Combine sugars, salt, peppercorns, and cardamom in a small bowl. Rub sugar mixture into salmon flesh, and pack the remaining rub around salmon. Wrap salmon tightly in plastic wrap and then in aluminum foil. Refrigerate 12 to 24 hours. Unwrap salmon, and rinse with cold water. Pat salmon dry.
Soak wood chips in water 30 minutes; drain well.
Prepare grill for indirect grilling, heating one side to high and leaving one side with low heat.
Place wood chips on hot coals. Place a disposable aluminum foil pan on the unheated side of grill. Pour 2 cups water in pan. Coat grill rack with cooking spray; place on grill. Place salmon on grill rack over foil pan on unheated side. Close lid; cook 15 minutes or until fish flakes easily when tested with a fork or until desired degree of doneness. Center of fish should be opaque and warm.