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Coherent communications over doubly-selective fading channels are attracting increasing research interests because of the performance advantage over their noncoherent counterparts. In this paper, we use a simple windowing and dewindowing technique to improve the accuracy of an existing basis expansion model (BEM) and develop a windowed least-squares (WLS) estimator for doubly-selective fading channels. We also design the optimum pilot pattern for the WLS estimator. Our designs can considerably improve the channel estimation performance. Simulations are provided to corroborate our theoretical analysis.