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Efficient random access is one of the key designs in code-division multiple-access (CDMA) cellular systems. Random access is used by user equipment for initial access, requesting dedicated channels and transmitting short packet data to a base station. In random access, a preamble part is usually devised for fast and reliable burst synchronization, which is essential in order to avoid excessive access delay and/or repeated transmissions that may reduce the overall system capacity. This paper investigates the issue of burst synchronization for the slotted random access with preamble power ramping in the reverse link of CDMA systems. A flexible burst synchronizer based on a parallel-serial code-phase detector is proposed, which can be easily configured to achieve different complexity/performance tradeoffs. A general analysis is also presented with important design parameters being taken into account, including the number of correlators, power control error, power ramping step, diversity order, frequency offset, multipath combining, and others. The analysis is verified by computer simulations.