Joint Power Allocation and Beamforming for Overlaid Secrecy Transmissions in MIMO-OFDM Channels

This paper considers that a transmitter superposes secrecy transmissions to a closer receiver with a high security level in the active MIMO-OFDM channel it is using to send data to a farther receiver with a low security level, by using NOMA techniques. A joint optimization of power allocation and beamforming is important to maximize the secrecy rate to the closer receiver, while keeping the requested data rate of the farther receiver unaffected. The optimization problem is challenging because of coupled variables, and has yet to be addressed. We propose to decouple the problem between subcarrier power allocation and beamforming. Given beamforming, we prove the subcarrier power allocation for the two receivers can be equivalently transformed to two convex problems with waterfilling structures and closed-form solutions. Given power allocation, beamforming can be decoupled between subcarriers by distributing the rate requirement of the farther receiver across the subcarriers. The per-subcarrier beamforming is convexified by applying semidefinite relaxation and the Dinkelbach method. Simulations show the proposed approach can outperform its existing alternatives in terms of secrecy rate, and holistic designs of power allocation and beamforming are critical.