# A Poisson Process-Based Random Access Channel for 5G and Beyond Networks +
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physical random access channel (RACH) through a four-step handshake process. Several UEs attempt to communicate over the same channel resources in a dense UE deployment. The UEs contend to control the common radio resources, which creates a massive collision problem. Due to simultaneous UE channel access, preamble collisions can obstruct the RA process. The problem of successful RA is crucial due to the increasingly growing number of connected UEs in the network [6]. A standard 5G network consists of two parts: the enhanced packet core (EPC) network and the radio access network (RAN) [7]. A high-level architecture of a typical 5G network with linked UEs' connectivity is shown in Figure 1, where the UEs are linked to the eNBs. The EPC is responsible for the ultimate regulation of mobile devices and creating an Internet Protocol (IP) packet transmission path. The RAN is responsible for wireless networking and radio resource usage. The RAN, which provides the requisite protocols for the user and control plane to communicate with mobile devices (UEs) in 5G network, is composed of eNBs. The eNBs are interconnected through the X2 interface. In addition, the eNB is connected to the EPC using an S1 interface [8].  
In a standard 5G network, the minimal resource scheduling unit for downlink (DL) and uplink (UL) transmission is referred to as a resource block (RB). An RB consists of 12 subcarriers in the frequency domain (FD), each size of 180 kHz and one subframe in the time domain (TD), length of 1 ms. This time-frequency resource is called RACH, and it is the RB on which RA is performed. RA helps UEs initialize an association, known as a contention-based RA (CB-RA) method [9]. In a CB-RA, UEs utilize preambles to launch the RA transmission attempt. There is a total of 64 preambles divided into two categories; preambles of contention-free RA (CF-RA) and preambles of CB-RA. For CF-RA, the eNB incorporates a few preambles and designates specific preambles for various UEs. Residual preambles are used for CB-RA, where every UE randomly chooses one preamble from a set of predefined uniform random variables (RV) [7].  
This uniform distribution (UD) of RVs is used to prevent the inevitable collisions in the 5G network when multiple UEs attempts to access the channel resources. However,  
Figure 1: A typical user equipment (UE) communication in a 5 th generation (5G) network.  
in a UD-based channel access mechanism, every UE has an equal chance to choose an identical contention preamble close to the mean value of the UD, that is, \(\frac{(a+b)}{2}\) for a lower bound \(a\) and an upper bound \(b\), which may cause an increase in a collision among the UEs. However, we may use a Poisson process-based distribution, which expresses the probability of a given RV of events independently and distributively occurring in a fixed interval of time or space with a known constant rate. Figure 2 shows a random variable (\(X\)) between a uniform random value and a Poisson process-based random value (that is an ED). In a Poisson process-based method, an ED distributes random values between two boundaries. Random variables exist constantly and independently with a constant average rate of \(\frac{1}{\lambda}\), for the \(\lambda\) as a constant rate parameter.