When you say carry on a backpack, that limits things.

US GI surplus closed cell foam pads can be found for around +/- $10. They weigh about 25 oz. They are much better than sleeping directly on the ground. They provide a little cushion and some insulation from the ground. They are easy to strap on a backpack. I have used one for backpacking. Your choice of colors is olive drab. They are great low-cost Boy Scout gear. OK, so they do not sleep like a feather bed, but did I mention weight of about 25 oz, cheap and durable?

If you want a little better and are not going so far with the pack, a self inflating pad is more comfortable. Costs more and weighs a little more without adding a great deal more bulk when rolled up. That is what I use for camping when I do not have to pack things in so far.

I perfer to sleep with ground cover and pad than on a folding cot even when I can park next to the camp area. I know some will agree and some will disagree.

On a limited budget, I would rather have the cheap GI pad with a good sleeping bag over an expensive pad or cot with a cheap bag.