A fast algorithm for signal subspace decomposition and its performance analysis

A fast signal-subspace decomposition (FSD) algorithm is presented for sample covariance matrices, which only needs O(M ²d) flops, where d(≪M) denotes the signal subspace dimension. A theoretical performance analysis was conducted, and it shows the strong consistency of the estimation of d and the asymptotic equivalence between the FSD estimate and the one obtained from an eigendecomposition. The approach can be easily implemented in parallel to further reduce the computation time to as little as O(Md) or O(log Md) by using O(M) or O(M²) multipliers, respectively