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UAV-to-UAV Communications in Cellular Networks

M. Mahdi Azari, Giovanni Geraci, Adrian Garcia-Rodriguez, Sofie Pollin

arXiv:1912.07534v1cs.ITeess.SP

TL;DR

The paper asks how cellular networks should share uplink spectrum between GUEs and direct U2U links. Using an analytical framework with realistic channels, antennas, and power control, it finds overlay preferable in urban scenarios for high GUE UL performance and minimum U2U coverage.

  • Problem

    The paper examines which spectrum-sharing strategy best supports direct UAV-to-UAV communications alongside cellular ground-user uplinks.

  • Method

    The authors analytically evaluate underlay and overlay U2U sharing using realistic channel models, antenna patterns, and power-control policies.

  • Results

    Overlay sharing is preferable in urban scenarios for maximizing GUE uplink performance while guaranteeing a minimum U2U coverage rate of 100 kbps to most UAV pairs.

  • Takeaways & Limitations

    Overlay sharing is the most suitable approach when urban deployments require high GUE uplink performance and a minimum guaranteed rate for most U2U pairs.

Abstract

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We consider a cellular network deployment where UAV-to-UAV (U2U) transmit-receive pairs share the same spectrum with the uplink (UL) of cellular ground users (GUEs). For this setup, we focus on analyzing and comparing the performance of two spectrum sharing mechanisms: (i) underlay, where the same time-frequency resources may be accessed by both UAVs and GUEs, resulting in mutual interference, and (ii)overlay, where the available resources are divided into orthogonal portions for U2U and GUE communications. We evaluate the coverage probability and rate of both link types and their interplay to identify the best spectrum sharing strategy. We do so through an analytical framework that embraces realistic height-dependent channel models, antenna patterns, and practical power control mechanisms. For the underlay, we find that although the presence of U2U direct communications may worsen the uplink performance of GUEs, such effect is limited as base stations receive the power-constrained UAV signals through their antenna sidelobes. In spite of this, our results lead us to conclude that in urban scenarios with a large number of UAV pairs, adopting an overlay spectrum sharing seems the most suitable approach for maintaining a minimum guaranteed rate for UAVs and a high GUE UL performance.

I. INTRODUCTION … Underlay in-band U2U:

The paper analyzes U2U pairs sharing cellular GUE uplink spectrum through underlay and overlay mechanisms, using stochastic-geometry models with realistic height-dependent channels, antennas, and power control. Its results identify conditions governing link coexistence and favor overlay in dense urban deployments when preserving UAV and GUE performance is essential.

  • A. Motivation and Related Work: Cellular-connected UAVs support search-and-rescue, mobile coverage enhancement, and automated logistics, while direct U2U communication enables swarms, collision avoidance, relaying, data transfer, and gathering.These applications motivate studying U2U communications alongside cellular connectivity.
  • B. Methodology and Contribution: The framework compares underlay, where UAVs and GUEs share PRBs and mutually interfere, with overlay, where their PRBs are orthogonally divided.Both U2U links and GUE uplinks are evaluated under the two sharing mechanisms.
  • B. Methodology and Contribution: Stochastic-geometry analysis evaluates how UAV altitude, density, power control, U2U distance, and PRB allocation affect aerial-ground coexistence.The framework accounts for realistic height-dependent propagation and antenna-related characteristics.
  • B. Methodology and Contribution: Exact coverage-probability expressions are derived for all links under both mechanisms, supplemented by tight practical approximations and simulation validation.Coverage probability is defined through the SINR distribution.
  • C. Summary of Results: Underlay U2U transmissions may degrade GUE uplink performance, but base-station sidelobe reception and generally low UAV transmit power limit this loss.Both U2U and GUE uplink performance worsen at higher UAV altitudes because increased LoS raises interference on aerial and ground-related links.
  • C. Summary of Results: Underlay UAV power control creates a tradeoff: increasing UAV transmit power improves U2U performance while worsening GUE uplink performance.Shorter U2U distances can benefit both link types because reduced path loss permits lower UAV transmit power and less interference.
  • C. Summary of Results: In underlay, increasing U2U PRB usage sharply degrades GUE performance unless UAV density and transmit powers are limited, whereas increasing UAV density causes limited UAV-rate degradation when GUE-to-UAV interference dominates.The stated spectrum-allocation takeaway supports overlay when maintaining high GUE uplink performance and a minimum UAV rate.
  • Underlay in-band U2U:: Underlay gives each U2U transmitter random access to ηu · n PRBs with interfering-UAV density ˆλu = ηu · λu, while overlay reserves ηu for U2U and ηg = 1 −ηu for GUE uplinks.Underlay uses frequency hopping; overlay confines interference within each orthogonal portion.

