Non-asymptotic performance analysis of eigenstructure spectral methods

A nonasymptotic theoretical analysis for the performance of eigenstructure spectral methods for direction-of-arrival (DOA) estimation is proposed. The performance analysis is based on perturbation analysis of covariance eigenstructure and directions-of-arrival. The performance is expressed in terms of signal-to-noise ratio (SNR), the number of snapshots, and other parameters including source locations, sensor locations, and sensor gains without utilizing asymptotic conditions. From the expression, it is proved that the absolute bias and the variance of MUSIC direction-of-arrival estimation is inversely proportional to signal-to-noise ratio and to the number of snapshots. Simulations confirm the inverse proportional relationship under conditions including a small-number of snapshots.<<ETX>>

[1]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[2]  D. Luenberger,et al.  Estimation of structured covariance matrices , 1982, Proceedings of the IEEE.

[3]  Petre Stoica,et al.  MUSIC, maximum likelihood and Cramer-Rao bound: further results and comparisons , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[4]  Mostafa Kaveh,et al.  The statistical performance of the MUSIC and the minimum-norm algorithms in resolving plane waves in noise , 1986, IEEE Trans. Acoust. Speech Signal Process..

[5]  Petre Stoica,et al.  MUSIC, maximum likelihood, and Cramer-Rao bound , 1989, IEEE Transactions on Acoustics, Speech, and Signal Processing.

[6]  Thomas Kailath,et al.  Asymptotic performance of eigenstructure spectral analysis methods , 1984, ICASSP.