This work assesses the performance of Long Term Evolution (LTE) downlink over aeronautical channels associated to arrival, parking and en-route scenarios. The huge velocity related to some of these scenarios poses the following challenges: (1) (Inter-Carrier-Interference) ICI due to Doppler Shift, (2) ICI due to Doppler spread and (3) channel estimation errors. Taking into account these problems a physical layer LTE modem has been implemented. Results reveals that LTE can achive good performance in air-to-ground communications with aircraft moving at 1500 km/h without a complex receiver.