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Low-complexity soft-in soft-out (SISO) equalizers based on time-varying linear filters and soft inter-symbol interference cancellation are known to be a viable alternative to the optimal trellis-based SISO equalizers when used in receivers based on iterative equalization and decoding. In particular, when the signal constellation is large and/or the channel impulse response is long, the computational complexity of trellis-based equalizers becomes prohibitive while linear equalizers can still be used. In this paper, a SISO linear equalization algorithm is derived for the case of a time-varying channel impulse response, which is either known or estimated. Simulation results are presented showing that the error rate performance of the SISO linear equalizer is close to that using an optimal trellis-based equalizer. The performance of iterative channel estimation is also investigated.