Paper derives and analyzes a novel block Fast Fourier Transform (FFT) based joint detection algorithm. The paper compares the performance and complexity of the novel block-FFT based joint detector to that of the Cholesky based joint detector and single user detection algorithms. The novel algorithm can operate at chip rate sampling, as well as higher sampling rates, unlike existing algorithms. For the performance/complexity analysis, the time division duplex (TDD) mode of a wideband code division multiplex access (WCDMA) is considered. The results indicate that the performance of the fast FFT based joint detector is comparable to that of the Cholesky based joint detector, and much superior to that of single user detection algorithms. On the other hand, the complexity of the fast FFT based joint detector is significantly lower than that of the Cholesky based joint detector and less than that of the single user detection algorithms. For the Cholesky based joint detector, the approximate Cholesky decomposition is applied. Moreover, the novel method can also be applied to any generic multiple-input-multiple-output (MIMO) system.