Analysis of Statistical Performance Measures
Final rept. 1 Oct 2002-31 Dec 2003
PURDUE UNIV LAFAYETTE IN
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When only a limited number of snapshots is available for estimating the spatial correlation matrix, a low-rank solution of the MVDR equations, obtained via a small number of iterations of Conjugate Gradients CG, can yield a higher SINR than the full-rank MVDR beamformer. A primary issue addressed in this effort is whether the unity gain constraint in the look direction should be enforced a-priori via the use of a blocking matrix, constituting Steering Dependent Conjugate Gradients SD-CG, or effected a-posteriori through simple scaling of the beamforming vector, constituting Steering Independent Conjugate Gradients SI-CG. A major contribution was that the two methods yield exactly the same low-rank beamformer. This is an important result since the construction, and application to the data, of a blocking matrix for each look direction is computationally burdensome. A simplified expression for the power estimate obtained with the SI-CG beamformer was also developed. Extensive simulations were conducted to verify the efficacy of the theory. While it was known that the optimal number of steps of SI-CG varies with look direction, simulations presented here reveal that the optimal number of principal eigenvectors for the PCI beamformer varies substantially with look direction.
- Theoretical Mathematics