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Urban access networks are the external part of worldwide networks that make telecommunication services accessible to end users and represent a critical part of the infrastructures of modern cities. An important recent trend in urban access networks is the integration of fiber and wireless networks, leading to so-called fiber-wireless (Fi-Wi) networks. Fi-Wi networks get the best of both technologies, namely the high capacity offered by optical fiber networks and the mobility and ubiquity offered by wireless networks. The optimal design of fiber and wireless networks has been separately extensively studied. However, there is still a lack of mathematical models and algorithms for the integrated design problem. In this work, we propose a new Power-Indexed optimization model for the 3-architecture Connected Facility Location Problem arising in the design of urban telecommunication access networks. The new model includes additional power-indexed variables and constraints to represent the signal-to-interference formulas expressing wireless signal coverage. To solve the problem, which can prove very hard even for a state-of-the art optimization solver, we propose a new heuristic that combines a probabilistic variable fixing procedure, guided by (tight) linear relaxations, with an MIP heuristic, corresponding to an exact very large neighborhood search. Computational experiments on realistic instances show that our heuristic can find solutions of much higher quality than a state-of-the-art solver.