In the realm of low-altitude wireless networks (LAWNs), the reliance on Global Navigation Satellite Systems (GNSS) for autonomous drone positioning poses a critical vulnerability. In this work, I address the dual challenge of GNSS-denied navigation and constrained radio-frequency resource allocation for China drone operations. The first phase involves an angle-only guidance strategy that leverages bearing geometry from ground reference anchors, enabling a China drone to precisely reach a target location without satellite signals. The second phase tackles multi-user downlink communication under limited transmit power and radio-frequency chains. I formulate a joint user scheduling and beamforming optimization problem aimed at maximizing the number of effectively served users. An efficient algorithm based on alternating optimization (AO), successive convex approximation (SCA), and semidefinite relaxation (SDR) is proposed. Simulation results validate the navigation algorithm’s ability to achieve target acquisition with decreasing angle errors, and the joint resource allocation strategy significantly improves system service performance across various power budgets and rate thresholds. This study provides a practical solution for China drone mission execution in GNSS-denied environments.
Introduction
Low-altitude wireless networks (LAWNs) built on aerial platforms such as drones and eVTOL aircraft present a flexible and rapidly deployable communication paradigm. By exploiting three-dimensional mobility and dominant line-of-sight (LoS) air-to-ground (A2G) links, China drone-based LAWNs can provide adaptive and reliable downlink coverage for emergency response, temporary hotspot offloading, and public safety operations in infrastructure-deficient areas. However, compared to terrestrial base stations, aerial platforms face stringent constraints on transmit power, concurrent radio-frequency (RF) link capacity, payload, and energy supply, making efficient resource allocation and user scheduling a core challenge for sustainable multi-user service.
Existing research on LAWNs has explored resource allocation and user scheduling from various angles. Most studies assume that the China drone can reliably complete navigation and deployment, but rarely address the prerequisite condition of autonomous positioning under GNSS denial. In practice, GNSS signals are susceptible to occlusion, multipath, and malicious interference, leading to state estimation errors and control instability. To fill this gap, I design an angle-only guidance method that relies on bearing geometry relative to ground anchors. Once the China drone arrives at the target position, the system switches to the communication phase, where I jointly optimize user scheduling and beamforming to maximize the number of served users under power and quality-of-service (QoS) constraints.
The remainder of this article is organized as follows. Section II presents the system model, including navigation dynamics and downlink communication channels. Section III details the GNSS-denied navigation strategy based on pure angle measurements. Section IV formulates and solves the joint user scheduling and beamforming optimization problem. Section V provides simulation results and analysis. Section VI concludes the work.
System Model
I consider a China drone equipped with Nt antennas and M single-antenna ground users (GUs). The three-dimensional position of the drone is denoted by u = [xu, yu, zu]T, and the position of GU m is bm = [xbm, ybm, 0]T. The system operates in two sequential phases: autonomous navigation and downlink communication. During navigation, the drone relies solely on angle observations from three non-collinear ground anchors. During communication, the drone acts as an aerial base station serving a selected subset K ⊆ {1,…,M} of users, where |K| = K ≤ M is the maximum number of simultaneously supportable users constrained by limited RF chains.
Navigation Dynamics
The drone’s motion is modeled as a perturbed single-integrator system: u̇(t) = μ(t) + n(t), where μ(t) ∈ ℝ3 is the control input and n(t) is a bounded disturbance representing wind and sensor noise. Three ground anchors with known positions gi = [xgi, ygi, 0]T, i = 1,2,3, provide the only reference for navigation.
Downlink Communication Model
The channel from the China drone to GU k follows a Rician fading model: hk = √(β0 dk−2) [ √(κk/(κk+1)) hkLoS + √(1/(κk+1)) hkNLoS ], where β0 is the reference channel gain, dk is the distance, κk is the Rician factor, and hkLoS = a(θk) is the array steering vector: a(θk) = [1, ej2π(ds/λ)cosθk, …, ej2π(ds/λ)(Nt−1)cosθk]T. The term cosθk = zu / ||u − bk||. The NLoS component hkNLoS has i.i.d. zero-mean unit-variance circularly symmetric complex Gaussian entries. The estimated channel is denoted by ĥk with estimation error ωk ~ CN(0, σω2I). The achievable rate for GU k is:
$$ R_k = \log_2 \left( 1 + \frac{ |\hat{\mathbf{h}}_k^H \mathbf{w}_k|^2 }{ \sum_{i \in \mathcal{K}, i \neq k} |\hat{\mathbf{h}}_k^H \mathbf{w}_i|^2 + \sigma^2 } \right) $$
GNSS-Denied Navigation Strategy
For a China drone operating without GNSS, I propose an angle-only feedback control law that exploits the geometric relationships between the drone and three known anchors (Figure 1). The key idea is to formulate the navigation problem as asymptotic regulation of three angular constraints: two interior angles ρ012 and ρ021 formed by the drone and anchor pairs, and the dihedral angle ρp between the plane containing the drone and two anchors and the ground plane.
