $\xi$, maximum iterations $T_{\max}$ |
| 2 | Set $t=0$, $E^{(0)} = +\infty$ |
| 3 | While $t < T_{\max}$ do |
| 4 | Update multipliers based on current trajectory |
| 5 | Compute first-order lower bounds for channel gains |
| 6 | Solve the convex problem P5 and obtain new trajectory |
| 7 | If the energy decrease is below $\xi$, break; otherwise update $\mathbf{Q}^*$ |
| 8 | End while |
| 9 | Output the optimized trajectory $\mathbf{Q}^*$ |
By alternately executing Algorithm 1 and Algorithm 2, I solve the joint power and trajectory optimization problem. The overall alternating optimization algorithm is given in Algorithm 3.
| Step | Procedure |
|---|---|
| 1 | Initialize $\mathbf{P}$, $\mathbf{Q}$, tolerance $\xi$, and maximum iterations $T_{\max}$ |
| 2 | Set $t=0$, $E^{(0)} = +\infty$ |
| 3 | While $t < T_{\max}$ do |
| 4 | Execute Algorithm 1 with fixed $\mathbf{Q}$ to obtain $\mathbf{P}$ |
| 5 | Execute Algorithm 2 with fixed $\mathbf{P}$ to obtain $\mathbf{Q}$ |
| 6 | Compute system energy $E$ |
| 7 | If $|E – E^{(t-1)}| < \xi$, break; otherwise update and continue |
| 8 | End while |
3.6 Device Grouping Based on Matching Theory
The device grouping problem can be cast as a many-to-one matching problem. Each device must be matched to exactly one time slot, and each time slot can accommodate $M$ devices. A matching $\Psi$ is a mapping from the set of time slots $\mathcal{N}$ to the set of devices $\mathcal{K}$ such that $|\Psi(n)| = M$ for all $n$, $|\Psi(k)| = 1$ for all $k$, and $k \in \Psi(n) \Leftrightarrow \Psi(k) = n$. I define the preference of a device $k$ over time slots $n$ and $n’$ based on the resulting system energy: device $k$ prefers the slot that yields lower total energy. Similarly, a time slot prefers the device that leads to lower total energy. A swapping operation between two devices $i$ and $j$ exchanges their matched time slots. A swapping operation is allowed if it strictly decreases the total system energy. The proposed algorithm starts from an arbitrary matching and repeatedly checks all possible swaps until no allowed swap remains, at which point the matching is swap-stable. The complexity of this algorithm is $O(C K^2)$ in the worst case, where $C$ is the number of rounds, whereas exhaustive search has factorial complexity. Table 3 shows an example of device grouping before and after optimization.
| Time slot | Group before optimization (device IDs) | Group after optimization (device IDs) |
|---|---|---|
| 1 | 3, 14, 31, 32, 41 | 15, 17, 23, 26, 43 |
| 2 | 6, 22, 42, 48, 50 | 9, 19, 28, 29, 33 |
| 3 | 5, 8, 21, 27, 42 | 4, 24, 36, 44, 49 |
| 4 | 16, 34, 36, 37, 43 | 1, 2, 5, 7, 37 |
| 5 | 17, 23, 26, 28, 49 | 16, 20, 30, 35, 38 |
| 6 | 9, 19, 23, 26, 28 | 13, 14, 25, 38, 47 |
| 7 | 4, 15, 38, 44, 47 | 10, 11, 18, 45, 46 |
| 8 | 1, 2, 7, 12, 39 | 8, 21, 27, 34, 42 |
| 9 | 13, 25, 35, 45, 46 | 6, 22, 44, 48, 50 |
| 10 | 10, 11, 18, 20, 30 | 3, 14, 31, 32, 41 |
3.7 Simulation Results
