LLM Assisted Alpha Fairness for 6 GHz WiFi and NR_U Coexistence: An Agentic Orchestrator for Throughput, Energy, and SLA

Unlicensed 6GHz is becoming a primary workhorse for high-capacity access, with Wi-Fi and 5G NR-U competing for the same channels under listen-before-talk (LBT) rules. Operating in this regime requires decisions that jointly trade throughput, energy, and service-level objectives while remaining safe and auditable. We present an agentic controller that separates policy from execution. At the start of each scheduling epoch the agent summarizes telemetry (per-channel busy and baseline LBT failure; per-user CQI, backlog, latency, battery, priority, and power mode) and invokes a large language model (LLM) to propose a small set of interpretable knobs: a fairness index α, per-channel duty-cycle caps for Wi-Fi/NR-U, and class weights. A deterministic optimizer then enforces feasibility and computes an α-fair allocation that internalizes LBT losses and energy cost; malformed or unsafe policies are clamped and fall back to a rule baseline. In a 6GHz simulator with two 160MHz channels and mixed Wi-Fi/NR-U users, LLM-assisted policies consistently improve energy efficiency while keeping throughput competitive with a strong rule baseline. One LLM lowers total energy by 35.3% at modest throughput loss, and another attains the best overall trade-off, finishing with higher total bits (+3.5%) and higher bits/J (+12.2%) than the baseline. We release code, per-epoch logs, and plotting utilities to reproduce all figures and numbers, illustrating how transparent, policy-level LLM guidance can safely improve wireless coexistence.