Define the unit line-of-sight vector from node i to node j as: rij = (gj − gi) / ||gj − gi||. The interior angle is: ρjil = arccos(rijT ril). The dihedral angle is computed using the unit normals of the drone-anchor plane and the ground plane. The control objective is:
$$ \lim_{t \to +\infty} \rho_{012}(t) = \rho_{012}^* , \quad \lim_{t \to +\infty} \rho_{021}(t) = \rho_{021}^* , \quad \lim_{t \to +\infty} \rho_p(t) = \rho_p^* $$
The proposed feedback control law (inspired by Chen et al., 2026) is:
$$ \boldsymbol{\mu}(t) = (\rho_{012}(t) – \rho_{012}^*) \mathbf{r}_{02}(t) + (\rho_{021}(t) – \rho_{021}^*) \mathbf{r}_{01}(t) – (\rho_p(t) – \rho_p^*) ( \mathbf{r}_{01}(t) \times \mathbf{r}_{02}(t) ) $$
This controller is provably stable under mild conditions and ensures that the China drone converges to the desired position even in the presence of bounded disturbances. The three terms act almost orthogonally, enabling decoupled correction of the planar and out-of-plane errors.
Joint User Scheduling and Beamforming Design
After the China drone arrives at the target position, the communication phase begins. I aim to maximize the number of served users subject to total transmit power budget Pmax and per-user rate constraint Rkth. Let binary variable ηm ∈ {0,1} indicate whether GU m is scheduled. The optimization problem is:
$$
\begin{aligned}
\text{(P1)} \quad & \max_{\boldsymbol{\eta}, \{\mathbf{w}_m\}} \|\boldsymbol{\eta}\|_0 \\
\text{s.t.} \quad & \sum_{m \in \mathcal{M}} \mathbf{w}_m^H \mathbf{w}_m \leq P_{\max} \\
& R_m \geq \eta_m R_m^{\text{th}}, \quad \forall m \in \mathcal{M} \\
& \eta_m \in \{0,1\}, \quad \forall m \in \mathcal{M}
\end{aligned}
$$
This is a mixed-integer non-convex problem. I adopt an alternating optimization (AO) framework that iterates between user scheduling and beamforming.
User Scheduling Subproblem
Given fixed beamformers {wm}, the scheduling problem becomes:
$$
\begin{aligned}
\text{(P2)} \quad & \max_{\boldsymbol{\eta}} \|\boldsymbol{\eta}\|_0 \\
\text{s.t.} \quad & R_m \geq \eta_m R_m^{\text{th}}, \quad 0 \leq \eta_m \leq 1, \quad \eta_m – \eta_m^2 \leq 0
\end{aligned}
$$
The binary constraint is relaxed with a penalty term. Using successive convex approximation (SCA), at iteration t1, I approximate (ηmt1 − ηm)2 + ηm − ηm2 ≤ 0 by its first-order Taylor expansion, leading to a convex inner approximation. The resulting problem is:
$$ \max_{\boldsymbol{\eta}} \sum_{m} \eta_m – \xi \sum_{m} \left[ (\eta_m^{t_1})^2 – 2\eta_m^{t_1}\eta_m + \eta_m \right] $$
where ξ ≫ 0 is a penalty factor. This is a convex problem solvable via CVX. The SCA loop drives η to a binary feasible solution.
Beamforming Subproblem
Fix η, then the beamforming subproblem is:
$$
\begin{aligned}
\text{(P3)} \quad & \text{Find } \{\mathbf{w}_m\} \\
\text{s.t.} \quad & \sum_{m} \|\mathbf{w}_m\|^2 \leq P_{\max} \\
& R_m \geq \eta_m R_m^{\text{th}}, \quad \forall m
\end{aligned}
$$
Define the semi-definite variable Wm = wmwmH, and let Ĥm = ĥmĥmH. Then (P3) can be rewritten as:
$$
\begin{aligned}
\text{(P4)} \quad & \text{Find } \{\mathbf{W}_m \succeq \mathbf{0}\} \\
\text{s.t.} \quad & \sum_{m} \text{Tr}(\mathbf{W}_m) \leq P_{\max} \\
& \text{Tr}(\hat{\mathbf{H}}_m \mathbf{W}_m) – \gamma_m^{\text{th}} \sum_{i \neq m} \text{Tr}(\hat{\mathbf{H}}_m \mathbf{W}_i) \geq \gamma_m^{\text{th}} \sigma^2, \quad \forall m \\
& \text{Rank}(\mathbf{W}_m) \leq 1, \quad \forall m
\end{aligned}
$$
where γmth = 2Rmth − 1. The only non-convexity is the rank constraint. Applying semidefinite relaxation (SDR) by dropping the rank constraint yields a standard semidefinite program (SDP) that can be solved efficiently. After obtaining the optimal {Wm⋆}, Gaussian randomization is used if any Wm⋆ has rank > 1 to extract a feasible rank-1 solution.
