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Interference Management in Reverse TDD HAPS-Ground Networks: A Large System Analysis

Shasha Liu, Abla Kammoun, Mohamed-Slim Alouini

arXiv:2609.39752v1eess.SP

TL;DR

Strong HAPS line-of-sight links can cause severe cross-tier interference when HAPS and terrestrial networks share spectrum, and tractable analysis for large integrated systems is limited. The paper proposes an RTDD framework and an RMT-based analysis using an analytical Kronecker channel model. Numerical results report close agreement with Monte Carlo simulations and near interference-free performance under RTDD.

  • Problem

    Strong HAPS LoS propagation creates severe cross-tier interference under spectrum sharing, while tractable analysis for large integrated HAPS–terrestrial networks is lacking.

    Source: §I · pp. 1–2

  • Method

    The paper combines opposite-direction RTDD operation with a Kronecker approximation of empirical terrestrial channels and RMT-based deterministic SINR analysis.

    Source: §I · p. 2

  • Results

    Numerical results show excellent agreement between deterministic approximations and Monte Carlo simulations, while RTDD suppresses cross-tier interference and achieves near interference-free performance.

    Source: §I · p. 2, §VI · p. 12

  • Takeaways & Limitations

    The authors present RTDD as a promising low-complexity approach that preserves TDD channel reciprocity for integrated HAPS–terrestrial networks.

    Source: §VI · p. 12

Abstract

from arXiv · show

High-altitude platform stations (HAPSs) are expected to coexist with terrestrial networks (TNs) to provide seamless wide-area wireless connectivity in future sixth-generation (6G) systems. However, the strong line-of-sight (LoS) propagation of HAPS links introduces severe cross-tier interference under spectrum sharing. This paper proposes a reverse time division duplexing (RTDD)-based transmission framework for integrated HAPS--TN systems, where the HAPS and terrestrial base station (BS) operate in opposite transmission directions to mitigate cross-tier interference while preserving TDD channel reciprocity. Standardized 3GPP channel models are adopted for both HAPS and terrestrial links. To enable tractable performance analysis, an analytical Kronecker channel model is developed to approximate the empirical 3GPP terrestrial BS channel, based on which a random matrix theory (RMT)-based large-system analysis is established to derive deterministic approximations for the uplink and downlink signal-to-interference-plus-noise ratios (SINRs). Numerical results demonstrate an excellent agreement between the proposed analysis and Monte Carlo simulations. Moreover, the proposed RTDD framework effectively suppresses cross-tier interference, achieves near interference-free performance.

I. Introduction

The paper targets cross-tier interference in shared-spectrum HAPS–terrestrial networks and proposes RTDD, with the two tiers transmitting in opposite directions. It also develops channel models and an analytical framework for evaluating the system.

I. Introduction

  • RTDD is proposed for integrated HAPS–terrestrial networks to mitigate cross-tier interference while preserving TDD channel reciprocity.The paper identifies strong HAPS LoS as a source of interference and tractable performance analysis as a gap.Source: §I · pp. 1–2

II. System Model

  • The modeled network has one HAPS serving HUEs and one terrestrial BS serving BUEs, with the HUEs outside the BS coverage region.The HAPS has M antennas and the BS has N antennas; both serve single-antenna users.Source: §II · p. 2

A. Transmission Protocol

  • The co-channel RTDD protocol reverses HAPS and BS transmission directions across two intervals, using HAPS null-space precoding in one interval and BS antenna down-tilt in the other.These mechanisms address HAPS-to-BS interference and limit BS-to-HAPS interference, respectively.Source: A. Transmission Protocol · pp. 2–3

B. Channel Model

  • HAPS–UE links are modeled with dominant LoS, while BS–UE links use Rician fading; a correlation-matched Kronecker model approximates empirical 3GPP terrestrial channels for analysis.The NLoS component also uses the standardized 3GPP channel model.Source: 1) HAPS-to-UE Channels · p. 3, 2) BS-to-UE Channels · pp. 3–4

III. Large System Analysis for RTDD

The analysis treats HAPS links with closed-form SINRs and terrestrial Rician links with random SINRs, using the Kronecker channel model for RMT-based analysis. For the first transmission interval, it derives deterministic large-system results for HAPS downlink and BS uplink performance.

