Communication and Sensing Coverage of UAV Corridor under Beam Misalignment Error

I. Introduction

• Aerial corridors constrain UAV mobility into predefined routes or volumes, addressing collision risk and traffic management while concentrating wireless coverage in specific aerial regions.The passage motivates corridor-assisted networks as a response to the management challenges of denser UAV traffic.Source: §I · p. 1
• Prior aerial JCAS work considers mobility, tracking, resource allocation, and beam management, while antenna misalignment remains a critical impairment for narrow directional links.The paper notes that prior studies typically use simplified beams or non-standard antenna assumptions.Source: §I · pp. 1–2
• The framework combines a finite cylindrical UAV corridor, probabilistic LoS/NLoS propagation, a realistic 3D 3GPP BS antenna, and correlated 3D beam-misalignment errors.It characterizes JCAS coverage under communication and clutter interference.Source: §I · p. 2

A. Spatial and Network Modeling

• A fixed number of UAV-UEs are independently and uniformly distributed in a finite 3D cylindrical corridor, forming a 3D binomial point process around a terrestrial BS.The corridor is centered at height h above the ground, with axial extent L and radius R.Source: A. Spatial and Network Modeling · p. 2
• The BS uses radar sensing to track a UAV-UE while that tracked UAV-UE communicates with the BS.Sensing and communication use different time-frequency resources.Source: A. Spatial and Network Modeling · p. 2

B. Antenna and Misalignment Error Modeling

• The terrestrial BS steers a directive beam toward the tracked UAV-UE using a 3GPP-based pattern with angle-dependent antenna gain.The pattern specifies vertical and horizontal radiation power patterns and a 3D antenna pattern.Source: B. Antenna and Misalignment Error… · p. 2
• The 3D beamsteering errors are modeled as a multivariate Gaussian with covariance describing the elevation and azimuth errors.Their standard deviations are set as fractions of the corresponding 3 dB beamwidths, using scaling constant c.Source: B. Antenna and Misalignment Error… · p. 3
• The covariance model includes correlation between elevation and azimuth angle errors.The correlation is represented by ρ.Source: B. Antenna and Misalignment Error… · p. 3

C. Blockage and Channel Models

• The model assigns a probabilistic LoS/NLoS state to each UAV-UE link using a modified sigmoid approximation for LoS probability.The cited environment parameters cover suburban, urban, and dense urban scenarios.Source: C. Blockage and Channel Models · p. 3
• LoS and NLoS links use different path-loss exponents, with path loss specified by a link-type-dependent law.The NLoS probability is defined as one minus the LoS probability.Source: C. Blockage and Channel Models · p. 3
• Channel amplitudes follow Nakagami distributions, so channel power gains are modeled as Gamma random variables.The shape parameter is m_t and the scale is 1/m_t, with integer m_t values assumed for analytical tractability.Source: C. Blockage and Channel Models · p. 3

D. Association Policy and SIR Definition

• The BS selects a UAV-UE for continuous tracking and fine trajectory adjustment; the remaining UAV-UEs model clutter and uplink interference.The tracked UAV-UE is denoted w0, and the others form the non-tracked set.Source: 1) UAV-UE Association Policy · p. 3

1) UAV-UE Association Policy:

• The BS measures the tracked UAV-UE’s echo, while the other N −1 UAV-UEs contribute clutter to the sensing SIR.The sensing SIR is expressed following the standard radar equation.Source: 2) Communication and Sensing SIR… · p. 3

2) Communication and Sensing SIR Definition:

• Under the Swerling I model, UAV-UE radar cross-sections are exponential random variables; the tracked UAV-UE communicates uplink while the other active UAV-UEs produce interference.The communication model treats interference from all remaining active UAV-UEs as a worst-case scenario.Source: 2) Communication and Sensing SIR… · p. 3

• JCAS CP is the probability that communication and sensing SIRs are simultaneously above their respective thresholds.Source: §III · p. 3
• The communication threshold represents the requirement for successful communication at the BS.Source: §III · p. 3
• The sensing threshold represents the requirement for successful tracking at the BS.Source: §III · p. 3

