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In a two-tier heterogeneous network (HetNet) where femto access points (FAPs) with lower transmission power coexist with macro base stations (BSs) with higher transmission power, the FAPs may suffer significant performance degradation due to inter-tier interference. Introducing cognition into the FAPs through the spectrum sensing (or carrier sensing) capability helps them avoiding severe interference from the macro BSs and enhance their performance. In this paper, we use stochastic geometry to model and analyze performance of HetNets composed of macro BSs and cognitive FAPs in a multichannel environment. The proposed model explicitly accounts for the spatial distribution of the macro BSs, FAPs, and users in a Rayleigh fading environment. We quantify the performance gain in outage probability obtained by introducing cognition into the femto-tier, provide design guidelines, and show the existence of …