  In this paper we present a generic framework for the asymptotic performance
analysis of subspace-based parameter estimation schemes. It is based on earlier
results on an explicit first-order expansion of the estimation error in the
signal subspace obtained via an SVD of the noisy observation matrix. We extend
these results in a number of aspects. Firstly, we derive an explicit
first-order expansion of the Higher- Order SVD (HOSVD)-based subspace estimate.
Secondly, we show how to obtain explicit first-order expansions of the
estimation error of ESPRIT-type algorithms and provide the expressions for
matrix-based and tensor-based Standard ESPRIT and Unitary ESPRIT. Thirdly, we
derive closed-form expressions for the mean square error (MSE) and show that
they only depend on the second-order moments of the noise. Hence, we only need
the noise to be zero mean and possess finite second order moments. Fourthly, we
investigate the effect of using Structured Least Squares (SLS) to solve the
overdetermined shift invariance equations in ESPRIT and provide an explicit
first-order expansion as well as a closed-form MSE expression. Finally, we
simplify the MSE for the special case of a single source and compute the
asymptotic efficiency of the investigated ESPRIT-type algorithms in compact
closed-form expressions which only depend on the array size and the effective
SNR. Our results are more general than existing results on the performance
analysis of ESPRIT-type algorithms since (a) we do not need any assumptions
about the noise except for the mean to be zero and the second-order moments to
be finite (in contrast to earlier results that require Gaussianity or
second-order circular symmetry); (b) our results are asymptotic in the
effective SNR, i.e., we do not require the number of samples to be large; (c)
we present a framework that incorporates various ESPRIT-type algorithms in one
unified manner.