III. Large System Analysis for RTDD

  • The framework analyzes the two transmission intervals separately, with closed-form SINRs for deterministic-LoS HAPS links and random SINRs for terrestrial Rician links.Unless otherwise specified, RMT analysis uses the Kronecker channel model.Source: §III · p. 4

A. Analysis for Transmission Interval T1

  • In T1, HAPS downlink ZF sacrifices one spatial degree of freedom to null interference toward the BS over the rank-one LoS HAPS–BS channel.The BS uses an MMSE receiver for its uplink; the HAPS nulling eliminates HAPS-to-BS cross-tier interference.Source: 1) HAPS Downlink · pp. 4–5
  • For T1 BS uplink, RMT turns an MMSE SINR quadratic form into a deterministic large-system quantity defined through fixed-point equations.The analysis introduces technical assumptions to control aggregate interference as the number of users grows; the stated scaling is an analytical convenience, not a physical requirement.Source: 1) HAPS Downlink · pp. 4–6

B. Analysis for Transmission Interval T2

In transmission interval T2, the HAPS receives uplink signals while the terrestrial BS serves BUEs downlink. The section analyzes these links separately, including a conditional large-system approximation for the BS downlink SINR.

B. Analysis for Transmission Interval T2

  • In T2, the HAPS receives HUE uplink signals while the terrestrial BS transmits downlink to BUEs.The links are analyzed separately because the HAPS and BS use different transmission and reception strategies.Source: B. Analysis for Transmission Interval T2 · p. 6
  • BS downlink interference to the HAPS is treated as negligible because of the BS antenna pattern and the large propagation distance.The HAPS uplink uses an MMSE receiver; for deterministic LoS HAPS channels, its SINRs can be computed directly without random matrix theory.Source: 1) HAPS Uplink · p. 6
  • BS downlink ZF eliminates intra-cell interference among BUEs, and the section defines its SINR using the BS channel and precoding vectors.The ZF precoder requires channel-Gram-matrix inversion.Source: 1) HAPS Uplink · p. 6
  • Under stated assumptions, the BUE downlink SINR satisfies a deterministic equivalent characterized by fixed-point equations.The analysis uses a Kronecker channel representation that preserves the 3GPP channel's spatial correlation; the ZF inversion assumptions require more transmit antennas than users and sufficiently many covariance eigenvalues bounded away from zero.Source: 1) HAPS Uplink · pp. 6–7

IV. TDD Scheme

Conventional TDD is used as a numerical benchmark for the proposed reverse-TDD scheme. The tiers share time-frequency resources and transmit or receive in the same direction.

IV. TDD Scheme

  • Conventional TDD serves as a benchmark for assessing the proposed reverse-TDD operation, with no separate theoretical analysis developed for it.Its performance is evaluated numerically in the next section.Source: §IV · p. 7
  • The HAPS and terrestrial BS operate in the same direction over the same time-frequency resources in conventional TDD.Both tiers transmit simultaneously in downlink and receive simultaneously in uplink.Source: §IV · p. 7
  • Simultaneous tier operation in conventional TDD results in cross-tier interference between the HAPS and terrestrial networks.Source: §IV · p. 7

A. Downlink Transmission

The downlink section describes simultaneous HAPS and BS service and contrasts conventional TDD with null-space-aided TDD. The latter projects HAPS transmission into a channel null space to suppress interference toward BUEs.

A. Downlink Transmission

  • The downlink formulation specifies received signals and SINRs for HUEs and BUEs, with ZF precoding vectors defined for both tiers.The transmitted symbols and additive noise are modeled as complex Gaussian variables.Source: A. Downlink Transmission · p. 7
  • In conventional TDD, each tier designs ZF precoding from its associated-user CSI, suppressing intra-tier but not explicitly mitigating cross-tier interference.The HAPS and BS serve their users simultaneously during the downlink phase.Source: A. Downlink Transmission · p. 7, 1) Conventional TDD · p. 8
  • NSA-TDD projects HAPS transmission into the null space of the HAPS–BUE channel, eliminating HAPS-induced interference to BUEs.The HAPS sacrifices part of its spatial degrees of freedom; the BS retains its conventional-TDD ZF precoder.Source: 2) Null-Space Aided TDD · p. 8

B. Uplink Transmission

During uplink, HUEs and BUEs transmit simultaneously to the HAPS and terrestrial BS. Each receiver experiences both multi-user and cross-tier interference, and MMSE combining is specified for the uplink SINRs.

B. Uplink Transmission

V. Numerical Results

The numerical evaluation finds that RTDD suppresses cross-tier interference to near-interference-free levels while preserving TDD reciprocity. It also validates the RMT analysis and the tractable Kronecker approximation against Monte Carlo simulations and 3GPP channels.

