Mathematical modeling, design, and optimization of mobile communiciation networks


R. Mathar,


        It is generally known that stochastic modeling and algorithms are an essential part of modern digital radio communication. Statistical Signal Detection and Information Theory are typical examples of fields which use complex mathematical models for optimum channel estimation and symbol detection, source and channel coding, as well as error correction methods. It is the intention of this work to show how methods from stochastic modeling and optimization, besides the above, influence the deployment of mobile communication networks. Mobile telephony and services are presently one of the fastest growing markets worldwide. In Europe, the existing second generation networks based on the GSM standard (GSM = global system for mobile communication) have more than 328.2 Million subscribers, worldwide there are more than 564.6 Million (July 2001). A similar success is expected for the upcoming UMTS networks (UMTS = universal mobile telecommunication system). According to these figures, the transmission medium itself, a total available bandwidth of 335 MHz in Europe, is an extremely scarce resource. Efficient data compression techniques, detection algorithms and spatial reuse of radio frequency bands are all-important to increase the capacity of such networks. To this aim, mathematical modeling and optimization techniques provide the appropriate tools as is shown in the following. Three particular subjects are selected to demonstrate the use of mathematics for improving mobile communication systems: channel allocation for frequency and time division multiple access (FD/TDMA, used in GSM), carrier-to-interference planning for code division multiple access (CDMA, mainly employed in UMTS), and capacity considerations for CDMA via spatial stochastic processes.

BibTEX Reference Entry 

	author = {Rudolf Mathar},
	title = "Mathematical modeling, design, and optimization of mobile communiciation networks",
	pages = "101-114",
	journal = "Jahresbericht Dt. Math.-Verein.",
	volume = "103",
	year = 2001,


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