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@nsmith You need an antenna of some sort, the Omega2+ has an antenna on it's little PCB, but the Omega2S is not on a PCB so it has no antenna. You have a choice a UFI antenna or an SMD antenna, the UFI antenna may give you better wifi but it's plugged in to the Omega2S UFI connector then you have to mount it somewhere. Just google UFI antenna there are loads available, I've tried several and they all functioned fine but personally I use an SMD antenna so it can be mounted discreetly on the board, the DigiKey part # is 712-1010-1-ND, they have 450,000+ in stock.
Your link was to the Omega2S which has 64MB RAM and 16MB Flash, if you need more you can use Omega2S+ which has 128MB RAM and 32MB Flash same as the Omega2+ you have been referring to in your recent posts.
https://www.digikey.com/en/products/detail/onion-corporation/om-o2sp/9922958
Here is the Omega2 reference schematic which helps you to design your PCB to use the Omega2S.
https://github.com/OnionIoT/Omega2/blob/master/Schematics/Omega2S-Reference-Schematic.pdf