The present disclosure relates to random access in wireless communication systems, and in particular to a wireless device, a preamble receiver, and methods for processing random access preamble signals. A disclosed method in a wireless device comprises generating (S11) one or more identical short sequences having a same time duration as an OFDM symbol used for carrying data traffic in a radio access network of the wireless device. The method also comprises generating (S12) at least one offset indicator sequence different from each of the short sequences, and constructing (S13) the preamble sequence by concatenating the at least one offset indicator sequence and the one or more identical short sequences in time, such that each of the at least one offset indicator sequence has a respective pre-determined location in the preamble sequence.