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_14: This paper addresses non-Gaussian statistical modeling of interference as a superposition of a large number of small effects from terminals scatterers distributed in the plane volume according to a Poisson point process. This problem is relevant to multiple access communication systems without power control and radar. Assuming that the signal strength is attenuated over distance r as 1 r m, we show that the interference clutter could be modeled as a spherically symmetric spl alpha -stable noise. A novel approach to stable noise modeling is introduced based on the LePage series representation. This establishes grounds to investigate practical constraints in the system model adopted, such as the finite number of interferers and nonhomogeneous Poisson fields of interferers. In addition, the formulas derived allow us to predict noise statistics in environments with lognormal shadowing and Rayleigh fading. The results obtained are useful for the prediction of noise statistics in a wide range of environments with deterministic and stochastic power propagation laws. Computer simulations are provided to demonstrate the efficiency of the spl alpha -stable noise model in multiuser communication systems. The analysis presented will be important in the performance evaluation of complex communication systems and in the design of efficient interference suppression techniques.
@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.
@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_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_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_5: The behavior of power-law shot noise, for which the associated impulse response functions assume a decaying power-law form, is explored. Expressions are obtained for the moments, moment generating functions, amplitude probability density functions, autocorrelation functions, and power spectral densities for a variety of parameters of the process. For certain parameters the power spectral density exhibits 1 f-type behavior over a substantial range of frequencies, so that the process serves as a source of 1 f sup alpha shot noise for alpha in the range 0 >
@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_12: A technique for characterizing multiuser interference and background noise in a direct-sequence spread-spectrum network is introduced, and packet error probabilities are calculated. The multiuser interference over a packet in the network is modeled as a compound Gaussian multivariate random variable for moderate to large values of the processing gain. The conditional variance is dependent on the number of users and their interference powers. The method works for any interference with statistics of the block interference having a spherically symmetric distribution. The best performance results, in terms of the expected total interference power, are obtained for the case of a large number of interferers with comparable interference powers. As the number of interferers approaches infinity, the performance is the same as that for Gaussian noise. For a small number of interferers, the block error probability curve is broader than that for Gaussian noise. For small values of SNR, the probability of error is smaller than that corresponding to Gaussian noise, and for large values of SNR it is larger. Modifications to the basic direct-sequence scheme that improve performance in the case of one strong interferer are suggested. >
@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 study of outage and throughput performance is related to the problem of interference characterization. Important results on the interference in large wireless systems have been derived by @cite_5 @cite_12 @cite_0 @cite_8 @cite_14 . In @cite_11 , outage probabilities for cellular networks are calculated for channels with Rayleigh fading and shadowing while @cite_6 determines outage probabilities to determine the optimum transmission range in a Poisson network. @cite_13 combined the two approaches to determine the optimum transmission range under Rayleigh fading and shadowing. @cite_1 provides a detailed analysis on outage probabilities and routing progress in Poisson networks with ALOHA.