Joint Precoder and Beamformer Design for Secure Relay Networks With Finite-Alphabet Inputs and Statistical CSI of Eve

Abstract

Because of discrepant deteriorations of the intended receiver and the unintended receiver, artificial noise (AN) can be invoked in conjunction with the precoder to wireless transmissions for enhancing the secrecy rate (SR) performance as long as we elaborately frame them. This paper studies a secure transmission strategy by jointly designing the precoder and AN beamformer at the relay network, where a passive eavesdropper and finite-alphabet inputs are taken into account. We propose a pair of solutions for low-order modulation and high-order modulation, respectively. To solve the first optimization problem, we propose a low-complexity algorithm with the aid of the invoked cut-off rate. Interestingly, we find that the phase of an optimum precoder for maximizing the SR has a correlation to both the channels spanning from the transmitter to the relays and spanning from the relays to the legitimate receiver. Furthermore, we reveal that the AN beamformer vector has at most one non-zero component, which only locates at the position corresponding to the minimum element of the channel between the relays and the intended receiver. According to these findings, the SR maximization problem over the two vectors is simplified as one only related to a pair of scalars. As for the high-order modulation, a new solution is further proposed for circumventing the predicament that the computational complexity exponentially increases as the size of the adopted modulation increases, where we not only eliminate two-layer summation over the legitimate symbols but also conceive a concave maximization SR problem. Finally, simulation results demonstrate the efficiency of the proposed algorithms in terms of the SR performance.