This paper explores the integration of Multiple-Input Multiple-Output (MIMO) and Non-Orthogonal Multiple Access (NOMA) technologies in Unmanned Aerial Vehicle (UAV) relay networks. The proposed system employs a UAV relay with \(Q\) antennas serving \(2M\) drone users equipped with \(N\) antennas (\(Q > N\)) in a downlink scenario. Users are spatially distributed in a 3D sphere \(\mathcal{D}^3\) of radius \(R_D\) following a Homogeneous Poisson Point Process (HPPP) with density \(\lambda\). The UAV relay operates under Amplify-and-Forward (AF) protocol to enhance spectral efficiency, addressing interference challenges through optimized precoding and clustering strategies.
The channel model incorporates Nakagami-\(m\) fading for small-scale variations, where channel gain \(|h|^2\) follows the probability density function (PDF):
$$f_{|h|^2}(x) = \frac{m_1^{m_1} x^{m_1-1}}{\Omega^{m_1} \Gamma(m_1)} \exp\left(-\frac{m_1 x}{\Omega}\right)$$
Here, \(m_1\) denotes the fading severity parameter, \(\Omega = \mathbb{E}\{|h|^2\}\) represents average channel gain, and \(\Gamma(\cdot)\) is the gamma function. Large-scale path loss is modeled as \(l_e(d) = d^{-\tau/2}\) for \(e \in \{\text{br}, m\}\), where \(\tau\) is the path-loss exponent.
Transmission occurs in two phases:
- BS to UAV Relay: The base station broadcasts signals using precoding matrix \(\mathbf{P}\):
$$\mathbf{y}_R = \frac{\sqrt{P_0}}{d_{\text{br}}^\tau \mathbf{H}_0 \mathbf{P} \mathbf{s} + \mathbf{n}_R$$
where \(\mathbf{s} = [\alpha_1 x_1 + \alpha_1′ x_1′, \dots, \alpha_M x_M + \alpha_M’ x_M’]^T\) is the superposition-coded signal vector, and \(\mathbf{n}_R \sim \mathcal{CN}(0, \sigma_R^2)\). - UAV Relay to Users: The relay amplifies and forwards signals:
$$\mathbf{y}_m = \frac{\sqrt{P_1 P_0}}{\mu d_m^\tau d_{\text{br}}^\tau \mathbf{V}_m \mathbf{H}_m \mathbf{H}_0 \mathbf{P} \mathbf{s} + \frac{\sqrt{P_1}}{\mu d_m^\tau} \mathbf{V}_m \mathbf{H}_m \mathbf{n}_R + \mathbf{V}_m \mathbf{n}_m$$
where \(\mu^2 = \frac{P_0}{d_{\text{br}}^\tau NQ + \sigma_R^2\) normalizes transmit power. Detection matrices \(\mathbf{V}_m\) align channel matrices to satisfy \(\mathbf{V}_m \mathbf{H}_m \mathbf{H}_0 = \mathbf{V}_{m’} \mathbf{H}_{m’} \mathbf{H}_0 = \mathbf{G}_m\), enabling interference suppression.
Precoding design eliminates inter-cluster interference. For the \(m\)-th cluster, \(\mathbf{P}_m = \mathbf{\widetilde{W}}_m \mathbf{\widehat{G}}_m^{-1}\), where \(\mathbf{\widetilde{W}}_m\) is derived from the null space of the inter-cluster channel matrix \(\mathbf{\widetilde{G}}_m = [\mathbf{G}_1^H, \dots, \mathbf{G}_{m-1}^H, \mathbf{G}_{m+1}^H, \dots, \mathbf{G}_M^H]^H\). This reduces the equivalent channel to \(K = 2N – Q\) SISO links:
$$|\mathbf{u}_m|^2 = \frac{1}{\text{tr}\left(\mathbf{P}_m \mathbf{P}_m^H\right)}$$
The signal-to-interference-plus-noise ratio (SINR) for near user \(U_m\) and far user \(U_{m’}\) after SIC are:
$$\text{SINR}_{m’ \to m’,k} = \frac{C_1 \alpha_{m’}^2 |\mathbf{u}_m|^2}{C_1 \alpha_m^2 |\mathbf{u}_m|^2 + C_2 + \frac{1}{2} \sigma_{m’}^2 d_{m’}^\tau}, \quad \text{SINR}_{m \to m,k} = \frac{C_1 \alpha_m^2 |\mathbf{u}_m|^2}{C_2 + \frac{1}{2} \sigma_m^2 d_m^\tau}$$
where \(C_1 = \frac{P_1 P_0}{\mu^2 d_{\text{br}}^\tau}\) and \(C_2 = \frac{P_1 Q}{4\mu^2} \sigma_R^2\).
