In this thesis, we investigate the CDMA (Code Division Multiple Access) multi- user detection scheme where the DD (Decorrelating Detector) is used to eliminate the multiple access interference. The DD algorithm need to compute the inverse of the matrix involves a great deal of computation, especially when the number of users is large. A recursive method with the LMS (Least-Mean-Square) algorithm, namely the decorrelating transversal filter, to detect users¡¦ signals adaptively can reduce greatly the computational complexity of a CDMA multi-user detector. In this thesis, we focus on the hardware FPGA (Fdield Programmable Gate Array) implementation of the decorrelating transversal filter. The functional system simulation of the decorrelating transversal filter is carried out by using Matlab first. Then this filter is implemented by the Xilinx FPGA and its system performance is also verified.