chirp spread spectrum with 2 users I am a beginner in digatal communications. I have 2 users and I want use a chirp spread spectrum. 

Can we take an up-chirp and a down-chirp as spreading signals for the 2 users? and if yes, why? The down-chirp is $x_{down}(t)=x_{up}(-t)$ with $x_{up}(t)$ the up-chirp.
Yes, you could. When you're using spread spectrum for multiple access, what's important is the cross-correlation between any two users' spreading signals. Any cross-correlation between two users' spreading sequences will cause "leakage" from one user's channel into another's; this causes an artficial noise floor that will limit your system's performance.

You'll find that an up-chirp and down-chirp have very little correlation with one another, so they would be usable for this purpose.