I'm wondering if System Sequence Diagram (SSD) belongs to design part or analysis part?
A System Sequence Diagram (SSD) is be a special type of UML sequence diagram that intends to document for one specific use case the the sequence of exchanges between the system under consideration and the outside actors.
It is not a standard UML diagram, but build upon such diagrams. The book "System analysis and design in a changing world" seem to have popularized this approach, but I could find articles dating back to the early 2000' (like this or this).
The above mentioned book places the SSD in the analysis activities. The reason is that analysis is about understanding the requirements, which often start with use-case. The SSD is then a fine-tuning of this analysis.
However, one could argue that it's part of the design activities, since the use case are the requirements, but how these requirements are addressed through a sequence of exchanges is already the start of the design of a solution, exactly as when you start to sketch an UI: more than one SSD could satisfy the needs and you have the choice.
So the answer depends on the purpose for which you're using the model.
My own point of view is that you're already drafting a solution, so it should be design, unless you do some reverse engineering of an existing application, or your client has very detailed requirements