This paper studies the behavior of the sum-rate of outdoor multi-user multiple input multiple output systems, where a uniform linear array is utilized at the base station (BS), as the number of BS antennas and the number of users increase. Two schemes are studied for the downlink, the zero-forcing and the maximum ratio transmission (MRT). To begin with, the channel matrix is described deterministically using direct scattering theory. Its matrix elements are the Fourier coefficients of functions that have a physical significance, being connected to the geometry of the environment. For the case when the energy is not arriving at the BS from every spatial direction, we prove for the ZF scheme that the achievable sum-rate behavior is sublinear in the number of antennas at the BS. For the MRT scheme, we prove that there is a link between the sum-rate and the distribution of the users in the city. To numerically evaluate the sum-rate for a given city, schematically described by its streets and its buildings, we introduce a model for the Fourier coefficients of the aforementioned functions, which mixes geometrical and statistical ingredients. We randomly distribute high buildings that will act as strong scatterers and look at the influence of their number on the sum-rate. With the ZF scheme, we perform the calculations for the case where the number of BS antennas, MT, is equal to the number of users, MR, and for the case where MTis larger than MR. We observe that the sum-rate first increases linearly with the number of BS antennas, and becomes sublinear after MTreaches a certain value. The threshold depends on the number of high buildings. With the MRT scheme, the calculations confirm the theoretical predictions, and the sum-rate is greater if the users are spread over all of the city.

Telecommunication systems have evolved, from being simple monolithic structures to complex ones. The present paper is an attempt to recast telecom systems in the language of complex systems. As a specific application of complex systems science to telecom systems, we tackle the problem of self-organizing frequency allocation. For this purpose, we model the problem of frequency assignment within the framework of cellular automata and we present an algorithm that reaches an interference-free allocation of the channels in a finite number of steps. By applying a measure of spatial structure and pattern to the two-dimensional lattice representing the frequency allocation, our study shows that autonomous networks assigning frequencies to their cells in a self-organized way, can be defined and therefore studied as complex systems. On the contrary, traditional networks based on centralized pre-planned frequency allocation cannot be considered as complex, according to the meaning given to the word by complex systems science. The present paper is to be considered as a step towards a comprehensive and rigorous study of Complex Communication Systems (CCS), adopting in communication networks design and analysis, the results and philosophy underlying the emerging multi-disciplinary field of Complex Systems Science.