It's also "suicide biased" (hFE dependent).
Yes - it is a bad biasing scheme. Horowitz/Hill: Don`t use such a circuit.
The reason is as follows: The BJT is a voltage controlled device (VBE controls Ic according to Shockley`s famous formula.).
Now - the resistor RE introduces current-controlled voltage feedback, which only works if the base voltage is as
stiff as possible.
That means: This feedback scheme is used in conjunction with a suitable voltage divider at the base (instead of a simple resistor as shown).
Nevertheless, one can compute the input resistance simply based on the feedback rules:
The input resistance (without feedback) is
hie=VT/IB with VT:Temperature voltage, IB:DC base current.
This resistance is increased due to feedback by the factor (1+RE*gm) with transconductance
gm=hfe/hieTherefore:
r,in=[hie*(1+RE*gm)]||RB = (hie+hfe*RE)||RB