"Perfect waveform" for cross-correlations? I am well versed in cross-correlations, as my masters thesis heavily relied on them for music classification and beat detection. So this question focuses more on the signals that I am running an xcorr on as opposed to the actual cross correlation process.

Here is a simplified version of my setup:
Suppose I have the original signal, which I time shift the signal (add a delay), and add noise/distort the signal. Then I run a cross-correlation on the two signals to find this time delay and get some value of R.

Is there some formulation to come up with a signal that will reduce ambiguity errors and optimize my value of R?
I know it will be some non-repeating, pseudo-random signal, but is there a formal formulation for this? Or should I be looking at other techniques?

Perhaps something like this would be perfect: http://tedxtalks.ted.com/video/TEDxMIAMI-Scott-Rickard-The-Wor. You see any issues with this?

I'm not talking about cross correlation processing techniques to improve the performance. I'm strictly talking about the shape of the waveform
In general, the resolution of the cross correlation is proportional to the bandwidth of the signal. This is way pseudo-random signals are common for that purpose.
So if you are looking for a signal that will produce sharp and distinct cross-correlation, you should use such signals.  

However, if you are looking to improve the time-delay estimation for a given signal, you should pre-filter the signal with high-pass filter as the lower frequencies tend to produce more smooth cross correlation.