Class11

The development of wireless communications in the 90’s has led to the emergence of decentralized and self-organized wireless networks, that do not require any fixed infrastructure in order to operate. In 2000, it has been shown by P. Gupta and P. R. Kumar that under some realistic assumtpions regarding state of the art wireless communications, the capacity of such networks only scales with the square root of the number of users, questioning therefore their feasibilty on a large scale. With the evolution of technology, there is however no reason to believe that the above mentioned realistic assumptions will still be realistic in 10, 20 or 30 years. One should therefore try to obtain information theoretic scaling laws, that do not rely on any particular assumption on the way communication is established in the network.

In this talk, I will present an information theoretic approach to the problem, that leads to the study of random Cauchy matrices. A precise estimate on the determinant of such matrices leads to a new scaling law on the capacity of one-dimensional networks (i.e., networks with users randomly distributed on a straight line). For the more realistic two-dimensional case, one recovers a scaling law close to Gupta-Kumar’s square root law; this involves a reduction to the one-dimensional problem, as well as the use of large deviations techniques.

This is joint work with Emmanuel Preissmann and Ayfer Ozgur.