In the era of big data, anonymity is recognized as an important attribute in privacy-preserving communications. The existing anonymous authentication and routing are applied at higher layers of networks, ignoring physical layer (PHY) also contains privacy-critical information. In this paper, we introduce the concept of PHY anonymity, and reveal that the receiver can unmask the sender's identity by only analyzing the PHY information, i.e., the signaling patterns and the characteristics of channel. We investigate two practical scenarios, where the receiver has more antennas than the sender in the strong receiver case, and vice versa in the strong sender case. For each scenario, we first investigate sender detection strategy at the receiver, and then we develop corresponding anonymous precoding to address anonymity while guaranteeing high receive signal-to-interference-plus-noise-ratio (SINR) for communications. In particular, an interference suppression anonymous precoder is first proposed, assisted by a dedicated transmit phase equalizer for removing phase ambiguity. Afterwards, a constructive interference anonymous precoder is further investigated to utilize the inter-antenna interference as a beneficial element without loss of sender's anonymity. Simulation demonstrates the proposed anonymous precoders are able to preserve the sender's anonymity and simultaneously guarantee high receive SINR, opening a new dimension on PHY anonymous designs.