A　variance　detection　(VD)-based　impulse　radio　ultra-wideband　(IR-UWB)　system　has　the　potential　of　mitigating　narrowband　interference　(NBI),　even　in　multipath　environments.　However,　as　a　highly　nonlinear　system,　which　involves　fourth-order　multiplications,　comprehensive　analysis　and　evaluations　of　its　performances　have　not　been　seen　so　far.　In　this　paper,　we　address　the　issues　by　developing　a　log-normal　random　distribution　model　for　the　VD-based　IR-UWB　receiver　and　deriving　the　analytical　bit-error-rate　formulas　for　the　system　in　both　additive　white　Gaussian　noise　and　CM1　multipath　channels　with　and　without　NBIs　for　the　first　time.　Furthermore,　through　both　theoretical　analysis　and　simulations,　we　show　that　the　presented　VD-based　receivers　can　outperform　the　conventional　energy-detection-based　and　the　fourth-order　detection-based　receivers　and　have　a　stronger　inherent　ability　to　mitigate　destructive　performance　degradation　caused　by　strong　NBIs.　This　makes　the　VD-based　IR-UWB　system　a　good　candidate　as　a　non-coherent　IR-UWB　receiver　for　low　power　and　low　complexity　applications.　©　2016　IEEE.