Performance analysis of MUSIC employing conjugate symmetric beamformers

If one incorporates a beamformer composed of conjugate centro-symmetric weight vectors as a preprocessor to an eigenstructure direction finding algorithm, a real-valued decomposition can be employed to estimate the noise and signal subspaces from the sample covariance matrix. The effect of employing the real processing methodology on the angle estimation performance of beamspace MUSIC is explored. Specifically, the distribution of the real-valued signal subspace eigenvectors is derived and used in an asymptotic analysis of the bias and variance of the MUSIC estimator. The theoretical analysis shows that processing the real part of the beamspace sample covariance matrix offers significant performance gains, in addition to the obvious computational benefit, relative to the conventional complex-valued procedure, particularly in the case of correlated sources. Monte Carlo simulations are included to verify the theoretical expressions. A trade-off study of the estimation accuracy versus the desire to provide adequate rejection of unwanted signals in a sector-based interrogation scheme for various beamforming architectures is also presented