Gauss-Poisson processes (GPPs) are a class of clustered point processes, which include the Poisson point process as a special case and have a simpler structure than the general Poisson cluster point processes. A key property of the GPP is that it is completely defined by its first- and second-order statistics. In this paper, we first show the properties of the GPP and provide an approach to fit the GPP to a given point set. A fitting example is presented. We then propose the GPP as a model for wireless networks that exhibit clustering behavior and derive the signal-to-interference-ratio distributions for different system models: 1) the basic model where the desired transmitter is independent of the GPP and all nodes in the GPP are interferers; 2) the non-cooperative model where the desired transmitter is one of the nodes in the GPP; and 3) the cooperative model, where the nodes in a GPP cluster transmit cooperatively. The simulation results indicate that a significant gain can be achieved with cooperation.

In all current models for cellular networks, independent randomness in the positions of the base stations (BSs) and the propagation conditions is assumed. In practice, however, in coverage-oriented deployments, where the goal is to achieve good baseline coverage, cellular operators place the base stations further apart if propagation is favorable, and vice versa. We thus propose a new class of cellular model, where BSs are deployed such that all cell edge users achieve a minimum target signal power level from the serving BS. The spatial structure of the BSs is a result of the propagation environment and the target signal power. We call such network models joint spatial and propagation (JSP) models. To formulate such models, we assume the path loss follows a power law with a variable path loss exponent, so that the target signal power is achieved at the cell edges, given the distribution of the BSs. The coverage probability, defined as the probability that the signal-to- interference-plus-noise-ratio (SINR) exceeds a threshold, is evaluated and compared with the standard Poisson and lattice models. Our results show that networks with Poisson distributed BSs appear to the user like lattice networks if the dependence between BS placement and propagation is accounted for.

In cellular network models, the base stations are usually assumed to form a lattice or a Poisson point process (PPP). In reality, however, they are deployed neither fully regularly nor completely randomly. Accordingly, in this paper, we consider the very general class of motion-invariant models and analyze the behavior of the outage probability (the probability that the signal-to-interference-plus-noise-ratio (SINR) is smaller than a threshold) as the threshold goes to zero. We show that, remarkably, the slope of the outage probability (in dB) as a function of the threshold (also in dB) is the same for essentially all motion-invariant point processes. The slope merely depends on the fading statistics. Using this result, we introduce the notion of the asymptotic deployment gain (ADG), which characterizes the horizontal gap between the success probabilities of the PPP and another point process in the high-reliability regime (where the success probability is near 1). To demonstrate the usefulness of the ADG for the characterization of the SINR distribution, we investigate the outage probabilities and the ADGs for different point processes and fading statistics by simulations.

In cellular network models, the base stations are usually assumed to form a lattice or a Poisson point process (PPP). In reality, however, they are deployed neither fully regularly nor completely randomly. Accordingly, in this paper, we consider the very general class of motion-invariant models and analyze the behavior of the coverage probability (the probability that the signal-to-interference-plus-noise-ratio (SINR) exceeds a threshold) as the threshold goes to zero. We show that, surprisingly, the slope of the outage probability (complementary to the coverage probability, in dB) as a function of the threshold (also in dB) is the same for essentially all motion-invariant point processes. The slope merely depends on the fading statistics. Using this result, we introduce the notion of the asymptotic deployment gain (ADG), which characterizes the horizontal gap between the coverage probability of the PPP and another point process in the high-reliability regime (where the coverage probability is near 1). To demonstrate the usefulness of the ADG for the characterization of coverage probabilities, we investigate the coverage properties and the ADGs for different point processes and fading statistics by simulations.

Gauss-Poisson processes (GPPs) are a class of clustered point processes, which include the Poisson point process as a special case and have a simpler structure than general Poisson cluster point processes. In this paper, we propose the GPP as a model for wireless networks that exhibit clustering behavior. We calculate the success probabilities and provide bounds for three kinds of GPP networks: (1) the basic model where the desired transmitter is independent of the GPP and all nodes in the GPP are interferers; (2) the non-cooperative model where the desired transmitter is one of the nodes in the GPP; (3) the cooperative model where both nodes in a two-node cluster of the GPP serve a receiver cooperatively using non-coherent joint transmission. Our results show that the bounds, especially the upper bounds, provide good approximations for different operating regimes.

The spatial structure of base stations (BSs) in cellular networks plays a key role in evaluating the downlink performance. In this paper, different spatial stochastic models (the Poisson point process (PPP), the Poisson hard-core process (PHCP), the Strauss process (SP), and the perturbed triangular lattice) are used to model the structure by fitting them to the locations of BSs in real cellular networks obtained from a public database. We provide two general approaches for fitting. One is fitting by the method of maximum pseudolikelihood. As for the fitted models, it is not sufficient to distinguish them conclusively by some classical statistics. We propose the coverage probability as the criterion for the goodness-of-fit. In terms of coverage, the SP provides a better fit than the PPP and the PHCP. The other approach is fitting by the method of minimum contrast that minimizes the average squared error of the coverage probability. This way, fitted models are obtained whose coverage performance matches that of the given data set very accurately. Furthermore, we introduce a novel metric, the deployment gain, and we demonstrate how it can be used to estimate the coverage performance and average rate achieved by a data set.

This paper presents an evolution framework of resource allocation by infection among secondary users (SUs) in an OFDMA-based cognitive radio cellular networks. Each primary user (PU) sells his extra sub-channels to SUs in his sensing range to achieve the highest payoff and each SU may come across another in his sensing range to make infection. Two different infection processes among SUs, the infection with and without local knowledge respectively, are considered. We prove the existence and convergence of evolutionary equilibrium (EE) for both cases, and show some interesting properties such as the impact of cheating of SUs in the above infection processes. Besides, we proposed two algorithms for the infection processes to converge to EE in a distributed manner. Simulation results show that the algorithms with local knowledge can equally share the extra resources among SUs efficiently, which is actually the overall optimal solution (OOS). While for the algorithm without local knowledge, we find that though EE exists, OOS cannot always be achieved. Furthermore, we optimize the second algorithm to make EE approximate to OOS.