Sizing a mixer circuit

Here's the problem:




So i already tried to size the circuit and here's what i got:



Here is the IF signal and RF signal:



I think the IF signal is a bit distorted but overall it's ok.

To bias the circuit i used a current mirror and 3 voltage dividers, is it ok if i do the biasing like that?

Also to compute the mixer noise, should i take into account the biasing circuit?

In razavi book i can compute the total output noise without the biasing and the 2 capacitors in parallel with RL:


But perhaps it's better to compute it using LTSpice or some other program (because doing it analytically taking into account the biasing circuit seems like a nightmare)?

Also i would like to add that if i drop the input signal amplitude below 0.4V the IF signal goes to 0.... Why does that happen?