Section: New Results

Design and Performance Analysis of Wireless Networks

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

This axis bears on 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 regard 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, distributed control algorithms, self organization protocols.

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 Orange Labs.

Effect of Opportunistic Scheduling on the Quality of Service Perceived by the Users in OFDMA Cellular Networks

Our objective in [20] is to analyze the impact of fading and opportunistic scheduling on the quality of service perceived by the users in an Orthogonal Frequency Division Multiple Access (OFDMA) cellular network. To this end, assuming Markovian arrivals and departures of customers that transmit some given data volumes, as well as some temporal channel variability (fading), we study the mean throughput that the network offers to users in the long run of the system. Explicit formulas are obtained in the case of allocation policies, which may or may-not take advantage of the fading, called respectively opportunistic and non-opportunistic. The main practical results of the present work are the following. Firstly we evaluate for the non-opportunist allocation the degradation due to fading compared to Additive White Gaussian Noise (AWGN) (that is, a decrease of at least 13% of the throughput). Secondly, we evaluate the gain induced by the opportunistic allocation. In particular, when the traffic demand per cell exceeds some value (about 2 Mbits/s in our numerical example), the gain induced by opportunism compensates the degradation induced by fading compared to AWGN. Partial results were presented at ComNet in 2009  [62] .

Impact of Shadowing on QoS in Cellular Networks

Shadowing is believed to degrade the quality of service (QoS) in wireless cellular networks. Assuming log-normal shadowing, and studying mobile's path-loss with respect to the strongest (serving) base station (BS) and the corresponding interference factor (the ratio of the sum of the path-gains form interfering BS's to the path-gain from the serving BS), which are two key ingredients of the analysis and design of the cellular networks, in [48] we discovered a more subtle reality. We observe, as commonly expected, that a strong variance of the shadowing increases the mean path-loss with respect to the serving BS, which in consequence, may compromise QoS. However, in some cases, an increase of the variance of the shadowing can significantly reduce the mean interference factor and, in consequence, improve some QoS metrics in interference limited systems, provided the handover policy selects the strongest BS as the serving one. We exemplify this phenomenon, similar to stochastic resonance, studying the blocking probability in regular, hexagonal networks in a semi-analytic manner, using a spatial version of the Erlang's loss formula combined with Kaufman-Roberts algorithm. More detailed probabilistic analysis explains that increasing variance of the log-normal shadowing amplifies the ratio between the strongest signal and all other signals thus reducing the interference. The above observations might shed new light, in particular on the design of indoor communication scenarios. Partial results were presented at IFIP WMNC'2010  [63] .

Self-Optimization of Radio Resources in Cellular Networks

In  [65] , we developed 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 were proposed. We focused on the optimization of transmit power and of user association. The method is applicable to both joint and separate optimizations. The global utility minimized is linked to potential delay fairness. The distributed algorithm adaptively updates the system parameters and achieves global optimality by measuring SINR and interference. The algorithms are built on Gibbs' sampler and offer a unified framework that can be easily used for different purposes.

In [32] , we investigated the joint optimization of radio resources in heterogeneous cellular networks made of a juxtaposition of macro and small cells. We showed that within this context, it is essential to use algorithms able to simultaneously solve the problems of channel selection, user association and power control. In such networks, the unpredictability of the cell and user patterns also requires self-optimized schemes. We proposed a generalized solution which is based on Gibbs' sampler. It can be implemented in a distributed way and nevertheless achieves minimal system-wide potential delay. Results show that it is effective in both throughput and energy efficiency.

In [35] , we extended it to an autonomous radio resource allocation and optimization scheme that chooses the transmit power and precoding vector among codebooks for multiple antennas transmitters to improve spectral and power efficiency and provide user fairness. Network self-optimization is an essential feature for supporting the cell densification in future wireless cellular systems. Besides, we included power pricing to parametrize and to enhance the energy efficiency. Simulation results show that the proposed scheme can outperform today's default modes of operation in network throughput, energy efficiency, and user fairness.

Three patents were filed under the INRIA/Alcatel–Lucent joint laboratory.

Best Signal Quality in a Wireless Network

In a wireless network composed of randomly scattered nodes, the characterization of the distribution of the best signal quality received from a group of nodes is of primary importance for many network design problems. The thesis of Van Minh Nguyen [7] developed a framework for analyzing this distributions using shot noise models for the interference field. The joint distribution of the interference and the maximum signal strength was identified. The best signal quality can be represented as a function of these two quantities. Particular practical scenarios were also analyzed where explicit expressions can be obtained.

