You are requesting no protection ring, but then you indicate one ring which can reverse traffic in the event of an upstream failure (which would be ring protection). The reason SONET is used is to provide for network protection. If a fiber cable is broken on the working traffic, the system reroutes it to the backup fibers.
You can operate the ONS without any network protection (only one, 2 fiber path between network nodes).
You could also operate the network with protection but the fibers share a common cable sheath.
SONET Collapsed Ring. The fibers that interconnect the ONS shelves are run in the same cable sheath. This type of architecture provides protection against a ONS card/port failure, but if the cable gets cut, all the fibers will be cut, so the circuits will not be protected.
Linear ADM
http://www.cisco.com/en/US/docs/optical/15000r9_1/15454/sonet/procedure/guide/454a91_turnupnetwork.html#wp154973
Same protection as SONET Collapsed Ring if fibers are run through the same cable sheath.
Share a little additional information on what your challenge is so we might be able to provide alternatives.
Thanx!