On the duration of blackouts due to primary user activity in cognitive networks

We derive probability distribution for the duration of total blackouts — periods in which no channel is idle — in the set of channels used by a cognitive network under random activity of independent primary users. We show that the mean value of blackout duration is very dependent on the number of channels in the network, and somewhat dependent on the activity factor (i.e., duty cycle) of primary user transmissions, with the impact of the latter being more pronounced in cases with smaller number of channels.