## Section: New Results

### Design and Performance Analysis of Wireless Networks

Participants : François Baccelli, Bartek Błaszczyszyn, Chung Shue Chen, Mir Omid Haji Mirsadeghi, Frédéric Morlot, Tien Viet Nguyen, Van Minh Nguyen.

This axis concerns the analysis and the design of wireless access communication networks. Our contributions are organized in terms of network classes: cellular networks, wireless LANs and MANETs, VANETs. We also have a section on generic results that concern more general wireless networks. We are interested both in macroscopic models, which are particularly important for economic planning and in models allowing the definition and the optimization of protocols. Our approach combines several tools, queueing theory, point processes, stochastic geometry, random graphs.

#### Cellular Networks

The activity on cellular networks has several complementary facets ranging from performance evaluation to protocol design. The work is mainly based on strong collaborations with Alcatel-Lucent and Sprint. We also have personal collaborations with two researchers of Orange Labs.

##### Dimensioning of OFDMA/LTE networks.

Building upon the scalable admission and congestion control schemes
developed in [38] , [34] ,
which allow for an exact representation of the geometry of
interference in networks, in collaboration with M.K. Karray [Orange Labs],
we continue developing a *comprehensive
approach to the performance evaluation of cellular networks* .
This approach, that resulted in
three patents filed by INRIA and FT,
is used by Orange. Some of our methods were in particular
integrated to Orange's dimensioning tool (initially SERT, now *UTRANDIM* ).

This year, the main focus was on the extension of our approach to cellular networks implementing Orthogonal Frequency-Division Multiple Access (OFDMA). The recent interest in OFDMA comes from the fact that it is used in the mobility mode of IEEE 802.16 WirelessMAN Air Interface standard, commonly referred to as WiMAX and OFDMA is currently a working assumption in 3GPP Long Term Evolution (LTE) downlink. Also, OFDMA is the candidate access method for the IEEE 802.22 Wireless Regional Area Networks. It is the context of LTE cellular networks that we have primarily on mind. However, our approach applies to other OFDMA downlink scenarios as well.

The primary objective is to build a *dimensioning method* for the
radio part of the downlink in wireless cellular OFDMA networks, i.e.;
a method allowing one to evaluate what is the minimal density of base stations
assuring a given quality of service (QoS) for a given traffic demand
per surface unit.

In [14] we use information theory to characterize the bit-rate in the channel from a base station to its mobile. It depends on the power and bandwidth allocated to this mobile. Then, we describe the resource (power and bandwidth) allocation problem and characterize feasible configurations of bit-rates of all users. As the key element, we propose some sufficient condition (in a multi-Erlang form) for a given configuration of bit-rates to be feasible. Finally, we consider an Erlang loss model, in which streaming arrivals whose admission would lead to the violation of this sufficient condition are blocked and lost. We evaluate the minimal density of base stations assuring acceptable blocking probabilities for a streaming traffic with a given load per surface unit. We validate this approach by comparison of the blocking probabilities to those simulated in a similar model in which the admission control is based on the original feasibility property (instead of its sufficient condition). Our sufficient bit-rate feasibility condition can also be used to dimension the network for elastic traffic.

In [15] we account for the effect of fading in the above approach. The main practical results of this work are the following. Firstly, for the non-opportunistic sub-channel allocation, we evaluate the degradation due to fading compared to AWGN (that is, a decrease of throughput of at least 13%). Secondly, we evaluate the gain induced by the opportunistic allocation. In particular, when the traffic demand per cell exceeds some value (about 2.5 Mbps in our example), the gain induced by opportunism compensates the degradation induced by fading compared to AWGN.

##### Self-Optimization of User Association and Power.

In the submitted paper [42] we develop mathematical and algorithmic tools for the self-optimization of mobile cellular networks. Scalable algorithms which are based on local measurements and do not require heavy coordination among the wireless devices are proposed. We focus on the optimization of power and of user association. The method is applicable to both joint and separate optimizations. The global utility minimized is linked to potential delay. The distributed algorithm adaptively tunes the system parameters and achieves global optimality by measuring SINR and interference. The algorithms are built on Gibbs' sampler, which offers a unified framework that can easily be reused for different purposes. This work is part of the joint laboratory with Alcatel-Lucent and was presented by C. Chen at the joint laboratory days in October.

