A method and apparatus for accessing a wireless communication system, and for processing random access attempts. A mobile communication device detects random-access information transmitted by a base station, transmits a random-access preamble to the base station according to the random-access information, and receives a random-access response from the base station. The random-access response includes at least an allocation of uplink resources to be used for the next step in the random access procedure. The mobile device also selects a reference signal sequence index from a pre-determined set of sequence indexes, and transmits a first message to the base station using the uplink resource allocation provided in the random-access response. The first message includes a device identifier and a first demodulation reference signal derived from a base reference sequence shifted according to the selected sequence index.