In recent years, the rapid growth of mobile devices and the emergence of the Internet of Things (IoT) have imposed stringent requirements on next-generation wireless communication networks, particularly in terms of spectral efficiency, energy efficiency, and connection density. Drone technology, especially Unmanned Aerial Vehicle (UAV) systems, has garnered significant attention due to its ability to provide flexible and reliable Line-of-Sight (LoS) links in various scenarios, such as emergency communications and IoT deployments. UAVs can act as aerial base stations or relays, extending network coverage and enhancing connectivity for ground and aerial users. However, the integration of multiple users in UAV networks introduces challenges related to interference and resource allocation. To address these issues, Non-Orthogonal Multiple Access (NOMA) and Multiple-Input Multiple-Output (MIMO) techniques have been proposed as promising solutions. NOMA allows multiple users to share the same time-frequency resources through superposition coding and successive interference cancellation (SIC), while MIMO leverages spatial diversity and multiplexing gains to improve system capacity. The combination of MIMO and NOMA in UAV relay networks, referred to as MIMO-NOMA, offers a powerful framework for achieving high spectral efficiency and reliable communication in dense user environments.
In this paper, we focus on the outage performance analysis of a multi-user UAV relay network based on MIMO-NOMA. We consider a downlink scenario where a ground base station (BS) communicates with multiple UAV users through an Amplify-and-Forward (AF) UAV relay. The network nodes are equipped with multiple antennas, and users are clustered using a three-dimensional stochastic geometry approach to facilitate NOMA implementation. Our primary contributions include the design of a precoding scheme that mitigates inter-cluster interference and enables efficient SIC within clusters, the derivation of analytical expressions for the outage probability (OP) of paired users, and the asymptotic analysis of OP under high signal-to-noise ratio (SNR) conditions. Furthermore, we validate our theoretical findings through extensive simulations and compare the performance of the proposed scheme with existing MIMO-NOMA transmission strategies.
The system model comprises a BS, a UAV relay, and 2M UAV users distributed in a three-dimensional space. The BS and UAV relay are equipped with Q antennas, while each user has N antennas, satisfying Q > N. The users are modeled using a homogeneous Poisson point process (HPPP) with density λ within a sphere of radius R_D. The UAV relay is positioned at the same height as the origin of the user distribution sphere, and the distances from the BS to the relay and from the relay to the origin are denoted as d_br and d_ro, respectively. User pairing is performed based on large-scale fading differences, with near users located within a distance R_p from the relay and far users beyond R_p. The channel matrices for the BS-to-relay and relay-to-user links follow independent and identically distributed (i.i.d.) Nakagami-m fading, which captures the LoS and Non-LoS (NLoS) components typical in drone technology environments. The path loss model is characterized by a path loss exponent τ, and the large-scale fading is assumed to be identical for all antennas at a given node due to their proximity.
The transmission process occurs in two phases. In the first phase, the BS broadcasts a superposition-coded signal to the UAV relay. The signal vector s is given by:
$$ \mathbf{s} = \begin{bmatrix} \alpha_1 x_1 + \alpha_{1′} x_{1′} \\ \vdots \\ \alpha_M x_M + \alpha_{M’} x_{M’} \end{bmatrix} $$
where E{ss^H} = I, α_m and α_{m’} are the power allocation coefficients for the near and far users in the m-th cluster, satisfying α_m^2 + α_{m’}^2 = 1. The received signal at the relay is:
$$ \mathbf{y}_R = \frac{\sqrt{P_0}}{d_{br}^{\tau/2}} \mathbf{H}_0 \mathbf{P} \mathbf{s} + \mathbf{n}_R $$
