soil-compaction - Question and answers

I manage a 3-acre plot for growing wheat and vegetables, and over the past few years, the soil has become increasingly compacted due to frequent tractor use and poor irrigation practices. I've tried deep plowing and adding some organic matter, but the improvements are temporary. I'm considering mixing sand into the soil, but I'm unsure about the right type of sand (e.g., coarse vs. fine), the ideal mixing ratio, and any potential drawbacks. Also, are there alternative methods like using cover crops or specific tillage techniques that might be more effective in the long run?