I wonder if a modem could be designed that used idle time when there is no data being transmitted in one direction or the other to send test patterns of certain types and thereby improve performance. A kind of continual training. Part of me thinks that this is i,possible, but then we already have opportunities for adaptation to changes in line conditions that are exploited now, in bitswap. Also when a retrain happens the modems make better choices than they did before, so it makes me think that more frequent retrains would be a very good thing. Of course we cannot practically do that with things as they are because it will upset the DLM gods and because it takes time.
I wonder about some system that would give us an opportunity for the application of some kind of detailed precoding though. What would happen if you regularly got a picture of the impulse respond if the line for example. Probably that never ever changes unless there is something rare and dramatically wrong so that is I suspect a really bad example. You could look out for nonlinearity in the link, if there ever is any, and you could look for echos too. But is there anything else that is actually worthwhile?