I conducted simulations with $K=50$ devices randomly distributed in a $50\times50$ m$^2$ area. The UAV flight period is divided into $N=10$ slots, with $M=5$ devices per slot. Task deadlines are randomly generated within $[5,10]$ s. Other parameters are listed in Table 4.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| Altitude $H$ | 15 m | Cycles per bit $C$ | $10^3$ cycles/bit |
| UAV speed $v$ | 2 m/s | Bandwidth $B$ | 1 MHz |
| UAV mass $W$ | 1 kg | Max transmit power $p_{\text{th}}$ | 10 W |
| Initial position $\mathbf{q}_0$ | [0,25,15] m | Task size $D$ | 100 Kbits |
| Distance constraint $d$ | 10 m | Noise power $\sigma^2$ | -100 dBm |
| UAV CPU frequency $f_{CPU}^U$ | 2 GHz | Tolerance $\xi$ | $10^{-3}$ |
| UAV effective capacitance $\kappa_U$ | $10^{-27}$ | Max iterations $T_{\max}$ | 50 |
| Final position $\mathbf{q}_F$ | [50,25,15] m | Reference path loss $\beta_0$ | -50 dB |
Figure 3 compares the total energy consumption of different schemes: the proposed optimal SIC order, channel-gain descending order, deadline ascending order, OMA scheme, and fixed UAV trajectory. The results show that the optimal SIC order yields the lowest energy consumption among the compared schemes. The OMA scheme performs the worst, indicating that NOMA provides significant energy savings. Also, optimizing the UAV trajectory reduces energy consumption compared to fixing the trajectory.
Figure 4 shows the total energy consumption versus the number of devices. When each slot serves only one device, all SIC orders have the same energy because there is no interference. As the number of devices per slot increases, the proposed optimal SIC order achieves increasingly lower energy consumption compared to other orders.
Figure 5 illustrates the convergence of the proposed device grouping algorithm. Each allowed swap operation reduces the total energy. The algorithm converges after about 180 swaps in the case of 50 devices. The resulting grouping is stable and optimal in the sense of no further reducing swaps.
Table 5 compares the system energy under different device grouping algorithms. The proposed matching-based grouping algorithm outperforms dynamic grouping, k-means-based grouping, and random grouping.
| Algorithm | Normalized system energy |
|---|---|
| Proposed matching-based grouping | 1.00 |
| Dynamic grouping | 1.18 |
| k-means-based grouping | 1.25 |
| Random grouping | 1.42 |
4. Security-Enhanced Design and Energy Consumption Optimization for NOMA-based UAV-assisted MEC with Covert Communication
4.1 System Model
In this section, I consider a NOMA-based UAV-assisted MEC system with an eavesdropper on the ground. The UAV acts as both a MEC server and a jammer. Each time slot serves two ground devices using NOMA: the device with stronger channel gain is denoted as Bob, and the weaker one as Roy. Since Bob transmits at higher power, it is more vulnerable to detection by the eavesdropper. To achieve covert communication, the UAV transmits artificial noise (AN) to confuse the eavesdropper. The UAV also receives the offloaded tasks from both devices and computes them locally.
