You may try to connect the LED to an earphone jack and stick it in your phone. Then play music. Don't expect too much of it. The power you can draw is very low. I don't have a phone with an audio jack socket so I connected an LED to the earphone socket of a radio and it worked. (By the way, if you decide to have a try, you'd better test the rig on something you don't mind frying.) If you play a regular music file the light will flicker. You should download or create a file with such frequencies that your eyes won't be able to see the LED alternately light and dim. You may try PWM. Rectification of the signal may help to gain some extra power but at the cost increased complexity and cumbersomeness. I hope this may help you.
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This document, section 1.5.1 addresses this.http://www.securecommconsulting.com/downloads/Android%20tethering%20March%202011.pdfIt is focused on android, but the theory will be similar across other smartphones. The relevant quote:"At the time of this writing there are no available commercial Android phones that supply power on their USB VCC pin3. This is likely due to the fact that a USB port that outputs 5V on the VCC pin would drain the battery of the smart phone faster. A potential, albeit temporary, solution is to provide power on the USB VCC pin from an external source, thereby tricking the USB Device that a Host is connected. This could be accomplished by using a USB hub or a special cable with a connection to a power supply. "