Simple self-biased cascoded current mirror
As shown below, the simplest self-biased cascoded current mirror progression would be that accomplished placing two diode-connected devices in series on the bias and mirror branches. However if we do this there is an extra vth that we incur as a headroom penalty.
This is because the VDS min for the bottom mirror M2 device is given by:
Vds_min = Veff_2 + Vth_2 = Vgs_2
This extra Vth needed appears in series and hence also contributes to the minimum VDS needed for the overall output branch.
Vds_min = Veff_2 + Vth_2 + Veff_3
For modern cmos processes with supplies in the order of 1.3V and below, the extra vth of headroom is simply prohibitive: hence this simple structure is seldom used in practice.