Cook 2 cups water and sugar in a medium saucepan over medium heat, stirring constantly, 5 minutes or until sugar is dissolved. Remove from heat, and cool.
Process sugar mixture, banana, and juices in a blender until smooth. Pour into a 13- x 9-inch pan, and freeze 3 hours or until almost firm.
Beat banana mixture in pan at medium speed with an electric mixer until smooth. Cover and freeze 8 hours. Garnish, if desired.