Covering-radius and Collinearity- Minimizing Pilots for Channel Estimation in TDD Systems

This letter studies pilot design for orthogonal frequency-division multiplexing-based time-division duplex (TDD) systems under a sliding-window latest-slot recovery framework that jointly exploits delay--Doppler sparsity across recent slots. Under contiguous-subband and fairness constraints, this viewpoint naturally leads to a geometry-aware time--frequency joint pilot assignment. We show that effective patterns should balance grid coverage and redundant-collinearity suppression, with an additional symmetry-avoidance refinement when complete collinearity elimination is infeasible. Based on these principles, we formulate a mixed-integer construction method compatible with practical TDD allocation. Numerical results show that minimum-coverage-radius and collinearity-control (MCC) pattern improves both surrogate geometry metrics and latest-slot recovery performance.