Equivalent Fisher Information for Wideband DOA Estimation With Unknown Sensor Phase Errors

Abstract

This letter derives the closed-form equivalent Fisher information matrix (EFIM) for single-source wideband DOA estimation with a uniform linear array in the presence of unknown sensor phase errors. Based on a deterministic frequency-domain model, the source coefficients are first concentrated out, and the phase-error nuisance parameters are then eliminated via the Schur complement, yielding a closed-form EFIM and the corresponding Cramér–Rao bound. The analysis reveals that unknown phase errors absorb the spectral-centroid component of the DOA information, while bandwidth expansion recovers part of the lost information through the increase of the power-weighted frequency variance. Consequently, under phase self-calibration, the effective DOA information is determined by the power-weighted frequency variance rather than the spectral second moment. Numerical results validate the derived closed-form expression.