We address the solution of a very challenging (and previously unsolved) instance of the quadratic 3-dimensional assignment problem, arising in digitalwireless communications.The paper describes the techniques developed to solve this instance to optimality, from the choice of an appropriate mixed-integer programming formulation, to cutting planes and symmetry handling. Using these techniques we were able to solve the target instance with moderate computational effort (2.5 million nodes and 1 week of computations on a standard PC).