Performance Analysis for DOA Estimation Using Compressive Measurements With Coprime Frequencies

Exploiting compressive measurements of two signals with coprime carrier frequencies to estimate direction-of-arrivals (DOAs) can obtain a high estimation performance with low system complexity. Coprime carrier frequencies can dramatically reduce the number of sensors, while compressive measurements effectively control the number of front-end circuit chains. However, the corresponding theoretical performance analysis has not been conducted. Therefore, we aim at revealing the estimation performance mathematically in this paper. First, the Cramér-Rao bound (CRB) expression with respect to the DOAs is derived to illustrate the performance limit. Then, the existence condition of the derived CRB expression is obtained, and the number of degrees of freedom (DOFs) is analyzed based on the condition. Finally, the CRB asymptotic properties are explicitly discussed, and it is found that, in the under-determined case, the CRB approaches a constant, which is similar as the asymptotic properties of sparse arrays. Through theoretical analysis in this paper, the superiorities of the proposed scheme are further verified. Specifically, the proposed scheme can obtain a higher estimation performance, including the number of DOFs and estimation accuracy, with the same number of front-end circuit chains than classical structure using coprime frequencies. From the simulation results, 24 targets can be resolved by the proposed scheme with 5 channels, while the classical structure can resolve only 20 targets. Other properties are also examined by numerical simulations.