Cellular Network Tomography

The Foschini-Miljanic's  [67] algorithm is used for power control in cellular networks whes users require a fixed bit rate. It leads to an optimal choice of power by the users in a distributed way when such a solution exists. If the users are too greedy or too many, the network saturates, and it is not possible to provide the required bit rates. We have been working on the question of residual bandwidth estimation in [61] . The residual bandwidth of a user is defined as the rate that this user should have to saturate the network when all other users stick to their initial rate requirement and all users use power control. The aim is to determine the residual bandwidth of a given user by local measurements. We showed that by simply changing their SINR target slightly and by listening to the evolution of interference, users can locally inverse Foschini-Miljanic's algorithm and compute their residual bandwidth.

Coverage in Cellular Networks

Cellular networks are usually modeled by placing the base stations according to a regular geometry such as a grid, with the mobile users scattered around the network either as a Poisson point process (i.e. uniform distribution) or deterministically. These models have been used extensively for cellular design and analysis but suffer from being both highly idealized and not very tractable. Thus, complex simulations are used to evaluate key metrics such as coverage probability for a specified target rate (equivalently, the outage probability) or average/sum rate. More tractable models have long been desirable. In a joint work with J. Andrews and R. Ganti [UT Austin, USA] [9] and [34] , we developed general models for multi-cell signal-to-noise-plus-interference ratio (SINR) based on homogeneous Poisson point processes and derived the coverage probability and rate. Under very general assumptions, the resulting expressions for the SINR cumulative distribution function involve quickly computable integrals, and in some important special cases of practical interest these integrals can be simplified to common integrals (e.g., the Q-function) or even to exact and quite simple closed-form expressions. We also derived the mean rate, and then the coverage gain (and mean rate loss) from static frequency reuse. We compared the coverage predictions obtained by this approach to the standard grid model and an actual base station deployment. We observed that the proposed model is pessimistic (a lower bound on coverage) whereas the grid model is optimistic. In addition to being more tractable, the proposed model may better capture the increasingly opportunistic and dense placement of base stations in urban cellular networks with highly variable coverage radii.

Cellular networks are in a major transition from a carefully planned set of large tower-mounted base-stations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well as distributed antennas. In a collaboration with H. Dhillon, J. Andrews and R. Ganti [UT Austin, USA] [66] , we extended the approach of we developed a model for a downlink heterogeneous cellular network (HCN) consisting of K tiers of randomly located BSs, where each tier may differ in terms of average transmit power, supported data rate and BS density. Assuming a mobile user connects to the strongest candidate BS, the resulting Signal-to-Interference-plus-Noise-Ratio (SINR) is greater than 1 when in coverage, Rayleigh fading, we derived an expression for the probability of coverage (equivalently outage) over the entire network under both open and closed access. One interesting observation for interference-limited open access networks is that at a given SINR, adding more tiers and/or BSs neither increases nor decreases the probability of coverage or outage when all the tiers have the same SINR threshold.

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, we worked on the analysis of MAC and routing protocols in multi-hop MANETS in collaboration with Paul Mühlethaler [INRIA HIPERCOM], and on a game theoretic view of Spatial Aloha in collaboration with E. Altman and M.K. Hanawal [INRIA MAESTRO] [68] .

Improvement of CSMA/CA's Spatial Reuse

The most popular medium access mechanism for such ad hoc networks is CSMA/CA with RTS/CTS. In CSMA-like mechanisms, spatial reuse is achieved by implementing energy based guard zones. In a new collaboration with Qualcomm ([26] and [14] ), we considered the problem of simultaneously scheduling the maximum number of links that can achieve a given signal to interference ratio (SIR). Using tools from stochastic geometry, we studied and maximized the medium access probability of a typical link. Our contributions are two-fold: (i) We showed that a simple modification to the RTS/CTS mechanism, viz., changing the receiver yield decision from an energy-level guard zone to an SIR guard zone, leads to performance gains; and (ii) We showed that this combined with a simple modification to the transmit power level – setting it to be inversely proportional to the square root of the link gain – leads to significant improvements in network throughput. Further, this simple power-level choice is no worse than a factor of two away from optimal over the class of all "local" power level selection strategies for fading channels, and further is optimal in the non-fading case. The analysis relies on an extension of the Matérn hard core point process which allows us to quantify both these SIR guard zones and this power control mechanism.

