Outage Probability Analysis of NOMA Enabled Hierarchical UAV Networks with Non-Linear Energy Harvesting

1. Problem Statement

Uncrewed Aerial Vehicles (UAVs) are critical for 6G networks due to their mobility and ability to cover remote areas. However, their deployment faces two major challenges:

• Energy Scarcity: UAVs have limited battery capacity, and the energy demands of flight and communication restrict mission duration.
• Realistic System Constraints: Existing literature often assumes ideal conditions, such as linear energy harvesting (EH) circuits and perfect hardware. In reality, EH circuits exhibit non-linear characteristics (saturation effects), and transceivers suffer from Hardware Impairments (HWI) like phase noise and amplifier distortion.

Furthermore, most studies focus on single-UAV or flat multi-UAV systems. There is a lack of research on hierarchical UAV networks that integrate Non-Orthogonal Multiple Access (NOMA) for spectral efficiency, non-linear EH for sustainable power, and HWI for realistic performance evaluation.

2. Methodology and System Model

The authors propose a hierarchical ad hoc UAV network designed to serve ground Internet of Things (IoT) devices. The system architecture and operational protocol are defined as follows:

• Network Architecture:
  • Cluster Head UAV (CHU): Acts as the source and coordinator, hovering at a fixed location. It is powered by solar cells.
  • Cluster Member UAVs (CMUs): Act as relays. They harvest energy from a terrestrial Power Beacon (PB) and forward data to ground IoT devices.
  • Ground Nodes: IoT devices and a Power Beacon (PB).
• Communication Protocol (Time Switching - TS):
  1. Energy Harvesting Phase ($\rho T$): CMUs harvest RF energy from the PB.
  2. Source Transmission Phase ($(1-\rho)T/2$): The CHU transmits superimposed NOMA signals to the CMUs.
  3. Relay Transmission Phase ($(1-\rho)T/2$): CMUs use harvested energy to decode and forward signals to ground IoT devices using Decode-and-Forward (DF) relaying.
• Key Modeling Assumptions:
  • Channel Model: Nakagami-$m$ fading. Air-to-Air (A2A) links are Line-of-Sight (LoS); Air-to-Ground (A2G) links are mixed LoS/Non-LoS.
  • Non-Linear EH: The paper utilizes a practical non-linear EH model where harvested energy saturates beyond a threshold ($P_{th}$), rather than assuming a linear relationship.
  • Hardware Impairments (HWI): Distortion noises at transmitters and receivers are modeled as additive Gaussian noise dependent on transmit power and impairment levels ($k^2$).
  • NOMA: Successive Interference Cancellation (SIC) is employed at both CMUs and ground devices.

3. Key Contributions

The paper makes three primary theoretical and analytical contributions:

1. Joint System Design: It proposes a novel framework integrating NOMA, non-linear EH, and HWI within a hierarchical UAV network, offering a more practical evaluation than previous linear/ideal models.
2. Analytical Derivation of Outage Probability: The authors derive closed-form analytical expressions for:
   • The outage probability of individual ground IoT devices.
   • The outage probability of a single CMU (CMU outage).
   • The overall system outage probability for the entire hierarchical network.
   • These derivations account for the complex interactions between non-linear saturation, HWI, and Nakagami-$m$ fading.
3. Benchmarking and Validation: The proposed system is compared against a non-EH system and validated through Monte Carlo simulations, demonstrating the superiority of the proposed approach.

4. Key Results and Findings

The numerical results, based on the derived analytical expressions, reveal several critical insights:

• Performance Gain of EH: The proposed NOMA system with Energy Harvesting significantly outperforms systems without EH. The study estimates a performance gain of 8–12 dB in terms of outage probability.
• Impact of Non-Linear Saturation:
  • As transmit power increases, outage probability decreases initially but eventually hits an "outage floor."
  • This floor is caused by the saturation threshold ($P_{th}$) of the non-linear EH circuit; beyond this point, increasing input power does not increase harvested energy, limiting further performance gains.
• Effect of Hardware Impairments (HWI):
  • The presence of HWI ($K > 0$) causes a noticeable degradation in system reliability compared to ideal hardware.
  • Higher saturation thresholds ($P_{th}$) help mitigate the negative impact of HWI by allowing more effective utilization of harvested energy.
• Role of Fading Parameters ($m$):
  • Increasing the Nakagami-$m$ shape parameter (indicating less severe fading) improves diversity gain and steepens the outage probability curves, leading to better reliability.
• Trade-off in Network Size:
  • Increasing the number of CMUs ($L$) improves coverage but paradoxically increases the overall outage probability.
  • This is because the system fails if any single CMU link fails; adding more relays increases the statistical probability of at least one link encountering unfavorable channel conditions.

5. Significance

This work is significant for the advancement of 6G and sustainable UAV communications because:

• Realism: It moves beyond idealized assumptions by incorporating non-linear energy harvesting and hardware impairments, providing a framework that aligns closer to physical hardware limitations.
• Sustainability: It demonstrates how hierarchical UAV networks can achieve self-sustainability through RF energy harvesting, extending mission lifetimes without relying solely on batteries.
• Design Guidelines: The findings offer practical guidelines for network planners, such as the optimal number of relay UAVs to avoid diminishing returns and the importance of selecting appropriate saturation thresholds for EH circuits to balance power efficiency and hardware constraints.

In conclusion, the paper establishes that while NOMA and EH significantly enhance UAV network performance, the non-linear nature of energy harvesting and hardware imperfections must be carefully managed to avoid performance ceilings and reliability degradation.