"Take up their cross"

In this reading from Matthew 16:21-28 Jesus states that his followers must "take up their cross" in order to follow him. Since he had not yet been condemned to crucifixion, I have to wonder if he told his disciples details about how he would be killed.

From that time on, Jesus began to show his disciples that he must go to Jerusalem and undergo great suffering at the hands of the elders and chief priests and scribes, and be killed, and on the third day be raised. And Peter took him aside and began to rebuke him, saying, ‘God forbid it, Lord! This must never happen to you.’ But he turned and said to Peter, ‘Get behind me, Satan! You are a stumbling-block to me; for you are setting your mind not on divine things but on human things.’Then Jesus told his disciples, ‘If any want to become my followers, let them deny themselves and take up their cross and follow me. For those who want to save their life will lose it, and those who lose their life for my sake will find it. For what will it profit them if they gain the whole world but forfeit their life? Or what will they give in return for their life?
‘For the Son of Man is to come with his angels in the glory of his Father, and then he will repay everyone for what has been done. Truly I tell you, there are some standing here who will not taste death before they see the Son of Man coming in his kingdom.’

Just wondering.