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

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 $k_\star(\Delta)$ and a spectral margin $\delta = k_\star(\Delta) - gH\rho(W)$ that compress topology, controller gain, and delay into a single design parameter. Under light assumptions on arrivals, we prove geometric ergodicity for $\delta>0$ and derive sub-Gaussian backlog and delay tail bounds with exponents proportional to $\delta$. 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.