Slot timing maximum likelihood estimation with bursty pilot signals for DS-CDMA in multipath fading channels

We consider timing initial acquisition in DS-CDMA when propagation is affected by multipath and fading and where the base-station broadcasts a synchronization pilot signal in the form of bursts of modulated chips transmitted periodically and separated by long silent intervals. Subject to certain simplifying assumptions we derive the maximum likelihood (ML) estimator by solving a constrained maximization problem by applying the Karush-Kuhn-Tucker conditions. Our ML timing estimator has constant complexity per observation sample. The relation to other estimation methods is addressed, and performance comparisons both in terms of estimation mean-square error and cumulative density function of the channel energy falling in a certain window are provided by simulation. The resulting estimator offers good results over all fading channels with delay spread not larger than a given maximum spread