The hairy reddish canes indicates wineberries. They are not raspberries, but they taste good. Your leaf description matches. Type wineberry into Google image search and you should get a better idea if you have a match.

Scott

Sounds like wineberry. They are Japanese raspberries that have naturalized in eastern US. Regarded as invasive as it will run like all raspberries but I don't find them hard to contain. The fruits ripe at the same time as my blackberries and they are very tasty for fresh eating or baking. You won't find the fruits at markets because they don't store well. They fruit on second year canes so if you cleared everything off last year you won't get any this year. But if you let the new growth grow out this year you will have berries next summer.