edit: you could just try this app:
https://play.google.com/store/apps/details?id=de.android.telnet
the below will work as well.
download Nova launcher from the play store. once installed, press the home button, you'll get a popup asking you which launcher to use. select nova launcher. don't set it as default (unless you want to, it's a great & fast launcher)
long press on the home screen, select "shortcuts" and then "activities"
scroll down to "settings" and click on it to expand that branch
find the entry under settings that says "Phone Info - RadioInfo" and select it
you'll now have a shortcut on your home screen (in nova launcher. it won't show up on your regular launcher) called Phone Info. click it
you'll see a bunch of debug/radio info, including signal strength in dbM. The less negative the number, the better the signal. ASU is another metric shown, for that one greater = better.