On generalized eigenvector space for target detection in reduced dimensions

The detection and estimation problems with large dimensional vectors frequently appear in the phased array radar systems equipped with, possibly, several hundreds of receiving elements. For such systems, a preprocessing stage reducing the large dimensional input to a manageable dimension is required. The present work shows that the subspace spanned by the generalized eigenvectors of signal and noise covariance matrices is the optimal subspace to this aim from several different viewpoints. Numerical results on the subspace selection for the radar target detection problem is provided to examine the performance of detectors with reduced dimensions.