We're not like Arabs. The Arab population in Iran is small. Arab migrations into Iran have only made an impact in Khuzestan (southwest Iran) and some parts of Hormozgan (southern Iran) but that was much later in history than what the BBC article talks about. Other Arab settlers to Iran didnt alter the population.
And we're not similar to South Asians either. This is just self-evident. The only similarities would have been with the original people that took Sanskrit language to India, but they obviously were not Indian and have died out in your main South Asian gene pool which the BBC article said is still just under half derived from the 'first Indians'.
In Iranian history South Asians have always been looked at as being a foreign race that is very different from Iranians and mostly described in the view of Persians as being dark skinned, thin/skinny bodies, different civilization with different customs, cultures, beliefs etc
You can see representations of how Persians viewed themselves and how they viewed foreigners like Indians/South Asians in Achaemenid royal reliefs at Perspolis. The differences are shown through body size/staure and facial differences, and differences in ethnic attire and way of life.
Iranians (Persians and Medes) according to their own view:
Indians from Hindush (modern Pakistan and northwest India) as represented in the view of the Achaemenid Persians:
These are the earliest surviving depictions of how Persians have viewed South Asians historically. In later writings they are described as foreign and being of a different race.