Finite Population Model for Performance Evaluation Between Narrowband and Wideband Users in the Shared Radio Spectrum Miroslava Raspopovic and Charles Thompson Center for Advanced Computation and Telecommunications Department of Electrical and Computer Engineering University of Massachusetts Lowell Lowell, MA 01854 Abstract— In this paper a theoretical evaluation of channel access availability of narrow and wideband users occupying a common range of frequencies in the radio spectrum is presented. User inter-request and call duration times are taken to be random and exponentially distributed. The number of available frequency channels is fixed. The differentiating feature between narrow and wideband users is the number of frequency channels required by each user to transmit their data. The probability of a given user being blocked from acquiring a spectral channel is determined. It is shown that the degree of blocking experienced by narrowband users can only be maintained by either throttling the offered load or limiting population size of wideband users requesting channel access. I. I NTRODUCTION Under a static frequency allotment scheme each licensed operator is allocated a frequency band in which its users can transmit. The licensed operator is charged with monitoring and regulating user transmissions. Fixed channel allotments allow one to minimize interference by users of adjacent frequency bands. With the addition of new services and the increase in the number of users requiring radio frequency access, underutilization of spectral resources is of concern. It has been demonstrated [1] that the spectrum may not be fully utilized either on a geographical or at a temporal level. These unused portions of the spectrum may offer opportunities for unlicensed user transmissions and applications. With the growth of the number of wireless users, efcient and secure usage of the radio spectrum has taken on greater importance. Interference and other factors that negatively impact the quality of service for the licensed users remains an obstacle to simply overlaying secondary users onto the licensed spectrum. The introduction of cognitive radio is seen as one possible solution for managing multiple networks using the same radio spectrum. Cognitive radio refers to smart radio that has capa- bility to detect and adopt appropriate transmission parameters to accommodate userVs communication needs[2][3]. Cognitive radios appear to be a prefect t for managing the spectrum for co-operating networks. However it is uncertain to what extent such unlicensed user activity may impact the performance of the exiting licensed user pool. The design and development of cognitive radios have motivated researchers to investigate method to better utilize the radio spectrum. Understanding the performance of systems that share a common spectral resource is essential for the design of communication networks that may use cognitive radio. Work has been done on modeling the performance of narrowband (NB) and wideband (WB) systems. Epstein and Schwartz [4] proposed an admission control algorithm. A multiclass prediction method is used for fair bandwidth sharing and blocking control. Kim[5] extended their work by creating a more general model which fairly admits NB and WB users. GimpelsonVs [6] access model for NB and WB sources allowed WB callers to be given an advantage when they can not gain access. In order to equalize the accessibility of both system Gimpelson introduced a switching model based on the blocking probabilities of both systems. Xing et al.[7] proposed a Markov model for the dynamic access allocation in open spectrum for NB and WB sources in which fairness based on airtime for both systems was analyzed. Giorgetti [8] investigated performance of UWB system in the presence of Bluetooth-like and GSM-like signals assuming Rake reception in Nakagami channels. The steady state blocking probabilities have been used to model performance of many communications systems such as multi-hop wireless networks[9], cellular[10] and optical networks[11]. However, their objectives and system charac- teristics are different than presented in this paper. Blocking probabilities in most optical networks papers are modeled based on wavelength availability. Multi-hop networks trans- mit by hoping the signal through multiple nodes before the signal reaches its nal destination. On the other hand, cellular networks communicate with the neighboring cells. We use a simple multi-server queueing Markov model to evaluate the impact of spectrum sharing between NB and WB systems. There are numerous interesting applications, both commer- cial and military, to which this model applies. Some of these applications are Bluetooth and Ultra-Wideband (UWB). Both