Outage probabilities and single-hop throughput are two important performance metrics that have been evaluated for certain specific types of wireless networks. However, there is a lack of comprehensive results for larger classes of networks, and there is no systematic approach that permits the convenient comparison of the performance of networks with different geometries and levels of randomness. The uncertainty cube is introduced to categorize the uncertainty present in a network. The three axes of the cube represent the three main potential sources of uncertainty in interference-limited networks: the node distribution, the channel gains (fading), and the channel access scheme (set of transmitting nodes). For the performance analysis, a new parameter, the so- called spatial contention, is defined. It measures the slope of the outage probability in an ALOHA network as a function of the transmit probability p at p = 0. Outage is defined as the event that the signal-to-interference ratio (SIR) is below a certain threshold in a given time slot. It is shown that the spatial contention is sufficient to characterize outage and throughput in large classes of wireless networks, corresponding to different positions on the uncertainty cube. Existing results are placed in this framework, and new ones are derived. Further, interpreting the outage probability as the SIR distribution, the ergodic capacity of unit-distance links is determined and compared to the throughput achievable for fixed (yet optimized) transmission rates.
@cite_1: An Aloha-type access control mechanism for large mobile, multihop, wireless networks is defined and analyzed. This access scheme is designed for the multihop context, where it is important to find a compromise between the spatial density of communications and the range of each transmission. More precisely, the analysis aims at optimizing the product of the number of simultaneously successful transmissions per unit of space (spatial reuse) by the average range of each transmission. The optimization is obtained via an averaging over all Poisson configurations for the location of interfering mobiles, where an exact evaluation of signal over noise ratio is possible. The main mathematical tools stem from stochastic geometry and are spatial versions of the so-called additive and max shot noise processes. The resulting medium access control (MAC) protocol exhibits some interesting properties. First, it can be implemented in a decentralized way provided some local geographic information is available to the mobiles. In addition, its transport capacity is proportional to the square root of the density of mobiles which is the upper bound of Gupta and Kumar. Finally, this protocol is self-adapting to the node density and it does not require prior knowledge of this density.
@cite_13: The evaluation of optimum transmission ranges in a packet radio network in a fading and shadowing environment is considered. It is shown that the optimal probability of transmission of each user is independent of the system model and is p sub o spl sime 0.271. The optimum range should be chosen so that on the average there are spl chi (G b) sup 2 spl eta terminals closer to the transmitter than the receiver, where G is the spread spectrum processing gain, b is the outage signal-to-noise ratio threshold, spl eta is the power loss factor and spl chi depends on the system parameters and the propagation model. The performance index is given in terms of the optimal normalized expected progress per slot, given by spl thetav (G b) sup 1 spl eta where spl thetav is proportional to the square root of spl chi . A comparison with the results obtained by using deterministic propagation models shows, for typical values of fading and shadowing parameters, a reduction up to 40 of the performance index. >
@cite_11: A novel mathematical method is presented to express the outage probability for a desired radio signal received from a mobile transmitter in the presence of multiple interfering signals with combined log-normal and Rayleigh fading. In contrast to previously reported analyses, this exact method avoids approximation of the PDF of the received powers of the various signals. This is useful in determining the spectrum efficiency and performance of (interference-limited) radio networks for high-capacity cellular telephony, two-way paging, packet radio and other mobile data networks. >
The Laplace transforms of the interference are particularly convenient for the determination of outage probabilities in Rayleigh fading. As was noted in @cite_11 @cite_13 @cite_1 , the success probability @math can be expressed as the product of the Laplace transforms of the interference and noise: