How can I improve my research experience for PhD application?
From my experience, there are three reasons why potential advisors want to see undergraduate research:


Show that the student cares enough about research to actually have participated in research during their undergraduate years.
Student is at least somewhat familiar with the ins-and-outs of performing academic research in a university setting.
The quality of the performed research may give some indication as to how "good" of a student the candidate will be.


If you perform research yourself outside of the university settings, you'll provide a strong showing for (1), nothing at all for (2), and given that you're unlikely to publish anything, nothing of much use to the advisor for (3).

To that end, I would try to get a job as a research assistant before applying. (I'm not sure this position exists in all fields.) This is usually a paid position, and will give you an experience to work with research, help run a lab, learn about academia, and and even possibly work towards being acknowledged--or even possibly a co-author, although that's unlikely--in a paper. It should help your application significantly.