**INTERFERENCE MODELING FOR CELLULAR NETWORKS UNDER BEAM FORMING TRANSMISSION**

** **

**ABSTRACT**

We propose analytical models for the interferencepower distribution in a cellular system employing MIMO beamformingin rich and limited scattering environments, whichcapture non line-of-sight signal propagation in the microwaveand mmWave bands, respectively. Two candidate models areconsidered: the Inverse Gaussian and the Inverse Weibull, bothare two-parameter heavy tail distributions. We further proposea mixture of these two distributions as a model with three parameters.To estimate the parameters of these distributions, threeapproaches are used: moment matching, individual distributionmaximum likelihood estimation (MLE), and mixture distributionMLE with a designed expectation maximization algorithm. Wethen introduce simple ﬁtted functions for the mixture modelparameters as polynomials of the channel path loss exponent andshadowing variance. To measure the goodness of these models, theinformation-theoretic metric relative entropy is used to capturethe distance from the model distribution to a reference one. Theinterference models are tested against data obtained by simulatinga cellular network based on stochastic geometry. The results showthat the three-parameter mixture model offers remarkably goodﬁt to simulated interference power. The mixture model is furtherused to analyze the capacity of a cellular network employing jointtransmit and receive beamforming and conﬁrms a good ﬁt withsimulation.

**EXISTING SYSTEM:**

We argue for the important role that interference character-ization plays in evaluating and predicting the network performancein both microwave and mmWave bands. Traditionally,mmWave bands are considered for backhaul in cellular systemsand for high-volume consumer electronics such as personalarea and local area networks, but not for cellular access dueto concerns about short-range and non-line-of-sight coverageissues. MmWave has, however, recently been shownto be suitable for cellular communications, provided short cellradius of the order of 100-200 meters and sufﬁcient beamforminggain between communicating nodes. Reducing thecell radius leads to dense base station (BS) deployments. Evenunder beamforming, these high BS and user densities can drivecellular networks to be more interference rather than noiselimited. While large adaptive arrays with narrow beams canboost the received signal power and hence reduce the impactof out-of-cell interferenc, this interference remainsan important performance-limiting factor in dense mmWavenetworks .In next generation of wireless networks with a large numberof subscribers and dense BSs deployment, interference modelingis an important step towards network realization. Existingstochastic geometry based work either uses the interferenceLaplace transform to evaluate simple transmission schemes or models the interference using moment matching gammadistribution. Gaussian distribution is another approximationthat is considered for the centered and normalizedaggregate wireless interference powe. The centrallimit theorem which justiﬁes the Gaussian approximation,however, does not apply when some of the interferers aredominant. Also, the Gaussian distribution does not modelthe interference very well at low density of interferers orwhen the exclusion region, the region with no interferers, isrelatively small, as the cell sizes shrink. The distribution ofthe interference power at relatively small exclusion regionshas a heavy tail which can not be captured by the Gaussiandistribution. Here we propose analytical distributionmodels characterized by only a few parameters, which canbe ﬁtted to simple polynomial functions of channel path lossexponent and shadowing variance, and test their ﬁtness againstnetwork simulation based on stochastic geometry. A closedform distribution of the interference helps in designing acellular system by allowing the analysis of system capacityand comparing different transmission techniques, which maynot be directly achievable with a characteristic function ofthe interference using the Laplace transform.

**PROPOSED SYSTEM:**

The main contributions and novelties of this paper are anew analytical model for interference power distribution andmethods for estimating its parameters for both rich scatteringand limited scattering environments, which are summarized as:1) We propose the use of two distributions to modelinterference power, each distribution characterized bytwo parameters: the inverse Gaussian (IG) as a light-toheavytailed distribution and the inverse Weibull (IW) asa heavy tailed one. Further, we propose a novel modelas a mixture of these two distributions with remarkablygood ﬁt to simulation data while having only threeparameters.2) We apply three approaches to estimate the interferencemodels parameters: moment matching (MM), individualdistribution MLE, and mixture distribution MLE. Inthe MM approach, a simple matching of the ﬁrst twointerference power moments is used. In the other twoapproaches, a combination of MM and MLE techniquesis used in designing an iterative EM algorithm whichmaximizes a log likelihood function of the interferencedata.3) We propose the use of the relative entropy or KullbackLeiblerdistance from information theory to measurethe goodness of each model. This metric measuresthe relative distance between a modeled distributionand reference (simulated) data, which gives a goodindication of how far the proposed interference modelis from the referenced interference.4) We provide simple polynomial functions with ﬁtted coefﬁcientsto express the mixture MLE model parametersin terms of channel characteristics, including the pathloss exponent and shadowing standard deviation. Thesepolynomials can be used as a simple representation ofnetwork interference in complex system-level simulations.5) We apply the interference models to evaluate the performanceof a cellular network with joint transmit andreceive beamforming. User’s outage probabilities usingthe MM and mixture MLE interference models are comparedto stochastic geometry based system simulation.6) Our proposed mixture model shows excellent ﬁt inboth interference distribution and network performanceevaluation for a wide range of channel propagationparameters, including path loss exponent from 2 to 5and shadowing standard deviation from 0 dB to 9 dB.

