Long Term Evolution (LTE) is the latest development in the field of mobile communication system. LTE physical layer uses single carrier modulation scheme SCOFDM as the uplink (from mobile to base station) due to its relatively low Peak to Average Power Ratio (PAPR) and uses OFDM as downlink (from base station to mobile) due to less complex equalizer. It is important for mobile device to synchronize with the base station in order to transmit or receive data. LTE downlink system uses synchronization signals to detect the frame timing and cell information. LTE uplink system needs time adjustment as mobile devices are at different distances with the base station. To time align the different mobiles, random access procedure is performed. Once uplink and downlink synchronized data transfer is carried between the mobile and base station. The thesis discusses and simulates the signals used during synchronization and random access procedure using MATLAB.