# Exploiting the Capture Effect to Enhance RACH Performance in Cellular-Based M2M Communications
## 1 Introduction
In [9], the authors analyzed the non-overlapping preamble separation, proposing the use of a load-adaptive throughput-maximizing preamble-allocation procedure, which automatically adjusted the preamble allocation to the priority classes, based on the access load. Both studies showed that the preamble-separation scheme increased the RA throughput, especially when the access load was heavy. The energy consumption of M2M devices is also a very important issue because most M2M devices are vulnerable to energy consumption. Therefore, many studies have been conducted on the energy consumption of the RA process. In [10], further improvement of traffic scattering for the group paging (FI-TSFGP) scheme was proposed to achieve high channel-access probability for M2M services. They also provided analysis of the scheme in terms of access latency and power consumption. Consequently, they argued that the FI-TSFGP scheme led to the reduction of both the channel access latency and the power consumption. In [11], group-based access control was studied in terms of the energy consumption of M2M devices. The authors introduced a coordinator to reduce massive access. In addition, they proposed a joint massive access control and resource allocation scheme that minimized total energy consumption. Analyzing the RA procedure is fundamental to understanding the RACH congestion problem and to providing the proper solutions. Various studies have analyzed an RA procedure to solve the RACH problem. These studies have mostly focused on the well-known multi-slotted Advocates of Linux Open-source Hawaii Association (ALOHA) model. The RA throughput, access delay, efficiency, and energy consumption of the RA procedure have been well analyzed using the multi-slotted ALOHA model [4; 5; 6; 12; 13; 14]. However, these studies used the classical collision model to interpret RA nature, which assumes that no signal is decoded when multiple nodes transmit simultaneously. This model allows for simple analysis but does not yield accurate results due to the characteristics of wireless communications. Other studies have used the slotted-ALOHA system in a capture model [15; 16]. This model assumed that a certain signal could be decoded when the received power of a specific signal was larger than a predefined threshold. Studies exploiting this model have provided more realistic results. In this paper, we provide novel solution to resolve the RACH congestion problem due to massive access of M2M devices by exploiting the capture effect: Msg3 power ramping (PR) scheme. The main contributions of this paper are summarized as follows:  
1. We formulated analysis models of the RA procedure considering the capture effect. Previous studies [4; 5; 6; 12; 13; 14] adopted the collision model to analyze the RA procedure and assumed that the RA performance degradation due to the collisions of the preambles (Msg1) could not be prevented. However, we provide an RA analysis model that considers the capture effect. Therefore, we consider RA performance improvements due to the capture effect of the physical layer, even if the collision occurs. We provide an RA performance analysis model, in terms of the RA throughput, the connection failure probability, and the average energy consumption of the devices. 2. Exploiting the capture effect to improve the RA performances, we propose the Msg3 PR scheme. This scheme causes a difference in the received power of messages at the eNB, so that the capture effect occurs frequently. In addition, it is easy to apply because the proposed scheme adopts the power ramping scheme that has already been used in the cellular system. Moreover, by applying this new technique, a device that has performed many retransmissions would have a higher RA success probability; thus, the connection failure probability could be reduced. 3. In the simulation, we demonstrate the accuracy of proposed analysis and the advantages of the Msg3 PR scheme. In addition, the effects of various network parameters on the performance of the technology are demonstrated.