Verizon Wireless’s newest phone, Samsung Electronics Co.’s Galaxy S4, is the first device that will be able to take advantage of the carrier’s next network upgrade, which will more than double Internet speeds. The Galaxy S4 includes components that allow it to work on Verizon’s Advance Wireless Service spectrum, said Mike Haberman, vice president of network support for the largest U.S. mobile-phone carrier. The phones will require a software upgrade to activate the connection to the AWS frequency, he said. Verizon has started construction of the next phase of its network using existing AWS airwaves and others it acquired last year from a group of cable companies led by Comcast Corp. The service is scheduled to start in major cities, including New York, in the next few months. Verizon is using the AWS airwaves to help increase the capacity of its long-term evolution, or LTE, network.