Hybrid Precoding Design for Secure Generalized Spatial Modulation With Finite-Alphabet Inputs

Technically, the security performance of generalized spatial modulation (GenSM) networks can be enhanced by dynamically adjusting the precoder allocated to the legitimate signal as communication channel varies. For this purpose, our paper proposes a secure transmission strategy upon designing both digital and analog precoders for hybrid GenSM systems, where an eavesdropper is taken into account. The concept of the hybrid GenSM system has arose to improve the spatial multiplexing (SMX) gain for remedying the shortcoming of the limited number of radio frequency chains in traditional GenSM systems. However, this may lead to a great deal of security degradation since the SMX gain of the unintended receiver will be also improved. To this end, we develop a secrecy enhancement scheme by devising both analog and digital precoders for hybrid GenSM networks. Specifically, we derive an efficiently closed-form alternative to the original secrecy rate (SR) expression for reducing the excessive computational complexity of the joint optimization problem over the hybrid precoder. Then, by using this alternative as our cost function, an iterative algorithm is proposed. In particular, we elaborately conceive a pair of concave maximization problems in order to optimize the digital and analog precoders, respectively. Our proposed strategy not only utilizes semi-positive definite relaxing technique over the analog precoder but also invokes a lower bound of the alternative to further simplify the optimization over the vectored digital precoder. Subsequently, both the convergence and computational complexity of the proposed alternating iteration algorithm are analyzed. Compared to existing designs, our proposed strategy strikes a compelling role in balancing the SR performance and complexity. Finally, our simulation results confirm the efficiency of the proposed algorithm in terms of the SR performance achieved.