##### Self-Optimization of Neighbour Cell List.

The configuration of the neighbour cell list (NCL) has an important impact on the number of dropped calls in cellular networks. In [55] a method for optimizing NCLs is presented. It consists of an initialization using a self-configuration phase, followed by a self-optimization phase that further refines the NCL based on measurements provided by mobile stations during the network operation. Algorithms for both initial self-configuration, and ongoing self-optimization are presented. The performance of the proposed methods is evaluated for different user speeds and different NCL sizes. In addition, the convergence speed of the proposed self-optimization method is evaluated.

##### Extremal Signal Quality in Small Cell Networks

In the papers [53] , [50] , we investigate two critical issues pertaining to small cell networks: best signal quality and user mobility management. We show that, in dense small cell networks, the extremal signal strength distribution tends, after renormalization, to a Gumbel distribution and that it is asymptotically independent of the total interference. Besides, we propose a simple random cell scanning scheme. We establish an analytical model to find the optimal number of cells to be scanned.

##### Best SINRs in Macro Cellular Networks

The distribution of the maximum of the SINRs, Y_{S} ,
received from a cell set S is useful for many problems in cellular
networks. By modelling the interference field as a shot noise process,
in an ongoing work [54]
we could analyze the joint distribution of the interference and
the maximum of the signal strengths, and deduce from this the
distribution of Y_{S} . This can in particular be used to determine
NCL sizes which minimize the real-time call dropping rate and maximize
the user data throughput in macro cellular networks.

#### Mobile Ad Hoc Networks

A MANET is made of mobile nodes which are at the same time terminals and routers, connected by wireless links, the union of which forms an arbitrary topology. The nodes are free to move randomly and organize themselves arbitrarily. Important issues in such a scenario are connectivity, medium access (MAC), routing and stability. This year, in collaboration with Paul Mühlethaler [INRIA HIPERCOM], we mainly worked on the analysis of MAC and routing protocols in multi-hop MANETS.

##### Opportunistic Aloha for MANETS.

Spatial Aloha is probably the simplest medium access protocol to be used in a large mobile ad hoc network: Each station tosses a coin independently of everything else and accesses the channel if it gets heads. In a network where stations are randomly and homogeneously located in a plane, there is a way to tune the bias of the coin so as to obtain the best possible compromise between spatial reuse and per transmitter throughput. In the paper [5] that complements [36] we showed how to address this questions using stochastic geometry and more precisely Poisson shot noise field theory. The theory that is developed is fully computational and leads to new closed form expressions for various kinds of spatial averages (like e.g. outage, throughput or transport). It also allows one to derive general scaling laws that hold for general fading assumptions. We exemplified its flexibility by analyzing a natural variant of Spatial Aloha which we call Opportunistic Aloha and which consists in replacing the coin tossing by an evaluation of the quality of the channel of each station to its receiver and a selection of the stations with good channel (e.g. fading) conditions. We showed how to adapt the general machinery to this variant and how to optimize and implement it. We also showed that when properly tuned, Opportunistic Aloha very significantly outperforms Spatial Aloha, with e.g. a mean throughput per unit area twice higher for Rayleigh fading scenarios with typical parameters.

##### Comparison of Slotted to Non-slotted Aloha for MANETS

In [29] we propose two analytically tractable stochastic models of non-slotted Aloha for MANETs: a first model assumes a static pattern of nodes while the other assumes that the pattern of nodes varies over time. Both models feature transmitters randomly located in the Euclidean plane, according to a Poisson point process with the receivers randomly located at a fixed distance from the transmitters. We concentrate on the so-called outage scenario, where a successful transmission requires a Signal-to-Interference-and-Noise Ratio (SINR) larger than a given threshold. With Rayleigh fading and the SINR averaged over the duration of the packet transmission, both models lead to closed form expressions for the probability of successful transmission. We show an excellent matching of these results with simulations. Using our models we compare the performances of non-slotted Aloha to the previously studied slotted Aloha. We observe that when the path loss is not very strong, both models, when appropriately optimized, exhibit similar performance. For stronger path loss, non-slotted Aloha performs worse than slotted Aloha. However when the path loss exponent is equal to 4 its density of successfully received packets is still 75% of that in the slotted scheme. This is still much more than the 50% predicted by the well-known analysis where simultaneous transmissions are never successful. Moreover, in any path loss scenario, both schemes exhibit the same energy efficiency.

