In order to show that the signal will be capable to retrieve the signal back on Earth, we can analyze a link budget equation and the noise floor with a transmit power of 5mW.
The link budget shows that our transmitted power will lose approximately 250 dB during the 10.5 year journey back to earth. Assuming Earth’s physical temperature at 290 K and an average low noise amplifier’s temperature at 100 K, the noise level can be calculated via the following.
The difference between the power received and the noise power shows that the signal to noise ratio of approximately 60 dB is much more than the 3 dB required by our turbo code. Although one may believe we could reduce the size of the antennas, it is almost guaranteed that there will be scattering of some power from objects in space which will consume some of this excess ratio. Clearly, wireless communication is possible even at 10.5 light years away.
For a detailed discussion of the formulas discussed in the proceeding sections, please refer to the link budget equations pdf file on the downloads page.