## Section: New Results

Keywords : Wireless LAN, IEEE 802.11, UMTS, association problem, rate control, ad hoc network, sensor network, coverage, connectivity, random matrix theory.

### Wireless networks

Participants : Sara Alouf, Eitan Altman, Konstantin Avrachenkov, Mouhamad Ibrahim, Arzad Alam Kherani, Giannis Koukoutsidis, Dinesh Kumar, Philippe Nain, Balakrishna Prabhu, Venkatesh Ramaiyan, Srinivas Shakkottai.

#### WLAN access

Participants : Sara Alouf, Mouhamad Ibrahim, Eitan Altman, Venkatesh Ramaiyan, Dinesh Kumar, Srinivas Shakkottai.

##### Analysis of IEEE 802.11

IEEE 802.11 represents the de facto standard for wireless local area networks. One of the well-known drawbacks of IEEE 802.11 is the low performance of its MAC protocol in terms of throughput in congested networks.

During his master internship, supervised by S. Alouf, M. Ibrahim has proposed an adaptive back-off mechanism whose contention window is set to an optimal size after a successful transmission. The proposed algorithm, called ``Adaptive BEB'', relies on on-line counts of error-free frames received at a given station. The optimality achieved by Adaptive BEB refers to a maximum overall system throughput. Simulation results show that Adaptive BEB substantially improves the IEEE 802.11 standard and that its performance is steady under a variety of network conditions and configurations [57] .

In [69] the same authors propose an alternative formulation of Adaptive BEB as well as an extension that enhances its performance over noisy channel. The extended algorithm, called Adaptive BEB++, makes use of an exponentially weighted moving average filter to estimate the packet error rate observed at a given station.

In [48] , E. Altman and D. Miorandi, in collaboration with A. Kumar and M. Goyal (both from IISc Bangalore, India), study the homogeneous case with saturated mobiles, in which all mobiles use the same back-off parameters (like in IEEE 802.11b). They obtain the throughput through a single fixed-point scalar equation. They also provide a computing procedure to compute the throughput of TCP over IEEE 802.11b.

In [53] , E. Altman jointly with V. Ramayan and A. Kumar (both from from IISc Bangalore, India), derives throughput expressions for the non-homogeneous case, which allows them to model service differentiation among several classes. Such differentiation exists in the "e" version of IEEE 802.11. They provide a vector valued fixed-point equation, and give conditions for the uniqueness of its solution. They also give examples of non-uniqueness. In case of uniqueness, they show that the solution of the fixed-point equation provides good approximations for the throughputs.

##### Rate selection in 802.11

In
[32] , E. Altman and D. Kumar and V. Ramaiyan, in collaboration with A. Kumar (
IISc Bangalore, India) derive closed-form expressions for the optimal PHY (physical) rate selection that achieves maximum throughput levels for the network at minimum power consumption. In the cooperative approach they seek to obtain the optimal
PHY rates under two different scenarios –
*max-min fair* rate (in which the objective is to obtain the highest value of a common rate to all users that satisfies the system's constraints) as well as a
*global multi-rate* allocation. In the non-cooperative approach a competitive
*multi-rate* allocation is studied. Single node throughputs corresponding to the optimal PHY rates are numerically computed.

##### The association problem for 802.11 WiFi networks

In [71] , S. Shakkottai and E. Altman, in collaboration with A. Kumar ( IISc Bangalore, India), investigate the so-called association problem: when a mobile has connectivity with several WiFi networks, to which network should it connect to? Since mobiles can frequently make such choices, and since they are in general not aware of each other, and are thus non-cooperative, the solution concept that these authors have developed uses a Nash equilibrium, which they explicitly compute.

#### Optimizing cellular networks using random matrix theory

Participants : Eitan Altman, Nicolas Bonneau, Laura Cottatellucci.

The work concerns applications of random matrix theory and unitary random matrix theory to cellular networks. In most cases of interest, explicit formulas depending only on a few meaningful system parameters can be derived.

In [36] , N. Bonneau and E. Altman, in collaboration with M. Debbah and G. Caire (both from Institut Eurecom , Sophia Antipolis), analyze base station deployment of CDMA cells along the line. Mobiles and base stations use spreading codes to simultaneously transmit their information, so that the receiving end can discriminate between the interfering users. Results are derived for three types of receiver structures: matched filter, Wiener filter and optimum filter. There is a uniformly distributed density dof users per meter as well as certain characteristics of the fading channel. The asymptotic regime of very dense networks are considered, where the spreading length Ntends to infinity, dtends to infinity but the ratio is constant. Using random matrix theory, simple expressions for the performance measures, such as SINR and spectral efficiency in the large system limit, are derived.

