For communications over large-scale antennas, noncoherent differential detection is an attractive option for avoiding expensive channel estimation, but it cannot maximally collect the performance benefits as the antenna number increases. For a desired performance-complexity tradeoff, this letter develops multiple symbol differential detection (MSDD) with simple implementation for single-input multiple-output (SIMO) systems, which jointly detects a block of symbols within the channel coherence time. The generalized likelihood ratio test criterion is adopted that maximizes the likelihood function over both the information symbols and the unknown channels. Simple formulas of the MSDD-SIMO detector are derived, whose performance is competitive to training-based coherent detection.