How to wake up iOS app with bluetooth signal (BLE)

From what I understand, if your app has not previously connected with the BLE Peripheral, then no.

If your app has previously connected with the BLE Peripheral, then use:

-connectPeripheral:options

Connection requests don't time out. The best place to call this method is when your app loses connectivity with the BLE peripheral. You will get notified when you lose connection to the peripheral in the CBCentralManagerDelegate Protocol:

-centralManager: didDisconnectPeripheral: error

So the next time your App comes in range of the BLE Peripheral, it will trigger this method. Also note that you will need to set up State Preservation and Restoration when you initialize a CBCentralManager.

If the app was running in the background and then closed (I mean here terminated - and you do not see it anymore in the list of background apps when you double click the home button) due to memory pressure from other apps, then the iOS will take care of waking it up again when a delegate is called (assuming you have background modes listed in .plist).

If the app was running in the background and then closed by the user (again I mean here terminated. So the user double clicked to get the list of apps running in the background and then clicked on your app in the background list until it wiggled and then pressed the 'x' next to the app to kill it) then this is a clear indication that the user does not want the app running in the background and the app will not be re-launched. The user has to relaunch the app for its delegates to start functioning again in the background (new in iOS7).

Update: I am not sure if this is in the documentation but it is in CoreBluetooth WWDC 2013 Video. I recommend you watch it. They spent a good portion of the video on how CoreBluetooth behaves in the background.