A Mathematical Theory of Network Interference and Its Applications

Abstract

In this paper, we introduce a mathematical framework for the characterization of network interference in wireless systems. We consider a network in which the interferers are scattered according to a spatial Poisson process and are operating asynchronously in a wireless environment subject to path loss, shadowing, and multipath fading. We start by determining the statistical distribution of the aggregate network interference. We then investigate four applications of the proposed model: 1) interference in cognitive radio networks; 2) interference in wireless packet networks; 3) spectrum of the aggregate radio-frequency emission of wireless networks; and 4) coexistence between ultrawideband and narrowband systems. Our framework accounts for all the essential physical parameters that affect network interference, such as the wireless propagation effects, the transmission technology, the spatial density of interferers, and the transmitted power of the interferers.

Area Model and Dimensioning Guidelines of Multisource Energy Harvesting for Nano–Micro Interface

“…In fact, sparse energy sources are present in a wide variety of physical phenomena. Among others, acoustic energy, mechanical, vibrational or RF energy [13], [14], [15] are considered representative examples of such sources, when considering a large time scale.…”

“…An exponentially distributed random process has been chosen as it presents the largest entropy, thus estimating the worst case [13]. Fig.…”

“…Alternatively, we have assumed that the power that the energy harvester consumes to sense the spectrum, to process this information and to tune the oscillating frequency of the energy harvester, referred as P loss , quadratically depends on the voltage range applied, V C , to an equivalent capacity of C eq = 1 µF, which is a reasonable value as reported in [10]. The voltage applied at the capacitor linearly depends to the number of frequency bands, as shown in (13).…”

5G green cellular networks considering power allocation schemes

“…Assume that the active interfering BSs set is modeled an independent thinning process on the BS Poisson point process, which still form a Poisson point process with intensity λ Inf [20], and generally satisfies 0 λ Inf λ B . Therefore, the interference power aggregated at the MS M S 0 is expressed as [34] …”

“…Based on the result in [34], the characteristic function Φ PI represents a alpha stable random process, which can be simply denoted as P I ∼ Stable (α = 2/σ, β = 1, δ, µ = 0), where α and δ are the stability parameter and the scale parameter, respectively. Based on the alpha stable characteristic function expression, Φ PI can be re-written as…”