We investigate a dual-unmanned aerial vehicle (UAV) cooperative covert communication system operating under the constraints of finite blocklength (short-packet) transmission and stringent covertness requirements. Our work is motivated by the growing need for high-reliability and low-latency links in sensitive aerial applications, particularly those involving China drone fleets deployed in urban or contested environments. In this scenario, a source UAV (Alice) must deliver critical commands to multiple ground users (Bobs) while an illegal eavesdropper (Willie) attempts to detect the presence of any transmission. To address this challenge, we employ rate-splitting multiple access (RSMA) at the source UAV and introduce a cooperative jamming UAV (Helper) that emits artificial noise to confuse Willie. The presence of a vigilant warden forces us to consider not only the reliability of the short-packet links but also the statistical detectability of the transmission. By analyzing Willie’s optimal detection threshold via the Kullback-Leibler (KL) divergence, we derive a closed-form covertness constraint. The resulting joint optimization of the source’s beamforming vectors, the Helper’s jamming vector, and the RSMA common-rate allocation is a non-convex problem. We solve it using block coordinate descent (BCD) and successive convex approximation (SCA). Extensive simulations demonstrate that our scheme, built around China drone platforms, achieves approximately a four-fold improvement in covert sum-rate compared to non-jamming baselines, and significantly outperforms space-division multiple access (SDMA) and non-orthogonal multiple access (NOMA) in terms of both reliability and covertness.
The rapid expansion of the low-altitude economy has propelled China drone technology into logistics, urban air mobility, emergency response, and security surveillance. In these critical missions, wireless communication is no longer solely about data encryption; it must also prevent the very existence of a transmission from being detected by sophisticated monitoring equipment. This is the domain of covert communication. The unique characteristics of UAV-to-ground channels—high mobility, line-of-sight (LoS) dominance, and severe time variation—make traditional physical-layer security measures insufficient. Short-packet communication, essential for ultra-reliable low-latency (URLLC) services, further complicates the design because finite blocklength incurs a non-negligible decoding error penalty. Multi-user interference must be managed intelligently. While NOMA has been widely studied for UAV networks, its reliance on successive interference cancellation (SIC) suffers from error propagation and inflexible resource allocation under low signal-to-noise ratio (SNR) conditions. RSMA emerges as a more robust alternative: it splits each user’s message into a common part and a private part, enabling flexible trade-offs between interference management and spectral efficiency. When combined with cooperative jamming, RSMA can simultaneously mask the transmission from Willie and improve the legitimate users’ achievable rates.
System Model
We consider a downlink covert communication system in an urban environment. The source UAV (Alice) is equipped with \(N_t\) antennas. The cooperative jamming UAV (Helper) is also equipped with \(N_t\) antennas. There are \(K\) single-antenna legitimate ground users (Bobs), indexed by \(k \in \mathcal{K} \triangleq \{1,2,\dots,K\}\), and one single-antenna warden (Willie). The geometry is as follows: Alice is deployed at a fixed altitude \(H\); Helper is positioned to provide jamming coverage; Bobs are randomly distributed in a ground area; Willie is located at a fixed point. All channels experience large-scale path loss and small-scale Rician fading. The channel vector from Alice to Bob \(k\) is denoted \(\mathbf{h}_{A,k} \in \mathbb{C}^{N_t \times 1}\), and from Helper to Bob \(k\) is \(\mathbf{h}_{H,k} \in \mathbb{C}^{N_t \times 1}\). Similarly, the channel from Alice to Willie is \(g_{A,W} \in \mathbb{C}^{1 \times N_t}\) and from Helper to Willie is \(g_{H,W} \in \mathbb{C}^{1 \times N_t}\). The channel model follows:
$$
\mathbf{h}_{i,j} = \sqrt{\beta_0 d_{i,j}^{-\eta}} \cdot \tilde{\mathbf{h}}_{i,j},
$$
where \(\beta_0\) is the reference channel gain at 1 m, \(d_{i,j}\) is the Euclidean distance, \(\eta\) is the path-loss exponent, and \(\tilde{\mathbf{h}}_{i,j}\) follows Rician fading with factor \(\kappa\). We assume quasi-static flat fading. Alice employs RSMA: the message for each user is split into a common part and a private part. All common parts are jointly encoded into one common stream \(s_c\). The private parts are individually encoded into private streams \(s_1,\dots,s_K\). All data symbols are normalized so that \(\mathbb{E}[|s_c|^2] = \mathbb{E}[|s_k|^2] = 1\). Alice transmits the superimposed signal:
$$
\mathbf{x}_A = \mathbf{w}_c s_c + \sum_{k=1}^{K} \mathbf{w}_k s_k,
$$
where \(\mathbf{w}_c \in \mathbb{C}^{N_t \times 1}\) and \(\mathbf{w}_k \in \mathbb{C}^{N_t \times 1}\) are the beamforming vectors for the common stream and the \(k\)-th private stream, respectively. Helper transmits jamming signal \(\mathbf{z} s_z\) with \(\|\mathbf{z}\|^2 \leq P_H\), \(s_z\) being a unit-power artificial noise. The received signal at Bob \(k\) is:
$$
y_k = \mathbf{h}_{A,k}^H \mathbf{w}_c s_c + \mathbf{h}_{A,k}^H \sum_{j=1}^{K} \mathbf{w}_j s_j + \underbrace{\mathbf{h}_{H,k}^H \mathbf{z} s_z}_{\text{jamming}} + n_k,
$$
where \(n_k \sim \mathcal{CN}(0, \sigma^2)\) is additive white Gaussian noise. Following the RSMA protocol, each user first decodes the common stream treating all private streams and jamming as noise, then performs SIC to remove the common stream, and decodes its own private stream. The signal-to-interference-plus-noise ratio (SINR) for decoding the common stream at user \(k\) is:
$$
\gamma_{c,k} = \frac{|\mathbf{h}_{A,k}^H \mathbf{w}_c|^2}{ \sum_{j=1}^{K} |\mathbf{h}_{A,k}^H \mathbf{w}_j|^2 + |\mathbf{h}_{H,k}^H \mathbf{z}|^2 + \sigma^2 }.
