DOA Estimation for Time-Modulated Linear Arrays via Hadamard Matrix Row Permutation

This paper proposes a Hadamard row-permutation based time-modulation matrix design for direction-of-arrival (DOA) estimation with time-modulated linear arrays (TMLAs). Fixed time-modulation schemes may lead to nonuniform harmonic observation energy, angle-dependent performance loss, and limited resolution for closely spaced sources. To address these issues, the proposed method optimizes the assignment between Hadamard binary switching sequences and physical array elements through row permutation, while preserving binary implementation and the underlying Hadamard row orthogonality. A whitened harmonic-domain MUSIC framework is adopted to handle the non-white noise induced by time modulation. Based on the whitened effective array manifold, a Cramér–Rao bound (CRB)-inspired projected-derivative metric and a steering-vector correlation penalty are combined to guide the row-permutation optimization, which is solved by a greedy row-exchange algorithm. Simulation results verify that the proposed design provides a more uniform nonzero-harmonic power distribution and achieves improved single-source accuracy, multi-source root-mean-square error (RMSE), and closely spaced source resolution compared with conventional and unoptimized Hadamard-based time-modulation schemes.