In the analysis of large random wireless networks, the underlying node distribution is almost ubiquitously assumed to be the homogeneous Poisson point process. In this paper, the node locations are assumed to form a Poisson cluster process on the plane. We derive the distributional properties of the interference and provide upper and lower bounds for its distribution. We consider the probability of successful transmission in an interference-limited channel when fading is modeled as Rayleigh. We provide a numerically integrable expression for the outage probability and closed-form upper and lower bounds. We show that when the transmitter-receiver distance is large, the success probability is greater than that of a Poisson arrangement. These results characterize the performance of the system under geographical or MAC-induced clustering. We obtain the maximum intensity of transmitting nodes for a given outage constraint, i.e., the transmission capacity (of this spatial arrangement) and show that it is equal to that of a Poisson arrangement of nodes. For the analysis, techniques from stochastic geometry are used, in particular the probability generating functional of Poisson cluster processes, the Palm characterization of Poisson cluster processes, and the Campbell-Mecke theorem.
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.  Non-Gaussian statistical signal processing is important when signals and or noise deviate from the ideal Gaussian model. Stable distributions are among the most important non-Gaussian models. They share defining characteristics with the Gaussian distribution, such as the stability property and central limit theorems, and in fact include the Gaussian distribution as a limiting case. To help engineers better understand the stable models and develop methodologies for their applications in signal processing. A tutorial review of the basic characteristics of stable distributions and stable signal processing is presented. The emphasis is on the differences and similarities between stable signal processing methods based on fractional lower-order moments and Gaussian signal processing methods based on second-order moments. > 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. In an electronically controlled sewing machine, new stitch position coordinate information is retrieved from a solid state memory and transferred to the sewing machine servo system one bit per some proportional clock period, at either a fast stepping rate or a slow stepping rate depending upon the speed of the sewing machine. By use of suitable logic gates, a low speed condition will initiate a slow stepping rate of some fraction of a predetermined clock period, whereas a high speed condition will initiate a fast stepping rate of once every clock period. The new data from the solid state memory is fed to a comparator wherein it is compared to the immediately prior stitch position coordinate information transferred to the servo system and retained in an up down counter. The comparator determines whether the new data requires an up or a down count of the counter. The signal from the up down counter is transferred to a pulse width modulator, the output of which is fed to a digital to analog converter for the appropriate bight or feed servo system of the sewing machine. In effect, the pulse width modulated signal transferred to the servo system is a ramp signal of steep or shallow slope dependent on whether the sewing machine is operating above or below a predetermined speed. We present a methodology for determining the outage probability of wideband ad hoc networks with random wireless channels. Assuming that the nodes are Poisson distributed and subject to a required SINR constraint, we develop a simple framework that gives upper and lower bounds on the outage probability. These bounds are important in that they can be manipulated to obtain bounds on the transmission capacity, i.e., the maximum permissible spatial density of transmissions ensuring an acceptably low outage probability. In this paper, we derive the outage probability of wireless ad hoc networks under path loss and shadowing, which are the dominant large-scale effects in wideband ad hoc networks. The analytical framework is rooted in stochastic geometry, employing marked point processes, void probabilities, Palm measure, and Campbell’s Theorem.