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This paper investigates a class of second-order blind channel estimation algorithms based on deterministic linear prediction, which includes double-sided as well as forward and backward single-sided, for single input multiple output (SIMO) finite impulse response (FIR) channels. By introducing the dual problem of well-known zero-forcing equalization concept, we first derive a double-sided deterministic linear prediction (D-DLP) algorithm that has, good channel estimation performance with the knowledge of exact channel order. By further exploiting the interference subspace cancellation technique and the triangular block-Toeplitz structure of a portion of the channel filtering matrix (upper-left or lower-right part), we obtain the forward and backward single-sided deterministic linear prediction (FS-DLP and BS-DLP) algorithms that can work in the absence of knowledge of channel order with a cost of relatively poor channel estimate. Moreover, a channel order estimation method is also studied based on results from both FS-DLP and BS-DLP. Simulation examples are finally presented to demonstrate the potential of the proposed methods.