My answer above is misleading. Simcha is from the shoresh SIN MEM CHES as in 砖讉指诪值纸讞址 and the spelling is 砖讉执诪职讞指芝讛.
Smicha comes from the shoresh of SAMACH MEM CHAF as in 讜职住指诪址郑讱职. The first time we see someone receive “smicha” is Yehoshua from Moshe (Bamidbar 27: 23): 讜址讬旨执住职诪支止讱职 讗侄转志讬指讚指譀讬讜 注指诇指謻讬讜 讜址讬职爪址讜旨值謶讛讜旨. I believe that YU on their CHAG HASMICHAH invitations spells it SAMACH MEM YUD CHAF HAY.