Subspace detection and scale evolutionary eigendecomposition

A measure of the potential of a receiver for detection is detectability. Detectability is a function of the signal and noise, and given any one of them the detectability is fixed. In addition, complete transforms of the signal and noise cannot change detectability. Throughout this work we show that "Subspace methods" as defined here can improve detectability in specific subspaces, resulting in improved Receiver Operating Curves (ROC) and thus better detection in arbitrary noise environments. Our method is tested and verified on various signals and noises, both simulated and real. The optimum detection of signals in noise requires the computation of noise eigenvalues and vectors (EVD). This process neither is a trivial one nor is it computationally cheap, especially for non-stationary noise and can result in numerical instabilities when the covariance matrix is large. This work addresses this problem and provides solutions that take advantage of the subspace structure through plane rotations to improve on existing algorithms for EVD by improving their convergence rate and reducing their computational expense for given thresholds.