Optimal Power Allocation for Superposed Secrecy Transmission in Multicarrier Systems

Superposition coding allows secret messages to be delivered stealthily on top of legacy signals. The effective allocation of the limited transmit power at a transmitter is critical to serve the data rate request of a legacy (untrusted) receiver while accomplishing the stealthy and secure transmissions of secret messages to a trusted receiver, which is challenging under OFDM settings due to the non-convexity of the secrecy rate. This paper presents a new iterative algorithm, which optimizes the allocation of the transmit power across the OFDM subcarriers to minimize the transmit power, subject to the data rate request of the (legacy) untrusted receiver and the required secrecy rate of the trusted receiver. The algorithm can also maximize the secrecy rate of the trusted receiver, subject to the data rate request of the untrusted receiver and the total transmit power. In particular, the proposed algorithm decouples the power allocations between the trusted and untrusted receivers. Semi-closed-form solutions are established for the powers, and can be alternately analyzed until convergence with local optimality. Corroborated by simulations, the proposed techniques outperform existing alternatives in terms of power saving and achievable secrecy rate. As the untrusted receiver moves further away from the transmitter, the number of subcarriers carrying superposed signals increases and the secret messages can be delivered unnoticed.