People tend to underestimate just how hard it is to detect radio transmissions from a distant source.

When a spacecraft communicates with the Earth using dish antennas on both ends, the received signal strength for a pure sinewave (unmodulated) carrier can be calculated as

$$P_R=\frac{P_TA_TA_R}{\lambda^2R^2},$$

where $P_T$ is the transmitter power, $A_T$ is the transmitter antenna's effective surface area, $A_R$ is the same for the receiver, $\lambda$ is the wavelength and $R$ is the distance between the transmitter and receiver.

By way of example, if I plug in the numbers for Pioneer 10 near the end of its mission (8 W transmitter, 80 AU from the Earth, a transmission frequency of roughly 2.3 GHz, a transmitter antenna diameter of 2.75 m, and 70 m dish antenna on the ground), I get a value of -165 dBm (decibel over milliwatts).

So now let me move the signal source from 80 AU to, say, 120 light years, which is a 100,000-fold increase. This reduces the signal strength by a whopping 100 dB. Further, let me assume that it is not transmitted by a dish transmitter aimed directly at the Earth (why would it be?) but rather, it is omnidirectional. At the wavelengths used by Pioneer, that's another ~30 dB decrease in the signal strength. On the other hand, let me assume that the transmitter is a lot more powerful, say, 8 MW instead of 8 W. That is a 60 dB increase in signal strength.

So a 70 m dish antenna (the largest used by NASA's Deep Space Network) would now see a signal at -245 dBm. Or rather, it would not see that signal; it is orders of magnitude below its detection threshold (maybe around -195 dBm).

OK, forget the DSN. Let's say we use the new Chinese radio telescope, FAST. Its dish is a whopping 500 meters in diameter. That is a 17 dB boost in the received signal level. Let me be generous and bump it to 20 dB; so now we are getting a -225 dBm signal.

It is still some three orders of magnitude less than what we can actually detect. And remember, this is just to detect the presence of a signal. Any modulation on that signal reduces the signal level, and detecting the modulation itself, even at a very low data rate, would be still orders of magnitude away.

So no, contrary to popular belief, civilizations that use radio are not shining beacons in the (radio) sky. Aliens won't be beaming back to us Hitler's 1936 Olympic opening speech from dozens of light years away. These "stray" radio broadcasts are immensely difficult simply to detect (never even mind decode or demodulate). And it's not a limit of technology, these are hard physical limits; an antenna of a given size only intercepts so many photons, so much radio energy, even if otherwise it if a "perfect", flawless instrument.