The Meta Distribution of the SIR for Cellular Networks With Power Control

The meta distribution of the signal-to-interference ratio (SIR) provides fine-grained information about the performance of individual links in a wireless network. This paper focuses on the analysis of the meta distribution of the SIR for both the cellular network uplink and downlink with fractional power control. For the uplink scenario, an approximation of the interfering user point process with a non-homogeneous Poisson point process is used. The moments of the meta distribution for both scenarios are calculated. Some bounds, the analytical expression, the mean local delay, and the beta approximation of the meta distribution are provided. The results give interesting insights into the effect of the power control in both the uplink and downlink. Detailed simulations show that the approximations made in the analysis are well justified.

[1]  Martin Haenggi,et al.  Analysis of D2D Underlaid Cellular Networks: SIR Meta Distribution and Mean Local Delay , 2017, IEEE Transactions on Communications.

[2]  Matthias Wildemeersch,et al.  D2D Enhanced Heterogeneous Cellular Networks With Dynamic TDD , 2014, IEEE Transactions on Wireless Communications.

[3]  Martin Haenggi,et al.  A Stochastic Geometry Analysis of Inter-Cell Interference Coordination and Intra-Cell Diversity , 2014, IEEE Transactions on Wireless Communications.

[4]  Tomasz Schreiber,et al.  Limit theorems for the typical poisson-voronoi cell and the crofton cell with a large inradius , 2005, math/0507463.

[5]  Nei Kato,et al.  A stochastic geometry analysis of D2D overlaying multi-channel downlink cellular networks , 2015, 2015 IEEE Conference on Computer Communications (INFOCOM).

[6]  Emil Björnson,et al.  Deploying Dense Networks for Maximal Energy Efficiency: Small Cells Meet Massive MIMO , 2015, IEEE Journal on Selected Areas in Communications.

[7]  Martin Haenggi,et al.  Stochastic Geometry for Wireless Networks , 2012 .

[8]  Jeffrey G. Andrews,et al.  Joint Rate and SINR Coverage Analysis for Decoupled Uplink-Downlink Biased Cell Associations in HetNets , 2014, IEEE Transactions on Wireless Communications.

[9]  J. Andrews,et al.  Correlation of link outages in low-mobility spatial wireless networks , 2010, 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers.

[10]  François Baccelli,et al.  A new phase transitions for local delays in MANETs , 2010, 2010 Proceedings IEEE INFOCOM.

[11]  Martin Haenggi,et al.  Spatial outage capacity of poisson bipolar networks , 2017, 2017 IEEE International Conference on Communications (ICC).

[12]  Jeffrey G. Andrews,et al.  Downlink MIMO HetNets: Modeling, Ordering Results and Performance Analysis , 2013, IEEE Transactions on Wireless Communications.

[13]  Robert W. Heath,et al.  Analyzing Uplink SINR and Rate in Massive MIMO Systems Using Stochastic Geometry , 2015, IEEE Transactions on Communications.

[14]  Marco Di Renzo,et al.  Stochastic Geometry Modeling of Cellular Networks: Analysis, Simulation and Experimental Validation , 2015, MSWiM.

[15]  Young Jin Sang,et al.  On the Uplink SIR Distributions in Heterogeneous Cellular Networks , 2014, IEEE Communications Letters.

[16]  Na Deng,et al.  A Fine-Grained Analysis of Millimeter-Wave Device-to-Device Networks , 2017, IEEE Transactions on Communications.

[17]  Holger Paul Keeler,et al.  Using Poisson processes to model lattice cellular networks , 2013, 2013 Proceedings IEEE INFOCOM.

[18]  Martin Haenggi,et al.  Downlink Coordinated Joint Transmission for Mutual Information Accumulation , 2017, IEEE Wireless Communications Letters.

[19]  Martin Haenggi,et al.  The Local Delay in Poisson Networks , 2013, IEEE Transactions on Information Theory.

[20]  Ekram Hossain,et al.  On Stochastic Geometry Modeling of Cellular Uplink Transmission With Truncated Channel Inversion Power Control , 2014, IEEE Transactions on Wireless Communications.

[21]  Jeffrey G. Andrews,et al.  A Primer on Cellular Network Analysis Using Stochastic Geometry , 2016, ArXiv.

[22]  Martin Haenggi,et al.  Spatiotemporal Cooperation in Heterogeneous Cellular Networks , 2015, IEEE Journal on Selected Areas in Communications.

[23]  Martin Haenggi,et al.  User Point Processes in Cellular Networks , 2016, IEEE Wireless Communications Letters.

[24]  Martin Haenggi,et al.  Coordinated Multipoint Joint Transmission in Heterogeneous Networks , 2014, IEEE Transactions on Communications.

[25]  Jeffrey G. Andrews,et al.  A tractable model for optimizing device-to-device communications in downlink cellular networks , 2014, 2014 IEEE International Conference on Communications (ICC).

[26]  Jeffrey G. Andrews,et al.  A Tractable Approach to Coverage and Rate in Cellular Networks , 2010, IEEE Transactions on Communications.

[27]  Martin Haenggi,et al.  The Meta Distribution of the SIR in Poisson Bipolar and Cellular Networks , 2015, IEEE Transactions on Wireless Communications.

[28]  J. Gil-Pelaez.  Note on the inversion theorem , 1951 .

[29]  Miklós Telek,et al.  A moments based distribution bounding method , 2006, Math. Comput. Model..

[30]  Angel Lozano,et al.  Ergodic Spectral Efficiency in MIMO Cellular Networks , 2016, IEEE Transactions on Wireless Communications.

[31]  Martin Haenggi,et al.  The Mean Interference-to-Signal Ratio and Its Key Role in Cellular and Amorphous Networks , 2014, IEEE Wireless Communications Letters.

[32]  Martin Haenggi,et al.  Stochastic Geometry for Modeling, Analysis, and Design of Multi-Tier and Cognitive Cellular Wireless Networks: A Survey , 2013, IEEE Communications Surveys & Tutorials.