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Publication# Fundamental limits and optimal operation in large wireless networks

Résumé

Wireless adhoc networks consist of users that want to communicate with each other over a shared wireless medium. The users have transmitting and receiving capabilities but there is no additional infrastructure for assisting communication. This is in contrast to existing wireless systems, cellular networks for example, where communication between wireless users heavily relies on an additional infrastructure of base stations connected with a high-capacity wired backbone. The fact that they are infrastructureless makes wireless adhoc networks inexpensive, easy to build and robust but at the same time technically more challenging. The fundamental challenge is how to deal with interference: many simultaneous transmissions have to be accommodated on the same wireless channel when each of these transmissions constitutes interference for the others, degrading the quality of the communication. The traditional approach to wireless adhoc networks is to organize users so that they relay information for each other in a multi-hop fashion. Such multi-hopping strategies face scalability problems at large system size. As shown by Gupta and Kumar in their seminal work in 2000, the maximal communication rate per user under such strategies scales inversely proportional to the square root of the number of users in the network, hence decreases to zero with increasing system size. This limitation is due to interference that precludes having many simultaneous point-to-point transmissions inside the network. In this thesis, we propose a multiscale hierarchical cooperation architecture for distributed MIMO communication in wireless adhoc networks. This novel architecture removes the interference limitation at least as far as scaling is concerned: we show that the per-user communication rate under this strategy does not degrade significantly even if there are more and more users entering into the network. This is in sharp contrast to the performance achieved by the classical multi-hopping schemes. However, the overall picture is much richer than what can be depicted by a single scheme or a single scaling law formula. Nowadays, wireless adhoc networks are considered for a wide range of practical applications and this translates to having a number of system parameters (e.g., area, power, bandwidth) with large operational range. Different applications lie in different parameter ranges and can therefore exhibit different characteristics. A thorough understanding of wireless adhoc networks can only be obtained by exploring the whole parameter space. Existing scaling law formulations are insufficient for this purpose as they concentrate on very small subsets of the system parameters. We propose a new scaling law formulation for wireless adhoc networks that serves as a mathematical tool to characterize their fundamental operating regimes. For the standard wireless channel model where signals are subject to power path-loss attenuation and random phase changes, we identify four qualitatively different operating regimes in wireless adhoc networks with large number of users. In each of these regimes, we characterize the dependence of the capacity on major system parameters. In particular, we clarify the impact of the power and bandwidth limitations on performance. This is done by deriving upper bounds on the information theoretic capacity of wireless adhoc networks in Chapter 3, and constructing communication schemes that achieve these upper bounds in Chapter 4. Our analysis identifies three engineering quantities that together determine the operating regime of a given wireless network: the short-distance signal-to-noise power ratio (SNRs), the long-distance signal-to-noise power ratio (SNRl) and the power path-loss exponent of the environment. The right communication strategy for a given application is dictated by its operating regime. We show that conventional multi-hopping schemes are optimal when the power path-loss exponent of the environment is larger than 3 and SNRs ≪ 0 dB. Such networks are extremely power-limited. On the other hand, the novel architecture proposed in this thesis, based on hierarchical cooperation and distributed MIMO, is the fundamentally right strategy for wireless networks with SNRl ≫ 0 dB. Such networks experience no power limitation. In the intermediate cases, captured by the remaining two operating regimes, neither multi-hopping nor hierarchical-MIMO achieves optimal performance. We construct new schemes for these regimes that achieve capacity. The proposed characterization of wireless adhoc networks in terms of their fundamental operating regimes, is analogous to the familiar understanding of the two operating regimes of the point-to-point additive white Gaussian noise (AWGN) channel. From an engineering point of view, one of the most important contributions of Shannon's celebrated capacity formula is to identify two qualitatively different operating regimes on this channel. Determined by its signal-to-noise power ratio (SNR), an AWGN channel can be either in a bandwidth-limited (SNR ≫ 0 dB) or a power-limited (SNR ≪ 0 dB) regime. Communication system design for this channel has been primarily driven by the operating regime one is in.

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We consider the issue of which criteria to use when evaluating the design of a wireless multihop network. It is known, and we illustrate in this paper, that maximizing the total capacity, or transport capacity, leads to gross imbalance and is not suitable. An alternative, which is often used in networking, is to consider the max-min fair allocation of rates, or of transport rates per node. We apply max-min fairness to the class of wireless, multi-hop networks for which the rate of a wireless link is an increasing functions of signal-to-noise ratio. This class includes CDMA and UWB. We show that, for a network in this class, the max-min fair allocation of bit or transport rates always gives the same rate to all flows. We show on one example that such an allocation is highly undesirable when the network is asymmetric. Another form of fairness, utility fairness, does not appear to have the same problem.

2003We consider the question of what performance metric to maximize when designing ad-hoc wireless network protocols such as routing or MAC. We focus on maximizing rates under battery lifetime and power constraints. Commonly used metrics are total capacity (in case of cellular networks) and transport capacity (in case of ad-hoc networks). However, it is known in traditional wired networking that maximizing total capacity conflicts with fairness, and this is why fairness oriented rate allocations, such as max-min fairness, are often used. We revisit this issue for wireless ad-hoc networks. Indeed, the mathematical model for wireless networks has a specificity that makes some of the findings different. On one hand, it has been reported in the literature on Ultra Wide Band that gross unfairness occurs when maximizing total capacity or transport capacity, and we confirm by a theoretical analysis that this is a fundamental shortcoming of such metrics in wireless ad-hoc networks, as it is for wired networks. In contrast, the story is different for max-min fairness. While it is perfectly viable for wired network, it is much less so in our setting. We show that, in the limit of long battery lifetime, the max-min allocation of rates always leads to strictly equal rates, regardless of MAC layer, network topology, choice of routes and power constraints. This is due to the ``solidarity" property of the set of feasible rates. This results in all flows receiving the rate of the worst flow, and leads to severe inefficiency. We show numerically that the problem persists when battery lifetime constraints are finite. This generalizes the observation reported in the literature that, in heterogeneous settings, 802.11 allocates the worst rate to all stations, and shows that this is inherent to any protocol that implements max-min fairness. Proportional fairness is an alternative to max-min fairness that approximates rate allocation performed by TCP in the Internet. We show by numerical simulations that proportional fairness of rates or transport rates is robust and achieves a good trade-off between efficiency and fairness, unlike total rate or maximum fairness. We thus recommend that metrics for the rate performance of mobile ad-hoc networking protocols be based on proportional fairness.

2003We consider the question of what performance metric to maximize when designing adhoc wireless network protocols such as routing or MAC. We focus on maximizing rates under battery lifetime and power constraints. Commonly used metrics are total capacity (in the case of cellular networks) and transport capacity (in the case of adhoc networks). However, it is known in traditional wired networking that maximizing total capacity conflicts with fairness, and this is why fairness oriented rate allocations, such as max-min fairness, are often used. We review this issue for wireless ad-hoc networks. Indeed, the mathematical model for wireless networks has a specificity that makes some of the findings different. It has been reported in the literature on Ultra Wide Band that gross unfairness occurs when maximizing total capacity or transport capacity, and we confirm by a theoretical analysis that this is a fundamental shortcoming of such metrics in wireless ad-hoc networks, as it is for wired networks. The story is different for max-min fairness. Although it is perfectly viable for a wired network, it is much less so in our setting. We show that, in the limit of long battery lifetime, the max-min allocation of rates always leads to strictly equal rates, regardless of the MAC layer, network topology, choice of routes and power constraints. This is due to the ``solidarity

2004