# Exploiting the Capture Effect to Enhance RACH Performance in Cellular-Based M2M Communications
## 2 System Model  
### Random Access Procedure  
An M2M device in the radio-resource-control (RRC) idle mode performs an RA procedure to set up a connection with an eNB before data transmission. There are two types of RA procedures: contention-free and contention-based. In this study, we focus on the contention-based RA procedure. Before beginning the RA, the device listens to the system information block (SIB) messages broadcasted periodically by the eNB. The SIB messages contain information about the RA, such as the physical random access channel (PRACH) configuration index and the frequency offset, which inform about what resource blocks are reserved for the subsequent RA. Furthermore, information about which preambles are reserved for groups and about power control is included in the SIB messages. The contention-based RA procedure includes four steps messages exchanging [17]; the RA procedure modeled in this study is as follows:  
1. Msg1. Preamble transmission The RA procedure is initiated by the transmission of a preamble that is randomly chosen from preamble set \(V\) at a predetermined RA slot. As a result, there are three cases: singleton preamble, collided preambleand empty preamble. Singleton preamble is chosen by exactly one device,the collided preamble preamble is chosen by multiple devices, and the empty preamble is chosen by none of the devices. An eNB can only detect whether a specific preamble is transmitted, but cannot determine whether it is a collided preamble or a singleton preamble [17; 18]. Devices that send Msg1 set the random-access-response (RAR) window.
2. Msg2. RAR When the eNB detects a preamble transmission, it sends an Msg2 for the corresponding preambles through the physical-downlink control channel (PDCCH). This Msg2 contains the radio-network temporary identifier (RA-RNTI), the timing-advance (TA) information, and the uplink grant. The RA-RNTI identifies the corresponding preamble, the TA information is used to adjust the synchronization of the corresponding device, and the uplink grant is used to schedule the transmission of Msg3. Because the eNB cannot distinguish between singleton and collided preambles, it sends Msg2 for either preamble. Therefore, multiple devices that select the same preamble during Msg1 transmission receive the same Msg2, which only indicates the corresponding preamble. If a device does not receive an Msg2 within the RAR window, it realizes that the current RA has failed.
3. Msg3. RRC-connection request After sending Msg1, the device observes the PDCCH for the RAR window. If it finds the corresponding Msg2, it sends the Msg3, containing its identifier, by using a physical-uplink shared channel (PUSCH) informed by the uplink grant in the Msg2. Devices that send Msg3 set the contention-resolution time. Devices that choose the same preamble (i.e., collided preamble) also send an Msg3 containing their own identifier by using the same uplink grant, and, therefore, an Msg3 collision can occur.
4. Msg4. RRC-connection setup The eNB transmits the Msg4 using the PDCCH to inform the device that an RRC connection has been set up. Because the Msg4 contains the device identifier received from successfully received Msg3, an RA collision can be resolved if a specific Msg3 is decoded by capture effect.  
If any of the four steps fails, an RA failure occurs. In this study, we assume that RA failure only occurs when the devices fail to receive an Msg 4. If a device does not receive an Msg 4 within the contention-resolution time, it performs a random back-off and re-attempts the RA, if the trial number does not exceed the maximum trial number, \(N_{max}\). If the trial number exceeds \(N_{max}\), a _connection failure_ occurs. Note that the trial number can be from 1 to \(N_{max}\). If the RA procedure is successful within \(N_{max}\) RA trials, the device successfully connects to the eNB. We do not consider the hybrid automatic repeat request (HARQ) procedure for Msg3 or Msg4, nor do we consider the PDCCH resource constraint.