Designing sparse extended nested arrays with high degrees of freedom and low coupling

The coupling effect significantly impacts Direction of Arrival (DOA) estimation. Employing coupling models to reduce this impact can be costly and sensitive to model fitting. Sparse arrays offer an effective means to mitigate coupling errors. Classical nested arrays in sparse arrays harbor numerous closely spaced sensor pairs, resulting in significant coupling errors. Traditional sparse arrays struggle to synchronize freedom degrees with coupling optimizations. Addressing these issues, this paper introduces Sparse Extended Nested Arrays (SENA). Comprising five subarrays, SENA effectively minimizes inter-element coupling by constraining sensor spacing within and between subarrays, maintaining freedom degrees. The paper derives and proves physical structure, continuous range of difference coarrays, and optimal choices for sensor count for SENA. Compared to traditional and improved sparse arrays with the same sensor count, SENA ensures higher freedom degrees with lower coupling errors, a superiority validated through experimental simulations.