Hi there. NSA here.
We'd like to ask everyone to stop copying our ideas. Unfortunately we can't patent them for obvious reasons, but we can block you just as much under the 'National Security' stamp, so just forget about it. Also just letting you know we are pushing for legislation to ban auto-frequency shifting routers and any rapidly moving iron object in the premises that may scatter signals.
But for the record; this works just as well with your cordless phone, cellphone, radio controlled car and microwave, so switching of your router really doesn't help you. And since you propagate the radio signals voluntarily the fourth amendment also doesn't apply. (Please don't conclude we care about the constitution - We've had this argument already)
Oh yeah, before I forget; dwellings that emit NO radio signals are automatically marked for surveillance and occupants placed on the no-fly list.