Standard studies of uplink CDMA schemes assume a multiple access communication scheme, where each user modulates his signal with a pseudo-random i.i.d. sequence. In [37] , N. Bonneau and E. Altman, in collaboration with M. Debbah and G. Caire ( Institut Eurecom ), investigate the possible gain of using orthogonal spreading codes in the uplink CDMA. The problem is analyzed in the asymptotic regime. The results are based on random unitary matrix theory.

Orthogonal Frequency Division Multiplexing Access (OFDMA) is a technique allowing multiple users to simultaneously transmit to a base station. The bandwidth is divided into carriers on which users send their information. However, efficient algorithms to schedule transmission tend to consume too many resources, because of the feedback requirements. Using the reciprocity of the channel on each carrier, N. Bonneau and E. Altman, in collaboration with M. Debbah ( Institut Eurecom and A. Hjørungnes (UniK, Norway) show in [38] how to optimize the use of OFDMA carriers in a decentralized context in which the choice of carriers is done at the transmitters rather than at the base station. This can be most relevant to 802.16 (WiMax) where FDMA is used.

In [65] , L. Cottatellucci, in collaboration with M. Debbah ( Institut Eurecom ) and R. R. Müeller (University of Trondheim, Norway), analyzes the performance of large asynchronous CDMA systems with linear multi-user detectors (e.g. minimum mean square error detector, multistage Wiener filter, multistage detectors) in the uplink channel. While the performance of synchronous systems with square-root Nyquist chip waveforms is independent of the chip bandwidth, the performance of asynchronous systems depends on the pulse shape and the bandwidth. It increases as the bandwidth increases beyond half on the chip rate and, in such a case, asynchronous systems outperform the synchronous ones. The analysis, based on the self-averaging properties of random matrices, provides also a terse description of asynchronous CDMA systems in terms of a few macroscopic system parameters, (noise variance, the system load, the fading distribution of the channel, the power distribution and some coefficients able to describe the effects of the pulse shape and the bandwidth on the system) that facilitates cross-layer design.

In [64] , L. Cottatellucci, in collaboration with M. Debbah ( Institut Eurecom ) and R. R. Müeller (University of Trondheim, Norway), provides a low complexity linear multistage detector for multiuser multiple-input multiple-output CDMA systems with correlated spatial diversity. The low complexity detector is based on the properties of random matrices and achieves near-linear minimum mean square error (LMMSE) performance with the same complexity order per bit of a conventional single user matched filter detector. The multistage detector performance is also investigated.

#### Ad hoc and sensor networks

Participants : Ahmad Al Hanbali, Eitan Altman, Robin Groenevelt, Arzad Alam Kherani, Dinesh Kumar, Philippe Nain.

##### Route lifetime in vehicular ad hoc networks

The work of D. Kumar, A. A. Kherani and E. Altman in
[56] aims to better understand the route lifetime dynamics in inter-vehicular mobile ad hoc networks (iv-MANETs or
VANETs), that are a special class of MANETs, but exhibit very different behavior from them. These authors solve the problem of finding an optimal multi-hop route between two vehicular nodes on a highway. Under a Markovian assumption on the process of the speed of nodes, they shown that
the optimal choice of speeds of relay nodes in a route attempts to equalize the lifetimes of adjacent links in a route. A monotone variation property of the speed of the relay nodes under the optimal policy is proved. The heuristics and structures developed can serve in designing a new
set of efficient
*interactive* routing protocols specifically tailored for high mobility ad hoc networks and iv-MANETs in particular.

##### Relaying performance in mobile ad hoc networks

In MANETs (Mobile Ad Hoc Networks) a route between two nodes often experiences failure when the mobility of nodes increases. This explains the poor performance of traditional ad hoc routing protocols. A well-known solution proposed, and analyzed by Tse and Grossglauser, is to use
intermediary nodes as relay nodes. A relay node stores in its buffer packets for other nodes, and then transmit a packet when it is sufficiently close to the destination. In
[54] , A. Al Hanbali, A. A. Kherani, R. Grenovelt, P. Nain, and E. Altman study the contribution of a relay node
in relaying data between a source and a destination, called
*relay throughput* . When all nodes move according to the same mobility model, a uniform steady-state node position distribution achieves the lowest relay throughput. Explicit and closed form expressions for the relay throughput are provided for the Random Waypoint and The Random
Direction mobility models, in both one and two dimensions. In addition, for the Random Walk mobility the mean waiting time of the packet in the relaying buffer of a relay node is derived for the high load case.

