Joint Track-While-Scan Beam Scheduling for 6G Sub-Terahertz Multi-UE Clusters Using Resolving-Window Metrics at 140 GHz and 300 GHz

At candidate 6G sub-terahertz (sub-THz) carriers near 140 GHz and 300 GHz, half-power beamwidths of 1°-6° create a scheduling regime that 5G beam management was never designed for: a base station must simultaneously hold high-SNR beams on active user equipments (UEs), monitor UEs drifting toward the edge of resolvability, and spend scarce beam time scanning for new arrivals-all within a thermally limited duty cycle. This is structurally the track-while-scan (TWS) problem of electronically scanned array (ESA) radar. Building on a companion paper that defined per-UE resolving-window metrics (normalized range separation W_R, SNR-gated angular separation W_θ^eff, LoS-convergence urgency C_k, and beam time-to-exit T_exit), this paper converts those metrics into an implementable control plane. We (i) formulate the joint tracking-scheduling problem as a constrained multi-objective optimization over outage probability, beam mis-association (ambiguity) probability, and discovery latency, subject to an RF-chain budget B_max and a thermal duty factor η; (ii) define a three-state UE classification-stable, boundary, ambiguous-driven by the resolving-window state with radar-consistent polarity (short time-to-exit and low separability escalate a UE's state, never relax it); and (iii) propose a low-complexity, priority-driven TWS scheduler that reserves scan capacity first, stabilizes boundary UEs preventively, and serves stable UEs at relaxed revisit rates bounded by their individual T_exit.