8 mars 2018

Catégorie : Doctorant

What: PhD position at IETR laboratory

Topic: Correlated spatial point processes for efficient resource allocations in dense and randomly deployed networks.

When: From 1/10/2018 to 30/09/2021

Supervising: Dr. Philippe Mary and Dr. Jean-Yves Baudais

Key words: Stochastic geometry, random matrix theory, MIMO signal processing, resource allocation

*Laboratory***: Institut d’électronique et de télécommunication de Rennes (IETR),**

** Start date : **October 1st, 2018

Stochastic geometry provided a mathematical framework to study large wireless communication networks by characterizing the distribution of interferences [1]. From this stochastic characterization, network performance metrics can be evaluated such as coverage probability and ergodic rate. Recent works have combined stochastic geometry and random matrix theory to evaluate the spectral-efficiency energy-efficiency (SE-EE) tradeoff of signal to leakage plus noise ratio (SLNR) compared to zero forcing (ZF) precoder [2]. Basically, the interest of spatial point processes in performance analysis is the possibility to express the main performance metrics with the Laplace transform of the interference which can be expressed in closed-form in some cases. However, same as the regular hexagonal grid model, the performance evaluation of wireless cellular networks with a fully stochastic spatial description strongly depends on the kind of process used, e.g. Ginibre, Matern, Poisson, and overall on hypothesis on the network (elastic flow, power constraint, Gaussian signals, etc) [1]. The challenge is to find a tradeoff between the relevance of the results and tractability.

A basic limitation of traditional stochastic geometry approach is that it does not catch the fact that users do not receive the same resources according to their location w.r.t. the base station. Hence the resources allocated to users are not related to the integration over the domain of the spatial process. A first challenge is to deal with different resource provisioning in the same time than averaging over the point process without increasing the complexity of the model. The key problem is that resource allocation strategy introduces correlation between users and BSs distributions. Moreover, cooperation between BSs used for resource allocation in a cluster cell also introduces correlation between point processes. A first attempt has been granted in [5], where users are separated into cell-edge and non cell-edge users. Different power allocations are then considered. However, to fully address the problem of resource allocation in multi-user randomly deployed networks, the joint distribution of a given statistic, e.g. SINR, among users in a cell should be derived.

The PhD thesis aims at designing tractable and constructive models based on stochastic geometry and random matrix theory in order to link the resource allocation and cooperation strategies to the randomly deployed network. A rigorous state of the art will be conducted first, including the cited references in particular, then theoretical model including those dealing with correlation between point processes will be proposed. In particular, the uplink case, less addressed in literature, will be dealt with. The validation of theoretical findings will be done by comparing with large Monte-Carlo simulations.

This work follows researches done in the project TEPN, funded by the labex Cominlabs, that gathered researcher from IRISA and IETR [2, 3, 4]. Interactions between teams of these two laboratories are envisaged during this PhD thesis. Moreover, this field of study is highly important for addressing the upcoming challenges of 5G and dense cellular networks in which the laboratory claims to contribute.

[1] H. ElSawy, A. Sultan-Salem, M. S. Alouini and M. Z. Win, "Modeling and analysis of cellular networks using stochastic geometry: A tutorial,'' *IEEE Communications Surveys Tutorials*, vol.~PP, no.~99, pp.~1--37, 2016.

[2] A. M. Alam, P. Mary, J.-Y. Baudais, and X. Lagrange, "Asymptotic Analysis of Area Spectral Efficiency and Energy Efficiency in PPP Networks With SLNR Precoder'' in *IEEE Transactions on Communications*, pp.~1--6, April 2017.

[3] A. M. Alam, P. Mary, J.-Y. Baudais, and X. Lagrange, “Energy Efficiency-Area Spectral Efficiency Tradeoff in PPP Network with SLNR Precoder'' in *Proc. 17 ^{th} IEEE SPAWC*, 2016.

[4] A. Mahbubul-Alam, P. Mary, J.-Y. Baudais, X. Lagrange, “Energy Efficiency-Spectral Efficiency Tradeoff in Interference-Limited Wireless Networks with Shadowing”, *In Proc. of IEEE VTC-Fall 2015,* Boston, USA.

[5] H. Zhuang and T. Ohtsuki, “A Model Based on Poisson Point Process for Analyzing MIMO Heterogeneous Networks Utilizing Fractional Frequency Reuse,” *IEEE Transactions on Wireless Communications*, vol. 13, no. 12, pp. 6839–6850, Dec 2014.

Stochastic geometry, Poisson point process, probabilities, resource allocations, random matrix theory, non-stationary point processes.

The candidate should have earned an MSc degree, or equivalent, in one of the following field: Signal processing, electrical engineering, applied mathematics. She/He should have a strong background in probabilities and in signal processing for wireless communications as well. The candidate should be familiar with Matlab and C/C++ languages.

- Email a motivation letter
- Full CV with project and courses that could be related to the subject
- Complete academic records (from Bachelor to MSc)
- 2 or 3 references
**Applications will be reviewed when they arrive until one candidate is select**

- Dr. Philippe Mary, INSA Rennes, IETR.

email: Philippe.mary@insa-rennes.fr

webpage: http://pmary.perso.insa-rennes.fr - Dr. Jean-Yves Baudais, CNRS, IETR.

email: jean-yves.baudais@insa-rennes.fr

webpage: http://jeanyves.baudais.free.fr

**Start date: 1/10/2018.**

(c) GdR 720 ISIS - CNRS - 2011-2018.