Fundamental limits and optimal operation in large wireless networks

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 qua