1156 IEICE TRANS. COMMUN., VOL.E92–B, NO.4 APRIL 2009 PAPER Blocking Probability Calculation for Cellular Systems with WCDMA Radio Interface Servicing PCT1 and PCT2 Multirate Traffic * Mariusz GL ˛ ABOWSKI †a) , Member, Maciej STASIAK † , Arkadiusz WI ´ SNIEWSKI †† , and Piotr ZWIERZYKOWSKI † , Nonmembers SUMMARY This article proposes a method that can calculate the blocking probability of multi-service cellular systems with Wideband Code Division Multiple Access radio interface. The method considers a finite and an infinite source population and takes into account the interdependency of calls service processes in neighboring cells and in both the uplink and the downlink directions. The basis of the proposed method is the fixed- point methodology. A comparison of the results of analytical calculations to those of simulations confirms the accuracy of the proposed method. The proposed scheme can realize cost-effective radio resource management in 3G mobile networks and can be easily applied to network capacity calcula- tions. key words: UMTS, WCDMA, blocking probability 1. Introduction Universal Mobile Telecommunications Systems (UMTS) using Wideband Code Division Multiple Access (WCDMA) radio interface is one of the standards proposed for the third generation cellular technologies (3G). According to the International Telecommunication Union (ITU) recom- mendations, 3G systems should include services with cir- cuit switching and packet switching, transmit data at speeds of up to 2 Mbit/s, and ensure access to multimedia services [2]. Due to the possibility of resource allocation for dif- ferent traffic classes, capacity calculation of the WCDMA radio interface is much more complex than in the case of Global System for Mobile Communications (GSM) system. Moreover, all users serviced by a given cell make use of the same frequency channel and a differentiation of the trans- mitted signals is possible, only and exclusively, by an appli- cation of orthogonal codes [3]. However, due to the multi- path propagation occurring in a radio channel, not all trans- mitted signals are orthogonal with respect to one another and, consequently, are received by users of the system as an interference adversely affecting the capacity of the sys- tem. Additionally, an increase in the interference is caused by users serviced by other cells of the system, who make Manuscript received May 8, 2008. Manuscript revised September 29, 2008. † The authors are with Pozna ´ n University of Technology, Chair of Communications and Computer Networks, Pozna´ n, Poland. †† The author is with PTK Centertel, Orange Group, Poland. ∗ This article is the extended version of the paper which re- ceived The Best Paper Award on Asia-Pacific Conference on Com- munications (Perth, Australia, 2005) [1]. a) E-mail: mariusz.glabowski@et.put.poznan.pl DOI: 10.1587/transcom.E92.B.1156 use of the same frequency channel, as well as by the users making use of the adjacent radio channels. To ensure appro- priate level of service in UMTS it is thus necessary to limit the interference by decreasing the number of active users or the allocated resources employed to service them. Several papers have been devoted to traffic modeling in cellular systems with the WCDMA radio interface i.e. [4]– [9]. The analytical method of blocking probability calcula- tion in a single cell serviced multi-rate traffic from an infini- tive number of sources was proposed in [4]. It was assumed that the service of a new call depended on the appropriate amount of free resources in the cell and the levels of the own cell and other cell interference. The total blocking proba- bility in [4] was calculated with the help of the so-called Kaufman-Roberts recursion [10]–[12], while other cell in- terferences were characterized by a random variable with the lognormal distribution. In [5], the Kaufman-Roberts re- cursion was applied to model isolated cell with prioritized handover traffic. The assumption of lognormal distribution was also used in [6] to determine the so-called Erlang ca- pacity of a single cell and cell coverage in WCDMA system with multi-rate traffic. In [7], the authors determined Erlang capacity of the WCDMA system based on the limited num- ber of channel elements in base station and on the assumed value of blocking probability calculated on the basis of Erlang-B formula. The convolution algorithm [13] has been used in [8] for blocking probability calculation of multi-rate traffic serviced in an isolated cell without inteferences. In [9] the concept of the so-called traffic equivalent distribu- tions was proposed to calculate the blocking probability in UMTS cells, using Gausian distribution. The proposed so- lution, limited to the systems with Poisson call streams, ex- ploits the relation between the interference power, the total transmit power and the traffic capacity of the systems. The present article proposes a complete methodology of modeling the WCDMA radio interface in multi-service wireless systems. The presented methods are the extension of the the models proposed by the authors in several earlier works [1], [14], [15]. In the article we model the WCDMA radio interface by the full-availability group servicing a mix- ture of multi-rate Erlang (infinite source population) and En- gset (finite source population) traffic streams. The basis of the proposed methodology is the fixed-point methodology [16] that makes it possible to take into account the interde- Copyright c  2009 The Institute of Electronics, Information and Communication Engineers