Optimal Pilot Pattern Design for LMMSE Channel Estimation in OFDM Systems with Finite Block Size over Doubly Dispersive Channels

Pilot pattern design over doubly dispersive channels has regained significant research interest, driven by emerging high-mobility applications in 5G-Advanced and 6G systems, as well as recent developments in Orthogonal Time Frequency Space (OTFS) modulation. This paper addresses the design of LMMSE-optimal pilot patterns for OFDM systems over doubly dispersive channels with finite time-frequency grids. We formulate the problem as A-optimal sensor selection and propose two heuristic algorithms, both combining an initialization stage with local swap refinement. The first employs convex relaxation with randomized rounding, while the second uses greedy selection. Simulations on practical resource block dimensions demonstrate that the proposed designs consistently outperform conventional rectangular and diamond lattice patterns.