In comparison with upper-layer authentication mechanisms, the tag-based Physical-Layer Authentication (PLA) attracts many research interests because of high security and low complexity. This paper mainly concerns two problems in prior tag-based PLA schemes, where the first one is extra overhead and vulnerability due to the reason that the parameter is broadcasted and the other one is the problem of setting the parameter empirically. Therefore, two new tag-based PLA schemes are proposed to address the above limitations. Specifically, a blind tag-based PLA scheme (BTP) is presented to achieve accurate authentication without knowing the tag parameter of the legitimate transmitter, which not only saves the communication overhead but also improves security. Then, an adaptive blind tag-based PLA scheme (ABTP) is further proposed, which adaptively sets the tag parameter according to the wireless channel state to achieve a better balance among robustness, security, and compatibility. Rigorous theoretical analyses are provided for the two proposed schemes and the prior schemes’ performance comparisons are given. The accuracy of the theoretical analyses is verified through simulation results. At last, the advantages and disadvantages of the two proposed schemes are discussed, and suggestions are given according to different scenarios.