On parameter estimation in long-code DS/CDMA systems: Cramér-Rao bounds and least-squares algorithms

The problem of parameter estimation in direct-sequence code division multiple access (DS/CDMA) systems employing long (aperiodic) spreading codes is considered. In particular, for an asynchronous network, the problem of estimating the amplitudes, phase offsets, propagation delays, and directions of arrival (DoAs) for the CDMA signals transmitted by the active users is examined. First, formulas are provided for the Cramér-Rao bound (CRB) on the error variance of any joint multiuser parameter estimation procedure exploiting a known training sequence. Further, least-squares adaptive algorithms are derived, which, based on the transmission of known pilot symbols, enable adaptive estimation of the parameters with a computational complexity that is only quadratic in the processing gain. In particular, the cases where either the parameters from all of the active users are to be estimated, or the relevant parameters of only one user are to be acquired (based on the knowledge of its spreading code and training sequence only), are considered. This study is completed by an analysis of the convergence properties of the proposed adaptive algorithms and by extensive computer simulation results illustrating the performance of the estimation procedures, also in comparison with the CRB, and the impact of the estimation errors on the performance of the linear minimum mean square error (LMMSE) multiuser detector.