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Performance Analysis of HAPS-Assisted Downlink RSMA under Orthogonal and Full Frequency Reuse

Farjam Karim, Prathapasinghe Dharmawansa, Nurul Huda Mahmood, Matti Latva-aho

arXiv:2609.16944v1eess.SP

TL;DR

The paper addresses the uncharacterized outage performance of HAPS-assisted RSMA under realistic propagation conditions and both orthogonal and reuse-based multibeam operation. It derives and validates analytical outage expressions, finding that full frequency reuse has a nonzero outage floor while orthogonal allocation continues to improve with transmit power.

  • Problem

    The outage performance of HAPS-assisted RSMA under orthogonal and full-reuse multibeam operation had not been analytically characterized with realistic HAPS propagation conditions.

    Source: §I · p. 1

  • Method

    The paper derives closed-form outage expressions for orthogonal allocation and approximates aggregate inter-beam interference with a moment-matched Gamma variable for full frequency reuse.

    Source: §I · p. 1

  • Results

    Under full frequency reuse, outage saturates to a nonzero floor, whereas under orthogonal allocation it continues to decrease as transmit power increases over the considered range.

    Source: §IV · p. 5, §V · p. 6

  • Takeaways & Limitations

    In full frequency reuse, increasing transmit power alone cannot overcome the interference-limited outage floor, which depends on the mainlobe-to-sidelobe gain difference.

    Source: §IV · p. 5

Abstract

from arXiv · show

This paper analyzes the outage performance of a high-altitude platform station (HAPS)-assisted downlink employing rate-splitting multiple access (RSMA). A realistic link budget accounting for free-space path loss, rain attenuation, and atmospheric absorption is combined with elevation-angle-dependent shadowed Rician fading. Closed-form outage probability and throughput expressions are derived for orthogonal frequency allocation and full frequency reuse, where the aggregate inter-beam interference is approximated by a moment-matched Gamma random variable, yielding a tractable finite-sum expression via its Laplace transform. The analytical expressions are validated through Monte Carlo simulations, showing close agreement. Numerical results show that the optimal common stream power allocation depends on the transmit power, while inter-beam interference under frequency reuse introduces an outage floor absent under orthogonal allocation, providing practical design insights for HAPS-RSMA systems

I. INTRODUCTION

The paper addresses the uncharacterized outage performance of HAPS-assisted RSMA under orthogonal allocation and full frequency reuse, where realistic propagation and interference conditions both matter. It develops an analytical framework for these operating regimes and models the network and its propagation geometry.

I. INTRODUCTION

  • RSMA splits each user's message into common and private parts, allowing interference to be partly decoded and partly treated as noise.The common stream is decoded by all users, while each private stream is decoded only by its intended recipient.Source: §I · p. 1
  • The outage performance of HAPS-assisted RSMA under interference-free and interference-limited multibeam operation had not been analytically characterized under realistic HAPS propagation conditions.The motivating conditions include free-space path loss, atmospheric absorption, rain attenuation, and elevation-dependent shadowed-Rician fading.Source: §I · p. 1
  • The paper derives closed-form outage expressions for orthogonal allocation and a Gamma-approximation framework for full frequency reuse, then validates the analysis by Monte Carlo simulation.It also uses the framework to quantify the effects of transmit power, RSMA power allocation, carrier frequency, and frequency reuse on outage and throughput.Source: §I · p. 1

A. Network and Geometric Model

  • The network model considers multiple HAPS beams serving multiple RSMA users, with either orthogonal frequency allocation or full frequency reuse.The orthogonal case excludes inter-beam interference; the reuse case accounts for it.Source: A. Network and Geometric Model · p. 2
  • The link budget combines antenna gains with free-space path loss, rain attenuation, and atmospheric absorption, using elevation angle to characterize user geometry.The slant propagation distance is related to platform altitude and user elevation angle.Source: A. Network and Geometric Model · p. 2

B. Small-Scale Fading: shadowed-Rician Model

The HAPS-to-ground link uses shadowed-Rician fading to represent a dominant line-of-sight component subject to random shadowing. The model yields a finite-series representation when the shadowing parameter is a positive integer.

B. Small-Scale Fading: shadowed-Rician Model

  • The HAPS-to-ground link is modeled with shadowed-Rician fading because its dominant line-of-sight component is susceptible to random shadowing.The model is applied to the small-scale fading of each link.Source: B. Small-Scale Fading: shadowed-Rician… · p. 2
  • Smaller positive-integer shadowing parameters correspond to more severe shadowing, while larger values approach conventional Rician fading.The parameter characterizes shadowing of the line-of-sight component.Source: B. Small-Scale Fading: shadowed-Rician… · p. 2
  • With a positive-integer shadowing parameter, Kummer's transformation makes the confluent hypergeometric function terminate as a finite polynomial, yielding a finite-series PDF.The CDF is obtained by integrating that PDF.Source: B. Small-Scale Fading: shadowed-Rician… · pp. 2–3

C. Transmit Signal and SINR Characterization

Within each beam, RSMA superposes one shared common stream and individual private streams, with power allocated between them. Under orthogonal allocation, users decode the common stream before their own private stream, while inter-beam interference is absent.

