The asymptotic behaviour of (Yn, n e N) is of fundamental importance in probability theory. Indeed, if the Xj have common mean fi and variance a, then by taking each an = n/u and b„ = n a, the celebrated Central Limit Theorem tells us that (Yn) converges in distribution to a standard normal. The class of random variables which appear as limits in distribution of (Yn) for more general (an) and (b„) are called the stable random variables and they have a number of elegant properties, such as the preservation of their distribution functions under convolution. A stochastic process is said to be stable if all its finite-dimensional distributions are themselves stable and it is the systematic study of such processes which is the aim of the present volume.

Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

This paper presents a tutorial on stochastic geometry (SG) based analysis for cellular networks. This tutorial is distinguished by its depth with respect to wireless communication details and its focus on cellular networks. The paper starts by modeling and analyzing the baseband interference in a basic cellular network model. Then, it characterizes signal-to-interference-plus-noise-ratio (SINR) and its related performance metrics. In particular, a unified approach to conduct error probability, outage probability, and rate analysis is presented. Although the main focus of the paper is on cellular networks, the presented unified approach applies for other types of wireless networks that impose interference protection around receivers. The paper then extends the baseline unified approach to capture cellular network characteristics (e.g., frequency reuse, multiple antenna, power control, etc.). It also presents numerical examples associated with demonstrations and discussions. Finally, we point out future research directions.

Modeling and Analysis of Cellular Networks using Stochastic Geometry: A Tutorial

This paper presents a tutorial on stochastic geometry (SG)-based analysis for cellular networks. This tutorial is distinguished by its depth with respect to wireless communication details and its focus on cellular networks. This paper starts by modeling and analyzing the baseband interference in a baseline single-tier downlink cellular network with single antenna base stations and universal frequency reuse. Then, it characterizes signal-to-interference-plus-noise-ratio and its related performance metrics. In particular, a unified approach to conduct error probability, outage probability, and transmission rate analysis is presented. Although the main focus of this paper is on cellular networks, the presented unified approach applies for other types of wireless networks that impose interference protection around receivers. This paper then extends the unified approach to capture cellular network characteristics (e.g., frequency reuse, multiple antenna, power control, etc.). It also presents numerical examples associated with demonstrations and discussions. To this end, this paper highlights the state-of-the-art research and points out future research directions.

Modeling and Analysis of Cellular Networks Using Stochastic Geometry: A Tutorial

We develop a general downlink model for multi-antenna heterogeneous cellular networks (HetNets), where base stations (BSs) across tiers may differ in terms of transmit power, target signal-to-interference-ratio (SIR), deployment density, number of transmit antennas and the type of multi-antenna transmission. In particular, we consider and compare space division multiple access (SDMA), single user beamforming (SU-BF), and baseline single-input single-output (SISO) transmission. For this general model, the main contributions are: (i) ordering results for both coverage probability and per user rate in closed form for any BS distribution for the three considered techniques, using novel tools from stochastic orders, (ii) upper bounds on the coverage probability assuming a Poisson BS distribution, and (iii) a comparison of the area spectral efficiency (ASE). The analysis concretely demonstrates, for example, that for a given total number of transmit antennas in the network, it is preferable to spread them across many single-antenna BSs vs. fewer multi-antenna BSs. Another observation is that SU-BF provides higher coverage and per user data rate than SDMA, but SDMA is in some cases better in terms of ASE.

