In LTE system, random access plays an important role in both uplink time adjustment and initial access of UE. This paper analyzes the theory of the related signal detection and the correlation calculation, and proposes a method to detect the received sequence in the receiver. And at last, it presents the implementation on DSP including the baseband signal processing module, Local frequency domain ZC sequence generation module and Correlation calculation module. In a word, it provides a solution for implement the PRACH receiver on hardware.