RF signal receiver is short distance and unstable. Can antenna sovle this? How?
Maybe add antenna?


Yes!

Yesterday I started with my 433 MHz wireless transmitter and I noticed as well that it only worked within 10 cm. Then I looked around on the interwebz to find a solution, just like you, and I found out that adding an antenna with a length equal to a quarter of the wavelength makes wonders. So now it works for a couple of meters. 

So you need to hook up two wires that is roughly \$\frac{c}{4f}=\frac{3×10^6}{4×315×10^6}=23.8\$ cm long. One for the sender and one for the receiver. 

The antenna will radiate in a donut shape around the wire. So the orientation of the antenna makes a huge difference.