Stochastic Geometry Modeling and Performance Evaluation of mmWave Cellular Communications

In this paper, a new mathematical framework to the analysis of millimeter wave cellular networks is introduced. Its peculiarity lies in considering realistic path-loss and blockage models, which are derived from experimental data recently reported in the literature. The path-loss model accounts for different distributions for line-of-sight and non-line-of-sight propagation conditions and the blockage model includes an outage state that provides a better representation of the outage possibilities of millimeter wave communications. By modeling the locations of the base stations as points of a Poisson point process and by relying upon a noise-limited approximation for typical millimeter wave network deployments, exact integral expressions for computing the coverage probability and the average rate are obtained. With the aid of Monte Carlo simulations, the noise-limited approximation is shown to be sufficiently accurate for typical network densities. Furthermore, it is shown that sufficiently dense millimeter wave cellular networks are capable of outperforming micro wave cellular networks, both in terms of coverage probability and average rate.Comment: Presented at 2015 IEEE International Conference on Communications (ICC), London, UK (June 2015). arXiv admin note: substantial text overlap with arXiv:1410.357

Stochastic Geometry Modeling of Cellular Networks: Analysis, Simulation and Experimental Validation

Due to the increasing heterogeneity and deployment density of emerging cellular networks, new flexible and scalable approaches for their modeling, simulation, analysis and optimization are needed. Recently, a new approach has been proposed: it is based on the theory of point processes and it leverages tools from stochastic geometry for tractable system-level modeling, performance evaluation and optimization. In this paper, we investigate the accuracy of this emerging abstraction for modeling cellular networks, by explicitly taking realistic base station locations, building footprints, spatial blockages and antenna radiation patterns into account. More specifically, the base station locations and the building footprints are taken from two publicly available databases from the United Kingdom. Our study confirms that the abstraction model based on stochastic geometry is capable of accurately modeling the communication performance of cellular networks in dense urban environments.Comment: submitted for publicatio

Diversity, Coding, and Multiplexing Trade-Off of Network-Coded Cooperative Wireless Networks

In this paper, we study the performance of network-coded cooperative diversity systems with practical communication constraints. More specifically, we investigate the interplay between diversity, coding, and multiplexing gain when the relay nodes do not act as dedicated repeaters, which only forward data packets transmitted by the sources, but they attempt to pursue their own interest by forwarding packets which contain a network-coded version of received and their own data. We provide a very accurate analysis of the Average Bit Error Probability (ABEP) for two network topologies with three and four nodes, when practical communication constraints, i.e., erroneous decoding at the relays and fading over all the wireless links, are taken into account. Furthermore, diversity and coding gain are studied, and advantages and disadvantages of cooperation and binary Network Coding (NC) are highlighted. Our results show that the throughput increase introduced by NC is offset by a loss of diversity and coding gain. It is shown that there is neither a coding nor a diversity gain for the source node when the relays forward a network-coded version of received and their own data. Compared to other results available in the literature, the conclusion is that binary NC seems to be more useful when the relay nodes act only on behalf of the source nodes, and do not mix their own packets to the received ones. Analytical derivation and findings are substantiated through extensive Monte Carlo simulations.Comment: IEEE International Conference on Communications (ICC), 2012. Accepted for publication and oral presentatio

The Intensity Matching Approach: A Tractable Stochastic Geometry Approximation to System-Level Analysis of Cellular Networks

The intensity matching approach for tractable performance evaluation and optimization of cellular networks is introduced. It assumes that the base stations are modeled as points of a Poisson point process and leverages stochastic geometry for system-level analysis. Its rationale relies on observing that system-level performance is determined by the intensity measure of transformations of the underlaying spatial Poisson point process. By approximating the original system model with a simplified one, whose performance is determined by a mathematically convenient intensity measure, tractable yet accurate integral expressions for computing area spectral efficiency and potential throughput are provided. The considered system model accounts for many practical aspects that, for tractability, are typically neglected, e.g., line-of-sight and non-line-of-sight propagation, antenna radiation patterns, traffic load, practical cell associations, general fading channels. The proposed approach, more importantly, is conveniently formulated for unveiling the impact of several system parameters, e.g., the density of base stations and blockages. The effectiveness of this novel and general methodology is validated with the aid of empirical data for the locations of base stations and for the footprints of buildings in dense urban environments.Comment: Submitted for Journal Publicatio

Outage Probability of Dual-Hop Selective AF With Randomly Distributed and Fixed Interferers

The outage probability performance of a dual-hop amplify-and-forward selective relaying system with global relay selection is analyzed for Nakagami-$m$ fading channels in the presence of multiple interferers at both the relays and the destination. Two different cases are considered. In the first case, the interferers are assumed to have random number and locations. Outage probability using the generalized Gamma approximation (GGA) in the form of one-dimensional integral is derived. In the second case, the interferers are assumed to have fixed number and locations. Exact outage probability in the form of one-dimensional integral is derived. For both cases, closed-form expressions of lower bounds and asymptotic expressions for high signal-to-interference-plus-noise ratio are also provided. Simplified closed-form expressions of outage probability for special cases (e.g., dominant interferences, i.i.d. interferers, Rayleigh distributed signals) are studied. Numerical results are presented to show the accuracy of our analysis by examining the effects of the number and locations of interferers on the outage performances of both AF systems with random and fixed interferers.Comment: 35 pages, 11 figures, accepted with minor revisions for publication as a regular paper in the IEEE Transactions on Vehicular Technology on 21/09/201

Stochastic Geometry Modeling and Analysis of Multi-Tier Millimeter Wave Cellular Networks