The positions and channel models are similar to the previous section. The channel gain between device $k$ and the UAV is denoted by $h_{k,u}[n]$, between device $k$ and the eavesdropper by $h_{k,e}$, and between the UAV and the eavesdropper by $h_{u,e}[n]$:
$$ h_{k,u}[n] = \frac{\beta_0}{H^2 + \|\mathbf{q}[n]-\mathbf{w}_k\|^2}, \quad h_{k,e} = \frac{\beta_0}{H_e^2 + \|\mathbf{q}_e-\mathbf{w}_k\|^2}, \quad h_{u,e}[n] = \frac{\beta_0}{H^2 + \|\mathbf{q}[n]-\mathbf{q}_e\|^2}. $$
In slot $n$, Bob and Roy offload tasks with powers $p_b[n]$ and $p_r[n]$, respectively. The UAV transmits AN with power $p_u[n]$, which is uniformly distributed in $[0, P_{u,\max}]$. The received signal at the UAV is
$$ y_u[n] = p_r[n] h_{r,u}[n] s_r + p_b[n] h_{b,u}[n] s_b + \rho \sqrt{p_u[n]} g_{u,u}[n] s_u + n_u, $$
where $\rho$ is the self-interference cancellation coefficient and $g_{u,u}[n]$ is the residual self-interference channel following Rayleigh fading. The achievable rates for Bob and Roy are
$$ R_b[n] = B \log_2\left(1 + \frac{p_b[n] h_{b,u}[n]}{p_r[n] h_{r,u}[n] + \rho^2 p_u[n] |g_{u,u}[n]|^2 + B\sigma^2}\right), $$
$$ R_r[n] = B \log_2\left(1 + \frac{p_r[n] h_{r,u}[n]}{\rho^2 p_u[n] |g_{u,u}[n]|^2 + B\sigma^2}\right). $$
The eavesdropper performs a binary hypothesis test to determine whether Bob is transmitting. The received signal at the eavesdropper under hypotheses $H_0$ (Bob absent) and $H_1$ (Bob present) is
$$ y_w[n] = \begin{cases} p_r[n] h_{r,e}[n] s_r + \sqrt{p_u[n]} h_{u,e}[n] s_u + n_w, & H_0, \\ p_r[n] h_{r,e}[n] s_r + p_b[n] h_{b,e}[n] s_b + \sqrt{p_u[n]} h_{u,e}[n] s_u + n_w, & H_1. \end{cases} $$
The eavesdropper compares the received power with a threshold $\tau[n]$. The false alarm probability $\alpha[n]$ and miss detection probability $\beta[n]$ can be derived from the distribution of $p_u[n]$. The minimum detection error probability is found by optimizing the threshold. Given the uniform distribution of $p_u[n]$, the minimum detection error probability in slot $n$ is
$$ \xi^*[n] = \frac{F[n]}{M[n]}, $$
where
$$ F[n] = \rho^2 p_r[n] |h_{r,e}[n]|^2 + P_{u,\max} |h_{u,e}[n]|^2, $$
$$ M[n] = \rho^2 p_r[n] |h_{r,e}[n]|^2 + \rho^2 p_b[n] |h_{b,e}[n]|^2 + P_{u,\max} |h_{u,e}[n]|^2. $$
To guarantee covertness, the following constraint must hold:
$$ \xi^*[n] \ge 1 – \varepsilon, $$
where $\varepsilon$ is a small positive constant indicating the required level of covertness.
4.2 Energy Consumption Model
The total energy includes offloading energy, computation energy, UAV flight energy, and UAV AN energy.
The offloading energy and AN energy in slot $n$ are
$$ E^{\text{off}}[n] = p_r[n] \frac{D_r[n]}{R_r[n]} + p_b[n] \frac{D_b[n]}{R_b[n]}, $$
$$ E^{\text{AN}}[n] = p_u[n] \frac{D_b[n]}{R_b[n]}, $$
where the AN is assumed to be transmitted only while Bob is offloading. The computation energy at the UAV is
$$ E^{\text{comp}}[n] = \kappa_U c_r[n]^2 D_r[n] s_r + \kappa_U c_b[n]^2 D_b[n] s_b, $$
with resource allocation constraints $c_r[n]+c_b[n] \le c_{u,\max}$, where $c_r[n]$ and $c_b[n]$ are the allocated CPU frequencies for the tasks of Roy and Bob, and $s_r$ and $s_b$ are the required CPU cycles per bit. The UAV flight energy is the same as before. Thus the total energy is
$$ E = \sum_{n=1}^{N} \left( E^{\text{off}}[n] + E^{\text{AN}}[n] + E^{\text{comp}}[n] \right) + E^{\text{fly}}. $$
4.3 Problem Formulation
Define $\mathbf{A}$ as the grouping matrix, $\mathbf{P}$ as device transmit powers, $\mathbf{P}_u$ as UAV AN powers, $\mathbf{Q}$ as UAV trajectory, and $\mathbf{C}$ as computation resource allocation. The optimization problem is
$$ \min_{\mathbf{A}, \mathbf{P}, \mathbf{P}_u, \mathbf{Q}, \mathbf{C}} E $$
subject to:
\begin{align}
& a_{k,n} \in \{0,1\}, \quad \sum_{n=1}^{N} a_{k,n}=1, \quad \sum_{k=1}^{K} a_{k,n}=2, \\
& \mathbf{q}[1]=\mathbf{q}_0, \quad \mathbf{q}[N+1]=\mathbf{q}_F, \quad \|\mathbf{q}[n+1]-\mathbf{q}[n]\| \le d, \\
& 0 \le p_u[n] \le P_{u,\max}, \quad \forall n, \\
& 0 \le p_k \le P_{d,\max}, \quad \forall k, \\
& c_r[n] + c_b[n] \le c_{u,\max}, \quad \forall n, \\
& \xi^*[n] \ge 1 – \varepsilon, \quad \forall n.
