The major objective of this paper is to reveal the performance of the turbo equalization using doped accumulator (TEQ-ACC) when it is combined with channel estimation, in broadband single carrier signalling. It is shown that the accuracy of the channel estimate in TEQ-ACC is inferior to that in conventional turbo equalization (TEQ-CVT), if TEQ-ACC generates the soft replica only from the soft information fed back from the decoder. To cope with this problem, this paper proposes a new soft replica generation method for TEQ-ACC which achieves asymptotically the equivalent accuracy of channel estimates to that with TEQ-CVT. Simulation results show that the gain in frame-error-rate (FER) with TEQ-ACC utilizing the proposed soft replica generation method is significant, 1 dB better than TEQ-CVT at FER = 10−3 under pedestrian mobility channel assumptions. Furthermore, this paper verifies that TEQ-ACC with channel estimation implemented by an adaptive subspace tracking technique, Low rank adaptive filtering (LO-RAF), achieves exactly the same FER performance as that with the sliding window singular value decomposition (SVD)-based technique.