Novel linear algorithms are proposed in this paper for estimating symbol spaced, time-varying FIR communication channels, without resorting to higher-order statistics. The proposed methods are applicable to channels where each time-varying tap coefficient can be described (with respect to time) as a linear combination of a finite number of basis functions. Examples of such channels include periodically varying ones or channels locally modeled by a truncated Taylor series or wavelet expansion. It is shown that the estimation of the basis expansion parameters is equivalent to estimating the parameters of an FIR single-input-many-outputs (SIMO) system. By exploiting this equivalence, a number of different blind subspace methods are applicable, which have been originally developed in the context of SIMO systems. Identifiability issues are investigated and some illustrative simulations are presented.