where P_0 is the BS transmit power, P is the precoding matrix, H_0 is the Q×Q channel matrix for the BS-to-relay link, and n_R is the additive white Gaussian noise (AWGN) vector with elements n_{R,i} ∼ CN(0, σ_R^2). In the second phase, the relay amplifies and forwards the received signal to the users. The received signal at the m-th user is:
$$ \mathbf{y}_m = \frac{\sqrt{P_1 P_0}}{\mu d_m^{\tau/2} d_{br}^{\tau/2}} \mathbf{V}_m \mathbf{H}_m \mathbf{H}_0 \mathbf{P}_m (\alpha_m x_m + \alpha_{m’} x_{m’}) + \text{inter-cluster interference} + \frac{\sqrt{P_1}}{\mu d_m^{\tau/2}} \mathbf{V}_m \mathbf{H}_m \mathbf{n}_R + \mathbf{V}_m \mathbf{n}_m $$
where P_1 is the relay transmit power, V_m is the detection matrix at the user, H_m is the N×Q channel matrix for the relay-to-user link, and n_m is the AWGN vector at the user with elements n_{m,i} ∼ CN(0, σ_m^2). The power normalization factor μ is defined as:
$$ \mu^2 = \frac{P_0}{d_{br}^{\tau}} \mathbb{E}\{\text{tr}(\mathbf{H}_0 \mathbf{H}_0^H)\} + \sigma_R^2 = \frac{P_0 N Q}{d_{br}^{\tau}} + \sigma_R^2 $$
To mitigate inter-cluster interference and enable SIC within clusters, we design the precoding matrix P and detection matrices V_m and V_{m’} based on signal alignment and zero-forcing principles. The detection matrices are constructed to align the small-scale fading matrices of paired users:
$$ \mathbf{V}_m \mathbf{H}_m \mathbf{H}_0 = \mathbf{V}_{m’} \mathbf{H}_{m’} \mathbf{H}_0 = \mathbf{G}_m $$
where G_m is the aligned channel matrix for the m-th cluster. The precoding matrix P is designed to eliminate inter-cluster interference by projecting the transmit signals onto the null space of the interference channel matrices. Specifically, P is composed of matrices P_m for each cluster, derived from the singular value decomposition (SVD) of the aggregated interference channel matrix. The resulting equivalent channel for each cluster is a set of parallel SISO channels, allowing for efficient SIC implementation.
The outage probability (OP) is a key performance metric, defined as the probability that the instantaneous data rate falls below a target rate. For the far user U_{m’}, the OP is given by:
$$ P_{O}^{m’} = \Pr\left\{ \log_2\left(1 + \frac{C_1 \alpha_{m’}^2 |u_m|^2}{C_1 \alpha_m^2 |u_m|^2 + C_2 + \frac{1}{2} \sigma_{m’}^2 d_{m’}^{\tau}} \right) < R_{m’} \right\} $$
where C_1 = \frac{P_1 P_0}{\mu^2 d_{br}^{\tau}}, C_2 = \frac{P_1 Q}{4\mu^2} \sigma_R^2, and R_{m’} is the target rate for the far user. After algebraic manipulation, the OP can be expressed as:
$$ P_{O}^{m’} = 1 – \frac{1}{\pi} \Gamma\left( \frac{1}{2}, \frac{\gamma_{m’} C_2 + \frac{1}{2} \gamma_{m’} \sigma_{m’}^2 d_{m’}^{\tau}}{2m_1 (C_1 \alpha_{m’}^2 – \gamma_{m’} C_1 \alpha_m^2)} \right) $$
where γ_{m’} = 2^{R_{m’}} – 1, and Γ(·,·) is the upper incomplete Gamma function. For the near user U_m, the OP accounts for the SIC process and is derived as:
$$ P_{O}^{m} = \Pr\left\{ |u_m|^2 < \epsilon_m C_2 + \frac{1}{2} \epsilon_m \sigma_m^2 d_m^{\tau} \right\} $$
where ε_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) and γ_m = 2^{R_m} – 1. The spatial distribution of users is incorporated using three-dimensional stochastic geometry, leading to integral expressions for the OP over the user regions.
Under high SNR conditions, we derive asymptotic expressions for the OP to gain insights into the system’s diversity order. Using first-order Taylor expansion, the asymptotic OP for the far user is approximated as:
$$ P_{\infty}^{m’} \approx \frac{2 \phi_{m’} C_2}{\pi} $$
where φ_{m’} = \frac{\gamma_{m’}}{2m_1 (C_1 \alpha_{m’}^2 – \gamma_{m’} C_1 \alpha_m^2)}. The diversity order, which characterizes the slope of the OP curve at high SNR, is found to be 1 for both near and far users. This result indicates that the proposed scheme sacrifices some diversity gain to reduce the antenna requirements for user clustering, making it suitable for practical drone technology applications.
