Two-Dimensional DOA Estimation via Shifted Sparse Arrays with Higher Degrees of Freedom

Sparse antenna arrays provide larger virtual arrays to estimate the direction of arrivals (DOAs) of more sources than the number of physical antennas in the array. While the degrees of freedom (DOF) can be increased by the special structure of the antenna array, a shift in the antenna positions can generate new lags in the difference co-array; hence, more sources can be resolved. In this paper, we propose shifted sparse array structures composed of two overlapping arrays shifted by one lag. It is shown that the shifting property fills the holes in the co-array, which yields larger virtual arrays. We derive stationary and moving array models where overlapping sparse arrays can be realized. The proposed shifting property is applied to coprime, nested and sparse linear arrays, and we show that the proposed technique guaranteed to increase the DOF. Using the proposed sparse array structures, we also propose a 2-D DOA estimation algorithm by utilizing the cross-covariance matrix of an L-shaped sparse array. The performance of the proposed approach is evaluated through numerical simulations, and we show that it can resolve more sources than the conventional sparse arrays with the same number of physical antennas, providing less computational complexity.