Overlay in-band U2U: … E. Key Performance Indicators

The paper compares overlay and underlay spectrum sharing while modeling height-dependent propagation, realistic BS antenna patterns, fading, power control, coverage, and rate. Overlay removes UAV interference to GUEs but confines each link type to a subset of resources.

  • Overlay in-band U2U:: Overlay lets UAV pairs share the same PRBs, increasing UAV-generated interference, while GUEs receive no UAV interference but access only a subset of PRBs.The overlay divides the spectrum into orthogonal portions for UAV and GUE communications.
  • C. Propagation Channel: Radio links combine path loss, antenna gain, and small-scale fading under large-scale fading ζxy.The model distinguishes propagation across different link types through these channel components.
  • Probability of LoS:: Links may be line-of-sight or non-line-of-sight, with their respective probabilities represented by pLxy and pNxy.LoS and NLoS conditions are denoted by superscripts L and N.
  • Path loss:: Distance-dependent path loss uses 3-D distance, 2-D distance, and height difference, with parameters depending on the communicating node types.The path-loss model includes reference path loss and a node-dependent exponent.
  • Antenna gain:: GUEs and UAVs use unit-gain omnidirectional antennas, whereas BSs use vertical ULAs with realistic sidelobe-aware radiation patterns.The total BS pattern combines element directivity and array-factor effects, and pairwise antenna gain is multiplicative.
  • Small-scale fading:: Small-scale fading follows a general Nakagami-m model, with LoS links typically having larger fading parameters than NLoS links.The fading parameter mxy is a positive integer.
  • D. Power Control: Fractional power control adjusts each node’s per-PRB transmit power according to the receiver, compensating for a fraction of large-scale fading subject to a maximum-power limit.The per-PRB maximum-power allocation is Pmax/nx, and εx controls the compensated fraction.
  • E. Key Performance Indicators: Coverage probability is the SINR CCDF beyond threshold T, while achievable rate is Rx = Bx log2(1 + SINRx) and rate coverage is its CCDF.Bandwidth Bx denotes the bandwidth accessed by node x.

III. EXACT PERFORMANCE ANALYSIS · A. Exact U2U Coverage Probability · B. Exact GUE UL Coverage Probability

The paper develops exact coverage-probability analyses for U2U and GUE uplink links under underlay and overlay spectrum sharing. The framework conditions coverage on link distance and propagation state and characterizes interference through Laplacians.

  • III. EXACT PERFORMANCE ANALYSIS: The exact performance analysis considers a typical BS receiver for U2U performance and a typical UAV receiver for GUE uplink performance, both located at the origin.Random variables and their realizations are denoted by uppercase and lowercase letters, respectively.
  • A. Exact U2U Coverage Probability: Theorem 1 gives the underlay U2U coverage probability.The result is the basis for evaluating U2U coverage when UAVs and GUEs share the same spectrum.
  • A. Exact U2U Coverage Probability: Underlay U2U coverage is conditioned on U2U-link distance and link condition, with aggregate interference represented through its Laplacian.The link condition is LoS or NLoS, and the aggregate interference is caused by interfering UAVs and GUEs.
  • A. Exact U2U Coverage Probability: Overlay U2U coverage follows from Theorem 1 by setting λb = 0 and ˆλu = λu, so UAVs perceive interference only from other UAVs.This specialization removes GUE-generated interference from the U2U coverage calculation.
  • B. Exact GUE UL Coverage Probability: Theorem 2 gives the underlay GUE uplink coverage probability, defined as the CCDF of the uplink SINR in the presence of U2U communications.The result is conditioned on the GUE distance to the typical BS and the LoS or NLoS link condition.
  • B. Exact GUE UL Coverage Probability: The underlay GUE uplink interference is characterized through its Laplacian, with the required expressions and indexing specified in the exact derivation.The formulation includes the index j(x) satisfying x ∈ [rj(x), rj(x)+1] and replaces rj(x) with x in the equation.
  • B. Exact GUE UL Coverage Probability: Overlay GUE coverage is obtained from Theorem 2 by replacing ˆλu = 0.This specialization excludes U2U interferers from the GUE uplink coverage calculation.

