A common approach for introducing security at the physical layer is to rely on the channel variations of the wireless environment. This type of approach is not always suitable for wireless networks where the channel remains static for most of the network lifetime. For these scenarios, a channel independent physical layer security measure is more appropriate which will rely on a secret known to the sender and the receiver but not to the eavesdropper. In this paper, we propose CD-PHY, a physical layer security technique that exploits the constellation diversity of wireless networks which is independent of the channel variations. The sender and the receiver use a custom bit sequence to constellation symbol mapping to secure the physical layer communication which is not known a priori to the eavesdropper. Through theoretical modeling and experimental simulation, we show that this information theoretic construct can achieve Shannon secrecy and any brute force attack from the eavesdropper incurs high overhead and minuscule probability of success. Our results also show that the high bit error rate also makes decoding practically infeasible for the eavesdropper, thus securing the communication between the sender and receiver.