Abstract: In this paper

firstly

changes the systems of time-hopping BPSK in UWB into a virtually linear model

secondly， writes least square criterion

one of the optimal criterion of adaptive filtering algorithm

into matrix form

and proposes a new adaptive multi-user detection algorithm by using recursion of Moore-Penrose Inverse Matrix to the code matrix for each user which can be defined based on its unique TH sequence. After following LS recursion of Moore-Penrose Inverse Matrix optimization procedures

the desired signal can be detected from the adaptive multi-user detection algorithm. Numerical examples illustrate the performance of the LS detector versus that of the conventional single-user UWB detector and the performance of LS adaptive filtering algorithm is better than the RLS algorithm.