Authenticated EC key exchange without a signing/signature scheme? From my little understanding of EC-based authenticated key exchange protocols,  I believe that it is not possible for authenticated key exchange without a signing/signature scheme. Is this correct?
Consider a scenario where neither client nor server have any certificates, and server has the pre-shared secret of User/client. In this scenario, what is the technique/protocol for using ECDHE-based authenticated key exchange?
For a pre-shared secret, you just use a secure MAC to authenticate the key exchange, e.g. for the exchanged public ephemeral keys $A$, $B$ and the resultant shared secret $S$, one side could send $HMAC(PSK, S, A, B)$ and the other $HMAC(PSK, S, B, A)$.  Each side can easily verify that the other is using the same exchanged values and shared secret, and that the message could only have come from someone with the same PSK.  They could then use $HMAC(PSK,S)$ for the encryption key, for example.

There are several public-key methods of authenticated key exchange that can work using EC, basically using DH with an ephemeral session key and a public key.  Although the use of the public key can be thought of as signing the key exchange, it's done in an integrated fashion so there's no explicit signing step, the proofs exchanged are as much a proof of the ephemeral keys as they are of the public keys.

An example is SRP-Z (the mutually-authenticating version) with keys instead of passwords (the method uses modular addition, but that's not necessary if the public key isn't subject to a dictionary attack, i.e. it's a strong key rather than a password).  You could also just use ordinary SRP if the verifier is kept secret and a strong key is used (instead of deriving the key from a salt and password), with the same reasoning as above.

Other examples are YAK, which has a very similar structure to SRP-Z, STS, and KEA+.

KEA+ is patented, as is SRP (though SRP is licensed for free for the non-Z form).