Anti-ship missile are impotent against major power. This is no more falkland war. CIWS makes anti-ship missile obsolete.Just arm them with anti ship missiles. Iran for example doesn't have aircraft carriers but anti ship missiles and claims they already defeated the U.S. Navy and holding them hostage. Taiwan is doing the same as well as Vietnam. Its enough to give China nightmares and feel like their navy is a hostage to their weaponry. And China is already freaking out over THAAD in South Korea.
Iran has better stuff.