Laplace Method
Performance Analysis of Wireless Networks
Rayleigh fading leads to exponentially distributed power

This presentation addresses aspects of managing the resources of radio spectrum in wireless networks for bursty multi-media traffic. A mathematical framework is presented based on Laplace transforms (characteristic functions) of probability density functions of received signal powers.

Starting from a few simple but generic examples, we develop an intuition for systems aspects that significantly affect the performance of radio networks, including the choice of the frequency reuse method, frequency hopping and direct sequence spread spectrum modulation, etc.

The cellular solution
The key design aspect behind cellular telephone networks is the regular reuse of radio frequencies in a certain geographic area. A crucial aspect in the evaluation and planning of such networks is the estimation of the effect of co-channel interference. The amount of interference that can be tolerated determines the required separation distance between transmit-receiver pairs that use the same radio resources. The performance of cellular telephone links was first studied around 1980. Initial analyses were limited to outage probabilities in continuous wave voice communication, i.e., the probability that the carrier-to-interference ratio drops below a minimum required value necessary to provide a reliable link. In the 1980's the technique for computing outage probabilities was refined step by step, considering among other things multipath fading, shadowing, multiple interfering signals, the modulation technique and error correction method.
The performance metric

To future data or multi-media services, queuing and retransmission delays are far more important performance measures than outage probability. Advanced methods to find link performance, as developed for cellular telephony, can still be used, but need to be extended to address the specific Quality of Service requirements for data or multi-media traffic. Messages lost due to interference from other cells can simply be retransmitted, so outage probabilities per sé may not be an appropriate criterion. The packet delay performance in the downlink, i.e., from base station to terminals, appears more appropriate.

For packet switched communication, it often is optimum to use the entire bandwidth in each cell. That is, it is suboptimum to split the spectrum in portions, and to avoid nearby reuse of the same portion of the spectrum. The corresponding high interference power levels from nearby transmitters in adjacent cells require a joint optimization and dynamic management of the spatial frequency reuse and the occupation of spectrum within cells.

Space-Time-Bandwidth resource management

Efficient mobile packet data transmission, as needed in networks for multimedia traffic or in an ambient intelligence setting, requires entirely different spectrum reuse than telephone nets. Several examples have been covered to support this insight. To optimize spectrum efficiency, user capacity and network performance, presumably a new class of access schemes is needed that dynamically combine random access within one cell with protection against interfering signals from other cells.

Jean-Paul Linnartz at the 5th Diderot Mathematical Forum, 2001

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