IV. APPROXIMATED PERFORMANCE ANALYSIS … C. Approximated GUE UL Coverage Probability

The paper develops compact approximations for coverage probabilities by simplifying fading, interference, and UAV transmit-power modeling. These approximations yield underlay and overlay expressions for both U2U and GUE uplink coverage.

  • IV. APPROXIMATED PERFORMANCE ANALYSIS: Exact coverage expressions may be numerically burdensome, especially because they require derivatives of the interference Laplacian.The proposed section therefore introduces simpler, tight approximations.
  • A. Preliminaries: Approximating Nakagami-m fading enables closed-form interference Laplacians and, consequently, compact coverage-probability expressions.The parameter b_xy is obtained by curve fitting as a function of m_xy.
  • A. Preliminaries: Neglecting NLoS UAV-to-UAV, GUE-to-UAV, and UAV-to-BS interference is justified by the high probability that LoS links dominate interference.This is the second approximation used in the analytical framework.
  • A. Preliminaries: Replacing random UAV transmit power with its mean removes one integral from coverage-probability computation.The approximation is motivated by LoS U2U links and their lower path-loss-exponent-induced power variation.
  • B. Approximated U2U Coverage Probability: Under Approximations 1-3, Corollary 1 provides a compact underlay U2U coverage-probability expression.The derivation accounts for interference contributions associated with LoS UAVs and LoS GUEs.
  • B. Approximated U2U Coverage Probability: The overlay U2U coverage probability follows from Corollary 1 by setting λ_b = 0 and λ̂_u = λ_u.Only UAV-generated aggregate interference remains in the overlay case.
  • C. Approximated GUE UL Coverage Probability: Under Approximations 1-3, Corollary 2 gives the compact underlay GUE uplink coverage probability, while overlay follows by setting λ̂_u = 0.The overlay substitution reflects aggregate interference generated only by GUEs.

V. NUMERICAL RESULTS AND DISCUSSION · A. Preliminaries · B. Analysis Validation and Impact of UAV Height

The numerical study validates the analytical framework and compares U2U and GUE uplink performance under overlay and underlay sharing in an urban scenario. It shows that UAV height and interference materially affect both link types, with U2U links more sensitive to altitude.

  • V. NUMERICAL RESULTS AND DISCUSSION: The study evaluates overlay and underlay U2U–GUE sharing in an urban scenario, varying UAV altitude, density, power control, link distance, and resource utilization.System parameters otherwise follow Table III and 3GPP specifications.
  • A. Preliminaries: The preliminary model assumes all UAVs share a common height hu and models U2U link distance with a truncated Rayleigh distribution.The UAV-distance distribution is parameterized by maximum distance rM and Rayleigh scale σu.
  • A. Preliminaries: LoS probability follows the ITU model with urban parameters {a1, a2, a3} = {0.3, 500, 20}, while NLoS probability is obtained complementarily.These channel assumptions support the subsequent mean UAV transmit-power calculation under practical power control.
  • B. Analysis Validation and Impact of UAV Height: The underlay coverage curves from approximated analysis, exact analysis, and simulations closely match, validating the analysis and its overlay special case.The comparison uses GUE UL and U2U coverage probability with ηu = 1.
  • B. Analysis Validation and Impact of UAV Height: At 50 m, U2U communications reduce median GUE UL performance by less than 3 dB because base stations receive UAV interference through sidelobes and UAVs transmit at low power.The low UAV transmit power is attributed to good U2U channel conditions.
  • B. Analysis Validation and Impact of UAV Height: U2U performance degrades as UAV height increases because UAV-to-UAV and GUE-to-UAV interference both increase with higher LoS probabilities.For GUE-to-UAV interference, the increased LoS probability outweighs the effect of larger GUE–UAV distances.
  • B. Analysis Validation and Impact of UAV Height: GUE UL performance also degrades at higher UAV heights, but less than U2U performance because interference from GUEs in other cells remains dominant.After validation, the study uses the approximated analytical expressions for the remainder of the section.

