FAST ALGORITHMS FOR UPDATING SIGNAL SUBSPACES

In various real-time signal processing and communication applications, it is often required to track a low-dimensional signal subspace that slowly varies with time. Conventional methods of updating the signal s ubspace rely on eigendecomposition or singular value decomposition, wh ich is computationally expensive and difficult to implement in paralle l. Recently, Xu and Kailath proposed fast and parallelizable Lanczos-b ased algorithms for estimating the signal subspace based on the data m atrices or the covariance matrices. In this paper, we shall extend the se algorithms to achieve fast tracking of the signal subspace. The com putational complexity of the new methods is O(M2d) per update, where M is the size of the data vectors and d is the dimension of the signal subspace. Unlike most tracking methods that assume d is fixed and/or k nown a priori, the new methods also update the signal subspace dimensi on. More importantly, under certain stationarity conditions, we can sh ow that the Lanczos-based methods are asymptotically equivalent to the more costly SVD or eigendecomposition based methods and that the esti mation of d is strongly consistent. Knowledge of the previous signal s ubspace estimate is incorporated to achieve better numerical propertie s for the current signal subspace estimate. Numerical simulations for some signal scenarios are also presented.