Matrix sign algorithms for signal subspace applications

Algorithms for computing the matrix sign function of nonsingular matrices are developed. These algorithms are used to estimate the signal and noise subspaces of the sample covariance matrix when a threshold which separates signal and noise eigenvalues is available. The computed subspaces are then utilized to develop high resolution methods such as MUSIC (multiple signal classification) and ESPRIT (estimation of signal parameters via rotational invariance techniques) for sinusoidal frequency and direction of arrival (DOA) problems. The main features of these algorithms are that they are stable and can be used to generate subspaces that are parameterized by the signal-to-noise ratio (SNR). Additionally, significant computational saving will be obtained due to the fast convergence of some of these iterations. Simulations showing the performance of these methods are also presented.