Achievable degree-of-freedom for three-level prime arrays

Due to their large aperture size, coprime arrays are good candidate in the presence of mutual coupling as most of the elements are separated by more than half-wavelength. However, the number of consecutive lags in their difference coarray is limited. Combining three uniform linear subarrays where the number of elements in the subarrays are pairwise coprime integers overcomes this limitation. The resultant array is referred to as three-level prime array (3LPA). The 3LPA has a closed form expression for antenna locations and can improve the DOF using smaller aperture size compared with coprime arrays. In this paper, we derive an approximate expression for the achievable DOF for the 3LPA configuration. Simulation results confirm the validity of the derived expressions compared with the exact DOF.