The recent publication of Omberg et al. (2012) has reminded me of the data of Henn et al. (2012) on Qatar which I don't believe I've used yet. I used the K12b calculator on ~20,000 SNPs that are common between it and the Affymetrix chip used.
Below is the population portrait of the Qatari population:
On the basis of the above, I conclude that there are several different groups represented in the Qatari population. I have absolutely no knowledge about the Qatari population, so it would be interesting to see if readers find correspondences between these and known social divisions in Qatar.
For example, I could wager that #5 which is a "Southwest Asian"+"Caucasus" mix represents a pure Arabian group with little outside influences. #1 and #2 are also Arab-like but with various degrees of admixture. #3 appears to include substantial African descendants and #4 a clear Iranian signal due to the high "Gedrosia" component. Of interest is that the "African" group #3 also scores high in the "South Asian" component.