Sergeant Alexander was a member of Battery C, 503rd Field Artillery Battalion, 2nd Infantry Division. He was taken Prisoner of War while fighting the enemy along the Chongchon River near Kunu-ri, North Korea, on 1 December 1950. He was presumed dead on 31 December 1953. His remains were not recovered. His name is inscribed on the Courts of the Missing at the Honolulu Memorial.

Alexander was awarded the Purple Heart with Oak Leaf Cluster, the Prisoner of War Medal, the Korean Service Medal, the United Nations Service Medal, the National Defense Service Medal, the Korean Presidential Unit Citation and the Republic of Korea War Service Medal.