Outage probability (OP) analysis leverages stochastic geometry. The cumulative distribution function (CDF) of \(\sum_{q=1}^Q X_q\) is:
$$F_{\sum X_q}(y) = \frac{1}{\pi} \Gamma\left(\frac{1}{2}, \frac{1}{2m_1 y}\right)$$
Far user \(U_{m’}\) OP is derived as:
$$P_{m’}^O = 1 – \frac{1}{V_2 \pi} \int_0^{2\pi} \int_{-\alpha}^{\alpha} \int_{R_p}^{l_1} \Gamma\left(\frac{1}{2}, \phi_{m’} C_2 + \frac{1}{2} \phi_{m’} \sigma_{m’}^2 r^\tau \right) r^2 \sin \phi d\theta d\phi dr$$
where \(\phi_{m’} = \frac{\gamma_{m’}}{2m_1 (C_1 \alpha_{m’}^2 – \gamma_{m’} C_1 \alpha_m^2)}\), \(\gamma_{m’} = 2^{R_{m’}} – 1\), and \(V_2\) is the volume of region \(\mathcal{D}_2^3\). Near user \(U_m\) OP is:
$$P_m^O = 1 – \frac{1}{V_1 \pi} \int_0^{2\pi} \int_{-\alpha}^{\alpha} \int_{l_2}^{R_p} \Gamma\left(\frac{1}{2}, \frac{1}{2m_1} \left( \epsilon_m C_2 + \frac{1}{2} \epsilon_m \sigma_m^2 r^\tau \right) \right) r^2 \sin \phi d\theta d\phi dr$$
with \(\epsilon_m = \max\left( \frac{\gamma_{m’}}{C_1 \alpha_{m’}^2 – \gamma_{m’} C_1 \alpha_m^2}, \frac{\gamma_m}{C_1 \alpha_m^2} \right)\).
Asymptotic OP at high SNR (\(\rho = P_0 / \sigma_m^2 \to \infty\)) reveals diversity order:
$$P_{m’}^\infty = \frac{2 \phi_{m’} C_2}{\pi}, \quad P_m^\infty = \frac{\epsilon_m C_2}{m_1 \pi}$$
Both users achieve unity diversity gain (\(D_{m’} = D_m = 1\)), confirming robustness in diverse drone communication environments.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| BS/UR Antennas (\(Q\)) | 7 | User Antennas (\(N\)) | 4 |
| Noise Power (\(\sigma^2\)) | -90 dBm | Distribution Radius (\(R_D\)) | 500 m |
| BS-UR Distance (\(d_{\text{br}})) | 1200 m | UR-Origin Distance (\(d_{\text{ro}})) | 1000 m |
| Near User Power (\(\alpha_m^2\)) | 0.35 | UR Transmit Power (\(P_1\)) | 10 dBm |
Simulations validate theoretical models. Key observations include:
- OP decreases with higher \(m_1\): At \(P_0 = 5\) dBm, OP for \(m_1 = 3\) is 5 dB lower than \(m_1 = 2\).
- Far users exhibit greater sensitivity to target rate \(R_{m’}\): A 3x increase in \(R_{m’}\) raises OP by 13 dB at \(P_0 = 10\) dBm and \(\tau = 2\).
- Path loss exponent \(\tau\) dominates performance: Increasing \(\tau\) from 2 to 4 degrades OP by 44 dB for near users.
NOMA-enhanced drone networks achieve 4.5 dB lower OP than OMA at \(P_0 = -5\) dBm and \(R_m = 2.75\) bps/Hz, demonstrating superior spectral efficiency for UAV applications.
This work establishes a framework for optimizing MIMO-NOMA in UAV relay networks. Future research will address mobile relays and joint resource allocation to further advance drone technology in 6G non-terrestrial networks.