Praying in an unclean place. I place my prayer mat there and then pray? Is my salah valid?

One of the fard conditions of prayer is cleanliness of place. I pray in my bedroom and I have carpet on the floor. When I am ready to pray I place the prayer mat on the carpet and then pray. But now I am wondering if my salah is valid, because the CARPET is somewhat unclean. In the past I have dropped sperm drops on the carpet. I do not have much space to pray in the room, so I place the prayer mat on the unclean carpet and then pray. Is my prayer valid? And can I continue to pray there? Please be specific regarding this. It is not practical to wash or replace the carpet, as it is very large. If I continue to pray like I mentioned, is salah still valid?