Asymptotic properties of 2-D MUSIC estimator and comparison to 2-D MP estimator (Q5906633)

The large sample estimation covariance of the MUSIC (Multiple Signal Classification) estimator [see, e.g. \textit{P. Stoica} and \textit{T. Söderström}, IEEE Trans. Signal Process. 39, 1836-1847 (1991; Zbl 0729.62088)] of two-dimensional (2-D) frequencies is derived for a model which is a sum of a complex Gaussian white noise and 2-D complex exponentials consisting of these frequencies, deterministic phases and positive amplitudes. MUSIC and MP (Matrix Pencil) methods are compared. Although the estimation covariances of the MP and MUSIC estimators are very close, in the single 2-D sinusoidal case, the MP has a better accuracy than the MUSIC, and in the multiple 2-D sinusoidal case, the MUSIC can perform slightly better than the MP. Both theoretical and simulated estimation variances are compared with the Cramer-Rao bound (CRB). The CRB is obtained by assuming a deterministic phase model. The results shown are valid for a median range of signal-to-noise ratio.