Calculating dBFS for I/Q I'm trying to figure out how to calculate the dBFS for a complex input. I have an AD9361 part which has a 16-bit A/D and I believe outputs I and Q samples. Now I know you can calculate the dBFS for a real valued 16 bit signal as 

20log10(abs(sample)/32768).

But I don't fully understand how to incorporate a second data stream into this calculation. 

My overall goal is to calculate the dBFS of the incoming signal and use it to compare against a set-point dBFS value for an AGC. and to adjust front-end attenuators as necessary.

Thanks!
The sensible way here is to realize that each complex sample has a magnitude $|z|=\left\lvert \Re z + j \Im z\right\rvert = \sqrt{\left(\Re z\right)^2+\left(\Im z\right)^2}$. 

In your case, the maximum non-clipping amplitude is $2^{15}$ (the maximum-power samples are on a circle around the origin).

Therefore, you'd calculate the magnitude of a sample, and compare that to $2^{15}$ to get your relation to full scale.