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_0: This paper deals with the distribution of cumulated instantaneous interference power in a Rayleigh fading channel for an infinite number of interfering stations, where each station transmits with a certain probability, independently of all others. If all distances are known, a necessary and sufficient condition is given for the corresponding distribution to be nondefective. Explicit formulae of density and distribution functions are obtained in the interesting special case that interfering stations are located on a linear grid. Moreover, the Laplace transform of cumulated power is investigated when the positions of stations follow a one- or two-dimensional Poisson process. It turns out that the corresponding distribution is defective for the two-dimensional models.
@cite_6: The authors obtain the optimum transmission ranges to maximize throughput for a direct-sequence spread-spectrum multihop packet radio network. In the analysis, they model the network self-interference as a random variable which is equal to the sum of the interference power of all other terminals plus background noise. The model is applicable to other spread-spectrum schemes where the interference of one user appears as a noise source with constant power spectral density to the other users. The network terminals are modeled as a random Poisson field of interference power emitters. The statistics of the interference power at a receiving terminal are obtained and shown to be the stable distributions of a parameter that is dependent on the propagation power loss law. The optimum transmission range in such a network is of the form CK sup alpha where C is a constant, K is a function of the processing gain, the background noise power spectral density, and the degree of error-correction coding used, and alpha is related to the power loss law. The results obtained can be used in heuristics to determine optimum routing strategies in multihop networks. >
@cite_8: In this paper we determine the probability distribution function of cumulated instantaneous interference power in a mobile radio network, when the positions of interfering stations are distributed according to a one- or two-dimensional Poisson point process, truncated at a finite horizon. The influences of Rice and Rayleigh fading, lognormal shadowing, near far effect and capture are taken into account. From the resulting distribution the probability of successful transmission and corresponding bit-error-rates are derived.
In early work, it is said that the convolution of exponential RVs of different means can be approximated by a Gamma distribution. This needs to be verified! @cite_6 determines the interference in Poisson random networks for @math . Since their interference is averaged over many network realizations, it turns out to be Gaussian. For a given network and a certain MAC scheme, the distribution obtained from a temporal trace will most likely look different (see @cite_0 @cite_8 ), since there will be a few dominant interferers, in particular for high @math . Hence, such Gaussian models have to be used with care for analysis and protocol design. We will characterize the distribution of the cumulated interference for single network realizations and different MAC schemes.