This paper focuses on a fast subspace tracking algorithm-approximated power iterations (API) algorithm

and its application to direction-of-arrival(DOA) estimation and blind multiuser detection (MUD) in CDMA system.The algorithm is derived by exerting an approximation on the power iterations method

which guarantees the orthonormality of the estimated subspace at each iteration

and satisfies a global convergence property.Its performance outperforms many subspace tracking algorithms

such as the projection approximation subspace tracking (PAST) method

the novel information criterion (NIC) method

and the Orthonormal PAST (OPAST) method

while keeping the same computational complexity as the above mentioned algorithms.The effectiveness is validated through some numerical simulations of DOA estimation in a narrowband source scenario and blind MUD in a synchronous DS-CDMA system

respectively.