Characterizing The SINR in Poisson Network Using Factorial Moment


  • Moubachir Madani Fadoul Wireless Communication Centre, Universiti Teknologi Malaysia
  • Razali Ngah Wireless Communication Centre, Universiti Teknologi Malaysia
  • Alireza Moradi Wireless Communication Centre, Universiti Teknologi Malaysia


Usually, cellular networks are modeled by placing
each tier (e.g macro, pico and relay nodes) deterministically
on a grid. When calculating the metric performances such
as coverage probability, these networks are idealized for not
considering the interference. Overcoming such limitation by
realistic models is much appreciated. This paper considered two-
tier two-hop cellular network, each tier is consisting of two-hop
relay transmission, relay nodes are relaying the message to the
users that are in the cell edge. In addition, the locations of the
relays, base stations (BSs), and users nodes are modeled as a point
process on the plane to study the two hop downlink performance.
Then, we obtain a tractable model for the k-coverage probability
for the heterogeneous network consisting of the two-tier network.
Stochastic geometry and point process theory have deployed to
investigate the proposed two-hop scheme. The obtained results
demonstrate the effectiveness and analytical tractability to study
the heterogeneous performance.

Author Biographies

Moubachir Madani Fadoul, Wireless Communication Centre, Universiti Teknologi Malaysia

received his B.Eng. degree in electrical and electronics from Azzaytuna University, Tarhona, Libya, 2009. M.Sc. and Ph.D. in electrical & electronics and telecommunication from Universiti Teknologi Malaysia (UTM), Malaysia in 2013 and 2019, respectively. His research interests include wireless communication, MIMO, cooperative communication, interference cancellation, information theory, beamforming, and stochastic geometry. He is serving as a reviewer for IEEE Access Journal.

Alireza Moradi, Wireless Communication Centre, Universiti Teknologi Malaysia

Postdoc Researcher


V. Chandrasekhar, J.G. Andrews, A. Gatherer, Femtocell networks: a survey

(9), 59 (2008)

R.N. Romain Chevillon, Guillaume Andrieux, J.F. Diouris, Effects of directional

antennas on outband d2d mmwave communications in heterogeneous networks,

International Journal of Electronics and Communications 96, 58 (2018)

T.S. Rappaport, R.W. Heath Jr, R.C. Daniels, J.N. Murdock, Millimeter wave

wireless communications (Pearson Education, 2014)

T. Shuminoski, T. Janevski, 5g terminals with multi-streaming features for real-

time mobile broadband applications, Radioengineering 26(2), 471 (2017)

P. Mitran, C. Rosenberg, in IEEE Wireless Commun. and Networking Conf.

(WCNC) (IEEE, 2012), pp. 2967–2972

J.G. Andrews, F. Baccelli, R.K. Ganti, A tractable approach to coverage and

rate in cellular networks, IEEE Trans. on Commun. 59(11), 3122 (2011)

H.S. Dhillon, R.K. Ganti, F. Baccelli, J.G. Andrews, Modeling and analysis of

k-tier downlink heterogeneous cellular networks 30(3), 550 (2012)

R. Bhagavatula, R.W. Heath, Adaptive bit partitioning for multicell intercell

interference nulling with delayed limited feedback 59(8), 3824 (2011)

M. Haenggi, Stochastic geometry for wireless networks (Cambridge University

Press, 2012)

B. B laszczyszyn, M.K. Karray, H.P. Keeler, Wireless networks appear

poissonian due to strong shadowing, IEEE Trans. Wireless Commun. 14(8),


H.P. Keeler, N. Ross, A. Xia, When do wireless network signals appear poisson?,

arXiv preprint arXiv:1411.3757 (2014)

H.S. Dhillon, R.K. Ganti, J.G. Andrews, in Inform. Theory and Applicat.

Workshop (ITA), 2011 (IEEE, 2011), pp. 1–6

H.S. Dhillon, M. Kountouris, J.G. Andrews, in 2012 Conf. Record of the Forty

Sixth Asilomar Conf. on Signals, Syst. and Comput. (ASILOMAR) (IEEE,

, pp. 683–687

S. Park, W. Seo, Y. Kim, S. Lim, D. Hong, Beam subset selection strategy for

interference reduction in two-tier femtocell networks 9(11), 3440 (2010)

S. Park, W. Seo, S. Choi, D. Hong, A beamforming codebook restriction for

cross-tier interference coordination in two-tier femtocell networks 60(4), 1651


V. Chandrasekhar, M. Kountouris, J.G. Andrews, Coverage in multi-antenna

two-tier networks, IEEE Trans. Wireless Commun. 8(10) (2009)

P. Madhusudhanan, J.G. Restrepo, Y. Liu, T.X. Brown, K.R. Baker, in Global

Telecommun. Conf. (GLOBECOM 2011), 2011 IEEE (IEEE, 2011), pp. 1–6

B. B laszczyszyn, M.K. Karray, H.P. Keeler, in INFOCOM, 2013 Proc. IEEE

(IEEE, 2013), pp. 773–781

H.P. Keeler, B. B

laszczyszyn, M.K. Karray, in Inform.Theory Proc. (ISIT),

IEEE Int. Symp. on (IEEE, 2013), pp. 1167–1171

M. Haenggi, A geometric interpretation of fading in wireless networks: Theory

and applications 54(12), 5500 (2008)

M. Haenggi, R.K. Ganti, Interference in large wireless networks (Now

Publishers Inc, 2009)

F. Baccelli, B. Blaszczyszyn, Stochastic geometry and wireless networks, vol. 1

(Now Publishers Inc, 2009)

C.H. Liu, J.G. Andrews, Multicast outage probability and transmission capacity

of multihop wireless networks 57(7), 4344 (2011)

H.U. Gerber, in Life Insurance Mathematics (Springer, 1997), pp. 23–33

J. Kingman, Poisson processes, Oxford University Press (1993)

B. Blaszczyszyn, H.P. Keeler, in Personal, Indoor and Mobile Radio Commun.

(PIMRC Workshops), 2013 IEEE 24th Inter. Symp. on (IEEE, 2013), pp. 153–

F. Olver, D. Lozier, R. Boisvert, C. Clark, Digital library of mathematical

functions, national institute of standards and technology from h ttp, dlmf. nist.

gov/(release date 2011-07-01), Washington, DC (2010)