An L-Shaped Sparse Array with Reduced Sensitivity to Parametric Mutual Coupling for 2D DOA Estimation

Mutual coupling among array receiving antennas in passive detection systems can introduce amplitude and phase inconsistencies between antenna elements. The resulting amplitude and phase errors across receiving channels not only affect the spectral peak values in subsequent MUSIC-based direction finding, but also cause shifts in the locations of the spectral peaks, thereby increasing detection errors. To reduce geometry-level sensitivity to this effect, this paper presents an analytically constructed L-shaped sparse array for two-dimensional direction-of-arrival (2D DOA) estimation. The array comprises two orthogonal three-subarray branches that share the sensor at the origin. The electrical angle of one branch is first estimated by a one-dimensional (1D) spatial spectrum; the corresponding electrical angle of the other branch is then obtained from a source-conditioned 1D spectrum, yielding paired 2D directional parameters. With 23 physical sensors, the proposed geometry provides 83 central contiguous difference-coarray lags and a one-arm aperture of 43d, where d is one-half wavelength. Under the normalized parametric coupling model adopted in this work, the reported numerical results show lower DOA-estimation RMSE than the compared L-shaped arrays over the investigated ranges. These results establish an analytical geometry and signal-model comparison rather than antenna-specific electromagnetic validation.