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Achieving ultra-reliable, low-latency and secure communications is essential for realizing the industrial Internet of Things (IIoT). Non-coherent massive multiple-input multiple-output (MIMO) has recently been proposed as a promising methodology to fulfill ultra-reliable and low-latency requirements. In addition, physical layer authentication (PLA) technology is particularly suitable for IIoT communications thanks to its low-latency attribute. A PLA method for non-coherent massive single-input multiple-output (SIMO) IIoT communication systems is proposed in this paper. Specifically, we first determine the optimal embedding of the authentication information (tag) in the message information. We then optimize the power allocation between message and tag signal to characterize the trade-off between message and tag error performance. Numerical results show that the proposed PLA is more accurate then traditional methods adopting the uniform tag when the communication reliability remains at the same level. The proposed PLA method can be effectively applied to the non-coherent system.