Analytical performance assessment of 1-D Structured Least Squares

In this paper, we derive the analytical performance of 1-D standard ESPRIT and 1-D Unitary ESPRIT using one iteration of Structured Least Squares to solve the shift invariance equations. First, we provide the estimation error of the fc-th spatial frequency as an explicit expression of the noise realization, which requires no assumptions about the statistics of the noise. Then, we compute the statistical expectation over zero mean circularly symmetric white noise and provide explicit formulas for the resulting mean square errors. All expressions are asymptotic in the effective SNR, i.e., they become exact as either the number of snapshots or the SNR tends to infinity.