$$
After successfully removing the common stream, the SINR for the private stream of user \(k\) is:
$$
\gamma_{p,k} = \frac{ |\mathbf{h}_{A,k}^H \mathbf{w}_k|^2 }{ \sum_{j \neq k} |\mathbf{h}_{A,k}^H \mathbf{w}_j|^2 + |\mathbf{h}_{H,k}^H \mathbf{z}|^2 + \sigma^2 }.
$$
In finite blocklength (FBL) regime with blocklength \(m\) and decoding error probability \(\epsilon\), the achievable rate (in nats per channel use) for stream \(x\) (common or private) is approximated by Polyanskiy’s formula:
$$
R_{x,k} \approx \log_2(1 + \gamma_{x,k}) – \sqrt{ \frac{V_{x,k}}{m} } \frac{Q^{-1}(\epsilon)}{\ln 2},
$$
with channel dispersion:
$$
V_{x,k} = 1 – \frac{1}{(1 + \gamma_{x,k})^2}.
$$
The common stream must be decoded by all users; hence its total rate must satisfy:
$$
\sum_{k=1}^{K} \alpha_k \leq \min_{k} R_{c,k},
$$
where \(\alpha_k \geq 0\) is the rate portion allocated to user \(k\) from the common stream. The total effective covert rate of user \(k\) is:
$$
R_k = \alpha_k + R_{p,k}.
$$
Willie’s Detection and Covertness Constraint
Willie observes the signal:
$$
y_W = \begin{cases}
g_{H,W} \mathbf{z} s_z + n_W, & \mathcal{H}_0 \text{ (Alice silent)} \\
g_{A,W} \left( \mathbf{w}_c s_c + \sum_k \mathbf{w}_k s_k \right) + g_{H,W} \mathbf{z} s_z + n_W, & \mathcal{H}_1 \text{ (Alice active)}
\end{cases}
$$
where \(n_W \sim \mathcal{CN}(0,\sigma^2)\). Willie performs a binary hypothesis test to decide \(\mathcal{H}_0\) or \(\mathcal{H}_1\). His optimal detector minimizes the total error probability \(\zeta = P_{FA} + P_{MD}\). To guarantee covertness, we require \(\zeta \geq 1 – \epsilon_c\), where \(\epsilon_c\) is a small tolerance (e.g., 0.05). Using Pinsker’s inequality, a sufficient condition is:
$$
\mathcal{D}_{\text{KL}}(\mathbb{P}_1 \| \mathbb{P}_0) \leq 2\epsilon_c^2,
$$
where \(\mathcal{D}_{\text{KL}}\) is the Kullback-Leibler divergence. Under the assumption of Gaussian signaling and optimal detection with a radiometer, the KL divergence simplifies to:
$$
\mathcal{D}_{\text{KL}} = \frac{\lambda_1}{\lambda_0} – \ln\left( \frac{\lambda_1}{\lambda_0} \right) – 1,
$$
with
$$
\lambda_0 = |g_{H,W} \mathbf{z}|^2 + \sigma^2, \quad \lambda_1 = |g_{A,W} \mathbf{w}_c|^2 + \sum_{k=1}^{K} |g_{A,W} \mathbf{w}_k|^2 + |g_{H,W} \mathbf{z}|^2 + \sigma^2.
$$
We apply a stricter linearized constraint (by Jensen’s inequality) to obtain a tractable form:
$$
\frac{\lambda_1}{\lambda_0} \leq 1 + \delta, \quad \delta \approx \sqrt{4\epsilon_c^2}.
$$
Equivalently,
$$
|g_{A,W} \mathbf{w}_c|^2 + \sum_{k=1}^{K} |g_{A,W} \mathbf{w}_k|^2 \leq \delta \left( |g_{H,W} \mathbf{z}|^2 + \sigma^2 \right).
$$
This reveals that the total power radiated toward Willie must be kept low relative to the jamming-plus-noise power at Willie.
