This paper analyzes the outage performance in finite wireless networks. Unlike most prior works, which either assumed a specific network shape or considered a special location of the reference receiver, we propose two general frameworks for analytically computing the outage probability at any arbitrary location of an arbitrarily-shaped finite wireless network: (i) a moment generating function-based framework which is based on the numerical inversion of the Laplace transform of a cumulative distribution and (ii) a reference link power gain-based framework which exploits the distribution of the fading power gain between the reference transmitter and receiver. The outage probability is spatially averaged over both the fading distribution and the possible locations of the interferers. The boundary effects are ac-curately accounted for using the probability distribution function of the distance of a random node from the reference receiver. For the case of the node locations modeled by a Binomial point process and Nakagami-m fading channel, we demonstrate the use of the proposed frameworks to evaluate the outage probability at any location inside either a disk or polygon region. The analysis illustrates the location dependent performance in finite wireless networks and highlights the importance of accurately modeling the boundary effects.

This paper presents a tractable analytical framework for the exact calculation of the probability of node isolation and the minimum node degree distribution when N sensor nodes are independently and uniformly distributed inside a finite square region. The proposed framework can accurately account for the boundary effects by partitioning the square into subregions, based on the transmission range and the node location. We show that for each subregion, the probability that a random node falls inside a disk centered at an arbitrary node located in that subregion can be expressed analytically in closed-form. Using the results for the different subregions, we obtain the exact probability of node isolation and minimum node degree distribution that serves as an upper bound for the probability of k-connectivity. Our theoretical framework is validated by comparison with the simulation results and shows that the minimum node degree distribution serves as a tight upper bound for probability of k-connectivity. The proposed framework provides a very useful tool to accurately account for the boundary effects in the design of finite wireless networks.

Abstract—This letter describes a direct method for computing the spatially averaged outage probability of a network with interferers located according to a point process and signals subject to fading. Unlike most common approaches, it does not require transforms such as a Laplace transform. Examples show how to directly obtain the outage probability in the presence of Rayleigh fading in networks whose interferers are drawn from binomial and Poisson point processes defined over arbitrary regions. We furthermore show that, by extending the arbitrary region to the entire plane, the result for Poisson point processes converges to the same expression found by Baccelli et al.. Index Terms—Outage probability, stochastic geometry, point processes, interference modeling, fading. I.

This paper characterizes the aggregate interference at the primary user (PU) due to M secondary users (SUs) in an underlay cognitive network, where appropriate SU activ-ity protocols are employed in order to limit the interference generated by the SUs. Different from prior works, we assume that the PU can be located anywhere inside an arbitrarily-shaped convex network region. Using the moment generating function (MGF) of the interference from a random SU, we derive general expressions for the n-th moment and the n-th cumulant of the aggregate interference for guard zone and multiple-threshold SU activity protocols. Using the cumulants, we study the convergence of the distribution of the aggregate interference to a Gaussian distribution. In addition, we compare the well-known closed-form distributions in the literature to approximate the complementary cumulative distribution function (CCDF) of the aggregate interference. Our results show that care must be undertaken in approximating the aggregate interference as a Gaussian distribution, even for a large number of SUs, since the convergence is not monotonic in general. In addition, the shifted lognormal distribution provides the overall best CCDF approximation, especially in the distribution tail region, for arbitrarily-shaped network regions.

Large-scale fading behavior for a cellular network with uniform spatial distribution

Abstract not found

This paper analyzes the performance of the primary and secondary users (SUs) in an arbitrarily-shaped underlay cognitive network. We consider different SU activity protocols and their effects on a primary receiver (PU-Rx) at an arbitrary location. We propose a framework, based on the moment generating function (MGF) of the interference due to a random SU, to analytically compute the outage probability in the primary network, as well as the average number of active SUs in the secondary network. The latter metric provides a measure of the efficiency of spectrum reuse in underlay cognitive networks. We also propose a cooperation-based SU activity protocol in the underlay cognitive network which includes the existing threshold-based protocol as a special case. A tradeoff analysis between the outage probability in the primary network and the average number of active SUs is provided in this paper, and we employ it as an analytical approach to compare the effect of different SU activity protocols on the performance of the primary and secondary networks.

We propose and implement an algorithm to compute the exact cumulative density function (CDF) of the distance from an arbitrary reference point to a randomly located node within an arbitrarily shaped (convex or concave) simple polygon. Using this result, we also obtain the closed-form probability density function (PDF) of the Euclidean distance between an arbitrary reference point and its ith neighbor node when N nodes are uniformly and independently distributed inside the arbitrarily shaped polygon. The implementation is based on the recursive approach proposed by Ahmadi and Pan [1] in order to obtain the distance distributions associated with arbitrary triangles. The algorithm in [1] is extended for arbitrarily shaped polygons by using a modified form of the shoelace formula. This modification allows tractable computation of the overlap area between a disk of radius r centered at the arbitrary reference point and the arbitrarily shaped polygon, which is a key part of the implementation. The obtained distance distributions can be used in the modeling of wireless networks, especially in the context of emerging ultra-dense small cell deployment scenarios, where network regions can be arbitrarily shaped. They can also be applied in other branches of science, such as forestry, mathematics, operations research, and material sciences.

▸ Interference exhibits a spatial correlation [1], that can be captured by evaluating the correlation coefficient of the outage probability at two reference receivers: r0 r net