I understand that when: receiving fixed coupons, you want rates to go down (bond price goes up), so you are long. (Like with other assets, you are long if you want prices to go up)
But what i don’t get is when: paying floating coupons, you want rates to go down (bond prices go up), so i thought you are also long, not short. (As mentioned, if you want prices to go up, you are long the asset)?