Cook barley according to package instructions, rinse, and set aside. In a large stockpot or dutch oven, heat oil to medium-high heat and add onion, carrots, celery, and sweet potato. Sauté for about 7 minutes and then add the garlic and sauté for another 1-2 minutes. Pour in broth and tomatoes. Add in paprika, oregano, thyme, salt, and pepper.