In　this　paper,　a　novel　nonlinear　signal　processing　technology,　which　is　denoted　as　the　polarity-invariant　square　law　(PISL)　algorithm,　is　proposed　to　compensate　nonlinear　distortions　caused　by　monobit　digitization　and　to　mitigate　the　performance　degradation　of　impulse　radio　ultra　wideband　(IR-UWB)　receivers　employing　monobit　analog-to-digital　converters　(ADCs).　An　analytical　framework　based　on　characteristic　functions　has　been　developed　to　evaluate　bit　error　rates　of　monobit　transmitted-reference　(TR)　receivers　and　performance　improvement　offered　by　the　PISL　algorithm.　Both　theoretical　analysis　and　simulations　show　that　by　employing　the　PISL　algorithm,　the　monobit　weighted　TR　(MWTR)　receivers　can　achieve　a　bit-error-rate　performance　that　is　more　than　10　dB　over　the　direct-reference　algorithm　and　is　less　than　1.5　dB　away　from　the　performance　bound　of　the　MWTR　receivers　in　intravehicle　UWB　channels.　Furthermore,　the　MWTR　receiver　employing　the　PISL　algorithm　is　insensitive　to　a　correlation　interval;　this　feature　not　only　reduces　complexity　of　the　receiver　design　but　also　ensures　performance　robustness　over　various　multipath　channels.　Therefore,　the　PISL　algorithm　can　be　considered　an　enabling　technology　for　the　monobit　IR-UWB　receivers　that　demand　high　performance,　lower　power　consumption,　and　low　complexity.