Coverage analysis using the Poisson point process model

doi:10.1017/CBO9781139061421.005

3 - Coverage analysis using the Poisson point process model

Published online by Cambridge University Press: 05 May 2013

Sayandev Mukherjee

Edited by

Tony Q. S. Quek ,

Guillaume de la Roche ,

İsmail Güvenç and

Marios Kountouris

Show author details

Sayandev Mukherjee: Affiliation:
NTT Docomo USA
Tony Q. S. Quek: Affiliation:
Singapore University of Technology and Design
Guillaume de la Roche: Affiliation:
Mindspeed Technologies
İsmail Güvenç: Affiliation:
Florida International University
Marios Kountouris: Affiliation:
SUPÉLEC (Ecole Supérieure d'Electricité)

Book contents

Get access

Summary

Introduction

The rapid rate of increase in data traffic means that future wireless networks will have to support a large number of users with high data rates. A promising way to achieve this is by spectrum reuse through the deployment of cells with small range, such that the same time-frequency resources may be reused simultaneously in multiple cells. At the same time, the traditional coverage requirement for wireless users (supporting a modest rate at cell-edge users) is most economically met with cells having large range, i.e., the traditional macrocellular architecture. Thus the wireless cellular networks of the future are likely to be heterogeneous, i.e., have one or more tiers of small cells overlaid on the macrocellular tier.

We consider the problem of network design from the point of view of a service provider considering the deployment of a network in a certain region. The primary metric we shall focus on is the coverage on the downlink: namely, the probability that a user at an arbitrary location in the deployed network has coverage. Later, we shall briefly discuss the distribution of the maximum rate that such a user could support from one of the base stations (BSs).

When we talk of the service provider designing a network to satisfy a certain coverage criterion, we mean the choice of deployment parameters for such a network, including:

Number of tiers of the network
Densities of the BSs in the tiers
Transmit powers of the BSs in the tiers.

Type: Chapter
Information: Small Cell Networks
Deployment, PHY Techniques, and Resource Management
, pp. 44 - 81

DOI: https://doi.org/10.1017/CBO9781139061421.005 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Book purchase

Temporarily unavailable

References

[1] L., Chen, W., Chen, B., Wang, X., Zhang, H., Chen, and D., Yang, “System-level simulation methodology and platform for mobile cellular systems,” IEEE Commun. Mag., vol. 49, no. 7, pp. 148–55, July 2011.Google Scholar

[2] R., Mallik, “A new statistical model of the complex Nakagami-m fading gain,” IEEE Trans. on Communications, vol. 58, no. 9, pp. 2611–20, Sep. 2010.Google Scholar

[3] A., Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd edn. McGraw-Hill, 1991.Google Scholar

[4] R. A., DeVore and G. G., Lorentz, Constructive Approximation. Springer, 1993.Google Scholar

[5] S., Atapattu, C., Tellambura, and H., Jiang, “A mixture gamma distribution to model the SNR of wireless channels,” IEEE Trans. Wireless Commun., vol. 10, no. 12, pp. 4193–203, Dec. 2011.Google Scholar

[6] J., Almhana, Z., Liu, V., Choulakian, and R., McGorman, “A recursive algorithm for gamma mixture models,” in Proc. IEEE Int. Conf. on Commun. (ICC), June 2006, pp. 197–202.Google Scholar

[7] J. G., Andrews, F., Baccelli, and R. K., Ganti, “A tractable approach to coverage and rate in cellular networks,” IEEE Trans. on Communications, vol. 59, no. 11, pp. 3122–34, Nov. 2011.Google Scholar

[8] P. C., Pinto and M. Z., Win, “Communication in a Poisson field of interferers-Part II: Channel capacity and interference spectrum,” IEEE Trans. Wireless Commun., vol. 9, no. 7, pp. 2187–95, July 2010.Google Scholar

[9] K., Gulati, B. L., Evans, J. G., Andrews, and K. R., Tinsley, “Statistics of co-channel interference in a field of Poisson and Poisson-Poisson clustered interferers,” IEEE Trans. Signal Processing, vol. 58, no. 10, pp. 6207–22, Dec. 2010.Google Scholar

[10] K. W., Sung, H., Haas, and S., McLaughlin, “A semianalytical PDF of downlink SINR for femtocell networks,” EURASIP J. Wireless Commun. Networking, vol. 2010, no. 4, 2010.Google Scholar

[11] R., Pupala, L. J., Greenstein, and D. G., Daut, “Throughput analysis of interference limited MIMO-based cellular systems,” IEEE Trans. Wireless Commun., vol. 9, no. 6, pp. 1946–51, June 2010.Google Scholar

[12] V. M., Nguyen, F., Baccelli, L., Thomas, and C. S., Chen, “Best signal quality in cellular networks: asymptotic properties and applications to mobility management in small cell networks,” EURASIP J. Wireless Commun. Networking, vol. 2010, no. 4, 2010.Google Scholar

