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Network-Optimised Spiking Neural Network (NOS) Scheduling for 6G O-RAN: Spectral Margin and Delay-Tail Control

Muhammad Bilal, Xiaolong Xu

TL;DR

The paper addresses scheduling in 6G O-RAN under interference and delay, introducing NOS, a delay-aware spiking scheduler that ties delay, topology, and controller gain into a single spectral-margin parameter δ. Through small-signal analysis, it derives a delay-aware threshold k⋆(Δ) and shows that δ>0 yields geometric ergodicity and sub-Gaussian backlog and delay tails, with tail exponents proportional to δ. A δ-proxy study calibrates NOS against PF and delayed BP across multiple interference topologies under 5–20 ms delays, using a single gain fixed at the worst spectral radius; NOS achieves higher utilization and tighter P99.9 delays, while remaining clique-feasible on integer PRBs. The framework provides an explainable, auditable baseline for O-RAN deployments, coupling near-RT tuning with efficient per-slot implementation and robust delay performance.

Abstract

This work presents a Network-Optimised Spiking (NOS) delay-aware scheduler for 6G radio access. The scheme couples a bounded two-state kernel to a clique-feasible proportional-fair (PF) grant head: the excitability state acts as a finite-buffer proxy, the recovery state suppresses repeated grants, and neighbour pressure is injected along the interference graph via delayed spikes. A small-signal analysis yields a delay-dependent threshold $k_\star(Δ)$ and a spectral margin $δ= k_\star(Δ) - gHρ(W)$ that compress topology, controller gain, and delay into a single design parameter. Under light assumptions on arrivals, we prove geometric ergodicity for $δ>0$ and derive sub-Gaussian backlog and delay tail bounds with exponents proportional to $δ$. A numerical study, aligned with the analysis and a DU compute budget, compares NOS with PF and delayed backpressure (BP) across interference topologies over a $5$--$20$\,ms delay sweep. With a single gain fixed at the worst spectral radius, NOS sustains higher utilisation and a smaller 99.9th-percentile delay while remaining clique-feasible on integer PRBs.

Network-Optimised Spiking Neural Network (NOS) Scheduling for 6G O-RAN: Spectral Margin and Delay-Tail Control

TL;DR

The paper addresses scheduling in 6G O-RAN under interference and delay, introducing NOS, a delay-aware spiking scheduler that ties delay, topology, and controller gain into a single spectral-margin parameter δ. Through small-signal analysis, it derives a delay-aware threshold k⋆(Δ) and shows that δ>0 yields geometric ergodicity and sub-Gaussian backlog and delay tails, with tail exponents proportional to δ. A δ-proxy study calibrates NOS against PF and delayed BP across multiple interference topologies under 5–20 ms delays, using a single gain fixed at the worst spectral radius; NOS achieves higher utilization and tighter P99.9 delays, while remaining clique-feasible on integer PRBs. The framework provides an explainable, auditable baseline for O-RAN deployments, coupling near-RT tuning with efficient per-slot implementation and robust delay performance.

Abstract

This work presents a Network-Optimised Spiking (NOS) delay-aware scheduler for 6G radio access. The scheme couples a bounded two-state kernel to a clique-feasible proportional-fair (PF) grant head: the excitability state acts as a finite-buffer proxy, the recovery state suppresses repeated grants, and neighbour pressure is injected along the interference graph via delayed spikes. A small-signal analysis yields a delay-dependent threshold and a spectral margin that compress topology, controller gain, and delay into a single design parameter. Under light assumptions on arrivals, we prove geometric ergodicity for and derive sub-Gaussian backlog and delay tail bounds with exponents proportional to . A numerical study, aligned with the analysis and a DU compute budget, compares NOS with PF and delayed backpressure (BP) across interference topologies over a --\,ms delay sweep. With a single gain fixed at the worst spectral radius, NOS sustains higher utilisation and a smaller 99.9th-percentile delay while remaining clique-feasible on integer PRBs.

Paper Structure

This paper contains 15 sections, 3 theorems, 24 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. NOS-Based Scheduler
  4. State evolution and networking interpretation
  5. Spike generation, fairness, and soft reset
  6. Spike-to-PRB mapping with feasibility and rounding
  7. Stability Analysis
  8. Local linearisation and topology
  9. Delay-aware threshold and spectral margin
  10. Perron–mode proxy and global margin.
  11. Early-warning signal
  12. Mean backlog and tail bounds
  13. Complexity and DU realisation
  14. Experimental Setup and Results
  15. Conclusion

Key Result

Corollary 1

For $\Delta=0$, $k_\star(0)=\min\{a-\bar{d},\; b-\bar{d}\}$ from eq:sch_kstar_nodelay. The zero-delay crossing frequency is For small $\Delta$ and $a\le b$, a first–order Padé approximation yields the conservative bound $k_\star(\Delta)\;\gtrsim\; \frac{k_\star(0)}{1+\tfrac{\Delta}{2}\,\omega_0}.$ For implementation we adopt the calibrated monotone envelope with $\tau_{\mathrm{ctrl}}$ fitted onc

Figures (5)

  • Figure 1: Left group (UEs, arrivals, queues) feeds the NOS kernel via a curved arrow. The right chain performs spike generation, fairness, clique allocation and integer PRB mapping. Dashed arrows denote neighbour spikes ($j\neq i$) and near-RT feedback via $\Delta_{\mathrm{eff}}$.
  • Figure 2: Utilisation headroom AUC across pair2, line4, and ring8 at $\Delta\in\{5,12,20\}$ ms. Nominal-cap normalisation; setup as in Sec. \ref{['sec:exp']}.
  • Figure 3: MaxQ proxy across pair2, line4, and ring8 at $\Delta\in\{5,12,20\}$ ms, computed from $\delta$ as in Corollary \ref{['cor:tails']}. Nominal-cap normalisation; setup as in Sec. \ref{['sec:exp']}.
  • Figure 4: P99.9 delay across pair2, line4, and ring8 at $\Delta\in\{5,12,20\}$ ms. Nominal-cap normalisation; setup as in Sec. \ref{['sec:exp']}.
  • Figure 5: Analytic delay tail bounds for line4 on a log scale. Bounds follow $\Pr\{D>\tau\}\le \exp(-\theta\tau^2)$ with $\theta$ from Corollary \ref{['cor:tails']}. Parameters and normalisation as in Sec. \ref{['sec:exp']}.

Theorems & Definitions (5)

  • Corollary 1: Delay envelope used in numerics
  • Definition 1: Effective margin used in tables and plots
  • Corollary 2: Tail proxy consistent with Theorem \ref{['thm:geo']}
  • Remark 1: Non-normal topology
  • Theorem 1: Geometric ergodicity under a spectral margin