1 Channel assignment and graph multicoloring

Cellular data and communication networks are usually modeled as graphs with each node representing a base station in a cell in the network, and edges representing geographical adjacency of cells. The problem of channel assignment in such networks can be seen as a graph multicoloring problem. We survey the models, algorithms, and lower bounds for this problem. — 1.1 INTRODUCTION In a cellular network, there are ongoing requests for communication links from mobiles in each cell to the base stations responsible for the cell. In FDMA or TDMA networks, the available spectrum is divided into narrow frequency channels, and each communication request is served by the assignment of a frequency channel. Spectrum is a scarce resource, and careful assignment of channels to calls is critical to being able to maximize the number of users in the network. Cellular networks employ a low power transmitter in every cell, which makes it possible to reuse the same frequency channel in different cells. Frequency reuse, however, is limited by two Ê Ì ÖÙÙÖÝ ½¸¾¼¼¾¸½¼¼¿¿¿Ñ Ê Ì ii CHANNEL ASSIGNMENT AND GRAPH MULTICOLORING kinds of radio interference. Co-channel interference is caused by two simultaneous transmissions on the same channel. To avoid this, once a channel is assigned to a certain call, it should not be reused by another call in an area where it may cause significant interference. Adjacent channel interference is the result of signal energy from an adjacent channel spilling over into the current channel. In this chapter, we model cellular data and communication networks as graphs with each node representing a base station in a cell in the network, and edges representing geographical adjacency of cells. Associated with each node Ú in the graph at any time is a set´Úµ which is the set of calls or active mobiles in the cell served by Ú. The size of the set´Úµ, is denoted Û´Úµ, and called the weight of the node Ú. Co-channel interference constraints are modeled in terms of reuse distance; it is assumed that the same channel can be assigned to two different nodes in the graph if and only if their graph distance is at least Ö. We do not deal with adjacent channel interference in this chapter; see [20] (in this book) for models and solutions for this problem. For our purposes, the objective of an algorithm for the channel assignment problem is, at time instant Ø, to …