One thing to note about authentication in DH-like systems is that you can derive symmetric key without authenticating the parties, establish secure (but unauthenticated) channel with the resulting symmetric key(s) and the do authentication inside that channel in a way that will only succeed if the symmetric key used by both parties is the same (this is called channel binding). For example SSH2 and many Active Directory related protocols do this.
Comments
One thing to note about authentication in DH-like systems is that you can derive symmetric key without authenticating the parties, establish secure (but unauthenticated) channel with the resulting symmetric key(s) and the do authentication inside that channel in a way that will only succeed if the symmetric key used by both parties is the same (this is called channel binding). For example SSH2 and many Active Directory related protocols do this.