[[abstract]]A cumulant based single-input multi-output (SIMO) blind channel estimation (BCE) algorithm, with a given set of non-Gaussian measurements, is proposed. It uses the multi-input multi-output (MIMO) inverse filter criteria (blind deconvolution criteria using higher-order cumulants) proposed by J.K. Tugnait (see IEEE Trans. Sig. Proc., vol.SP-41, p.549-58, 1993) and C.-Y. Chi and C.-H. Chen (see IEEE Trans. Sig. Proc., 2001). Then a time delay estimation (TDE) algorithm is proposed that estimates P-1 time delays from the phase information of the estimated single-input P-output (P⩾2) system obtained by the proposed SIMO BCE algorithm. Some simulation results are presented to support the efficacy of the proposed SIMO BCE and TDE a...