Ok, a little background: My senior design project consists of building a "spotter" scope (a ballistics computer) that takes range and wind reading puts them through some Arduinos and farts out a result. We have gone through three options: triangulation using the webcam and laser method, hard core engineering a rangefinder using the phase shifting method, and buying a rangefinder (the option we went with). We are still trying to build a back up just in case the bought rangefinder goes out. We have the schematic and have talked to a professor about the feasibility of building one. So we can do it but we want to find a way to do this without using an XOR logic gate because it reduces our range to 250 yards and we need a minimum of 300 yards. Any help will be greatly appreciated.

A mixer will operate in the frequency domain to produce a signal proportional to phase difference.

Any saturated amplifier that behaves in a non-linear mode will also do the same thing.
A simple 'badly' designed one transistor amplifier that produces a lot of distortion in the large signal (as opposed to small signal) environment.

We usually use a lot of feedback around amplifiers to AVOID creating phase related harmonics.

You WANT a crappy design.

We were originally planning to use a heterodyne mixer but we don't have time to build one. I'm intrigued with your amp design though. Please forgive me if I seem noobish.

Any device you can drive into non-linear operation will do the job.

Make the signal big enough to drive a Schottky diode on and off and you will have the harmonics you want.
A 2N2222 amp in large signal mode (even on-off) will do the job.

Ok! Is it just a 2N2222? Or can I use any BJT (i.e 2N3904)? By Schottky diode you mean like a 1N914? Sorry but my EE professors have never gone over Schottky diodes in their classes.

You can use just about any device that has gain and can be driven hard enough to be non-linear.

Just watch out how much power is getting dissipated by both the DC bias and the large AC signal.

A 1N914 is NOT a Schottky diode.
It is a 'conventional' semiconductor diode.
They still need 0.7 V to turn on.

Schottky diodes only need about 0.3  They are metal junction diodes instead of conventional P-N junction diodes.

Sounds like you need to read ahead in your textbook or choose a better book.