My solution is far simpler than most and it appears to have been proven effective; keep illegal aliens from being able to find work. We saw with the recession in 2008 that illegal immigration went way down; there was no reason for people to come because they couldn't support themselves as there were no jobs. We see that anytime the job market falls in the US.
We don't need a wall that costs billions, causes all sorts of issues, etc. What we need is to put in serious penalties for businesses hiring illegal aliens, as well as requiring employers to use a well managed and up to date, E-Verify system to screen employees for their ability to work. Then you can also have ICE go to known "hangouts" of illegals who are looking for day work, such as checking the parking lots of Home Depot on a daily basis. If illegal aliens can't earn money in the US, they aren't going to come.