A school that I am applying has a list of available topics, along with their descriptions, which I can choose from. I already select one topic which matches my interest and background, I also contact a professor who will supervise on that topic and he encourages me to go for it. However, as the application process, I need to write a research proposal. It makes me confused as the topic and research description are already defined. I can add some comments on the topic and then relate my background to it, but it will be a personal statement instead of research proposal. So, I wonder in other universities, what students are expected to write in their research proposals when they select a pre-defined topics.
I would ask the professor who encouraged you to apply what the best strategy is.
In any case, a good idea is to take the topic proposed in the list you mention and write about that. Make it your own. Try to develop your own approach to the topic. Elaborate more on what needs to be done. Explore some related work a find out what has been written. This will help demonstrate that you have what it takes to be a (top) PhD student.
Avoid simply writing a personal statement on top of the research proposal. They probably want to see how you think about the research topic and would approach it.
If possible, get the professor to help you out. Not by doing the writing, but by providing comments and possibly related work. (Note that professors are busy, so s/he may not have time to do this.)
A research proposal should address several things, whether the topics are predefined or not. Yes, you propose a topic but you also want to address: why you selected your topic, any background you might have in that area, how you intend to approach your research, methodologies you intend to employ, relevant standards and rigor, and (possibly the most important) how your research on the chosen topic will advance the related body of knowledge in your discipline. Of course this would all be at a very high level but it should all work toward advancing your argument. I think it also helps to keep in mind that any research proposals or statements that you write are intended to be persuasive in nature. When the reader finishing reviewing their proposal there should be no doubt that you're the best person to do what you want to do, and if you don't do it there will be a potential void of knowledge in your discipline. All you have to do is convince them of that.
Final tips: edit often, get lots of test readers, revise-revise-revise, and when you submit it - let it go and don't let it get to you. I've seen people drive themselves nuts waiting to hear back.