A blind code timing estimator and its implementation for DS-CDMA signals in unknown colored noise

Commonly, the channel noise is assumed as temporally white when we estimate the PN code timing for direct-sequence code-division multiple-access (DS-CDMA) systems. However, it may be invalid in practice due to, for instance, the presence of some narrow-band interference or lumping the secondary users into the noise. In this paper, we introduce the matrix decomposition technique in a subspace-based code timing estimator. The new code timing estimator can robustly work in unknown colored noise. The Cramer-Rao bound for the code timing estimator is outlined. Furthermore, we propose a practical implementation method, which includes reducing the number of eigendecompositions and an adaptive eigendecomposition algorithm based on subspace tracking using the unconstrained gradient-descent technique. The performance of the new method is evaluated by computer simulation and compared with the MUSIC method. It is proved that the proposed code timing estimation algorithm outperforms the MUSIC method in colored noise or when the number of users is large.