##### A New Phase Transitions for Local Delays in MANETs

Consider again a slotted version of Aloha for MANETS. As above, our model features transmitters randomly located in the Euclidean plane, according to a Poisson point process and a set of receivers representing the next-hop from every transmitter. We concentrate on the so-called outage scenario, where a successful transmission requires a SINR larger than some threshold. In [24] we analyze the local delays in such a network, namely the number of times slots required for nodes to transmit a packet to their prescribed next-hop receivers. The analysis depends very much on the receiver scenario and on the variability of the fading. In most cases, each node has finite-mean geometric random delay and thus a positive next hop throughput. However, the spatial (or large population) averaging of these individual finite mean-delays leads to infinite values in several practical cases, including the Rayleigh fading and positive thermal noise case. In some cases it exhibits an interesting phase transition phenomenon where the spatial average is finite when certain model parameters (receiver distance, thermal noise, Aloha medium access probability) are below a threshold and infinite above. To the best of our knowledge, this phenomenon, has not been discussed in the literature. We comment on the relationships between the above facts and the heavy tails found in the so-called "RESTART" algorithm. We argue that the spatial average of the mean local delays is infinite primarily because of the outage logic, where one transmits full packets at time slots when the receiver is covered at the required SINR and where one wastes all the other time slots. This results in the "RESTART" mechanism, which in turn explains why we have infinite spatial average. Adaptive coding offers another nice way of breaking the outage/RESTART logic. We show examples where the average delays are finite in the adaptive coding case, whereas they are infinite in the outage case.

##### Opportunistic Routing in MANETs.

In classical routing strategies for wireless ad-hoc (mobile or mesh)
networks packets are transmitted on a pre-defined route that is
usually obtained by a shortest path routing protocol.
In [6] we review some recent ideas
from [33] , [35] concerning a new routing technique
which is *opportunistic* in the sense that each packet at each hop
on its (specific) route from an origin to a destination
takes advantage of the actual pattern of nodes that captured its recent
(re)transmission in order to choose the next relay.
The paper focuses both on the distributed algorithms
allowing such a routing technique to work and on the evaluation
of the gain in performance it brings compared to classical mechanisms.
On the algorithmic side, we show that it is possible to implement this
opportunistic technique in such a way that the current transmitter of
a given packet does not need to know its next relay a priori, but the
nodes that capture this transmission (if any) perform a *self selection*
procedure to chose the packet relay node and acknowledge the transmitter.
We also show that his routing technique works well with various
medium access protocols (such as Aloha, CSMA, TDMA)
Finally, we show that the above relay self selection procedure
can be optimized in the sense that it is the node that optimizes some
given utility criterion (e.g. minimize the remaining distance to the
final destination) which is chosen as the relay.
The performance evaluation part is based on stochastic geometry
and combines simulation a analytical models. The main result is that
such opportunistic schemes very significantly outperform classical routing
schemes when properly optimized and provided at least a small number of
nodes in the network know their geographical positions exactly.

Mathematical analysis of asymptotic properties of opportunistic routing on large distances (when the Euclidean distance between the source and destination node tends to infinity) reviles the following surprising negative result: Under Poisson assumption for the repartition of nodes and some natural assumptions on the wireless channels, the mean delay per unit of distance is infinite. The main positive result states that when adding a periodic node infrastructure of arbitrarily small intensity to the Poisson point process, this “delay rate” is positive and finite (see Section 6.4.4.3 for more details).