C. Effect of Power Control and Resource Allocation · D. Coverage Rate Comparison: Underlay vs. Overlay · VI. CONCLUSION

Power control and resource allocation create clear interference tradeoffs between U2U and GUE uplinks. Across coverage-rate comparisons, overlay generally provides the strongest combined guarantee for GUE performance and a 100 kbps U2U rate in urban scenarios.

  • C. Effect of Power Control and Resource Allocation: Increasing εu improves U2U performance at the expense of GUE UL performance, with U2U deficient below 0.4, increasing from 0.4–0.9, and saturating above 0.9.For εu > 0.9, GUE performance stabilizes because almost all aerial devices reach maximum transmit power.
  • C. Effect of Power Control and Resource Allocation: Smaller U2U link distances improve U2U performance for every εu and also benefit GUE UL when εu > 0.4 by reducing UAV transmit power and UAV-to-BS interference.The gains arise from stronger U2U received signals and reduced UAV-to-UAV interference at shorter distances.
  • C. Effect of Power Control and Resource Allocation: Increasing ηu sharply degrades GUE UL performance, except when λu = 1e-6 and εu = 0.6; increasing UAV density or transmit power also reduces GUE SINR.U2U performance remains almost constant with ηu for λu = 1e-6 when UAV-to-UAV interference is limited.
  • D. Coverage Rate Comparison: Underlay vs. Overlay: In overlay, U2U coverage is affected only by UAV-to-UAV interference, so higher UAV density has a more noticeable impact than the UL power-control strategy.In underlay, GUE-generated interference mainly affects U2U coverage, making the degradation from increasing λu from 1e-6 to 5e-6 limited at εu = 0.8 and almost negligible at εu = 0.6.
  • D. Coverage Rate Comparison: Underlay vs. Overlay: Underlay and overlay exhibit a crossover for εu = 0.6 and λu = 5e-6 because interference dominance differs across the worst and best U2U links.Worst underlay links benefit from overlay’s absence of GUE interference, whereas best underlay links can be worse because UAV-to-UAV interference dominates.
  • D. Coverage Rate Comparison: Underlay vs. Overlay: Maintaining high GUE UL rates requires overlay or underlay with εu = 0.6, but εu = 0.6 reduces median U2U rates almost by one order of magnitude.This reduction occurs for both λu = 1e-6 and λu = 5e-6.
  • D. Coverage Rate Comparison: Underlay vs. Overlay: For both λu = 1e-6 and λu = 5e-6, overlay offers the best guaranteed GUE UL performance while generally allowing more UAVs to achieve 100 kbps.The comparison considers underlay and overlay with εu = 0.6 and εu = 0.8.
  • VI. CONCLUSION: The analytical framework evaluates underlayed and overlayed U2U communications using realistic channel, antenna, and power-control models, with exact coverage expressions and tight compact approximations.The conclusions identify overlay as preferable in urban scenarios for maximizing GUE UL performance and guaranteeing 100 kbps U2U coverage to most UAV pairs.

APPENDIX · A. Proof of Theorem 1

The appendix proves Theorem 1 by deriving the U2U coverage probability through fading and interference calculations, then completing a recursive computation of the Laplacian derivative. The derivation uses integration by parts, incomplete gamma and hypergeometric-function identities, and linear dependencies on the transform variable.

