Performance comparison of subspace rotation and MUSIC methods for direction estimation

The statistical performance of subspace rotation (SR) methods (such as the Toeplitz approximation method and a variant of ESPRIT) for direction estimation using arrays composed of matched sensor doublets is studied. The distributional properties of these methods are established, and a compact explicit formula for the covariance matrix of their estimation error is provided. Next, using this formula and a similar formula for MUSIC covariance matrix, it is shown that the SR methods are statistically less efficient than MUSIC, at least for a sufficiently large number of snapshots. The difference in statistical performance between the commonly used SR method and MUSIC may be substantial if the number of sensors in the array is large. An optimally weighted SR method which may approach the MUSIC level of statistical performance for one direction parameter (specified by the user) is introduced