OK, so you want to receive a signal from alpha centauri.

There is a tiny red shift for light between here and there due to relative motion of the stars.

The sender would need a pretty powerful laser with a wavelength known to the receiver. They point the laser at the earth and send the message. In astronomical terms, this is not a long distance, the red shift is minimal and the receiver knows the red shift involved and the transmission wavelength of the light. The transmission is also consists of billions of photons all in the same wavelength. Sneding signals over interstellar distances would also involve repeating the message over the course of days with error correction bits.

It would not be a problem to filter out background noise over that range and correct for the minimal red shift.

As long as you are using a highly directional transmitter and know where your receiver is going to be when the signal should arrive, this works fine for distances of many thousands of lightyears. The transmitter power has to be increased to overcome signal attenuation over the distance. The next big problem would be stuff getting in the way. That's unlikely to be a problem under ranges of 100 light years, maybe up to thousands because space is big and mostly empty.