APPLICATION OF FAST SUBSPACE DECOMPOSITION TO SIGNAL-PROCESSING AND COMMUNICATION PROBLEMS

In [1], we described a class of fast subspace decomposition (FSD) algo rithms. Though these algorithms can be applied to solve a variety of s ignal processing and communication problems with significant computati onal reduction, we shall focus our discussion on two typical applicati ons. i.e., sensor array processing and time series analysis. In many c ases, replacing usual eigenvalue decomposition (EVD) or singular value decomposition (SVD) by FSD is quite straightforward. However, the FSD approach can exploit more structure of some special problems to furth er simplify the implementation. In this paper, we shall first discuss the implementation details of FSD such as how to choose an optimal sta rting vector, how to handle correlated noise, and how to exploit addit ional matrix structure for further computational reduction. Then, we d escribe an FSD approach targeted at data matrices (rectangular N x M, N greater-than-or-equal-to M), which requires only O(NMd) flops where d denotes the signal subspace dimension versus a regular O(N M2 + M3) SVD. The computational reduction is substantial in tropical scenarios d much less than M less-than-or-equal-to N. In the spectrum estimation problems, the data matrix has additional structure such as Toeplitz o r Hankel, we shall finally show how FSD can exploit such structure for further computational reduction.