I currently have:

server{
...
if ($remote_user = "") {
return 401;
}
...
}

But what I really want is:

server{
...
if ($remote_user = "") {
add_header WWW-Authenticate 'Basic realm="mydomainhere.com"';
return 401;
}
...
}

But nginx won't allow me to use the add_header directive inside an if block. How can I achieve this?