It is shown that spatial modulation (SM) can be effectively combined with single-carrier (SC) transmission to obtain the advantages in both aspects for broadband wireless communications. However, the signal detection methods for the cyclic-prefix (CP) based SC-SM system are generally not sophisticated enough to provide good performance in many scenarios. In this paper, to lower the frequency-domain equalization complexity, we first consider employing a special recursive method to invert the Gram matrix in the minimum mean-squared-error (MMSE) weight calculation. Second, energy detection is used to locate the active transmit antennas for each SM symbol. Simple single-symbol maximum likelihood (ML) detection can then be used to extract the transmitted modulated symbols in those active transmit antennas with negligible loss in the error-rate performance. On the other hand, M -algorithm is applied for enhancing the error rate to various extents. Results show that a better compromise between the computational complexity and the error rate can.