Operating voltage range of frequency mixers using diodes
I'm not really sure what your question is.

What application are you thinking of?  A normal receiver?

The threshold voltage of the diodes is not really an issue.

For most mixer applications there is a local oscillator signal that is supplied locally and it can be made as large as necessary - it is not dependent upon the strength of the received signal.

This local oscillator signal will be made large enough so that the diodes are fully conducting - there is then no threshold for the received signal to overcome.

Tutorial on Double Balanced Mixers