Opportunistic versions of CSMA/CA

In collaboration with Gustavo de Veciana and Yuchul Kim [UT Austin, ECE] we studied the benefits of channel-aware (opportunistic) scheduling of transmissions in ad-hoc networks using CSMA/CA [36] . The key challenge in optimizing the performance of such systems is finding a good compromise among three interdependent quantities, the density and channel quality of the scheduled transmitters, and the resulting interference at receivers. We propose two new channel-aware slotted CSMA protocols: opportunistic CSMA (O-CSMA) and quantile-based CSMA (QT-CSMA) and develop stochastic geometric models allowing us to quantify their performance in terms of spatial reuse and spatial fairness. When properly optimized these protocols offer substantial improvements in terms of both of these metrics relative to CSMA - particularly when the density of nodes is moderate to high. Moreover, we show that a simple version of QT-CSMA can achieve robust performance gains without requiring careful parameter optimization. The paper supports the case that the benefits associated with channel-aware scheduling in ad hoc networks, as in centralized base station scenarios, might far outweigh the associated overhead, and this can be done robustly using a QT-CSMA like protocol.

Cognitive Radio Networks

We wrote a survey [22] on the probabilistic framework which can be used to model and analyze cognitive radio networks using various classes of MAC protocols (including carrier sensing based multiple access schemes and Aloha schemes). For each model, analytical results were derived for important performance metrics. This leads to a quantification of the interplay between primary and secondary users in such networks.

Generic Wireless Networks

Power Control in Wireless Networks

In [10] , in collaboration with N. Bambos, [Stanford] and N. Gast [EPFL], we formulated a delay-power control (DPC) scheme for wireless networking, which balances delay against transmitter power on each wireless link. The DPC scheme is scalable, as each link autonomously updates its power based on the interference observed at its receiver; no cross-link communication is required. It is shown that DPC converges to a unique equilibrium power and several ke properties are established, concerning the nature of channel bandwidth sharing achieved by the links. The DPC scheme is contrasted to the well-known Foschini-Miljanic (FM) formulation for transmitter power control in wireless networks, and some key advantages are established. Based on the DPC and FM schemes, two protocols are developed, which leverage adaptive tuning of DPC parameters. One of them is inspired by TCP and exhibits analogous behavior.

In [21] , we studied the weighted sum rate maximization problem in wireless networks consisting of multiple source-destination pairs. The optimization problem is to maximize a weighted sum of data rates by adjusting the power of each user. The problem is in general a non-convex optimization problem that will lead to multiple local maxima. A Gauss-Seidel type iterative power control algorithm was presented. We showed by simulation that the proposed algorithm converges to the global maximum with very high probability, if we initialize the initial power allocation uniformly at random. The proposed algorithm also has the favorable properties that only simple operations are needed in each iteration, and the convergence is fast. Performance comparison under different user densities has also indicated its effectiveness. Finally, we discussed some simple and optimal power allocation strategies under special cases of the problem if the network can be represented by a certain approximation.

Simultaneous Decoding

In  [15] , in collaboration with A. El Gamal [Stanford, USA] and D. Tse [UC Berkeley, USA], we analyzed a network made of a collection of transmitter-receiver links where each link is considered to be part of a Multiple Access Channel (MAC) together with a collection of co-transmitters, rather than treating the messages of the latter as noise. This MAC extension is meant to improve the rate of the link and not to decode the messages of the co-transmitters. The necessary and sufficient condition for the feasibility of some rate when using successive interference cancellation and simultaneous decoding were provided. The reasons why simultaneous decoding is preferable to successive interference cancellation were also given. The gain obtained when using this type of simultaneous decoding rather than treating interference as noise was then quantified in a network made of a large random collection of such links. The gains in coverage and in rate were analyzed in terms of ensemble averages, evaluated using stochastic geometry. Closed form or integral expressions were obtained for the outage/coverage probability in networks where nodes are randomly distributed like a Poisson point process on an infinite plane. In the CDMA limit (large bandwidth, low SINR per hertz, high density), the ensemble average of the link rates tends to 0 when interference is treated as noise whereas it tends to a positive constant when simultaneous decoding of infinite order is used. The whole analysis was conducted in the AWGN case.