R. Groenevelt and P. Nain (in collaboration with G. Koole from the Vrije Universiteit of Amsterdam, The Netherlands) have introduced in [44] a generic stochastic model that accurately predicts the message delay in a mobile ad hoc network when nodes can relay messages. The model has only two input parameters: the number of nodes and the intensity of a finite number of homogeneous and independent Poisson processes modeling instances when any pair of nodes come within transmission range of one another. Explicit expressions are obtained for the Laplace-Stieltjes transform of the message delay, from which the expected message delay is derived in closed-form. These calculations are carried out for two relay protocols: the two-hop relay and the unrestricted relay protocols. Despite its simplicity, the model is able to accurately predict the performance of both relay protocols for a number of mobility models (Random Waypoint, Random Direction and Random Walker Mobility Models), as shown by simulations.

In [67] nodes move according to independent Brownian motions on a line and R. Groenevelt, E. Altman and P. Nain compute the expected time before a message reaches its destination when node relaying is used.

##### Coverage and connectivity

One important issue in ad hoc wireless networks is the characterization of the limiting performance, in terms of both connectivity and coverage. After studying in 2004 one-dimensional networks using a queueing theory approach, E. Altman, in collaboration with D. Miorandi ( Create-Net , Italy), has studied in [51] the two-dimensional problem under various assumptions on the channel gains.

In [49] , P. Nain, in collaboration with B. Liu (University of Massachusetts-Lowell, USA), P. Brass, O. Dousse (both from Epfl , Switzerland) and D. Towsley (University of Massachusetts, USA), has studied dynamic aspects of the coverage of a mobile sensor movement, and showed that sensor mobility can be exploited to compensate for the lack of sensors and improve the network coverage. This work has been further extended to the case of non-zero sensing duration (an intruder entering the detection area of a sensor cannot be detected before a minimum amount of time).

#### Analysis of UMTS networks

Participants : Eitan Altman, Giannis Koukoutsidis.

In [47] , G. Koukoutsidis analyzes a Wideband Code Division Multiple Access (WCDMA) multiservice system. This system is composed of real-time traffic having dedicated channel access, admission control and limited rate control, and non real-time traffic with limited resource reservation and processor sharing rate control. A non-homogeneous quasi-birth-death process is used to model the system and evaluate its performance.

In [46] , G. Koukoutsidis and E. Altman, in collaboration with J.-M. Kelif ( France Telecom R&D , Issy-les-Moulineaux), describe a modeling approach for studying fair rate sharing in a CDMA link with simultaneous transmissions with Poisson and Engset flow arrivals. The approach revisits and extends the Generalized Processor Sharing (GPS) scheme introduced, and analyzed, by J. M. Cohen in 1979, and it allows the authors to derive various performance metrics (expected transfer time, blocking probabilities, etc.).

#### Optimization and control of mobile networks

Participants : Eitan Altman, Konstantin Avrachenkov, Arzad Alam Kherani, Grigoriy Miller, Balakrishna Prabhu.

In [39] , A. A. Kherani and B. Prabhu, in collaboration with V. S. Borkar ( Tata Institute, Mombai, India), study the structure of the optimal policy in a decision problem faced by a wireless device. The device wants to transmit packets with minimal delay but it also wants to minimize the energy consumed by each transmission. The optimal policy for such a decision problem is shown to be of threshold type, where the threshold depends on the number of packets in the queue and the remaining energy in the battery.

E. Altman, K. Avrachenkov and G. Miller, along with R. Márquez (University of Los Andes, Merida, Venezuela), have worked on the problem of decentralized dynamic control of power and transmission rate in cellular networks. It is assumed that each mobile knows only the state of its own channel, and takes decisions on the power levels based on that information. For each mobile, its SINR (which is the ratio between the power received at a base station from the mobile and the sum of the powers corresponding to interferences from other mobiles and of noize) determines the transmission rate that the mobile can achieve. In [17] the authors consider the case of two mobiles, where the first mobile seeks for a power control strategy so as to maximize its transmission rate, whereas the other mobile, assumed to be malicious, tries to minimize the rate of the first mobile by the intereference that it causes. Both mobiles have constraints on their average power consumption. This problem is formulated as a stochastic zero-sum game, with a non-standard information structure. Foundations for solving such problems are laid in [17] , and then implemented to derive structural properties of the optimal policies for each of the mobiles.