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, wherein the MFH branches are configured to receive respective frequency offsets in the plurality of frequency offsets; and a MFH branch selector coupled to the MFH branches, wherein, for each iteration of the MFH testing, the MFH branch selector is configured to: determine a selected MFH branch in the plurality of MFH branches, wherein the selected MFH branch has a highest primary synchronization sequence (PSS) correlation peak magnitude in the plurality of MFH branches, and perform a consistency check on cell identification (ID) information of a radio frame for the selected MFH branch.