Sparse Array Source Enumeration Via Coarray Subspace Optimization

Linear sparse arrays, where the sensors are placed with non-uniform spacing, identify more source direction-of-arrivals (DOAs) than sensors. In contrast, uniform linear arrays (ULAs) can only find fewer source DOAs than sensors. To resolve these DOAs in practice, the sources have to be enumerated first. However, existing source enumerators are either designed for ULAs or computationally challenging for sparse arrays. This paper proposes sparse array source enumeration via coarray subspace optimization (SASE-CSO). The SASE-CSO algorithm first establishes multiple batches of array outputs. In each batch, we estimate the projection matrix onto the signal subspace on the difference coarray. Next, we propose the coarray subspace optimization (CSO) to combine these estimated projection matrices. The explicit relation between the optimal solution to the CSO and the estimated projection matrices reduces the complexity for implementation. Finally, the sources are enumerated from the most significant gap in the eigenvalues of the optimal solution to the CSO. The SASE-CSO can enumerate up to U sources, where U denotes the largest element in the central ULA segment in the difference coarray. Numerical examples demonstrate that the SASE-CSO increases the probability of detection for more sources than sensors and two closely-spaced sources with unequal powers.