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Have we started looking for modulations like this with SETI? A signal would have to be quite loud to be ordinarily detectable, but someone might embed e.g. digits of Pi into an ultra-wide spread spectrum transmission that could be detected even though it's far below cosmic microwave background.

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These modulation methods require knowledge and synchronization of coding by both receiving station and transmitting station. Without knowledge of the sender's modulation schema, the received signal appears as noise.

Indeed, more and more of the Earth's electromagnetic radiation will be designed to be indistinguishable from noise. Or it will propagate in optical fibers. Based on our own experience, I give a civilization a roughly 100 year period during which their radio emanations will be intelligible. A planet interconnected by optical fibers is kind of a poor man's dyson sphere. ;-)

Yes. Some years ago I went to a talk on SETI at Stanford, where they talked about detecting "carriers". Anything they could detect is obsolete technology now. Analog TV was 80% carrier (video was AM, the audio part was FM) with a huge sine wave component. Digital TV looks like narrowband noise.

Analog TV was probably Earth's biggest detectable RF export. Lots of transmitters in the megawatt range transmitting 24/7.

I think technological progress in modulation might be a really good explanation for the "great silence." Advanced aliens could be all over the place, but if they're really advanced their transmissions are low-power, directional or cellular, and look like noise if you don't know the codec.

I thought I remembered reading somewhere that even our most powerful emissions were unlikely to be detectable to any type of receiver we could conceive of further than a light-year or two, less than half of the distance to the nearest star.

I believe the answer is yes. One example would be the use of the Karhunen–Loève transform [1] promoted by Claudio Maccone [2].

[1] https://en.wikipedia.org/wiki/Karhunen–Loève_theorem

[2] https://doi.org/10.22323/1.056.0034

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