Differential spatial modulation (DSM) is a multiple-input multiple-output (MIMO) transmission scheme. It has attracted extensive research interest due to its ability to transmit additional data without increasing any radio frequency chain. In this paper, DSM is investigated using two mapping algorithms: Look-Up Table Order (LUTO) and Permutation Method (PM). Then, the bit error rate (BER) performance and complexity of the two mapping algorithms in various antennas and modulation methods are verified by simulation experiments. The results show that PM has a lower BER than the LUTO mapping algorithm, and the latter has lower complexity than the former.