In this paper, a new mathematical framework to the analysis of millimeter wave cellular networks is introduced. Its peculiarity lies in considering realistic path-loss and blockage models, which are derived from recently reported experimental data. The path-loss model accounts for different distributions of line-of-sight and non-line-of-sight propagation conditions and the blockage model includes an outage state that provides a better representation of the outage possibilities of millimeter wave communications. By modeling the locations of the base stations as points of a Poisson point process and by relying on a noise-limited approximation for typical millimeter wave network deployments, simple and exact integral as well as approximated and closed-form formulas for computing the coverage probability and the average rate are obtained. With the aid of Monte Carlo simulations, the noise-limited approximation is shown to be sufficiently accurate for typical network densities. The proposed mathematical framework is applicable to cell association criteria based on the smallest path-loss and on the highest received power. It accounts for beamforming alignment errors and for multi-tier cellular network deployments. Numerical results confirm that sufficiently dense millimeter wave cellular networks are capable of outperforming micro wave cellular networks, both in terms of coverage probability and average rate.Comment: Submitted to IEEE Transactions on Wireless Communication

Average Rate of Downlink Heterogeneous Cellular Networks over Generalized Fading Channels - A Stochastic Geometry Approach

In this paper, we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks. The framework leverages recent application of stochastic geometry to other-cell interference modeling and analysis. The heterogeneous cellular network is modeled as the superposition of many tiers of Base Stations (BSs) having different transmit power, density, path-loss exponent, fading parameters and distribution, and unequal biasing for flexible tier association. A long-term averaged maximum biased-received-power tier association is considered. The positions of the BSs in each tier are modeled as points of an independent Poisson Point Process (PPP). Under these assumptions, we introduce a new analytical methodology to evaluate the average rate, which avoids the computation of the Coverage Probability (Pcov) and needs only the Moment Generating Function (MGF) of the aggregate interference at the probe mobile terminal. The distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions, including composite fading channels with small- and mid-scale fluctuations. In addition, our method can efficiently handle correlated Log-Normal shadowing with little increase of the computational complexity. The proposed MGF-based approach needs the computation of either a single or a two-fold numerical integral, thus reducing the complexity of Pcov-based frameworks, which require, for general fading distributions, the computation of a four-fold integral.Comment: Accepted for publication in IEEE Transactions on Communications, to appea

Power Beacon-Assisted Millimeter Wave Ad Hoc Networks

Deployment of low cost power beacons (PBs) is a promising solution for dedicated wireless power transfer (WPT) in future wireless networks. In this paper, we present a tractable model for PB-assisted millimeter wave (mmWave) wireless ad hoc networks, where each transmitter (TX) harvests energy from all PBs and then uses the harvested energy to transmit information to its desired receiver. Our model accounts for realistic aspects of WPT and mmWave transmissions, such as power circuit activation threshold, allowed maximum harvested power, maximum transmit power, beamforming and blockage. Using stochastic geometry, we obtain the Laplace transform of the aggregate received power at the TX to calculate the power coverage probability. We approximate and discretize the transmit power of each TX into a finite number of discrete power levels in log scale to compute the channel and total coverage probability. We compare our analytical predictions to simulations and observe good accuracy. The proposed model allows insights into effect of system parameters, such as transmit power of PBs, PB density, main lobe beam-width and power circuit activation threshold on the overall coverage probability. The results confirm that it is feasible and safe to power TXs in a mmWave ad hoc network using PBs.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Bit Error Probability of Space Modulation over Nakagami-m Fading: Asymptotic Analysis

International audienceRecently, the Average Bit Error Probability (ABEP) of Space Shift Keying (SSK) and Spatial Modulation (SM) over Nakagami-m fading has been computed as a single integral involving the Meijer-G function. Even though the frameworks are very accurate, the use of special functions hides some fundamental properties of the aforementioned new modulation schemes, e.g., coding and diversity gains. In this Letter, we exploit a notable limit involving the Meijer-G function near the singular point −1, and provide a simple, closed-form, and asymptotically tight upper-bound of the ABEP. The result is applicable to SM and SSK modulation, to correlated Nakagami-m fading, and to general Multiple-Input Multiple-Output (MIMO) wireless systems. As a case study, numerical examples showing the accuracy for SSK modulation are given, and it is proved that, unlike conventional modulations, the diversity gain is independent of the fading severity m

Space Shift Keying (SSK) Modulation With Partial Channel State Information: Optimal Detector and Performance Analysis Over Fading Channels

International audienceSpace Shift Keying (SSK) modulation is a new and recently proposed transmission technology for Multiple–Input–Multiple–Output (MIMO) wireless systems, which has been shown to be a promising low–complexity alternative to several state–of–the–art MIMO schemes. So far, only optimal or heuristic transceivers with Full Channel State Information (F–CSI) at the receiver have been investigated, and their performance analyzed over fading channels. In this paper, we develop and study the performance of the optimal Maximum–Likelihood (ML) detector with unknown phase reference at the receiver (i.e., Partial–CSI, P–CSI, knowledge). A very accurate analytical framework for the analysis and optimization of this novel detector over generically correlated and non–identically distributed Nakagami–m fading channels is proposed, and its performance compared to the optimal receiver design with F–CSI. Numerical results will point out that: i) the performance of SSK modulation is significantly affected by the characteristics of fading channels, e.g., channel correlation, fading severity, and, particularly, power imbalance among the transmit–receive wireless links, and ii) unlike ordinary modulation schemes, there is a substantial performance loss when the receiver cannot exploit the phase information for optimal receiver design. This latter result highlights the importance of accurate and reliable channel estimation mechanisms for the efficient operation of SSK modulation over fading channels. Analytical frameworks and theoretical findings will also be substantiated via Monte Carlo simulations