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