To validate our theoretical analysis, we conduct Monte Carlo simulations under various channel conditions and system parameters. The simulation parameters are summarized in Table 1.
| Parameter | Value |
|---|---|
| Number of BS/Relay Antennas (Q) | 7 |
| Number of User Antennas (N) | 4 |
| Noise Power (σ²) | -90 dBm |
| User Distribution Radius (R_D) | 500 m |
| User Density (λ) | 10⁻⁶ |
| BS-to-Relay Distance (d_br) | 1200 m |
| Relay-to-Origin Distance (d_ro) | 1000 m |
| Relay Transmit Power (P_1) | 10 dBm |
| Near User Power Allocation (α_m²) | 0.35 |
The results demonstrate that the theoretical OP expressions closely match the simulation results across different Nakagami-m fading parameters (m_1). For instance, when m_1 = 2 and the BS transmit power P_0 = 5 dBm, the near user’s OP is approximately 5 dB lower than that for m_1 = 1, highlighting the impact of channel fading on performance. Additionally, the asymptotic OP curves converge to the simulation results at high SNR, confirming the accuracy of our analysis. The diversity order of 1 is consistent across all scenarios, as predicted.
We further investigate the effect of path loss exponent τ and target rates on the OP. Table 2 presents a comparison of OP for different values of τ and target rates at P_0 = 10 dBm.
| Path Loss Exponent (τ) | Near User Target Rate (R_m) | Far User Target Rate (R_{m’}) | Near User OP | Far User OP |
|---|---|---|---|---|
| 2 | 1 BPCU | 0.5 BPCU | 0.12 | 0.08 |
| 2 | 3 BPCU | 1.5 BPCU | 0.23 | 0.21 |
| 4 | 1 BPCU | 0.5 BPCU | 0.56 | 0.47 |
The data shows that increasing the path loss exponent or target rates significantly degrades the OP, with far users being more sensitive to rate changes. This underscores the importance of careful rate selection and power allocation in drone technology networks.
In terms of system throughput, we define the outage sum rate as R_m (1 – P_O^m) + R_{m’} (1 – P_O^{m’}). Figure 1 illustrates the outage sum rate versus BS transmit power P_0 for different fading parameters and target rates. The results indicate that systems with higher m_1 values achieve higher sum rates due to better channel conditions. Moreover, the sum rate saturates at high SNR as the OP approaches zero, approaching the sum of the target rates. Compared to existing MIMO-NOMA schemes, such as those based on zero-forcing detection, the proposed precoding scheme achieves superior outage sum rate performance, particularly in low to moderate SNR regions. This advantage stems from the effective interference management and the exploitation of spatial degrees of freedom in Unmanned Aerial Vehicle networks.
Another critical aspect is the comparison between NOMA and Orthogonal Multiple Access (OMA) in UAV relay networks. We evaluate the system OP, defined as the product of the near and far user OPs, for both multiple access schemes. The results, summarized in Table 3, reveal that NOMA consistently outperforms OMA across various target rates and transmit powers. For example, at P_0 = -5 dBm and R_m = 2.75 BPCU, the system OP under NOMA is approximately 4.5 dB lower than that under OMA. This demonstrates the superior spectral efficiency of NOMA in leveraging user channel disparities, which is particularly beneficial in drone technology applications where user densities and service demands vary.
| Multiple Access Scheme | Near User Target Rate (R_m) | Far User Target Rate (R_{m’}) | System OP at P_0 = -5 dBm |
|---|---|---|---|
| NOMA | 2.75 BPCU | 1 BPCU | 0.15 |
| OMA | 2.75 BPCU | 1 BPCU | 0.60 |
| NOMA | 1 BPCU | 0.5 BPCU | 0.08 |
| OMA | 1 BPCU | 0.5 BPCU | 0.25 |
The complexity of the proposed precoding scheme is analyzed based on the number of operations required for matrix computations. The overall complexity is dominated by two SVD operations and one matrix inversion, with the worst-case complexity being O(Q³). This is manageable for practical implementations in drone technology, given the typical antenna configurations.
In conclusion, this paper has presented a comprehensive analysis of the outage performance in MIMO-NOMA-based multi-user UAV relay networks. The proposed transmission scheme effectively addresses interference and clustering challenges through innovative precoding and detection matrix design. Theoretical derivations and simulations confirm that the system achieves a diversity order of 1 for both near and far users, with performance gains over existing schemes. The insights gained from this work can guide resource allocation and network optimization in future drone technology deployments, particularly in scenarios requiring high reliability and spectral efficiency. Future research directions include extending the analysis to mobile UAV relays and developing joint optimization frameworks for precoding, power allocation, and user clustering.