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Impulse radio ultra-wideband (UWB) communication systems employ a time-hopping technique to enable multiple access. Each user is assigned a distinct time-hopping sequence, either periodic or aperiodic, to suppress multiuser interferences. Aperiodic codes have many promising features compared with periodic codes, such as smoothed spectrum and enhanced security. But they pose additional challenges to channel estimation. This paper studies channel estimation issues in aperiodic time-hopping systems. Both a least squares technique and a correlation matching technique are developed. An instantaneous estimate of the mean or correlation of received signals is exploited for simultaneous estimation of all users' channels based on a pulse-rate discrete-time model. If only the desired user's time-hopping codes are available, single-user channel estimators are developed by utilizing the time-varying property of aperiodic time-hopping codes. Performance of each proposed channel estimator is analyzed and numerically evaluated by computer simulations. This paper shows that the correlation matching approach has better performance while the least squares approach has lower complexity. Matched filter receivers based on proposed channel estimators yield detection performance close to corresponding ones with known channel state information. Significant improvement of detection performance is observed by using modified matched filter receivers or multiuser receivers that explicitly take into account interferences to the desired signal.