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Various performance metrics of impulse-radio (IR) ultrawideband (UWB) receivers are closely connected to the correlation functions of the multipath channel responses to UWB pulses. Interpulse interference is related to the autocorrelation function (ACF) of the received pulse (RP), the RP energy and its fading correspond to the ACF at zero lag, and multiple access interference is connected to the cross-correlation function (CCF) between two channel pulse responses. Each realization of the multipath channel shows different correlation functions due to the ldquorandomnessrdquo of the UWB propagation environment. This paper derives the first- and second-order statistics of the ACF and CCF, capturing this randomness. Such results are useful for incorporating the multipath channel into the performance and design optimization studies of UWB systems. The analysis is based on a model of the received UWB pulse. The model describes the random channel response by two continuous functions of the excess delay time-one expresses the power, the other expresses power variations-and by a prototype pulse shape representing all linear system components including the band limitation of the RP and antenna effects. The analytical results are validated through the analysis of simulated and measured channel responses.