Application of fast subspace decomposition to signal processing and communication problems

The authors previously described a class of fast subspace decomposition (FSD) algorithms. Though these algorithms can be applied to solve a variety of signal processing and communication problems with significant computational reduction, they focus their discussion on two typical applications, i.e., sensor array processing and time series analysis. In many cases, replacing the usual eigenvalue decomposition (EVD) or singular value decomposition (SVD) by the FSD is quite straightforward. However, the FSD approach can exploit more structure of some special problems to further simplify the implementation. They first discuss the implementation details of the FSD such as how to choose an optimal starting vector, how to handle correlated noise, and how to exploit additional matrix structure for further computational reduction. Then, they describe an FSD approach targeted at data matrices (rectangular N×M,N⩾M), which requires only O(NMd) flops where d denotes the signal subspace dimension versus a regular O(NM²+M³) SVD. The computational reduction is substantial in typical scenarios i.e., d≪M⩽N. In the spectrum estimation problems, the data matrix has additional structure such as Toeplitz or Hankel, they finally show-how the FSD can exploit such structure for further computational reduction