A. Sensing Coverage Probability

• Communication-phase interferers use an independent BPP; modeling dependent locations would couple aggregate interference terms and falls beyond this work’s scope.Source: A. Sensing Coverage Probability · p. 3
• UAV-UE locations are independently and uniformly distributed within the finite cylindrical corridor.Source: A. Sensing Coverage Probability · p. 4
• The aggregate clutter interference is characterized by a conditional Laplace transform given the tracked UAV’s location and misalignment error.Source: A. Sensing Coverage Probability · p. 4
• The conditional sensing CP is characterized using the tracked UAV’s location and beam-misalignment error.Source: A. Sensing Coverage Probability · p. 4

B. Communication Coverage Probability

• The tracked UAV-UE communicates uplink to the BS while the other N −1 UAV-UEs interfere.Source: B. Communication Coverage Probability · p. 4
• A conditional Laplace transform characterizes the aggregate communication interference given the tracked UAV’s location and misalignment error.Source: B. Communication Coverage Probability · p. 4
• The conditional communication CP is derived for the terrestrial BS given the tracked UAV’s location, misalignment error, and propagation state.Source: B. Communication Coverage Probability · p. 4

C. JCAS Coverage Probability

• The overall JCAS CP is derived by jointly deconditioning the sensing and communication coverage factors.Source: C. JCAS Coverage Probability · p. 4
• The theorem gives the JCAS CP for a terrestrial BS in a UAV corridor-assisted network.Source: C. JCAS Coverage Probability · p. 4
• The theorem’s proof is provided in Appendix B.Source: C. JCAS Coverage Probability · p. 4

IV. Numerical Results & Discussions

• Unless otherwise stated, the numerical evaluation uses L = 100 meters, R = 5 meters, N = 10, and h = 100 meters.The stated antenna beamwidths are (45°, 45°), with Gmax = 8 dBi, SLA = 30 dB, and σ = 0.7 m².Source: §IV · p. 4
• JCAS CP falls as corridor length increases, then stabilizes only at higher UAV deployment heights; 4.5° misalignment is tolerant, while 9° substantially reduces performance.The reported mechanism at sufficiently high altitude is that the LoS advantage and spread of interferers compensate for added pathloss.Source: Figure 2 · p. 5, §IV · p. 5
• Narrower beams suppress interference more effectively but are more sensitive to pointing errors; wider beams resist misalignment but are more susceptible to interference.For wider beams, angular deviation up to 2.25° hardly affects JCAS performance; the optimal UAV height increases with corridor length.Source: Figure 3 · p. 5, §IV · p. 5
• JCAS performance varies more strongly with corridor length than radius, and its reported optimal (L, R) pair uses the smallest corridor length.The passage attributes the difference to L controlling axial UAV spread, desired-link pathloss, and LoS probability, while R controls spread around corridor height.Source: Figure 4 · p. 5, §IV · p. 5

V. Conclusion

• The proposed framework uses a 3D BPP for UAV-UE swarms in corridor-enabled networks and studies JCAS coverage with a terrestrial BS equipped with a 3D 3GPP antenna.The analysis models 3D beam misalignment with a multivariate normal distribution.Source: §V · p. 5
• At higher deployment heights, JCAS performance decreases as corridor length increases, then eventually stabilizes.Source: §V · p. 6
• Narrower beams reduce interference more effectively but are more sensitive to pointing errors.Source: §V · p. 6

Appendix A Proof of Lemma 2

• The conditional Laplace transform of sensing interference is formed using the fading moment-generating function, averaging over interfering UAV-UE RCS values, and conditioning on their LoS/NLoS states.Source: Appendix A · p. 6
• The Lemma 2 expression is completed by deconditioning over LoS/NLoS states and averaging over the 3D locations of interfering UAV-UEs.Source: Appendix A · p. 6

Appendix B Proof of Theorem 1

• Theorem 1 follows by factoring the conditional joint event into independent sensing and communication interference terms, inserting Propositions 1 and 2, and averaging over w0 and ϵ.Source: Appendix B · p. 6