A wireless device includes a preamble detector configured to identify a plurality of preambles transmitted via a random access channel of a wireless network. The preamble detector includes a noise floor estimator. The noise floor estimator is configured to: estimate, for a given preamble root sequence identified by the preamble detector, a noise floor value as mean energy of received signal samples, excluding detected preamble samples on the give preamble root sequence, below a noise floor threshold assigned to the given preamble root sequence. The noise floor estimator is configured to compute the noise floor threshold as a product of: average energy of the received signal samples less total signal energy contained in each cyclic prefix window in which a preamble is detected using the given preamble root sequence; and a predetermined normalized relative noise floor threshold based on a target false preamble detection rate.