Online Frequency Assignment in Wireless Communication Networks

Abstract

Wireless communication has many applications since its invention more than a century ago. The frequency spectrum used for communication is a scarce resource and the Frequency Assignment Problem (FAP), aiming for better utilization of the frequencies, has been extensively studied in the past 20-30 years. Because of the rapid development of new wireless applications such as digital cellular network, cellular phone, the FAP problem has become more important.

In Frequency Division Multiplexing (FDM) networks, a geographic area is divided into small cellular regions or cells, usually regular hexagons in shape. Each cell contains one base station that communicates with other base stations via a high-speed wired network. Calls between any two clients (even within the same cell) must be established through base stations. When a call arrives, the nearest base station must assign a frequency from the available spectrum to the call without causing any interference with other calls. Interference may occur, which distorts the radio signals, when the same frequency is assigned to two different calls emanating from cells that are geographically close to each other. Thus the FAP problem can be viewed as a problem of multi-coloring a hexagon graph with the minimum number of colors when each vertex of the graph is associated with an integer that represents the number of calls in a cell.

FAP has attracted more attention recently because of the following:

a) Online analysis techniques: FAP problem is known to be NP-complete and many approximation algorithms have been proposed in the past. As frequency assignments have to be done without knowledge of future call requests and releases, online algorithms have been proposed and competitive analysis has been used to measure their performance.

b) New technology and application: Wideband Code-Division Multiple-Access (W-CDMA) technology is a new technology used for the implementation of 3G cellular system. Orthogonal Variable Spreading Factor (OVSF) codes are used to satisfy requests with different data rate requirements. FAP with OVSF code trees representing the frequency spectrum becomes an important problem.