We present an iterative semiblind suboptimal maximum-likelihood sequence estimation (MLSE) method for single-carrier block transmission over stationary multipath channels. This suboptimal ML detector is based on an iterative least squares with projection (ILSP) algorithm exploiting both the finite alphabet properties of the transmitted signal and its cyclic prefixed structure in order to approach ML detection in a cheap way. Since the initial channel estimate is crucial for the convergence speed of the ILSP algorithm, we propose a new low-complexity stochastic method for providing an initial channel estimate. We therefore rely on some known symbols that are provided by a variant of cyclic prefix only (CP-Only) transmission, known as the known symbol padding only (KSP-Only) technique. The resulting channel model is sufficiently accurate to be used as a starting point for the iterations. The final result is a direct symbol estimation method that is characterised by its low computational complexity and its promising results in terms of bit error rate (BER).