Dynamic Channel Assignment with Cumulative Co-Channel Interference Karen Daniels Kavitha Chandra Sa Liu Sumit Widhani kdaniels@cs.uml.edu Kavitha Chandra@uml.edu sliu@cs.uml.edu swidhani@cs.uml.edu Center for Advanced Computation and Telecommunications, University of Massachusetts, Lowell, MA, USA This paper studies the problem of centralized dynamic channel assignment (DCA) in wire- less cellular systems under space and time-varying channel demand. The objective is to minimize the number of channels required to satisfy demand while also satisfying co- channel interference constraints. Cumulative co-channel interference constraints govern channel reuse, via a threshold decision criterion based on the carrier-to-interference ratio. The paper makes two contributions. First, it provides an empirical bound on the difference between the minimal number of channels required based only on geographic reuse distance versus the cumulative interference case in the context of linearly increasing demand. The bound is characterized using only the reuse distance. It is obtained with an Integer Pro- gramming (IP) based strategy that uses channel assignments for one demand state to assign channels for the next state. Geographic locality constraints are applied to limit reassign- ments. The impact of cumulative interference constraints is observed to be small for small geographic localities. Second, the paper presents a new, fast DCA heuristic that is based on the characteristic channel reuse patterns used by the IP-based strategy. The heuristic and IP-based method yield similar results for the zero blocking condition. The DCA heuristic is applied to the problem of estimating the blocking probabilities of call arrivals modeled by a two state discrete-time Markov chain and uniformly distributed holding times. The blocking performance for an ensemble of spatial load imbalance distributions is uniquely characterized using the heuristic and IP solutions. I. Introduction Emerging wireless communication systems will in- creasingly rely on smart systems and intelligent net- works to optimize resources and maximize perfor- mance. Internet data services with highly variable ap- plication specific bandwidth requirements will repre- sent a major traffic component on wireless networks. Protocols and algorithms that support bandwidth ef- ficient distribution of resources for such applications are critical to the new generation of wireless systems. The adaptive allocation of wireless spectrum based on traffic characteristics and their performance require- ments may be examined in the context of a Dynamic Channel Assignment (DCA) model. The channel assignment problem has been exam- ined in a number of studies [1, 2, 3, 4, 5] over the last three decades. Typically, each cell is associated with an interference region that is based on geographic distance. In some cases, a predefined channel com- patibility matrix [6] specifies the required frequency separation between cells. Within this interference re- gion, channel reuse is prohibited. Engineering ap- proaches to this problem have addressed how the fixed channel assignment (FCA) policies applied to cellu- lar networks may be adapted when cells experienced more calls than the number of available channels. As- signment strategies have involved channel borrowing schemes where channels from the richest neighbor- ing cells are borrowed to minimize future call block- ing probability. Chuang [5] and Anderson [3] dis- cuss simulation studies of these algorithms and show that the number of search steps required impacts the time to solution. Modifications that reduce the num- ber of search steps have also been considered [7]. These involve channel ordering schemes where the fixed-to-borrowable channel ratio is dynamically var- ied according to changing traffic conditions. A sur- vey of fixed, dynamic and hybrid channel assignment schemes is provided by Katzela and Naghshineh [8]. Mathematical programming (MP) models for chan- nel assignment find assignments through minimiza- tion of a cost function such as the allocated band- width under the constraint that channel reuse takes place above specified interference levels. Murphey et al. [9] provide a comprehensive survey of algorithmic approaches to the problem. Graph coloring and IP formulations have been used for graph-theoretic ab- Mobile Computing and Communications Review, Volume 1, Number 2 1