Multicell network duality with instantaneous and statistical channel information: A nonlinear Perron-Frobenius characterization

This paper studies a joint optimization of beamforming and power control to enforce egalitarian fairness for all users in a multicell setting. In a single cell downlink with instantaneous channel information, the well-known uplink-downlink duality via Lagrange interpretation helps in algorithm design. By leveraging nonlinear Perron-Frobenius theory, we establish the network duality for the max-min weighted SINR problem in a general multicell network with multiple serving users per cell, whose generic feature reduces to two special scenarios: the single cell multiuser scenario and the multiuser ad hoc network scenario. The network duality can be observed through Perron-Frobenius characterization, and holds for both forms of channel information: the instantaneous channel information and statistical channel information. This characterization of network duality further enables the design of distributed algorithms with geometrically fast convergence rate, which are readily applicable to practical implementation.