Precoding and Transmit Antenna Subarray Selection for Secure Hybrid Spatial Modulation

Spatial modulation (SM) is a particularly important form of multiple-input multiple-output (MIMO), which uses both modulation symbols and antenna indices to carry information. In this paper, to avoid the high cost and circuit complexity of SM, we consider the hybrid SM system with a hybrid precoding transmitter architecture, combining a digital precoder and an analog precoder. In such a system, we carried out secure hybrid precoding and transmit antenna subarray selection (TASS) methods. Two hybrid precoding methods, called maximizing approximate secrecy rate (SR) via gradient ascent (Max-ASR-GA) and maximizing approximate SR via alternating direction method of multipliers (Max-ASR-ADMM), are proposed to improve the SR performance. As for TASS, a high-performance method of maximizing the approximate SR (Max-ASR) is first presented. To reduce its high complexity, two low-complexity TASS methods, namely maximizing eigenvalue (Max-EV) and maximizing product of signal-to-interference-plus-noise ratio and artificial noise-to-signal-plus-noise ratio (Max-P-SINR-ANSNR), are proposed. Simulation results demonstrate that the proposed Max-ASR-GA and Max-ASR-ADMM hybrid precoders harvest substantial SR performance gains over existing method. For TASS, the proposed three methods Max-ASR, Max-EV, and Max-P-SINR-ANSNR perform better than existing leakage method. Particularly, the proposed Max-EV and Max-P-SINR-ANSNR are of low-complexity at the expense of a little performance loss compared with Max-ASR.

I. Introduction

As an essential key technique for future generation wireless communications like six generation (6G), multiple-input multiple-output (MIMO) has attracted a lot of research activities, which can greatly improve the system performance in wireless communications. Two typical forms of MIMO are Bell laboratories layer space-time (BLAST) in [1] and space time coding (STC) in [2]. Extensive investigations have been performed in both spatial multiplexing and diversities in MIMO systems. However, as the third form of MIMO, spatial modulation (SM) is attracting more and more research attention from industry and academia due to its advantages of no inter-channel interference (ICI) and inter-antenna synchronization (IAS) [3]. It works by mapping a block of information bits into two information-carrying units. The first information carrying unit is an amplitude/phase modulation (APM) symbol chosen from the signal-constellation diagram. The second information-carrying unit is a transmit antenna index chosen, while other transmit antennas are not activated [3]–[5].