We study a wireless communication system based on a magnetic tunnel junction (MTJ) spin-torque nano-oscillator (STNO) by employing amplitude shift keying modulation. By varying the pulse modulation frequency (fm) from 1 kHz to 2 MHz and distance (D) between the antenna from 25 cm to 150 cm, we show a maximum data rate of 6 Mbps (at D = 25 cm and fm = 1 MHz), a limit imposed by our set-up and noise generated by the STNO itself. We also report the average amplitude noise (Sa) and average white frequency noise (Swh) of the wireless communication system and discuss their dependence on the distance between the antennas.