Select the rectangle formed by the two ends of the microstrip, then, in the port definition add some distance to the edges of the ports.
Otherwise, model it as you are going to actually feed it, for instance with micro-strip or coax, and put the port on that.
This antenna is only partly log-periodic. In a true log-periodic the separation between the two antennas would also increase along the antenna, and the width of the centre track would also increase. It might do what you want, though.