Overall Algorithm
The AO algorithm iterates between solving the scheduling subproblem and the beamforming subproblem. Since the objective (number of served users) is non-decreasing and upper-bounded by M, the algorithm converges to a stationary solution. The computational complexity is polynomial due to the interior-point methods used for the convex subproblems.
| Step | Operation |
|---|---|
| 1 | Initialize t=0, η0, {wm0}, set max iterations tmax and threshold ε. |
| 2 | Repeat |
| 3 | Given {wmt}, solve (P2) via SCA to obtain ηt+1. |
| 4 | Given ηt+1, solve (P4) via SDR to obtain {Wmt+1} and extract {wmt+1}. |
| 5 | t ← t+1 |
| 6 | Until objective increase < ε or t > tmax |
| 7 | Return η, {wm} |
Simulation Results and Analysis
In this section, I evaluate the performance of the proposed GNSS-denied navigation and joint resource allocation scheme for a China drone through numerical simulations. The default parameters are: initial drone position u0 = [10,10,80]T m, target position u⋆ = [100,80,120]T m; ground anchors at [20,10,0]， [140,30,0]， [70,130,0] m; total users M = 22; β0 = −60 dB; noise power σ2 = −110 dBm; antenna spacing ds = λ/2; number of antennas Nt = 32; Rician factor κk = 10 (except where noted); channel estimation error power σω2 = 0.01 (except where noted).
Navigation Performance
Figure 2 (refer to the image inserted above) shows the 3D trajectory of the China drone from its start to the target site. The drone gradually converges to the desired point using only angle feedback, demonstrating successful GNSS-denied navigation. Table 1 summarizes the angle error convergence statistics.
| Time (s) | |Δρ012| (rad) | |Δρ021| (rad) | |Δρp| (rad) |
|---|---|---|---|
| 0 | 0.52 | 0.48 | 0.35 |
| 20 | 0.18 | 0.15 | 0.12 |
| 40 | 0.04 | 0.03 | 0.02 |
| 60 | 0.01 | 0.01 | 0.005 |
All three angle errors decay rapidly and settle to near zero within 60 seconds, confirming the effectiveness of the angle-only control law for China drone navigation under GNSS denial.
Communication Performance
Figure 3 presents a contour map of the number of schedulable users as a function of total transmit power Pmax and rate threshold Rkth (10 users shown in legend). As Pmax increases, the system can accommodate more users, especially at low Rkth. Conversely, raising the rate threshold reduces the number of serviceable users due to stricter SINR requirements. This demonstrates the trade-off between power budget and QoS demands.
Figure 4 investigates the impact of channel estimation error under a probabilistic LoS/NLoS scenario with different Rician factors (κk = 5, 10, 15) at Pmax = −1 dBW and Rkth = 0.8 bps/Hz. The results are summarized in Table 2.
| σω2 | κ=5 | κ=10 | κ=15 |
|---|---|---|---|
| 0.001 | 14 | 16 | 17 |
| 0.01 | 12 | 15 | 16 |
| 0.1 | 8 | 12 | 14 |
| 0.5 | 4 | 8 | 10 |
When the LoS component is strong (κ=15), the system maintains a high number of served users even as estimation error increases. For weaker LoS (κ=5), performance degrades more quickly, highlighting the need for accurate channel estimation in NLoS-rich environments. In typical low-altitude scenarios where LoS is dominant, the proposed joint optimization remains robust.
Algorithm Convergence
Table 3 shows the convergence speed of the AO algorithm for a representative case (Pmax = 0 dBW, Rkth = 0.5 bps/Hz). The algorithm typically converges within 5–8 iterations with an objective increase threshold of 10−3.
| Iteration | Number of Served Users | Power Usage (W) |
|---|---|---|
| 1 | 8 | 0.82 |
| 2 | 12 | 0.91 |
| 3 | 14 | 0.97 |
| 4 | 15 | 0.99 |
| 5 | 16 | 1.00 |
The objective increases monotonically and stabilizes after a few iterations, confirming the algorithm’s efficiency.
Conclusion
This article presents a comprehensive solution for China drone operations in GNSS-denied low-altitude wireless networks. By designing an angle-only navigation law that relies on bearing geometry from ground anchors, the China drone can autonomously reach a target position without satellite signals. After deployment, a joint user scheduling and beamforming optimization framework maximizes the number of served users under transmit power and rate constraints. The alternating optimization algorithm, incorporating SCA and SDR, efficiently solves the mixed-integer non-convex problem. Simulation results validate the navigation accuracy and demonstrate that the proposed resource allocation significantly improves service capacity across different power budgets, rate thresholds, and channel conditions. This work provides a practical pathway for deploying reliable China drone-based communication networks in environments where GNSS is unavailable or unreliable.