# CeRA-eSP: Code-Expanded Random Access to Enhance Success Probability of Massive MTC
## 1 Introduction
In a conventional RA scheme, the BS can accurately discern the actual transmitted preamble sequence for each RA slot. By contrast, the CeRA method deduces the preamble codeword based on the preamble observation for each random access slot, allowing it to recognize the preamble codewords that have not been transmitted. For example, we consider a situation in which \(n\) devices transmit a preamble codeword of length \(l_{c}\). If the devices transmit different preamble sequences in all RA slots, the actual number of preamble codewords transmitted by the devices is equal to the number of devices \(n\). However, the BS deduces the number of \(n^{l}\) possible combinations based on the preamble sequence observations for each RA slot. A preamble codeword that the device did not actually transmit was deduced by the BS, which is defined as a phantom codeword. The codeword ambiguity problem refers to a problem in which it becomes difficult to identify the actual preamble codeword as the proportion of phantom codewords increases. The codeword ambiguity problem causes a shortage of PUSCH resources. In the legacy RA scheme, the BS recognizes the transmitted preamble sequences and sends a random access response (RAR) message to the user-sent preamble sequences. The device allocates a dedicated PUSCH resource using an RAR message when the preamble transmission is successful. The PUSCH resource is a limited uplink resource for the device to transmit data packets and control signals after the preamble transmission. The PUSCH shortage problem occurs when PUSCH resources are wasted on phantom codewords. Specifically, the majority of deduced preamble codewords are phantom codewords when codeword ambiguity is high. If the BS randomly allocates PUSCH resources, most of them are allocated to the phantom codeword. Because the phantom codeword is not a preamble codeword transmitted by an actual device, this results in a waste of PUSCH resources. If PUSCH resources are wasted, the PUSCH resources that need to be allocated to the transmitted preamble codewords become insufficient. Because devices that are not allocated PUSCHresources are dropped during the RA process, the shortage of PUSCH resources is directly related to the degradation of the RA performance. As mentioned previously, two main factors contribute to the degradation of the RA performance: preamble collision and codeword ambiguity. If the BS attempts to solve the high collision rate by using a large-scale preamble codeword set, the codeword ambiguity problem occurs because of a non-overlapping preamble transmission, which incurs a large, deduced preamble set. By contrast, if the BS utilizes a small preamble codeword set to solve the codeword ambiguity problem, the performance of the RA deteriorates owing to the preamble collision. Because both factors are closely related to performance according to the size of the preamble codeword set, preamble collision and codeword ambiguity have a trade-off relationship. To maximize the RA performance, CeRA studies that consider both factors should be conducted. In this paper, we propose a code-expanded random access to enhance success probability (CeRA-eSP) scheme that considers preamble collision and codeword ambiguity to increase the RA success rate and PUSCH resource utilization. The proposed scheme consists of a preamble codeword-set selection phase and PUSCH resource allocation phase. In the preamble codeword set selection algorithm, we design three probabilistic analysis models with respect to the preamble transmission success rate, preamble codeword utilization rate, and PUSCH timeout rate. Because the three factors have a trade-off relationship, we analyze the random-access success rate by considering these three factors and select the preamble codeword set that maximizes the random access success rate. In the PUSCH resource allocation phase, we propose an improved PUSCH allocation procedure that utilizes the PUSCH waiting message.