## 2 Preliminaries
### Random Access Procedure in LTE-A System  
In the Long Term Evolution-Advanced (LTE-A) system, a Random Access (RA) method, called Random Access Procedure, has been proposed for MTC [24]. The Random Access Procedure is identified as a key step for initial access [25]. In the Random Access Procedure, two uplink channels are required, i.e., Physical Random Access Channel (PRACH) and Physical uplink Shared Channel (PUSCH). PRACH is used for preamble transmission, and user data is scheduled to be transmitted through PUSCH. Random Access Channels (RACHs) are time-frequency resource blocks (RBs) repeated in the system periodically. There is a set of codes called preambles which are shared by all users in their random access. Each node requesting an uplink channel transmits a random access preamble in a RACH. There are two types of access modes in RACHs [3]. The first one is contention-free, eNodeB allocates a dedicate preamble sequence to each UE to ensure that no other UE will use the same preamble in the same PRACH at the same time. In this case, there is no collision in random access procedure [26]. The second type is contention-based, where a user selects a preamble randomly from the set of available preambles. In this case, two nodes may select the same preamble, resulting in a conflict. Most of the current studies are discussed in contention-based random access.  
The traditional contention-based access mode is comprised of four steps. The corresponding signaling is Msg1-Msg4:  
* Msg1: preamble transmission. Once an MTC device launches an access request to the RACH, it randomly selects a preamble with equal probability and transmits the selected preamble to the eNodeB via PRACH (i.e., the same uplink time-frequency resources). When two or more nodes select identical preambles and send them at the same time, there could be a collision.
* Msg2: random access response. If a preamble has been received correctly, the eNodeB computes an identifier and then transmits a random access response (RAR) to the UE devices. The RAR includes a RA preamble identifier (ID), an uplink grant for MSG3, timing alignment (TA) command for corresponding UEs, and assignment of a temporary identifier (the cell radio network temporary identifier, CRNTI). UE is expected to receive RAR within a timing window.
* Msg3: data transmission. A UE first finds its random access response by looking up the index of the preamble it has used in its random access request, and then uses the dedicated resource block (RB) on PUSCH to transmit a Connection Request message with a UE identifier to the eNodeB. If two or more UEs select an identical preamble in Step 1, they will implement uplink scheduling in the same RBs, thus scheduled message will not be correctly decoded by eNB due to the co-channel interference. This section is the main reason of random access conflict.
* Msg4: contention resolution. Upon reception of a Connection Request in Step 3, the eNodeB transmits a Connection Resolution message as an response to Step 3. Therefore, if a device does not receive Step 4, it will indicate a failure in the Contention Completion and launch a new access request after a random backoff.  
As we have introduced the ACB scheme in Section 2.1, the Random Access Procedure through the ACB mechanism is depicted in Figure 1.