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Analytical Channel Models for Millimeter Wave UAV Networks under Hovering Fluctuations
Mohammad Taghi Dabiri, Hossein Safi, Saeedeh Parsaeefard, Walid Saad
TL;DR
Hovering-induced vibrations and orientation fluctuations can misalign directional mmWave antennas and undermine UAV link reliability. The paper derives analytical models for three UAV communication scenarios, validates them against simulations, and finds that the preferable antenna directivity depends on SNR and hovering stability.
Problem
Random hovering vibrations and orientation fluctuations can cause antenna gain mismatch and SNR fluctuations, motivating channel models that capture mmWave propagation and UAV instability.
Method
The paper derives accurate, computationally efficient channel models for U2U, U2U2U, and G2U2G links, including random vibrations, orientation fluctuations, mmWave propagation, and outage probability.
Results
Simulation results corroborate the analytical expressions and show that higher antenna directivity performs better at low SNR, whereas lower directivity is more reliable at high SNR.
Takeaways & Limitations
Reliable hovering-UAV mmWave communication requires optimizing antenna radiation patterns for instability and operating conditions rather than simply increasing directivity gain.
Abstract
from arXiv · showhide
The integration of unmanned aerial vehicles (UAVs) and millimeter wave (mmWave) wireless systems has been recently proposed to provide high data rate aerial links for next generation wireless networks. However, establishing UAV-based mmWave links is quite challenging due to the random fluctuations of hovering UAVs which can induce antenna gain mismatch between transmitter and receiver. To assess the benefit of UAV-based mmWave links, in this paper, tractable, closed-form statistical channel models are derived for three UAV communication scenarios: (i) a direct UAV-to-UAV link, (ii) an aerial relay link in which source, relay, and destination are hovering UAVs, and (iii) a relay link in which a hovering UAV connects a ground source to a ground destination. The accuracy of the derived analytical expressions is corroborated by performing Monte-Carlo simulations. Numerical results are then used to study the effect of antenna directivity gain under different channel conditions for establishing reliable UAV-based mmWave links in terms of achieving minimum outage probability. It is shown that the performance of such links is largely dependent on the random fluctuations of hovering UAVs. Moreover, higher antenna directivity gains achieve better performance at low SNR regime. Nevertheless, at the high SNR regime, lower antenna directivity gains result in a more reliable communication link. The developed results can therefore be applied as a benchmark for finding the optimal antenna directivity gain of UAVs under the different levels of instability without resorting to time-consuming simulations.
I. INTRODUCTION
UAVs can extend next-generation wireless coverage and support high-capacity mmWave links, but hovering fluctuations and directional-beam misalignment complicate reliable communication. Accurate models must jointly capture mmWave propagation, fading, path loss, and UAV orientation effects.
- UAV-enabled networks: UAVs can serve as flying base stations or mobile relay backhaul nodes to enhance heterogeneous-network coverage.Their maneuverability, flexibility, and adaptive altitude adjustment support varied communication scenarios.
- UAV-enabled mmWave: Directional mmWave arrays on small UAVs offer high-capacity links, while line-of-sight propagation remains important for exploiting mmWave frequencies.UAVs can establish air-to-air and air-to-ground links, including in dense urban environments where long terrestrial LoS links are impractical.
- Channel challenges: Hovering fluctuations can misalign directional transceivers, causing antenna gain mismatch, receiver-SNR fluctuations, and degraded link reliability.The mismatch arises from random UAV vibrations and affects the directional transmit pattern.
- Modeling gap: Reliable UAV-based mmWave assessment requires channel models that incorporate path loss, fading, mmWave propagation, and UAV orientation fluctuations.Prior sub-6 GHz channel models do not directly extend to mmWave systems, while some mmWave studies use omnidirectional antennas and omit UAV fluctuation effects.
B. Major Contributions and Novelty
The paper develops analytical channel and outage models for direct and relay-based UAV mmWave links while accounting for random vibrations and orientation fluctuations. Simulations validate the models and show that reliability depends on instability, SNR regime, and antenna directivity, motivating adaptive pattern selection.
