Cramér-Rao lower bound
Sounds like you have read reference 8 and understand that for an infinite $N$ you can one could theoretically achieve the CRLB. But clearly in practice you need to drop that idea and think about what your constraints are for your problem. That is, do you really need an estimate with such low variance and if you do then how long are you willing to wait? Since increasing $N$ means you need more and more samples of your signal to come but if you are doing offline processing then maybe you can afford this and can take a very large $N$.