@article {Bennani20161,
	title = {Achieving QoS in Virtual MIMO systems: a satisfaction equilibrium analysis},
	journal = {Eurasip Journal on Wireless Communications and Networking},
	volume = {2016},
	number = {1},
	year = {2016},
	note = {cited By 0},
	pages = {1-13},
	abstract = {This paper presents a game theoretic framework to analyze a cellular-WLAN heterogeneous network from a virtual multiple-input multiple-output (VMIMO) perspective. Namely, we restrict to the uplink case and consider a non-cooperative game where each user seeks to meet some quality of service (QoS). Moreover, mobile users are allowed to re-inject, through their WLAN interfaces, a part of their throughput in the induced game. Thus, the interaction among users defines a distributed VMIMO with a possibly throughput exchange. This mechanism will help all users to meet their respective QoS expressed by the perceived average throughput. The average throughput is considered to be the utility function used in this framework. Now, each mobile user experiences a certain throughput composed of two parts: (1) the throughput received from cellular subsystem and (2) the throughput received from WLAN subsystem. Naturally, we use the concept of satisfaction equilibrium to predict the behavior of the network. Indeed, we provided a sufficient condition for the existence of such an equilibrium. Next, we prove the uniqueness of the equilibrium and compute it explicitly. Afterward, we propose a fully distributed algorithm inspired from the well-known Banach-Picard learning algorithm. Our scheme has many good features facilitating its implementation and usability. Indeed, it accurately converges to the equilibrium (if exists), it is very fast, and it requires no external information. Simulation results validate the algorithm and show its robustness and illustrate numerically the proposed learning scheme for quality-of-service management in such a heterogeneous network. {\textcopyright} 2016, Bennani et al.},
	doi = {10.1186/s13638-016-0612-6},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84966280664\&doi=10.1186\%2fs13638-016-0612-6\&partnerID=40\&md5=e67ac437a619c2d9ac7539dace4426e6},
	author = {Bennani, H.a and Sabir, E.b and Kobbane, A.a and Ben-Othman, J.c and El-koutbi, M.a}
}
@conference {Bennani201456,
	title = {A tax-inspired mechanism design to achieve QoS in VMIMO systems: Give to receive!},
	booktitle = {IWCMC 2014 - 10th International Wireless Communications and Mobile Computing Conference},
	year = {2014},
	note = {cited By 0},
	pages = {56-62},
	abstract = {In this paper, we model a Virtual MIMO system using a game-theoretic approach. We are interested in the uplink, considering a non-coopertive game, where each user try to satisfy a quality of service. The uplink of a direct-sequence code division multiple access (DS-CDMA) data network is considered and a non-cooperative game is proposed in which users are allowed to choose their uplink receivers as well as to satisfy their quality of service. The utility function used in this framework is defined so that the throughput used by the user is divided into two components: the throughput received from cellular Network, and throughput received from Virtual MIMO System. In addition, this framework is used to study a constrained Nash equilibrium for the proposed game, and the impact of the interaction among users. {\textcopyright} 2014 IEEE.},
	doi = {10.1109/IWCMC.2014.6906332},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84908622993\&doi=10.1109\%2fIWCMC.2014.6906332\&partnerID=40\&md5=8f8afb3e0c78e9a74a2e145125d111ac},
	author = {Bennani, H.a and Sabir, E.b and Kobbane, A.a and Walid, A.a and Ben-Othman, J.c}
}
@conference {Bennani201477,
	title = {Virtual MIMO systems: A game theoretical approach},
	booktitle = {WCCCS 2014 - Proceedings; 2014 5th Workshop on Codes, Cryptography and Communication Systems},
	year = {2014},
	note = {cited By 0},
	pages = {77-80},
	abstract = {In this work, we present a new game theoretic approach in order to build a Virtual MIMO system. The utility function used in this framework is defined so that the user throughput is divided into two components: the real, received by the base station, and the virtual throughput received by the neighboring users. A non-cooperative game is proposed where each user are allowed to choose its uplink receiver as well as to maximize its utility function. Simulation results validate our model and and illustrate numerically the proposed scheme under different scenarios. {\textcopyright} 2014 IEEE.},
	doi = {10.1109/WCCCS.2014.7107924},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-84983134494\&doi=10.1109\%2fWCCCS.2014.7107924\&partnerID=40\&md5=7908ed0bd120abe099e5dea1bce6962f},
	author = {Bennani, H.a and Sabir, E.b and Kobbane, A.a and El Koutbi, M.a}
}
