A fast method for subspace decomposition is proposed.Given the training sequences of a desired signal

the signal subspace and noise subspace can be obtained quickly.The dimension of subspace can be correctly estimated while the signal subspace and noise subspace are acquired.The presented method does not require the formation of the covariance matrix and its eigendecomposition

thereby reducing the computational complexity significantly.Finally

numerical results show that the novel approach can achieve the asymptotic performance of the classical method.