A fast maximum-likelihood (ML) detection algorithm with low computational complexity was proposed for double space-time block codes (DSTBCs) recently. However, it only provides hard outputs. In this thesis, we extend the fast ML detection algorithm to offer soft outputs such that near-optimum performance of the DSTBC is obtained. This extension is done by using the single-tree search (STS) technique which was developed for spatial multiplexing in multiple-input multiple-output communication systems. Simulation results show that the proposed soft-output algorithm outperforms the hard-output one approximately by 3 dB while its complexity is lower than the brute-force algorithm around 61.15%.