Robbie Morrison, 31, who had previously served with the First Battalion Scots Guards, was found dying in an alleyway in Wester Hailes, Edinburgh, at around 4.30pm last Friday.
Today, a week on, detectives will try to jog the memories of witnesses to the killing of the former guardsman. No arrests have yet been made and the appeal will be directed at anyone who was in the area last Friday afternoon or who may have information about the death.
Mr Morrison served two tours of duty in Iraq in 2008. He lived in the Colinton area of the city and had been in the Dumbryden Gardens area of Wester Hailes two days before his death.
He is thought to have returned to Dumbryden Gardens on the day he was found critically injured.
Despite being taken to Edinburgh Royal Infirmary for treatment, doctors were unable to save Mr Morrison's life.
Police Scotland's Major Investigation Team said soon after that the case was being treated as murder and they were pursuing various lines of inquiries.
Officers now believe a member of the public may hold a key piece of information needed to catch the killer.
Last week, Detective Inspector Grant Johnston, who is leading the investigation, said: "We are appealing to anyone who saw anything in and around Dumbryden Gardens on Friday afternoon to get in touch as soon as possible."
Police have been carrying out high-visibility patrols in the area since the death in an attempt to reassure local residents about their safety. They have stressed the killing appears to be an isolated incident. Flowers have been left at the spot where Mr Morrison was found.
His mother Lynn has been too upset to talk about his death. In 2008, she told a newspaper of her concerns for him in Iraq. She said then: "You're obviously worried when your son is in a war zone."