Random Correlation Detector

No, it really isn't limited by the ADC resolution. If you have enough noise and/or other patterns going, the effect will be to dither across the LSBs in the converter. You only need a converter good enough to ensure that when a significant part of the span is used, the lowest few bits are the noise. Once you have that situation, averaging over time effectively adds bits.

If you really want to be silly about it, you can just use a comparitor and a noise source as the ADC and do a whole lot of averaging on the one bit values to get enough bits. I have actually seen this done and seen it "kind of" work. In a world where ADCs exist, it is better to use one.

I forgot for a moment how great spreading really is.

You are very correct: you can get a signal from an A/D converter that is well below its noise floor (or dynamic range) using the despreading correlation - the stuff of this post - thanks to the "processing gain" of the correlator.

When a signal is despread, the noise tends to stay at the same noise level. Ambient bias tends to filter out toward zero. The teeny tiny signal is increased by many dB. A 2^11-1 pattern should produce a processing gain of about 26 dB; longer patterns can give larger gain but the despreading gain is generally limited by the lowpass frequency.

I'd like to see what can be accomplished with a simple ADC-based system. Perhaps there's a way to combine this project with the LED light sensor talked about on this newsgroup?

Make that 66 dB processing gain. Some days numbers just bounce through my brain wrong.