**CONCLUSION**

We introduced new interference models based on moment matching and maximum likelihoodestimation techniques for both the rich scattering and limited scattering NLOS propagations. Anovel model as a mixture between the Inverse Gaussian and Inverse Weibull presents remarkablygood ﬁt with simulation, capturing the heavy-tail characteristics of interference especially inhigh shadowing environments. We designed an expectation maximization algorithm to estimatethe parameters of this mixture model. We also ﬁtted the mixture model parameters to simplepolynomial functions of the channel propagation features, which provide a simple way to modelthe interference without any optimization. The ﬁtted mixture model can then be integrated intoa more complex system level simulation to evaluate and predict cellular performance, or usedto aid system design. The next step would be to test the mixture model with appropriatelyadjusted parameters and functional ﬁtting coefﬁcients against data from measurement campaignsto evaluate the model in an actual system setting.

**REFERENCE:**

[1] S. Rajagopal, S. Abu-Surra, and M. Malmirchegini, “Channel feasibility for outdoor non-line-of-sight mmwave mobilecommunication,” in IEEE Vehicular Tech. Conf. (VTC Fall), Sept 2012, pp. 1–6.

[2] W. Roh, J.-Y. Seol, J. Park, B. Lee, J. Lee, Y. Kim, J. Cho, K. Cheun, and F. Aryanfar, “Millimeter-wave beamformingas an enabling technology for 5G cellular communications: theoretical feasibility and prototype results,” IEEE Comm.Magazine, vol. 52, no. 2, pp. 106–113, February 2014.

[3] F. Boccardi, R. Heath, A. Lozano, T. Marzetta, and P. Popovski, “Five disruptive technology directions for 5G,” IEEEComm. Magazine, vol. 52, no. 2, pp. 74–80, Feb. 2014.

[4] T. Bai, V. Desai, and R. W. Heath, “Millimeter wave cellular channel models for system evaluation,” in IEEE ICNC,2014, pp. 178–182.

[5] T. Bai, A. Alkhateeb, and R. Heath, “Coverage and capacity of millimeter-wave cellular networks,” IEEE Comm. Magazine,vol. 52, no. 9, pp. 70–77, September 2014.

[6] M. Rebato, M. Mezzavilla, S. Rangan, F. Boccardi, and M. Zorzi, “Understanding noise and interference regimes in 5gmillimeter-wave cellular networks,” in European Wireless 2016; 22th European Wireless Conference, May 2016, pp. 1–5.

[7] A. Giovanidis and F. Baccelli, “A stochastic geometry framework for analyzing pairwise-cooperative cellular networks,”CoRR, vol. abs/1305.6254, 2013.

[8] J. Andrews, F. Baccelli, and R. Ganti, “A tractable approach to coverage and rate in cellular networks,” IEEE Trans. onComm., vol. 59, no. 11, pp. 3122–3134, November 2011.

[9] H. ElSawy, E. Hossain, and M. Haenggi, “Stochastic geometry for modeling, analysis, and design of multi-tier andcognitive cellular wireless networks: A survey,” IEEE Comm. Surveys Tutorials, vol. 15, no. 3, pp. 996–1019, 2013.

[10] R. Heath, M. Kountouris, and T. Bai, “Modeling heterogeneous network interference using Poisson point processes,” IEEETrans. on Signal Processing, vol. 61, no. 16, pp. 4114–4126, Aug 2013.