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This paper explores the use of various antenna configurations at the base station for acquisition of the preamble signal sent on a random access channel (RACH) in a 3G wireless network such as UMTS and CDMA2000. Conventional base-station receivers employ two widely-spaced antennas for spatial diversity reception, which has been thought to be a critical feature for successful acquisition on the RACH. However, alternate antenna configurations in which there is no spatial diversity (such as four closely-spaced antennas) have been shown to provide a tremendous capacity benefit for dedicated channels used in voice and data applications. In this paper, we develop both optimal and efficient suboptimal detectors for the RACH preamble with several candidate antenna configurations which are attractive for enhancing voice and data capacity. Analytic results, as well as extensive simulation results covering a variety of propagation environments, confirm that acceptable RACH preamble detection can be achieved even with a simple fixed-beam detector applied to configurations containing only closely-spaced antennas.