Locals in Portobello say they have been routinely disturbed in the early hours by the low hum of helicopter rotors as the operation continues throughout the month, while those in Corstorphine have also reported hearing the aircraft overhead.
The 'medium-sized' exercise will be taking place between September 1 and September 21, the MoD said.
Air space over Inchcolm, Leuchars, Gin Head and Red Craig will also be used.
Inchcolm sits in the shadow of the Forth Rail Bridge and is reached by boat from South Queensferry. There are only a few buildings on the island including Inchcolm Abbey which dates back to the 12th century.
Around 20,000 people visit the island every year and weddings are held in the ruins of the abbey. English raiders repeatedly attacked the island during the Wars of Scottish Independence.
Exact details of the nature of the training exercise haven't been released by the MoD.