V. Numerical Results

  • The simulations use one HAPS and one terrestrial BS, with BUEs in the BS area and HUEs in the HAPS area outside the BS region; parameters follow 3GPP specifications.The setup describes uniformly distributed users in the respective coverage areas.Source: §V · p. 9

A. Performance Evaluation

  • RTDD improves HUE downlink SINR over conventional TDD and NSA-TDD, while BUEs gain substantially over conventional TDD and NSA-TDD matches BS-only performance.The Fig. 3 CDFs cover downlink and uplink SINR under different transmission schemes.Source: A. Performance Evaluation · p. 9, Figure 3 · p. 10
  • Under RTDD, HUE and BUE uplink SINRs are nearly those of their respective isolated-tier configurations; NSA-TDD matches conventional TDD.Cross-tier interference is attenuated by propagation distance and building penetration loss; null-space projection affects only the HAPS downlink precoder.Source: A. Performance Evaluation · pp. 9–10, Figure 3 · p. 10
  • As HAPS antennas increase, HUE downlink and uplink SINRs rise, while BUE downlink SINR stays unchanged under RTDD, BS-only, and NSA-TDD.Under conventional TDD, BUE downlink SINR rises as the larger HAPS array reduces interference leakage.Source: A. Performance Evaluation · p. 10, Figure 4 · p. 11
  • As BS antennas increase, BUE downlink and uplink SINRs improve, while HUE uplink SINR stays unchanged and HUE downlink SINR falls under conventional TDD and NSA-TDD.Conventional TDD has the lowest BUE downlink performance because of HAPS interference.Source: A. Performance Evaluation · p. 10, Figure 5 · p. 11

B. Validation of the Proposed Kronecker-Based RMT Model

  • RMT deterministic equivalents closely match Kronecker-model Monte Carlo results, while the Kronecker model agrees well with 3GPP channels with a small performance gap.The antenna-sweep validation also reports consistent performance trends across the Kronecker and 3GPP models.Source: B. Validation of the Proposed… · pp. 10, 12

VI. Conclusion

  • RTDD effectively suppresses cross-tier interference and achieves near-interference-free performance while preserving TDD channel reciprocity.The conclusion presents it as a low-complexity solution for integrated HAPS–terrestrial networks.Source: §VI · p. 12

Appendix A Supporting Lemmas and Proofs

This appendix develops auxiliary random-matrix results for resolvents and leave-one-out quadratic forms used in the analysis. The results concern sample covariance matrices with a deterministic component and correlated random columns under a high-dimensional regime.

Appendix A Supporting Lemmas and Proofs

  • The appendix develops deterministic-equivalent results for the resolvent of a sample covariance matrix with a deterministic component and correlated random columns.It also introduces a leave-one-out quadratic-form result for the matrix formed by removing one column.Source: Appendix A · p. 12, A. Technical Lemma · p. 13
  • The matrix model is Σ = A + Y, with Y assembled from random columns whose correlation is represented by their correlation matrices.The analysis proceeds under stated high-dimensional and randomness assumptions.Source: A. Technical Lemma · p. 12
  • The leave-one-out analysis relates the resolvent with a column removed to the full deterministic equivalent.The appendix combines these relations to obtain the stated quadratic-form result.Source: A. Technical Lemma · p. 13

B. Deterministic Equivalent of the ZF Resolvent

This section obtains deterministic equivalents for the ZF resolvent by taking the regularization parameter to zero under stated assumptions. It establishes fixed-point characterizations and a leave-one-out quadratic-form result for ZF.

B. Deterministic Equivalent of the ZF Resolvent

  • As the regularization parameter tends to zero, the fixed-point quantities and derivatives require scalings that yield finite, nonvanishing limits.The section states assumptions ensuring the relevant limits exist and remain bounded away from zero.Source: B. Deterministic Equivalent of the ZF… · p. 14
  • Theorem 2 gives a deterministic equivalent for the ZF resolvent, characterized by fixed-point equations under the lemma and proposition assumptions.The theorem applies to deterministic matrices with uniformly bounded spectral norm.Source: B. Deterministic Equivalent of the ZF… · p. 15
  • Under the assumptions of Lemma 1 and Proposition 2, Proposition 3 defines the ZF leave-one-out quadratic form Q_u = lim_{z→0}(−z)Q_u(z) and δ_u = (1/n)tr(Ω_uΘ).The proof says it recalls Proposition 1.Source: B. Deterministic Equivalent of the ZF… · p. 16

Appendix B Proof of Theorem 1

The proof analyzes BS desired-signal power using deterministic equivalents for ZF precoding. It applies the full-system deterministic equivalent and uses a law-of-large-numbers step to obtain the stated expression.

Appendix B Proof of Theorem 1

  • The proof derives the BS desired-signal power using the limiting deterministic equivalents established for ZF precoding.The subsection focuses on the normalized channel vector and the corresponding desired-signal-power expression.Source: Appendix B · p. 16
  • The ZF precoder is connected to a regularized inverse to obtain the desired-signal expression for the normalized precoding vector.The proof collects the deterministic LoS components of the BUE channels.Source: Appendix B · p. 16
  • Applying Theorem 2 to the full system and then using the law of large numbers yields the deterministic-equivalent expression.The derivation combines the resulting relations with Proposition 4.Source: Appendix B · pp. 16–17
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