##### Cognitive Radio

In [52] we propose a probabilistic model based on stochastic geometry to analyze cognitive radio in a mobile ad hoc network using carrier sensing multiple access. Analytical results are derived on the impact of the interaction between primary and secondary users on their medium access probability, coverage probability and throughput. These results give insight on the guarantees which can be offered to primary users and more generally on the possibilities offered by cognitive radio to improve the effectiveness of spectrum utilization in such networks.

#### Vehicular Ad-Hoc Networks (VANETs)

Vehicular Ad Hoc NETworks (VANETs) are special cases of MANETs where the network is formed between vehicles. VANETs are today the most promising civilian application for MANETs and they are likely to revolutionize our traveling habits by increasing safety on the road while providing value added services.

##### Optimizing Throughput in Linear VANETs.

In [16] we adapted the stochastic geometry framework previously worked out for planar MANETs to propose two models of point to point traffic for Aloha-based linear VANETs. The first one uses a SINR capture condition to qualify a successful transmission, while the second one express the transmission throughput as a function of SINR using Shannon's law. Assuming a Poisson repartition of vehicles, a power-law mean path-loss and a Raleigh fading, we derive explicit formulas for the probability of a successful transmission on a given distance and the mean throughput, respectively. Furthermore, we optimize two quantities directly linked to the achievable network throughput: the mean density of packet progress and the mean density of information transport. This is realized by tuning the communication range and the probability of channel access. We also present numerical examples and study the impact of the thermal noise on the optimal tuning of network parameters. The mathematical tools for its analysis are borrowed from [36] and [5] .

##### Performance of VANETs under Different Attenuation and Fading Conditions

In [17] we perform a more massive simulation study of the performance of current wireless MAC protocols unsuitable for use in VANETs without modifications. These protocols can be tuned to design a VANET with optimal network throughput. We study two popular MAC schemes (Aloha and CSMA) in a linear VANET and analyze them in terms of density of progress of the transmissions under different attenuation and fading conditions. The results show how network performance deteriorates with changes in the conditions and how we can improve it by tuning the MAC protocols. The results presented in this paper can be useful for the design and optimal tuning of VANETs in varying network conditions (attenuation, fading and noise).

#### Generic Wireless Networks

##### Power Control in Wireless Networks

In [43] , we study the weighted sum rate maximization problem in wireless networks consisting of multiple source-destination pairs. The optimization problem is in general non-convex and there are multiple local maxima. A simple iterative power control algorithm for the system optimization is presented. Convergence property holds. By comparing against benchmark problem instances and two other algorithms, we show by simulation that if we choose the initial power allocation randomly, the proposed algorithm converges to the global maximum with very high probability. Performance comparison under different network densities has also indicated its effectiveness. Two variants of the design are offered for different needs. Besides, some optimal properties under special cases are developed.

##### Conflict-Avoiding Codes

Conflict-avoiding codes are used in the multiple access collision channel without feedback. The number of codewords in a conflict-avoiding code is the number of potential users that can be supported in the system. In [43] , a new upper bound on the size of conflict-avoiding codes is proved. This upper bound is general in the sense that it is applicable to all code lengths and all Hamming weights. Several existing constructions for conflict-avoiding codes, which are known to be optimal for Hamming weights equal to four and five, are shown to be optimal for all Hamming weights in general.

##### User Mobility Models

In [49] ,
we analyze phenomena related to user
clumps and hot spots occurring in mobile networks at the occasion of large
urban mass gatherings like the *Fête de la Musique* in French
cities. Our analysis is based on observations made on mobility
traces of GSM users in several large cities. Classical
mobility models, such as the random waypoint, do not
allow one to represent the observed dynamics of clumps
in a proper manner. This motivates the introduction and the
mathematical analysis of a new interaction-based mobility model.
This model is shown to allow one to describe the dynamics
of clumps and in particular to predict key phenomena such as
the building of hot spots and the scattering between hot spots,
which play a key role in the engineering of wireless networks
during such events.
We show how to obtain the main parameters of this model
from simple communication activity measurements and we
illustrate this calibration process on real cases.