Neutral hydrogen around high– z QSO and an optical depth \tau \sim 0.17 can be reconciled if reionization is more complex than a single transition at z \simeq 6 - 8 .
Tracing its details could shed a new light on the first sources of radiation .
Here we discuss how far such details can be inspected through planned experiments on CMB large-scale anisotropy and polarization , by simulating an actual data analysis .
By considering a set of double reionization histories of Cen ( [ 2003 ] ) type , a relevant class of models not yet considered by previous works , we confirm that large angle experiments rival high resolution ones in reconstructing the reionization history .
We also confirm that reionization histories , studied with the prior of a single and sharp reionization , yield a biased \tau , showing that this bias is generic .
We further find a monotonic trend in the bias for the models that we consider , and propose an explanation of the trend , as well as the overall bias .
We also show that in long-lived experiments such a trend can be used to discriminate between single and double reionization patterns .