Here is my solution for your situation. Using simple signals is not sufficient: the west track is shared between two trains, using simple signal on it will lead to two trains blocking each other on this signal. Using no signal at all would lead, as Ters described, to tracks occupied for too long periods.
Red marks are simple signals, their use is to divide tracks in sections to prevent trains from occupying the track for too long before arriving at their station.
Yellow marks are presignals, when a train departs, they ensure that the train can proceed after the simple signals, avoiding the blocked situation I described above.
Of course, all of this works as long as there is only one train for each station. If you have more, the simple signals must be replaced by presignals, and the signals out of what we can see must be adjusted too.