how to adjust drain bias to keep power dissipation constant (HEMT)
Presumably the signals to be measured are very small with respect the gate bias voltage. So there is a single operating point for the HEMT transistor (and the input and output signals represent small-signal variations about that point). 

So you pick an operating point (in this case you pick Id * Vds) and a load resistor. Say you pick 100uW and 510\$\Omega\$.  

For every Vds from 50mV to 450mV there is a corresponding Id. So you can pick, say 200mV Vds. So Id must be 500uA. So the gate bias voltage is approximately -0.575V. You set the drain bias voltage to exactly 200mV + 255mV + 255mV (2x 510 ohms), and then trim the gate bias voltage so that the DC drain voltage (VD) reads 200mV. 



P.S. If that thesis is available online it would be interesting to read.