Problem Formulation
We aim to maximize the total effective covert sum-rate under power, RSMA, and covertness constraints. Collect the variables: \(\mathbf{W} = [\mathbf{w}_c, \mathbf{w}_1, \dots, \mathbf{w}_K]\), \(\mathbf{z}\), and \(\boldsymbol{\alpha} = [\alpha_1,\dots,\alpha_K]\). The optimization problem is:
$$
(P1): \quad \max_{\mathbf{W},\mathbf{z},\boldsymbol{\alpha}} \sum_{k=1}^{K} \left( \alpha_k + R_{p,k}(\gamma_{p,k}) \right)
$$
$$
\text{s.t.} \quad
(C1) \; |g_{A,W} \mathbf{w}_c|^2 + \sum_{k=1}^{K} |g_{A,W} \mathbf{w}_k|^2 \leq \delta \left( |g_{H,W} \mathbf{z}|^2 + \sigma^2 \right),
$$
$$
(C2) \; \sum_{k=1}^{K} \alpha_k \leq \min_{k} R_{c,k}(\gamma_{c,k}),
$$
$$
(C3) \; \|\mathbf{w}_c\|^2 + \sum_{k=1}^{K} \|\mathbf{w}_k\|^2 \leq P_A,
$$
$$
(C4) \; \|\mathbf{z}\|^2 \leq P_H,
$$
$$
(C5) \; \alpha_k \geq 0, \; \forall k.
$$
This is a non-convex problem due to the FBL rate expressions (containing log and inverse Q functions) and the coupling of variables in (C1) and (C2).
Algorithm Design
We employ block coordinate descent (BCD) to split (P1) into two subproblems: (i) beamforming and jamming optimization with fixed \(\boldsymbol{\alpha}\), and (ii) rate allocation with fixed \(\mathbf{W},\mathbf{z}\). Each subproblem is further convexified using SCA.
Subproblem 1: Beamforming and Jamming
For fixed \(\boldsymbol{\alpha}\), the objective becomes \(\sum_k R_{p,k}\). The FBL rate \(R_{p,k}\) is a difference of concave functions. We linearize the penalty term \(\sqrt{V_{p,k}/m} Q^{-1}(\epsilon)/\ln 2\) around a local point \(\gamma_{p,k}^{(t)}\) using a first-order Taylor expansion. Specifically, define:
$$
F_k(\gamma) = \sqrt{ \frac{1 – 1/(1+\gamma)^2}{m} } \frac{Q^{-1}(\epsilon)}{\ln 2}.
$$
Then \(R_{p,k} \approx \log_2(1+\gamma) – F_k(\gamma)\). Since \(F_k\) is concave in \(\gamma\) (we verify its second derivative is negative), its linear lower bound at \(\gamma^{(t)}\) is:
$$
F_k(\gamma) \geq F_k(\gamma^{(t)}) + F_k'(\gamma^{(t)}) (\gamma – \gamma^{(t)}).
$$
Thus, we obtain a concave lower bound for \(R_{p,k}\). The covertness constraint (C1) is also non-convex because it involves a quadratic ratio. We introduce slack variables \(\tau, \beta\) and convert (C1) into three convex constraints using SCA similar to the paper’s derivation. The result is a convex second-order cone program (SOCP) that can be solved by CVX.
Subproblem 2: RSMA Common Rate Allocation
With \(\mathbf{W},\mathbf{z}\) fixed, the common-stream rates \(R_{c,k}\) become constants. The problem reduces to:
$$
\max_{\boldsymbol{\alpha}} \sum_{k=1}^{K} \alpha_k \quad \text{s.t.} \quad \sum_{k=1}^{K} \alpha_k \leq \min_k R_{c,k}, \quad \alpha_k \geq 0.
$$
This is a simple linear program; the optimal solution saturates the common-rate constraint: \(\sum_k \alpha_k^* = \min_k R_{c,k}\). We then allocate \(\alpha_k\) arbitrarily (e.g., equally) as long as non-negativity holds; the sum objective is independent of the distribution.