C. Transmit Signal and SINR Characterization

  • RSMA combines users' common message parts into one shared stream and encodes each user's private part in an individual stream, with power allocated across the streams.All users in the beam can decode the common stream; each private stream is intended for its user.Source: C. Transmit Signal and SINR… · p. 3

1) Case I: Orthogonal Frequency Allocation:

  • Under orthogonal frequency allocation, each beam uses an exclusive frequency resource, eliminating inter-beam interference.The case's received-signal model includes additive white Gaussian noise.Source: 1) Case I: Orthogonal Frequency… · p. 3
  • Users first decode the common stream while treating private streams as interference, then decode their own private stream after subtracting the common stream.The common-stream rate is limited by the user with the lowest common-stream SINR.Source: 1) Case I: Orthogonal Frequency… · p. 3

2) Case II: Full Frequency Reuse:

Under full frequency reuse, all HAPS beams share the same frequency resource, so each user receives its desired beam signal alongside inter-beam interference and noise. The resulting common- and private-stream SINRs characterize this scenario for the performance analysis.

2) Case II: Full Frequency Reuse:

  • With full frequency reuse, each user's received signal includes the desired transmission, inter-beam interference, and additive white Gaussian noise.The interference term represents transmissions from other beams.Source: 2) Case II: Full Frequency Reuse · p. 3
  • The full-reuse model characterizes both common-stream and private-stream SINRs in the presence of inter-beam interference.The common-stream SINR and the post-SIC private-stream SINR are specified for this scenario.Source: 2) Case II: Full Frequency Reuse · p. 3
  • The SINR expressions for both allocation scenarios form the basis of the subsequent performance analysis.The expressions cover common and private streams.Source: 2) Case II: Full Frequency Reuse · p. 3

III. PERFORMANCE ANALYSIS

The section derives outage probability and throughput expressions for HAPS-RSMA under orthogonal frequency allocation and full frequency reuse. For reuse, it averages over aggregate interference using a moment-matched Gamma approximation and its Laplace transform.

III. PERFORMANCE ANALYSIS

  • The analysis treats outage as failure to meet the common- or private-stream decoding thresholds in either frequency-allocation case.The section considers orthogonal allocation and full frequency reuse separately.Source: §III · p. 3
  • For orthogonal allocation, Proposition 1 gives the outage probability, with probability one when the stated parameter conditions fail.The supplied passage states conditions A2 > 0 and A3 > 0, respectively.Source: §III · p. 4
  • For full frequency reuse, aggregate inter-beam interference makes the decoding threshold random, so outage is averaged over its distribution.The derivation approximates the interference by a moment-matched Gamma random variable and uses its Laplace transform to obtain a closed form.Source: §III · p. 4

A. Moments of a Single Interferer

The supplied passage directs the proof to Appendix B but provides no substantive details about the moments of a single interferer.

A. Moments of a Single Interferer

B. Gamma Approximation of the Aggregate Interference

For full frequency reuse, the section approximates aggregate interference with a moment-matched Gamma random variable to derive outage probability.

B. Gamma Approximation of the Aggregate Interference

IV. NUMERICAL RESULTS

The numerical results validate the outage analysis and show that frequency reuse creates a high-power outage floor, while common-stream power allocation produces a user-dependent trade-off.

IV. NUMERICAL RESULTS

  • Higher carrier frequency and rain attenuation degrade outage by reducing net link gain, requiring more transmit power to achieve the same outage.The resulting outage curves shift rightward.Source: §IV · p. 5
  • Analytical curves closely match Monte Carlo simulations for both frequency-allocation scenarios, validating the derived outage expressions.The section presents results for two downlink users, although the expressions apply to N users in both cases.Source: §IV · p. 5
  • Under orthogonal allocation, outage keeps decreasing with transmit power, but full frequency reuse saturates at a non-zero floor because desired signal and interference scale together.At high power, the SINR approaches a power-independent desired-to-interference ratio; the floor is nearly the same at 2 GHz and 5 GHz for the considered sidelobe gains.Source: §IV · p. 5
  • For common-stream power splits at or below 0.5, outage is one; beyond that cutoff, it first decreases and then rises as the private-stream power budget shrinks.The resulting overall outage is non-monotonic because common- and private-stream outage terms compete.Source: §IV · p. 5
  • U2 needs a larger common-stream power split than U1 to reach comparably low outage, so one fixed split cannot equally favor both users.The results motivate fairness-aware or adaptive power-split design.Source: §IV · p. 5

V. CONCLUSION

The paper concludes that HAPS-assisted downlink RSMA can be analyzed under realistic fading and link-budget conditions, with frequency reuse introducing an outage floor absent under orthogonal allocation.

V. CONCLUSION

  • Full frequency reuse produces an outage floor, whereas orthogonal allocation continues to improve with increasing transmit power; the analysis informs power-allocation and frequency-reuse design.The paper reports Monte Carlo validation of its analytical results.Source: §V · p. 6
  • The analysis derives closed-form outage expressions for orthogonal allocation and uses a tractable Gamma approximation for aggregate inter-beam interference under full reuse.The interference approximation supports characterization of the reuse case.Source: §V · p. 6
  • The fading derivation models the channel power as a line-of-sight component plus independent scattering, using conditional moments and total variance to obtain its result.Conditioned on the line-of-sight power, the channel power follows a noncentral chi-squared distribution with two degrees of freedom.Source: §V · p. 6

APPENDIX C Proof. Rearranging Υ(k)

Appendix C averages the shadowed-Rician channel distribution over random interference to obtain an approximated outage expression.

APPENDIX C Proof. Rearranging Υ(k)

  • The random-interference case replaces the fixed threshold with an interference-dependent threshold, provided the feasibility condition holds.The supplied proof passage identifies this condition as ˜A2 > 0.Source: Appendix C · p. 6
  • Because interference is random, outage is obtained by averaging the shadowed-Rician CDF over that interference..Source: Appendix C · p. 6
  • A binomial expansion and the Gamma approximation's interference moment reduce the averaging to a finite-sum expression.The derivation substitutes the moment back into the expansion and outer CDF summation.Source: Appendix C · p. 6
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