Recently, we proposed a frequency-domain block signal detection using maximum likelihood detection (MLD) employing QR decomposition and M-algorithm (QRM-MLD) for the cyclic prefix inserted single-carrier (CP-SC) block transmissions. However, if the number of surviving-symbol candidates is small, the achievable bit error rate (BER) performance degrades, because the probability of removing the correct symbol-candidates at early stages increases. In this paper, to solve this problem, we insert the known training sequence into each data block instead of CP. This SC transmission is called the training sequence-aided SC (TA-SC) block transmissions. We show by computer simulation that the TA-SC can achieve much better BER performance than the CP-SC if the number of surviving symbol-candidates is limited.