  • A. Proof of Theorem 1: The U2U coverage probability is expressed from the small-scale fading CDF and the Laplacian of aggregate interference.The interference terms are characterized by node condition, active-GUE density, and a transform parameter s.
  • A. Proof of Theorem 1: A change of variables is used to evaluate the integral term in the interference calculation.The transformed integral is subsequently evaluated through the expressions developed in the proof.
  • A. Proof of Theorem 1: Integration by parts and the incomplete gamma function reduce the interference integral to a closed expression used in the coverage derivation.The resulting expression is substituted back into the preceding integral relations.
  • A. Proof of Theorem 1: The expectation under Nakagami-m fading is obtained using an integral identity and hypergeometric-function transformations.These steps produce the expectation needed in the coverage-probability expression.
  • A. Proof of Theorem 1: The proof concludes after substituting the derived expressions into the coverage formula and evaluating the relevant terms at P L and P N.The final substitution completes the proof.
  • A. Proof of Theorem 1: The Laplacian’s derivative is computed recursively by applying Leibniz’s formula to the i-th derivative of LIu(su).The proof then exploits the linear dependence of µ and K on su and applies a hypergeometric-function identity.
  • A. Proof of Theorem 1: Substituting the derived hypergeometric expressions into the recursive relations completes the computation of the Laplacian’s derivative.The final step uses equations (64) and (63) in equation (62), yielding equation (61).

C. Proof of Theorem 2

The proof derives the GUE uplink coverage by characterizing interference terms and evaluating the resulting integrals. It then substitutes these intermediate expressions through the Laplacian calculation to obtain the final coverage expression.

  • Coverage derivation: The GUE uplink coverage is expressed through an intermediate derivation involving Ig(sg) and related terms.The derivation follows expressions analogous to (44) and identifies Ig(sg) in (67).
  • Interference characterization: Interference from other GUEs is characterized through Iξ, with LIL ug and LIN ug obtained similarly to (57).This interference characterization supports the subsequent integral reformulation.
  • Proof completion: Substituting (72) into (71) evaluates (70), which yields the interference Laplacian and completes the proof through (68), (67), and (66).The proof proceeds by using (70) in (69), then propagating the result through the preceding coverage expressions.
  • Antenna-gain approximation: The BS antenna gain is approximated as constant within each interval [ri, ri+1], using ggb(r) = ggb(ri).The approximation is considered tight because the interval can be chosen arbitrarily small.

D. Proof of Corollary 1

The proof of Corollary 1 applies Approximation 2, uses Approximation 1 to rewrite the resulting expression, and neglects interference from NLoS links. It then derives I_L^gu by replacing P_u with its mean and substitutes this result into equations (75), (74), and (73).

  • Proof of Corollary 1: Approximation 2 provides the starting expression for C_N.The proof explicitly begins from Approximation 2.
  • Proof of Corollary 1: Approximation 1 is used to rewrite the expression obtained under Approximation 2.This rewrite is part of the derivation preceding the corollary.
  • Proof of Corollary 1: Under Approximation 2, interference generated by NLoS links is neglected.This assumption simplifies the interference expression used in the proof.
  • Proof of Corollary 1: I_L^gu is derived from (57) by replacing P_u with its mean, then substituted into (75), (74), and (73).These substitutions complete the derivation of Corollary 1.

E. Proof of Proposition 1

The proof derives the mean UAV transmit power by expressing it through an integral and evaluating the constituent integrals before substitution into the preceding expressions. Proposition 1 follows from these substitutions.

  • E. Proof of Proposition 1: The mean UAV transmit power is formulated through an integral involving the UAV-distance distribution.The supplied passage introduces the mean transmit power and the integral representation used in the derivation.
  • E. Proof of Proposition 1: The first integral in the derivation is evaluated using the defined variable substitutions.The proof defines yi and related parameters before evaluating the first integral.
  • E. Proof of Proposition 1: The second integral on the right-hand side is evaluated analogously.The passage states that the second integral is obtained in the same manner as the first.
  • E. Proof of Proposition 1: Proposition 1 follows by substituting the evaluated integrals into the preceding expressions for the mean UAV transmit power.The final step substitutes (82) and (83) into (77), and then into (76).
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