A method and apparatus reduce latency of Long Term Evolution (LTE) uplink transmissions. A Downlink Control Information (DCI) message can be transmitted in a first subframe. The DCI message can indicate a resource assignment and a modulation and coding scheme and indicating a plurality of cyclic shifts from which a User Equipment (UE) may select one cyclic shift for transmission in a second subframe on an uplink carrier. A data packet can be received on a Physical Uplink Shared Channel (PUSCH) in a resource indicated by the resource assignment and modulation and coding scheme, and using a Demodulation Reference Signal (DMRS) based on a selected cyclic shift in the second subframe on the uplink carrier.