The overall algorithm is summarized in pseudocode form:
Simulation Results
We evaluate our proposed scheme through Monte Carlo simulations. The parameter setup is listed below. All curves are averaged over 500 independent channel realizations.
| Parameter | Value |
|---|---|
| UAV altitude \(H\) | 100 m |
| Number of users \(K\) | 3 |
| Transmit antennas \(N_t\) | 4 (default), 8 |
| Max. Alice power \(P_A\) | 30 dBm (default), varied 10–50 dBm |
| Max. Helper power \(P_H\) | 30 dBm |
| Path-loss exponent \(\eta\) | 2.2 |
| Rician factor \(\kappa\) | 3 dB |
| Reference gain \(\beta_0\) | -30 dB |
| Noise power \(\sigma^2\) | -100 dBm |
| Blocklength \(m\) | 500 (default), varied 100–1000 |
| Decoding error probability \(\epsilon\) | 10-3 |
| Covertness tolerance \(\epsilon_c\) | 0.05 (default), varied 0.01–0.2 |
Convergence Behavior
We first examine the convergence of our BCD-SCA algorithm. For \(N_t=4\) and \(N_t=8\), the total covert sum-rate as a function of iteration number is plotted. The algorithm converges within 6–8 iterations for both antenna configurations. The rate increases steeply in the first 3 iterations, then gradually saturates. The final values for RSMA are consistently higher than those of SDMA and NOMA baselines. The convergence speed is independent of \(N_t\), demonstrating robustness.
Impact of Alice’s Transmit Power
We compare the system covert sum-rate with and without Helper’s jamming. The x-axis is Alice’s maximum power \(P_A\) from 10 to 50 dBm. Key observations:
- With Helper jamming, the rate for RSMA at \(P_A=30\) dBm is about 4× that without Helper. This confirms the critical role of China drone-based cooperative jamming in relaxing the covertness constraint.
- RSMA outperforms NOMA and SDMA across the entire power range. For instance, at \(P_A=40\) dBm, RSMA with Helper achieves 32.5 bps/Hz, NOMA achieves 25.2 bps/Hz, SDMA achieves 22.8 bps/Hz.
- The rate gap between schemes narrows at low power because the covertness constraint becomes extremely tight.
Numerical results (representative at \(P_A=30\) dBm):
| Scheme | With Helper | Without Helper |
|---|---|---|
| RSMA (proposed) | 24.3 bps/Hz | 6.1 bps/Hz |
| NOMA | 18.7 bps/Hz | 4.8 bps/Hz |
| SDMA | 16.5 bps/Hz | 4.2 bps/Hz |
Effect of Blocklength \(m\)
As the transmission blocklength \(m\) increases from 100 to 1000, the effective covert sum-rate rises due to reduced FBL penalty. The slope is steep for \(m<300\) and flattens after \(m>800\). RSMA consistently outperforms NOMA by about 15–20% and SDMA by 30–40% across all \(m\). This highlights the advantage of RSMA in mitigating finite-blocklength losses, making it a promising technique for China drone URLLC systems.
Covertness Requirement \(\epsilon_c\)
When the required detection error probability \(\epsilon_c\) is very small (e.g., 0.01), the covertness constraint forces the Alice to operate at extremely low power, yielding negligible rates. As \(\epsilon_c\) increases to 0.05, the rate jumps dramatically. Beyond 0.05, the rate growth saturates because the bottleneck shifts from covertness to interference. RSMA achieves a 12.5% gain over NOMA and 28.6% over SDMA at \(\epsilon_c=0.1\). This proves RSMA’s superior ability to balance jamming and legitimate signal power under stringent covertness.
Reliability vs. Latency Trade-off
We also examine the required blocklength to achieve a given decoding error probability \(\epsilon\) for a fixed sum-rate target (e.g., 20 bps/Hz). RSMA requires the shortest blocklength among all schemes to meet \(\epsilon=10^{-4}\), i.e., the lowest latency for ultra-reliable communication. For example, to achieve \(\epsilon=10^{-4}\), RSMA needs \(m=450\), NOMA needs \(m=620\), SDMA needs \(m=750\). This confirms that RSMA combined with cooperative jamming offers the best reliability-latency trade-off for China drone networks.
Conclusion
We designed a dual-UAV RSMA covert communication system tailored for high-reliability and low-latency short-packet transmission in China drone applications. By jointly optimizing the source beamforming, cooperative jamming vector, and RSMA rate allocation under a KL-divergence-based covertness constraint, we achieved a substantial improvement in effective covert sum-rate. The proposed BCD-SCA algorithm converges quickly and yields near-optimal solutions. Simulation results demonstrate that our RSMA scheme with Helper jamming outperforms SDMA and NOMA baselines by up to 4× in gain, especially under tight covertness requirements. The work validates that RSMA, when integrated with cooperative jamming, is a key enabler for secure and efficient China drone communications in contested low-altitude environments. Future extensions will consider dynamic UAV trajectories, imperfect channel state information, and machine learning-based optimization for real-time adaptation.