You're experiencing the Dawn Phenomenon. Thats when your liver dumps out glucose during the night when you're sleeping.
Here's some solutions I have received from others.
l. Glass of red wine before bed.
2. Small snack before bed, preferably with some fat and some fiber
3. Some light weight training before bed.
4. If all else fails, ask your doctor to prescribe some medication or insulin before bed. I have found that to be the only solution that worked for me, but others have had success with the above.