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This paper develops a general framework for communication over time-varying multipath fading channels via orthogonal short-time Fourier (STF) basis functions. In general, STF basis functions interfere with each other due to the loss of orthogonality by channel dispersion. It is shown that the channel spread factor, the product of multipath and Doppler spreads, plays a key role in determining system performance. Smaller spread factors result in lower interference. A simple and approximately optimal pulse scale adaptation rule is derived to minimize interference by matching pulse properties to channel characteristics. For sufficiently small channel spread factors, a scale-adapted STF basis serves as a set of approximate eigenfunctions of the channel. However, for relatively larger spread factors, residual interference may cost a large degradation in performance. A highly effective iterative interference cancellation technique, sequential iterative interference cancellation (SIIC), is proposed to mitigate the residual interference between basis functions. Analytical and simulation results demonstrate the excellent performance of the proposed signaling framework.