Design of two MUSIC-like estimators based on bias minimization
Wenyuan Xu, M. Kaveh · IEEE Transactions on Signal Processing · 1996
Two classes of MUSIC-like estimators are considered. One class, called weighted norm MUSIC, possesses an optimizing functional, or null spectrum, which is the product of the MUSIC null spectrum and an angle-dependent weight. The second class, which is denoted the D/sub r/ estimator, has an optimizing functional that is dependent on a parameter r and is a generalized distance between two particular vectors in the signal subspace. It is shown that the asymptotic mean-square errors of these estimators are the same as MUSIC. By determining an appropriate weight, based on a derived large-sample expression for the estimator bias, a weighted norm MUSIC estimator is found that gives zero bias of order N/sup -1/, where N is the sample size. Using an approximate relation between the two types of estimators under consideration, a data-dependent parameter r(/spl theta/) is derived for the D/sub r/ estimator, which results in small bias over a wide range of signal-to-noise ratios (SNRs) for two closely spaced sources.