Long Term Evolution (LTE) is considered one of the main candidate to provide wireless broadband access to mobile users. Among main LTE characteristics, flexibility and efficiency can be guaranteed by resorting to suitable resource allocation schemes, in particular by adopting adaptive OFDM schemes. This paper proposes a novel solution to the sub-carrier allocation problem for the LTE downlink that takes into account the queues length, the QoS constraints and the channel conditions. Each user has different queues, one for each QoS class, and can transmit with a different data rate depending on the propagation conditions. The proposed algorithm defines a value of each possible sub-carrier assignment as a linear combination of all the inputs following a cross-layer approach. The problem is formulated as a Multidimensional Multiple-choice Knapsack Problem (MMKP) whose optimal solution is not feasible for our purposes due to the too long computing time required to find it. Hence, a novel efficient heuristic has been proposed to solve the problem. Results shows good performance of the proposed resource allocation scheme both in terms of throughput and delay while guarantees fairness among the users. Performance has been compared also with fixed allocation scheme and round robin.