pdf/downlink-mimo-hetnets-modeling-ordering-results-and-14y7y45smm.pdf

Downlink MIMO HetNets: Modeling, Ordering Results and Performance Analysis

The forthcoming 5G cellular network is expected to overlay millimeter-wave (mmW) transmissions with the incumbent micro-wave ( $\mu\text{W}$ ) architecture. The overall mm- $\mu\text{W}$ resource management should, therefore, harmonize with each other. This paper aims at maximizing the overall downlink (DL) rate with a minimum uplink (UL) rate constraint, and concludes: mmW tends to focus more on DL transmissions while $\mu\text{W}$ has high priority for complementing UL, under time-division duplex (TDD) mmW operations. Such UL dedication of $\mu\text{W}$ results from the limited use of mmW UL bandwidth due to excessive power consumption and/or high peak-to-average power ratio (PAPR) at mobile users. To further relieve this UL bottleneck, we propose mmW UL decoupling that allows each legacy $\mu\text{W}$ base station (BS) to receive mmW signals. Its impact on mm- $\mu\text{W}$ resource management is provided in a tractable way by virtue of a novel closed-form mm- $\mu\text{W}$ spectral efficiency (SE) derivation. In an ultra-dense cellular network (UDN), our derivation verifies mmW (or $\mu\text{W}$ ) SE is a logarithmic function of BS-to-user density ratio. This strikingly simple yet practically valid analysis is enabled by exploiting stochastic geometry in conjunction with real three-dimensional (3-D) building blockage statistics in Seoul, South Korea.

Tractable Resource Management With Uplink Decoupled Millimeter-Wave Overlay in Ultra-Dense Cellular Networks

This paper addresses the performance of space-time coding over fading channels with impulsive noise which is known to accurately capture network interference. We use the symmetric alpha stable noise distribution and adopt two models which assume dependent and independent noise components across receive antennas. We derive pairwise error probability (PEP) of orthogonal space-time block codes (STBC) with a benchmark genie-aided receiver (GAR), or the minimum distance receiver (MDR) which is optimal in the Gaussian case. For general space-time codes we propose a maximum-likelihood (ML) receiver, and its approximation at high signal-to-noise ratio (SNR). The resulting asymptotically optimal receiver (AOR) does not depend on noise parameters and is computationally simple. Monte-Carlo simulations are used to supplement our analytical results and compare the performance of the receivers.

pdf/space-time-coding-over-fading-channels-with-stable-noise-4q650dwmih.pdf

Space-Time Coding over Fading Channels with Stable Noise

This paper addresses the performance of space-time coding over fading channels with impulsive noise, which is known to accurately capture network interference. We use symmetric alpha stable noise distribution and adopt two models that assume dependent and independent noise components across receive antennas. We derive the pairwise error probability (PEP) of orthogonal space-time block codes (STBCs) with a benchmark genie-aided receiver (GAR) or the minimum distance receiver (MDR), which is optimal in the Gaussian case. For general space-time codes, we propose a maximum-likelihood (ML) receiver and its approximation at high signal-to-noise ratio (SNR). The resulting asymptotically optimal receiver (AOR) does not depend on noise parameters and is computationally simple. Monte Carlo simulations are used to supplement our analytical results and compare the performance of the receivers.

Space-Time Coding Over Fading Channels With Stable Noise

This paper considers signal detection in coexisting wireless sensor networks. We characterize the aggregate signal and interference from a Poisson random field of nodes and define a binary hypothesis testing problem to detect a signal in the presence of interference. For the testing problem, we introduce the maximum likelihood (ML) detector and simpler alternatives. The proposed mixed-fractional lower order moment detector is computationally simple and close to the ML performance, and robust to estimation errors in system parameters. We also derived asymptotic theoretical performances for the proposed simple detectors. Monte-Carlo simulations are used to supplement our analytical results and compare the performance of the receivers.

Distributed Detection in Coexisting Large-Scale Sensor Networks

The present invention relates to a transmitting method of a base station including: a step of generating a physical channel or physical signal using a PRB which is a resource allocation unit on frequency axis; and a step of transmitting the physical channel or physical signal, wherein intervals of sub-carriers for a plurality of numerologies are defined to be different from each other, the number of sub-carriers belonging to a first PRB to which a first numerology from among the plurality of numerologies is applied is equal to the number of sub-carriers belonging to a second PRB to which a second numerology from among the plurality of numerologies is applied, and the boundary of the first PRB is arranged at the boundary of the second PRB.

Transmitting method and device using numerology, and scheduling method and device using numerology

The fifth generation (5G) communication system is developed to provide wireless services to various use cases. Specifically, 5G is provisioned to support eMBB services to users moving at 500km/h which primarily aims for high speed train application. Although millimeter wave is one of the essential elements of 5G, most of 5G research were focused on below 6GHz to support high mobility users. In this paper, a promising network architecture and physical layer improvements of the legacy NR have been proposed to provide live high-definition video streaming service to users within high speed train under millimeter wave band.

Enabling 5G Techniques to Support HD Video Streaming to High Speed Train Users

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