[13] S., Mukherjee, “Analysis of UE outage probability and macro-cellular traffic offloading for WCDMA macro network with femto overlay under closed and open access,” in Proc. IEEE Int. Conf. on Commun. (ICC), June 2011.Google Scholar

[14] A. J., Ganesh and G. L., Torrisi, “Large deviations of the interference in a wireless communication model,” IEEE Trans. Inform. Theory, vol. 54, no. 8, pp. 3505–17, Aug. 2008.Google Scholar

[15] B., Blaszczyszyn, M. K., Karray, and F. X., Klepper, “Impact of the geometry, path-loss exponent and random shadowing on the mean interference factor in wireless cellular networks,” in Proc. IEEE Wireless Mob. Netw. Conf. (WMNC), Oct. 2010.Google Scholar

[16] A., Berman and R. J., Plemmons, Nonnegative Matrices in the Mathematical Sciences. Society for Industrial and Applied Mathematics, 1994.Google Scholar

[17] A. M., Hunter, J. G., Andrews, and S., Weber, “Transmission capacity of ad hoc networks with spatial diversity,” IEEE Trans. Wireless Commun., vol. 7, no. 12, pp. 5058–71, Dec. 2008.Google Scholar

[18] J. F. C., Kingman, Poisson Processes. Oxford University Press, 1993.Google Scholar

[19] R. W., Heath Jr and M., Kountouris, “Modeling heterogeneous network interference,” in Proc. Inform. Theory and Appl. Workshop (ITA), Feb. 2012.Google Scholar

[20] S., Mukherjee, “UE coverage in LTE macro network with mixed CSG and open access femto overlay,” in Proc. IEEE Int. Conf. on Commun. (ICC), June 2011.Google Scholar

[21] S., Mukherjee, “Downlink SINR distribution in a heterogeneous cellular wireless network,” IEEE J. Select. Areas Commun. (JSAC), vol. 30, no. 3, pp. 575–85, Apr. 2012.Google Scholar

[22] M. L., Kleptsyna, A., Le Breton, and M., Viot, “General formulas concerning Laplace transforms of quadratic forms for general Gaussian sequences,” Journal of Applied Mathematics and Stochastic Analysis, vol. 15, no. 4, pp. 309–25, 2002.Google Scholar

[23] S., Mukherjee, “Downlink SINR distribution in a heterogeneous cellular wireless network with max-SINR connectivity,” in Proc. Allerton Conference on Communication, Control, and Computing, Sep. 2011.Google Scholar

[24] H. S., Dhillon, R. K., Ganti, F., Baccelli, and J. G., Andrews, “Modeling and analysis of K-tier downlink heterogeneous cellular networks,” IEEE J. Sel. Areas Commun. (JSAC), vol. 30, no. 3, pp. 550–60, Apr. 2012.Google Scholar

[25] P., Madhusudhanan, J. G., Restrepo, Y., Liu, T. X., Brown, and K. R., Baker, “Multi-tier network performance analysis using a shotgun cellular system,” in Proc. IEEE Global Telecommun. Conf. (GLOBECOM), Dec. 2011, pp. 1–6.Google Scholar

[26] NTT DoCoMo, “Discussions on UE capability for dual-antenna receiver,” 3GPP Standard Contribution (R4-070745), May 2007.

[27] H. S., Jo, Y. J., Sang, P., Xia, and J. G., Andrews, “Outage probability for heterogeneous cellular networks with biased cell association,” in Proc. IEEE Global Telecommun. Conf. (GLOBECOM), Dec. 2011.Google Scholar

[28] S., Mukherjee, “Downlink SINR distribution in a heterogeneous cellular wireless network with biased cell association,” in Proc. IEEE Int. Conf. on Commun. (ICC), Small Cells Workshop (SmallNets), June 2012.Google Scholar

[29] 3GPP TS 36.304 Release 9 V9.3.0 (2010–2006), “Technical specification group radio access network; evolved universal terrestrial radio access (E-UTRA); user equipment (UE) procedures in idle mode (release 9),” June 2010.

[30] Femto Forum, “Interference management in OFDMA femto-cells,” http://www.femtoforum.org, Mar. 2010.

[31] C., Tepedelenlioglu, A., Rajan, and Y., Zhang, “Applications of stochastic ordering to wireless communications,” IEEE Trans. Wireless Commun., vol. 10, no. 12, pp. 4249–57, Dec. 2011.Google Scholar

[32] M., Aljuaid and H., Yanikomeroglu, “Investigating the Gaussian convergence of the distribution of the aggregate interference power in large wireless networks,” IEEE Trans. Veh. Technol., vol. 59, no. 9, pp. 4418–24, Nov. 2010.Google Scholar

[33] A., Lapidoth, “Nearest neighbor decoding for additive non-gaussian noise channels,” IEEE Trans. Inform. Theory, vol. 42, no. 5, pp. 1520–29, Sep. 1996.Google Scholar

[34] M. S., Pinsker, V. L., Prelov, and S., Verdu, “Sensitivity of channel capacity,” IEEE Trans. Inform. Theory, vol. 41, no. 6, pp. 1877–88, Nov. 1995.Google Scholar