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Some applications of the hypergeometric and Poisson distributions
Published in Henry C. Tuckwell, Elementary Applications of Probability Theory, 2018
Definition A point process N is an homogeneous Poisson point process in the plane with intensity λ if:for any subset A of ℝ2, the number of points N(A) occurring in A is a Poisson random variable with parameter λ|A|, where |A| is the area of A;for any collection of disjoint subsets of ℝ2, A1, A2,…,An, the random variables {N(Ak),k = 1,2,…,n}are mutually independent.
Exponential ergodicity of some Markov dynamical systems with application to a Poisson-driven stochastic differential equation
Published in Dynamical Systems, 2019
Dawid Czapla, Joanna Kubieniec
For a Poisson point process , by its intensity we mean the intensity of the Poisson random measure , i.e. for . If satisfies where κ is some non-negative measure on , then is called a stationary Poisson process, and κ is said to be the characteristic measure of .
Flexible Beamforming in 5G Wireless for Internet of Things
Published in IETE Technical Review, 2019
Mukesh Kumar Maheshwari, Mamta Agiwal, Navrati Saxena, Abhishek Roy
In this article, we first examine various human-centric and machine-centric requirements expected in a connected living. Understanding the heterogeneity of wireless landscape would lay a strong foundation for effective communication design. We infer that antenna system for future wireless communication should be configured for scalability and flexibility. Therefore, we propose FBF (flexible beamforming) antenna system to accommodate different application demands efficiently. FBF promises to resolve dynamic scalability by capturing advantages of variable downtilt adaptations and scalable power levels. The contributions of this paper are summarized as follows: We propose multiple antenna arrays at every BS, operating at variable power levels, to achieve intended throughput. A typical link budget analysis, with actual 5G testbed parameters, helps FBF achieve variable Gbps data rates. Variable Gbps data rates in FBF would address dense connectivity expected in IoT ecosystem.We design FBF scheme based on 3D directional antenna patterns, horizontal and vertical antenna gains and variable downtilt adaptations. We propose an algorithm to flexibly adjust downtilt in order to enhance the coverage and reduce the overlap region.We derive the closed-form expressions for throughput and network energy efficiency in 5G beam-based networks by incorporating recent mmWave channel model and energy-efficient power allocations.In order to statistically model deployment similar to real-world trends, we consider Poisson Point Process (PPP). Geographical distribution of BSs is considered with the density of Poisson distribution ρ.System-level simulations are executed for performance evaluation of FBF using real testbed parameters.