Fast subspace decomposition of data matrices

The authors present a fast subspace decomposition method (Bi-FSD) for (rectangular) data matrices, employing the bidiagonalization Lanczos algorithm. It only requires O(NMd) flops for a N ×M data matrix and achieves almost an order of magnitude computational reduction over the O(NM² +M³) SVD (singular value decomposition) or ED (eigendecomposition) approach. A novel detection scheme is also presented that can be implemented at each intermediate step of estimating the signal subspace. Unlike many fast algorithms that trade performance for speed, rigorous performance analysis shows that Bi-FSD has the same asymptotic performance as the more costly SVD, and the Bi-FSD detection scheme is strongly consistent. Also, the most computationally intensive part (i.e., O(NM) operations) is O(d) matrix-vector products, which can be easily implemented in parallel for even faster computation. All these features of the Bi-FSD algorithm make it easier to implement a class of high-resolution array signal processing algorithms in real time