We have an ancient Assyrian (East Semitic) sample from north Iraq. He is dated to Shalmaneser I period. It has no Steppe and has a shift toward Levant. Something expected for a Semitic person. His Y dna also points toward Semitic background J1. We discussed a lot here modern Assyrian (West Semitic) gene pool. It is quite obvious now that they acquired significant ancestry from neighbouring Indo Europeans later than Assyrian empire existed.