- Scope: The paper models three links: direct U2U, aerial-relay U2U2U, and ground-relay G2U2G communications.The G2U2G scenario uses a hovering UAV to connect a ground source and ground destination.
- Analytical models: Closed-form channel and outage expressions are derived for U2U links and for amplify-and-forward U2U2U and G2U2G relays.The relay analysis includes closed-form end-to-end destination SNR expressions.
- Performance findings: Simulation results corroborate the analytical expressions and show that link performance is strongly dependent on hovering-UAV fluctuations.Higher antenna directivity performs better at low SNR, whereas lower directivity is more reliable at high SNR.
- Pattern selection: Optimal antenna directivity is selected under different UAV instability levels by balancing antenna beam width and directivity gain to minimize outage probability.The resulting analytical models provide a benchmark for selecting directivity without time-consuming simulations.
II. SYSTEM MODEL
The system model represents hovering UAV mmWave links with directional antenna arrays, fading, path loss, orientation deviations, and outage capacity. It assumes fixed-position hovering nodes with no Doppler spreading and uses a Nakagami fading model alongside an instantaneous directivity gain.
- A vertical directional pattern uses a uniform linear array of N elements with λ/2 spacing, while the horizontal pattern is approximately constant.
- The instantaneous SINR combines normalized thermal noise, small-scale fading, path loss, and interference terms from Doppler spread and other transmitters.
- Fixed-position hovering UAVs with no relative velocity eliminate Doppler spreading, simplifying the SINR model.
- The directivity gain is modeled as the product of transmitter and receiver actual array gains, Gt(θty) and Gr(θry).
- Small-scale fading is modeled with a Nakagami random variable because this distribution can represent various channel conditions.
- Outage capacity is defined through the CDF of instantaneous SNR relative to the threshold γth = 2Cth −1.
III. CHANNEL DISTRIBUTION FUNCTION
The paper develops channel distributions for direct U2U and aerial-relay links, including U2U2U and G2U2G configurations. These distributions are intended to support end-to-end SNR analysis for hovering-UAV networks.
- The channel-distribution analysis first derives a model for the U2U link, then determines end-to-end SNR for U2U2U and G2U2G relay links.
A. U2U Link
The U2U model approximates directional antenna gain with a sectorized-cosine pattern and derives closed-form SNR distributions for UAV links affected by orientation fluctuations. Its accuracy depends on the sector count M, creating a tradeoff between analytical fidelity and complexity.
- Antenna-gain approximation: The antenna array gain is approximated using only its main lobe, which is reasonable for large antenna-array sizes because the main-lobe peak exceeds the side-lobe peak.The approximation is introduced to derive a tractable PDF for the U2U-link SNR.
- Antenna-gain approximation: The sectorized-cosine model divides the antenna pattern into M sectors, with larger M improving approximation accuracy at the cost of greater complexity.The model uses d = 2.5 because it more accurately approximates the actual array gain than d = 2.
- Analytical channel model: Closed-form expressions are derived for the PDF and CDF of the instantaneous receiver SNR in the considered UAV-based mmWave links.The derivation uses the directivity-gain distribution together with the channel model.
- Analytical channel model: The analytical model supports closed-form derivation of U2U performance metrics, including channel capacity, outage probability, and bit error rate, without time-consuming simulations.The outage probability follows from the CDF of the instantaneous SNR.
- Accuracy-complexity tradeoff: The approximation becomes more accurate as M increases, while M = 20 is reported as a good choice that closely matches simulation results.The selected M must satisfy both a predefined accuracy requirement and a tolerable complexity level.
B. U2U2U Link
The U2U2U relay model analyzes a fixed-gain amplify-and-forward link whose source, relay, and destination are hovering UAVs. It derives end-to-end SNR distributions and a simpler CDF-based outage expression for analytical reliability evaluation.
- System model: The U2U2U scenario uses a single aerial relay with directional receive and transmit antennas aimed toward the source and destination.The relay has separate array gains for its source-facing and destination-facing antennas.
