Input resistance of differential LNA
The basic way to find \$R_i\$ is to find the bias point of the circuit, then apply:
\$ R_i = dV/dI\$

Essentially, pretend that the voltage changes by just a little bit.  How much does the current change?  The change in voltage / the change in current will give you the input resistance.  

This is called small signal analysis.  Using this technique you can convert the LNA amplifier schematic shown into a series of voltage/current sources and resistors.  You can also add capacitors but for calculating R and the gain, this is not necessary.  Including capacitors is done for frequency analysis.

Below is a picture showing the simplest FET model.



Once you have built up a suitable circuit model you can apply very simple math to determine the input resistance. 

See the link for a walkthrough on using small signal analysis to analyze a simple MOS single stage amplifier; starting with differential feedback amplifier may be a bit much:
single-stage-mos-example-ssa

Alternatively, you could apply small signal analysis on smaller pieces of the full amplifier.  Using two-port network theory you can 'characterize' the separate pieces (for example H-parameters).  Then using the parameters you can quickly analyze the whole circuit.
two-port-wiki