A frequency-domain block signal detection (FDBD) using QR decomposition with M-algorithm maximum likelihood detection (QRM-MLD) can significantly improve the bit error rate (BER) performance of the cyclic prefix inserted single-carrier (CP-SC) block transmission in a frequency-selective fading channel. However, the use of a fairly large number of the surviving paths is required in the M-algorithm, leading to high computational complexity. In this paper, we propose the use of the training sequence-aided SC (TA-SC) block transmission instead of CP-SC block transmission. We show that TA-SC using FDBD with QRM-MLD can achieve the BER performance close to the matched-filter (MF) bound while reducing the computational complexity compared to CP-SC.