In　this　paper,　a　systematic　framework　is　developed　for　the　first　time　for　theoretically　analyzing　performance　of　the　nonlinear　Teager-Kaiser　operator　(TKO)　employed　in　energy　detection　(ED)　based　impulse　radio　ultra-wideband　(IR-UWB)　receivers.　Closed-form　formulations　are　derived　for　various　nonlinear　terms　in　the　TKO　output　as　well　as　for　the　performance　gain　of　the　IR-UWB　systems　with　the　TKO　technique　(over　those　without　the　TKO　technique).　Both　theoretical　analysis　and　computer　simulations　show　that　the　TKO　technique　can　effectively　mitigate　not　only　performance　degradation　caused　by　narrowband　interference　(NBI)　but　also　that　by　additive　white　Gaussian　noise.　As　a　result,　the　TKO　technique　can　be　used　to　improve　overall　performance　of　ED　based　IR-UWB　receivers　regardless　of　an　NBI　being　present　or　not.