- End-to-end SNR analysis: The analysis derives the PDF of the end-to-end destination SNR for the U2U2U link under the fixed-gain relay scheme.The derivation accounts for source-to-relay and relay-to-destination directivity gains and fading terms.
- System model: A fixed-gain amplify-and-forward protocol relays the source signal without decoding and does not require instantaneous channel-state information to control amplifier gain.Its simplicity makes it suitable for UAV relaying.
- Outage analysis: A simpler closed-form CDF expression enables analytical calculation of U2U2U outage probability without simulations.The outage probability is obtained from the behavior of the end-to-end SNR CDF at low SNR values.
C. G2U2G Link
The G2U2G link models an aerial relay system connecting fixed ground source and destination nodes through a hovering UAV. The derived PDF and CDF of end-to-end SNR enable tractable characterization of key performance metrics.
- G2U2G is a special aerial relay case with ground source and destination nodes.
- The analysis derives PDF and CDF expressions for the destination’s end-to-end SNR.
- Ground nodes are assumed firmly fixed, so their slight vibrations are ignored and their antenna gains are set to N.
- The resulting expressions tractably characterize channel capacity, outage probability, and bit error rate for G2U2G links.
IV. SIMULATION RESULTS AND ANALYSIS
The evaluation uses Monte Carlo simulation to verify the analytical models and assess outage probability under orientation fluctuations. Simulations impose matched fluctuation deviations within each link and equal relay-segment lengths for U2U2U.
- Monte Carlo simulations use over 50 × 10^6 independent runs to verify channel-model expressions and evaluate outage probability.
- The U2U simulations set σty = σry, while U2U2U simulations set σs = σd = σr.
- For U2U2U, the source–relay and relay–destination link lengths are assumed equal.
A. Accuracy of the Derived Channel Models
The analytical models capture SNR distributions for direct and aerial-relay links under orientation deviations. Increasing antenna elements strengthens and narrows the main-lobe gain, widening SNR variation and increasing sensitivity to beam deviations.
- SNR distributions as functions of antenna-element count N are derived for both U2U and U2U2U links.
- Increasing N produces a wider range of receiver SNR values because stronger, narrower main-lobe gain increases sensitivity to beam deviations.
- For sufficiently large sector count M, analytical results exactly match simulations, whereas small M can miss low-SNR values.
- When N is small, the M = 4 analytical model remains reasonable for both links.
B. Performance Analysis and Optimal Pattern Selection
Outage performance depends on SNR, antenna directivity, orientation fluctuations, and angular offset. The results identify an instability- and offset-dependent antenna-element choice that balances beam gain against alignment robustness.
- Higher N improves outage performance at low SNR, whereas lower N provides more reliable U2U communication at high SNR.
- The U2U2U outage analysis offers a perfectly matching analytical approach and a simpler expression with acceptable accuracy.
- Increasing N does not necessarily improve outage performance because higher directivity narrows the main lobe and increases vulnerability to hovering vibrations.
- Increasing σs, σr, and σd from 10 mrad to 30 mrad reduces the optimal N from 16 to 6.
- The optimal N depends on both angular offset and orientation-deviation variance, motivating accurate estimation of UAV positions and antenna boresight directions.
- Large beam width improves robustness under large instantaneous orientation deviations, while angular offset adversely affects system performance.
- Increasing angular offset from 5 to 20 mrad reduces optimal N from 17 to 12 at SNR = 20 dB and from 15 to 11 at SNR = 30 dB.
V. CONCLUSION
The paper develops analytical mmWave channel models for three UAV link types and shows that hovering stability and antenna directivity jointly determine reliability. Its results support selecting antenna directivity gains according to UAV stability without time-consuming simulations.
- The study derives accurate, computationally efficient channel models for U2U, U2U2U, and G2U2G mmWave links.
- Hovering UAV antenna stability considerably affects communication performance, unlike in ground communication links.
- Increasing antenna directivity gain does not necessarily improve performance when UAVs experience hovering fluctuations.
- Optimizing the antenna radiation pattern is important for reliable hovering UAV-based mmWave communication.
- The analytical results enable selection of optimal antenna directivity gains under different UAV stability levels without time-consuming simulations.