Adaptive algorithms for solving generalized eigenvalue signal enhancement problems

In this paper, we investigate adaptive algorithms for solving generalized eigenvalue problems that arise in the context of signal enhancement. This problem applies in general to any setup involving vectors of signal and interference samples, including wideband temporal processing, diffuse spatial (array) processing, or any combination thereof. The algorithms attempt to solve a generalized eigenvalue (GEV) problem using only snapshots of signal and interference training vectors, and the goal is to do this with a minimum amount of data and computational resources. The algorithms considered fall into two classes: two-step approaches that first estimate the covariance matrices and then solve the GEV problem; and, stochastic gradient type algorithms that recursively update the solution in one step for each new set of data vector snapshots. The algorithms are compared on the basis of convergence rate and computational complexity.