WEIGHTED SUBSPACE METHODS AND SPATIAL SMOOTHING - ANALYSIS AND COMPARISON

In this paper, the effect of using a spatially smoothed forward-backward covariance matrix on the performance of weighted eigen-based state space methods/ESPRIT, and weighted MUSIC for the direction-of-arrival (DOA) estimation is analyzed. Expressions for the mean-squared error in the estimates of the signal zeros and the DOA estimates, along with some general properties of the estimates and optimal weighting matrices are derived. A key result of the analysis is that optimally weighted MUSIC and weighted state space methods/ESPRIT have identical asymptotic performance. It is also shown that by properly choosing the number of subarrays, the performance of unweighted state space methods can be significantly improved. Then it is shown that the mean-squared error in the DOA estimates obtained using subspace based methods is independent of the exact distribution of the source amplitudes. This results in an unified framework for dealing with DOA estimation using a uniformly spaced linear sensor array (ULA), and the time series frequency estimation problem. The resulting analysis of the time series case is shown to be more accurate than previous results.