# CeRA-eSP: Code-Expanded Random Access to Enhance Success Probability of Massive MTC
## 4 Proposed Scheme  
In this section, we describe the proposed code-expanded random access to enhance the success probability (CeRA-eSP). The CeRA-eSP is a random access scheme to reduce the preamble collision rate in the mMTC environment and improve the actual random access success rate while considering uplink resource limitations. The overview of the proposed CeRA-eSP is shown in Figure 4. The CeRA-eSP consists of four phases: estimation of the number of active devices, SIB-2 broadcasting, preamble transmission, and RAR response. First, the number of active devices estimation phase aims to estimate the current access intensity indicator, which is utilized in the preamble codeword set selection algorithm. We use the Bayesian rule-based estimation scheme proposed in [28] to measure the number of active devices in each RAO. The Bayesian estimation scheme requires an a priori distribution and the number of idle preambles in the previous RAO to estimate the posterior distribution of the current RAO. Because the posterior distribution estimated at time slot \(t\) is used as an a priori distribution in the next time slot \(t+1\), it is possible to obtain the number of active devices in the current RAO using a recursive Bayesian estimation. The number of active devices for all RAOs is calculated using the following recursive calculation based on the Bayesian rule:  
\[\
u\leftarrow\
u\bigg{(}1-\frac{I}{M}\bigg{)}\bigg{(}1-e^{-\frac{\
u}{M}} \bigg{)}^{-1}, \tag{3}\]  
where \(I\) is the number of unselected preambles and \(\
u\) is the mean value of the activated device. Second, the SIB-2 message broadcasting phase is a process for selecting the optimal preamble codeword set to optimize random access performance. In a legacy CeRA scheme, an oversized preamble codeword set, which increases exponentially as the codeword length increases, causes the codeword ambiguity problem mentioned in Section 1. We refine the scale of the codeword set by limiting the transferable preamble sequences in the first RA to solve the codeword ambiguity problem. Due to the trade-off relationship between codeword utilization and the collision rate, it is necessary to select the optimal preamble codeword set considering both factors in order to improve the overall RA success rate. We design mathematical models for three key RA performance indicators, (1) preamble transmission success rate, (2) preamble codeword utilization rate, and (3) PUSCH timeout rate, which are described in Section 4.1, to implement the preamble codeword selection algorithm. The BS determines the number of preamble sequences that can be transmitted in the first random access slot for the current RA cycle according to a mathematical model based on the estimation of the number of active devices. The BS sequentially allocates the preamble sequences of the first random access slot and continuously records the last number of the preamble indexes of the first RA slot that were used in the previous RA cycle. Through the last preamble index and preamble sequence scale information, the BS broadcasts the available preamble sequence indexes of the first random access slot in the current RA cycle using the SIB-2 message. The devices can identify the transferable preamble codeword set in the current RA cycle based on the SIB-2 message information. Third, the preamble codeword transmission phase aims to reduce the collision rate in the preamble transmission phase by transmitting a large-scale preamble codeword. In Figure 4, the devices randomly transmit one of the transferable preamble sequences in the first RA slot. Thereafter, the devices randomly transmit one of the \(M\) preamble sequences in the second RA slot. Through two consecutive preamble sequences, the device can transmit one preamble codeword. Devices that have transmitted the preamble codeword monitor the signal on the physical downlink shared channel for a predefined RAR receive timer, which is used in legacy random access procedures.