A new method is proposed for the blind subspace-based identification of the coefficients of time-varying (TV) single-input multiple-output (SIMO) FIR channels. The TV channel coefficients are represented via a finite basis expansion model, i.e. linear combination of known basis functions. In contrast to earlier related works, the basis functions need not be limited to complex exponentials, and therefore do not necessitate the a priori estimation of frequency parameters. This considerably simplifies the implementation of the proposed method and provides added flexibility in applications. The merits of the proposed technique, including asymptotic consistency, are demonstrated by numerical simulations.