I have had a little progress. I removed the 'period' parameter in vpulse. Instead, I connect 4 vpulses in series. The first one has an offset of 0ns, pulse width 50ns. Second one: offset 100ns, width 50ns ... Fourth one: offset 300ns, pulse width not specified(Infinite, I guess). With this, I managed to make pss converge.
Indeed. You're right. pss analysis seems automatically detecting the steady state. The last switching activity in the circuit occurs at 300ns and 'pss' simulation widows shows several time windows: time = (0s-> 301.2ns), time = (301.2ns-> 301.4ns), time = (301.2ns-> 301.401ns), time = (301.2ns-> 301.401ns)... The pss seems to find the circuit after 301.2ns to be stable and converges.
I think you're right on windowed FFT. I think what I'm looking for is to do FFT from 300ns. I have also been suggested something like time-domain noise simulator from Berkeley. Anyway, I think this is the correct track to go.
Thanks for your help!