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That really depends. If you are working for an SME, the roles of sysadmin and network admin will usually merge. In bigger corporate environment they tend to be distinct.
In this case, I would say network administration would be the best way to start. Get your Cisco, Juniper and other relevant network equipment vendor certification, that would be a good start. Since you are in telecom, at least from the hardware point of view things will be more or less the same, but from the appliance software point of view, that's where you need the requisite skill set and certs.
Playing a role in systems administration would be a good fit for somebody with a background in telecommunications. The "sysadmin" role requires somebody who understands network infrastructure, and coming from a telecommunications background, you would have at least some familiarity with that. It can be a rewarding career for someone who is technical and detail-oriented. Best of luck in your career pursuit!