Explicit Asymptotic Performance Analysis of ESPRIT-Type Methods Exploiting the Difference Co-Array Concept

Over the past decade, the difference co-array (DCA) processing technique based on sparse arrays has attracted significant attention given its capability of addressing underdetermined direction-of-arrival (DOA) estimation problems. ESPRIT-type methods have been widely studied in this context; however, their closed-form asymptotic performance analysis for the underdetermined case remains an open problem. In this paper, the explicit asymptotic performance expression for the co-array-based standard ESPRIT method is first derived, followed by the derivation of closed-form performance bound for the co-array-based unitary ESPRIT (achieving reduced computational complexity compared to standard ESPRIT method). Simulation results confirm the tightness of derived performance bounds compared to the existing Cramér-Rao bound (CRB), providing an effective evaluation metric for both sparse array design and performance analysis.