275 IETE JOURNAL OF RESEARCH | VOL 55 | ISSUE 6 | NOV-DEC 2009 Time and Angle of Arrival Statistics of Mobile- to-Mobile Communication Channel Employing Circular Scattering Model Babu Sena Paul, Abul Hasan, Himanshu Madheshiya and Ratnajit Bhaacharjee Department of Electronics and Communication Engineering, Indian Institute of Technology Guwahati, Assam, India ABSTRACT Mobile-to-mobile communicaon becomes necessary in many emerging wireless communicaon systems. Characteriscs of mobile-to-mobile communicaon channel have been studied through a geometrical single bounce scaering model and analycal expressions for angle of arrival and me of arrival probability density funcons have been derived for such models. Analycal expressions have been verified through computer simulaons. This paper aims to provide a beer understanding of mobile-to-mobile channel behavior in terms of the parameters studied. Keywords: Angle of arrival, Time of arrival, Channel model, Geometry based single bounce modeling, Mobile-to-mobile communicaon. 1. INTRODUCTION Studies on mobile-to-mobile (M2M) communication and relay based communication have been attracting significant attention of the research community [1-5] with the advent and popularity of wireless adhoc net- works, advanced cellular networks and wireless sensor networks. In an M2M channel both the transmitter and receiver are surrounded by local scatterers. Making it channel different from a conventional macro cellular channel. In a scattering environment the angle of arrival (AOA) and time of arrival (TOA) probability density func- tions (PDF) depend on the location as well as distribution of scatterers. Beam steering and interference mitigation, in a wireless environment using antenna arrays, require prior knowledge of the AOA of signals. Information on the TOA statistics helps determine data rates and symbol periods so as to avoid ISI. As in the case of the macro cellular scenario [6,7], it is necessary to develop appro- priate models representing M2M channels and study the distribution of TOA and AOA pertaining to such models. A widely used geometrical model for macro cellular scenario consists of a uniformly distributed circular scattering region around the mobile station [8,9]. This modeling technique has been extended for the M2M case by considering uniformly distributed circular scattering region around both transmitter and receiver. Further, only single scattered waves have been considered sig- nificant. The analytical expressions for AOA and TOA PDFs for the single bounce geometrical model for M2M communication have been derived and verified through simulation studies. The paper is organized as follows: Section 2 elaborates on the model under consideration. Analytical expres- sions for time and angle of arrival have been derived in section 3 and section 4 respectively. Finally, conclusions are drawn in section 5. 2. MODEL DESCRIPTION The M2M channel model under consideration may be considered a geometry-based single bounce model as shown in Figure 1. M 1 and M 2 denote the transmitting and receiving mobile communicating devices respec- tively, separated by a distance D. The model can take into account mobile devices with one or more antennas. In this model, scatterers are assumed to be distributed in two circular regions around M 1 and M 2 . In general, the distribution of scatterers may be arbitrary, and it will affect the AOA and TOA PDFs evaluated using the model. The analysis presented here has been carried out assuming uniform distribution of scatterers. R 1 and R 2 respectively denote the radii of the scattering regions around M 1 and M 2 . N 1 and N 2 represent the number 5  0  0  5  ' Figure 1: Uniformly distributed circular scaering regions surrounding mobile nodes modeling mobile-to-mobile propagaon environment.