To dream that you are fighting with your doppelganger means that you are struggling between good and evil and right and wrong.
If you kill your own doppelganger, then it indicates that you have successfully repressed certain negative emotions from surfacing.
To see your own doppelganger in your dream is a reflection of your negative actions.
The dream is showing you the consequences of your actions and what you should not do.
Alternatively, the dream signifies bad luck, danger, and/or illness.