Low-Complexity DOA Estimation for Acoustic Vector Sensors Based on Dimensionality Reduction and Semi-Spectrum Search

To alleviate the heavy computational burden of full-space spectral peak search in high-resolution direction-of-arrival (DOA) estimation with acoustic vector sensors, this paper presents a low-complexity approach that couples dimensionality reduction with a semi-spectrum search strategy. First, a joint pressure-velocity transformation converts the high-dimensional complex-valued measurements into low-dimensional real-valued data. The resulting equivalent steering vector becomes real, and its spatial phase difference depends solely on the sine of the target azimuth. Because the sine function is not monotonic over −180°, 180°, distinct azimuth angles can produce the same sine value. This sine ambiguity causes the reduced-dimensional spatial spectrum to be symmetric about 0° and 90°. By exploiting this symmetry, the spectral peak search needs to be conducted only within 0°, 90°. Each detected peak is subsequently expanded via the sine ambiguity relation into four candidate azimuths that cover the full angular space. For each candidate, the corresponding full-dimensional steering vector is reconstructed, and its spectral value is evaluated against the noise subspace of the original data. Subspace orthogonality then resolves the ambiguity: only the steering vector of the true azimuth is orthogonal to the noise subspace and hence yields the maximum spectral value, whereas the three spurious candidates are strongly suppressed. Monte Carlo simulation results indicate that the proposed method preserves unambiguous super-resolution direction-finding capability while cutting the computation time per DOA estimate by approximately 75% compared with conventional full-dimensional search methods.