\end{align}
This problem is highly coupled and non-convex. I adopt a two-stage iterative approach: first, for a fixed grouping, I alternately optimize the power variables and the trajectory/computation variables; then, I update the device grouping using a low-complexity dynamic grouping algorithm.
4.4 Iterative Optimization Algorithm
For fixed grouping, I decompose the problem into two subproblems.
Subproblem 1: Optimize $\mathbf{P}, \mathbf{P}_u$ with fixed $\mathbf{Q}, \mathbf{C}$. Since the time slots are independent, I can solve each slot separately. The objective function after applying quadratic transform becomes
$$ f(p_r,p_b,p_u) = D_r \left(2\sqrt{p_r} x_1 – x_1^2 R_r\right) + D_b \left(2\sqrt{p_b} x_2 – x_2^2 R_b\right) + D_b \left(2\sqrt{p_u} x_3 – x_3^2 R_b\right), $$
where $x_1,x_2,x_3$ are updated iteratively. The covertness constraint is transformed into
$$ p_r h_{r,e}^2 + p_b h_{b,e}^2 + P_{u,\max} h_{u,e}^2 \le \frac{1}{1-\varepsilon} \left( p_r h_{r,e}^2 + P_{u,\max} h_{u,e}^2 \right). $$
The problem becomes convex after approximation and can be solved by CVX. Algorithm 4 summarizes this step.
| Step | Procedure |
|---|---|
| 1 | Initialize $p_r^*[n], p_b^*[n], p_u^*[n]$ for all $n$ |
| 2 | For each slot $n$ |
| 3 | Repeat |
| 4 | Update multipliers $x_1,x_2,x_3$ |
| 5 | Solve convex approximation of subproblem 1 |
| 6 | Until convergence |
| 7 | End for |
Subproblem 2: Optimize $\mathbf{Q}, \mathbf{C}$ with fixed $\mathbf{P}, \mathbf{P}_u$. The objective function after quadratic transform and SCA becomes convex. The computation resource variables appear linearly in the computation energy, so they can be optimized jointly. Algorithm 5 gives the procedure.
| Step | Procedure |
|---|---|
| 1 | Initialize $\mathbf{Q}^*$, $\mathbf{C}^*$ |
| 2 | Repeat |
| 3 | Update multipliers and SCA lower bounds |
| 4 | Solve convex subproblem 2 to obtain $\mathbf{Q}$ and $\mathbf{C}$ |
| 5 | Until convergence |
By alternately solving the two subproblems, the system energy decreases monotonically and converges to a local optimum. Algorithm 6 provides the overall alternating optimization.
