Make sure that double-tapping is turned on in your phone. Go to Settings > display+touch, and swipe to touch. Make sure that you’ve checked the Double tap to wake up the phone checkbox.
You can also try to adjust the display sensitivity. Go to Settings > display+touch, swipe to touch, and switch Touch sensitivity to High.
If you still find it hard to wake up the screen, make sure that you double-tap the middle of the screen. Double-tapping doesn’t work on the edges of the screen.