Performance analysis of ESPRIT-Type algorithms for co-array structures

In the recent field of co-array signal processing, sparse linear arrays are processed to form a virtual uniform linear array (ULA), termed co-array, that allows to resolve more sources than physical sensors. The extra degrees of freedom (DOFs) are leveraged by the assumption that the signals are uncorrelated, which requires a large sample size. In this paper, we first review the Standard ESPRIT and Unitary ESPRIT algorithms for co-array processing. Secondly, we propose a performance analysis for both methods, which is asymptotic in the effective signal-to-noise ratio (SNR), i.e., the results become exact for either high SNRs or a large sample size. Based on the derived analytical expressions, we study the effects of a small sample size such as the residual sample signal correlation and the sample noise contribution on the estimation accuracy of the proposed algorithms. Simulation results verify the derived analytical expressions.