Cramér-Rao Bound for Generalized Multi-Level Prime Array with and without Compression

Sparse antenna arrays like multi-level prime arrays (MLPA) and MLPA with compressed subarray (MLPAC) use multiple uniform linear subarrays where the number of elements in the subarrays is pairwise coprime integer. Both configurations have large degrees of freedom (DOF), i.e. large number of consecutive lags and few/or no holes in the difference coarray. MLPA and MLPAC require a small aperture size compared with nested and coprime arrays. This paper derives the Cramér-Rao bound (CRB) of the MLPA and MLPAC based on the second order difference coarray, when the number of estimated sources is larger than the number of antenna elements. Simulation results confirm the derived CRB using MUSIC algorithm.