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This paper proposes two robust binary quadratic formulations for wireless downlink (DL) Orthogonal Frequency Division Multiple Access (OFDMA) networks when using adaptive modulation. The first one is based on a scenario uncertainty approach from Kouvelis and Yu [1] and the second is based on an interval uncertainty approach from Bertsimas and Sim [2]. Both robust models allow to decide what modulations and what sub-carriers are going to be used by a particular user in the system depending on its bits rate requirements. Thus, we derive for each, two semidefinite relaxations and by numerical results, we get a near optimal average tightness of 4.12% under the scenario approach and 1.15% under the interval uncertainty approach when compared to the optimal solution of the problem derived by linearizing the two quadratic models with Fortet linearization method.
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