FPDF background images: what size for a good background A4

I tried a bit hard to try to add a nice background to my PDF file created using the FPDF class. I tried a Photoshop document based on international A4 paper, but that was too big. Also converting it from 300dpi to 72dpi (as stated in the manual) is not very good, it just looks pixelated now.

I found various settings on the network (~ 1062px width), but this is too wide and when testing with something that should match, it just creates a pixelated version instead of a nice background image.

Thanks in advance.