The growing number of wireless devices and wireless systems present many challenges on the design and operation of these networks. We focus on massively dense ad hoc networks and cellular systems. We use the continuum modeling approach, useful for the initial phase of deployment and to analyze broad-scale regional studies of the network. We study the routing problem in massively dense ad hoc networks, and similar to the work of Nash, and Wardrop, we define two principles of network optimization: user- and system-optimization. We show that the optimality conditions of an appropriately constructed optimization problem coincides with the user-optimization principle. For different cost functions, we solve the routing problem for directional and omnidirectional antennas. We also find a characterization of the minimum cost paths by extensive use of Green’s theorem in directional antennas. In many cases, the solution is characterized by a partial differential equation. We propose its numerical analysis by finite elements method which gives bounds in the variation of the solution with respect to the data. When we allow mobility of the origin and destination nodes, we find the optimal quantity of active relay nodes. In Network MIMO systems and MIMO broadcast channels, we show that, even when the channel offers an infinite number of degrees of freedom, the capacity is limited by the ratio between the size of the antenna array at the base station and the mobile terminals position and the wavelength of the signal. We also find the optimal mobile association for the user- and system-optimization problem under different policies and distributions of the users.
