# Improvement and Performance Evaluation When Implementing a Distance-Based Registration
## 1 Introduction  
To cope with the continuous increase of mobile subscribers and provide various multimedia services with good quality, the efficiency of radio channels, which are limited resources, must be maximized. Due to the nature of the mobile network, two functions must be performed to connect calls to user equipment (UE): location registration, performed by the UE, and paging, performed by the base station (BS). Location registration refers to a process to update the location area (LA) information of the subscriber in the system database when the LA of the subscriber changes in the mobile network. Paging refers to a process in which the network pages the UE to identify the exact location (BS) of the UE in order to connect the incoming call to the UE. Because future mobile networks deal with smaller cells, higher user density, and higher mobility, it is essential to adopt effective mobility management schemes for location registration and paging [1; 2; 3; 4; 5].  
Many studies have been performed to reduce the signaling cost on radio channels in terms of location registration and paging. Studies on location registration have been most frequently performed regarding zone-based registration (ZBR) [2; 3; 5; 6; 7; 8] because ZBR shows a rather good performance and its implementation in real networks is easy. In addition, studies on distance-based registration (DBR) [9; 10; 11; 12; 13; 14; 15], movement-based registration (MBR) [9; 16; 17; 18; 19], time-based registration [20], tracking area list (TAL)-based registration [4; 21; 22; 23], and auxiliary location registrations such as power-on registration, power-off registration, and implicit location registration have also been performed for next-generation networks [1; 5]. Studies on the problem of paging load optimization [24; 25] can also be included in the studies on location registration by default since they basically relate to the trade-off between paging load and registration load closely.  
To analyze the performance of location registration, the mobility model of subscribers is very important. Thus, the objective of this study was to analyze the performanceof DBR based on a 2-D random walk model. Previous studies on DBR using random walk mobility models [9; 11; 15; 16] have presented the optimal size of the LA assuming that an LA is composed of rings of cells to compare the performance with ZBR [6] or MBR [9; 16]. However, this kind of ring-by-ring system environment assumed in previous studies [6; 12; 16; 17] has significant problems for real-world systems since the number of cells comprising the LA increases discretely and steeply.  
In this study, we considered DBR, which is known to have better performance than ZBR, assuming a random walk mobility model and an LA increasing on a ring-by-ring basis [6]. In this study, we proposed a DBR with an LA increasing on a cell-by-cell basis, rather than a conventional LA increasing on a ring-by-ring basis, and obtained the optimal number of cells of the LA that minimizes signaling cost on the radio channels. Throughout this study, we will show that the optimal LA can be constructed in an environment that is not possible if only a ring-by-ring DBR is considered and therefore, for an accurate evaluation of DBR, the performance should be evaluated for the LA increasing on a cell-by-cell basis.  
This paper is organized as follows: Section 2 describes DBR; Section 3 describes the system environment and mobility model for analyzing location registration and paging cost, as well as the LA configuration according to the increase of the number of cells in the LA; Section 4 presents an analytical model for obtaining signaling cost on radio channels; Section 6 presents numerical results; Section 7 describes conclusions and discussion.