| Step | Procedure |
|---|---|
| 1 | Initialize $\mathbf{Q}, \mathbf{C}, \mathbf{P}, \mathbf{P}_u$ |
| 2 | Repeat |
| 3 | Execute Algorithm 4 to update $\mathbf{P}, \mathbf{P}_u$ |
| 4 | Execute Algorithm 5 to update $\mathbf{Q}, \mathbf{C}$ |
| 5 | Compute total energy $E$ |
| 6 | Until energy decrease is below tolerance |
4.5 Dynamic Device Grouping
To avoid exhaustive search, I propose a low-complexity dynamic grouping algorithm. In the considered NOMA-based system with two devices per slot, the achievable sum rate in slot $n$ is approximately
$$ R_{\text{sum}}[n] \approx B \log_2\left(1 + \frac{p_r[n] h_{r,u}[n] + p_b[n] h_{b,u}[n]}{\rho^2 p_u[n] |g_{u,u}[n]|^2 + B\sigma^2}\right). $$
To maximize the sum rate, the two devices with the largest values of $p_k h_{k,u}[n]$ should be grouped together. Therefore, I compute the product of the current transmit power and channel gain for each unassigned device, sort the products in descending order, and pick the top two devices as a group for the current slot. This process is repeated for each slot, updating the channel gains as the UAV moves. This algorithm has linear complexity and yields a near-optimal grouping.
4.6 Simulation Results
I set $K=20$ devices in a $50\times50$ m$^2$ area, $N=10$ slots, two devices per slot. The eavesdropper is located at $[25,25,0]$ m. Other parameters are listed in Table 6.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| $H$ | 15 m | Cycles per bit $s_r,s_b$ | $10^3$ cycles/bit |
| $\mathbf{q}_e$ | [25,25,0] m | Self-interference cancellation $\rho$ | 0.01 |
| $\sigma_u^2=\sigma_w^2$ | -10 dB | $\lambda_{u,u}$ | 1 |
| $P_{d,\max}$ | 10 dB | $P_{u,\max}$ | 20 dB |
| $c_{u,\max}$ | 2 GHz | $\kappa_U$ | $10^{-27}$ |
| $\varepsilon$ | 0.01 / 0.05 / 0.1 | Task sizes | $50-150$ Kbits |
Figure 6 shows the system energy convergence for different covertness levels $\varepsilon$. As $\varepsilon$ decreases, the covertness requirement becomes stricter, forcing the UAV to transmit higher AN power, which increases energy consumption. The proposed algorithm converges within a limited number of iterations.
Figure 7 compares the energy with and without UAV trajectory optimization under different covertness constraints. Trajectory optimization significantly reduces the total energy, highlighting its importance in UAV-assisted systems.
Figure 8 compares the dynamic grouping algorithm with random grouping and two existing grouping algorithms. The proposed dynamic grouping yields the lowest system energy, confirming its effectiveness.
| Algorithm | Normalized energy |
|---|---|
| Proposed dynamic grouping | 1.00 |
| Random grouping | 1.25 |
| Sum-rate maximizing grouping [78] | 1.12 |
| Distance-based grouping [74] | 1.19 |
5. Conclusion
In this thesis, I have studied the energy consumption optimization problem in NOMA-based UAV-assisted mobile edge computing systems from two perspectives: task delay and security.
First, I proposed a novel optimal SIC order that jointly considers channel gain and task delay constraints for uplink NOMA offloading. The optimization problem was formulated to minimize the total system energy, including offloading, computation, and UAV flight energy. I solved the non-convex problem by alternating optimization of transmit power and UAV trajectory, and used matching theory to design a low-complexity device grouping algorithm. Simulation results demonstrated that the proposed optimal SIC order achieves lower energy than conventional SIC orders, and the matching-based grouping algorithm obtains near-optimal solutions with acceptable complexity.
Second, I integrated covert communication into the NOMA-based UAV-assisted MEC system to protect the offloading behavior from eavesdroppers. The UAV transmits artificial noise to degrade the detection performance of the eavesdropper, while also serving as a MEC server. I formulated a joint optimization problem involving device grouping, transmit power, AN power, UAV trajectory, and computation resource allocation. A two-stage iterative algorithm based on quadratic transform and successive convex approximation was developed to minimize the system energy under covertness constraints. Simulation results verified the effectiveness of the proposed scheme and showed that dynamic grouping outperforms other grouping algorithms.
Future work may extend this research to multi-UAV MEC systems with partial task offloading and consider cloud-edge collaboration. In addition, the impact of imperfect channel state information and practical UAV energy harvesting on system design is worth investigation.