Random Access process plays two main roles - establishment of uplink synchronization and establishment of a unique UE ID (C-RNTI) known to both the network and the UE.So Random Access is used not only for initial access, but also after periods of uplink inactivity when uplink sync got lost in LTE_ACTIVE states.
i) UE initiate a Random Access Procedure on the (uplink) Random Access Channel (RACH).(The location of RACH in the frequency/time resource grid the RACH is known to the mobile via the (downlink) Broadcast Channel (BCH). The random access message itself only consists of 6 bits and the main content is a random 5 bit identity)
ii) Network sends a Random Access Response Message(RARM) at a time and location on the Physical Downlink Shared Channel (PDSCH) (The time and location of RARM on PDSCH can be calculated from the time and location the random access message was sent. This message contains the random identity sent by the device, a Cell Radio Network Temporary ID (C-RNTI) which will be used for all further bandwidth assignments, and an initial uplink bandwidth assignment)
iii) The mobile device then uses the bandwidth assignment to send a short (around 80 bits) RRC Connection Request message which includes it's identity which has previously been assigned to it by the core network
Only the step i) uses physical-layer processing specifically designed for random access. The remaining steps utilizes the same physical layer processing as used for normal uplink and downlink data transmission.
For more detailed explanation about this procedure, refer to http://www.sharetechnote.com/html/RACH_LTE.html