1. A baseband processor for processing communication signals in a wireless communication device, comprising: a mixing frequency generator configured to select a plurality of frequency offsets for an iteration of multiple frequency hypothesis (MFH) testing; a plurality of MFH branches, coupled to the mixing frequency generator, configured to receive respective frequency offsets in the plurality of frequency offsets; and an MFH branch selector, coupled to the plurality of MFH branches, wherein, for each iteration of the MFH testing, the MFH branch selector is configured to: determine, based on respective primary synchronization sequence (PSS) correlation peak magnitudes of the plurality of MFH branches, a selected MFH branch in the plurality of MFH branches, and check a consistency of cell identification (ID) information between a first portion of a radio frame for the selected MFH branch and a second portion of the radio frame for the selected MFH branch.