Low-Complexity Linear Precoding for Secure Spatial Modulation

In this work, we investigate linear precoding for secure spatial modulation. With secure spatial modulation, the achievable secrecy rate does not have an easy-to-compute mathematical expression, and hence, has to be evaluated numerically, which leads to high complexity in the optimal precoder design. To address this issue, an accurate and analytical approximation of the secrecy rate is derived in this work. Using this approximation as the objective function, two low-complexity linear precoding methods based on gradient descend (GD) and successive convex approximation (SCA) are proposed. The GD-based method has much lower complexity but usually converges to a local optimum. On the other hand, the SCA-based method uses semi-definite relaxation to deal with the non-convexity in the precoder optimization problem and achieves near-optimal solution. Compared with the existing GD-based precoder design in the literature that directly uses the exact and numerically evaluated secrecy capacity as the objective function, the two proposed designs have significantly lower complexity. Our SCA-based design even achieves a higher secrecy rate than the existing GD-based design.Comment: 11pages, 8figure

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). Unlike traditional MIMO, it uses both modulation symbols and antenna indices to carry information. In this paper, to avoid the high cost and circuit complexity of fully-digital SM, we mainly consider the hybrid SM system with a hybrid precoding transmitter architecture, combining a digital precoder and an analog precoder. Here, the partially-connected structure is adopted with each radio frequency chain (RF) being connected to a transmit antenna subarray (TAS). In such a system, we made an investigation of secure hybrid precoding and transmit antenna subarray selection (TASS) methods. Two hybrid precoding methods, called maximizing the approximate secrecy rate (SR) via gradient ascent (Max-ASR-GA) and maximizing the 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) TASS method is first presented. To reduce its high complexity, two low-complexity TASS methods, namely maximizing the eigenvalue (Max-EV) and maximizing the product of signal-to-interference-plus-noise ratio and artificial noise-to-signal-plus-noise ratio (Max-P-SINR-ANSNR), are proposed. Simulation results will 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 is low-complexity at the expense of a little performance loss compared with Max-ASR.Comment: 13 pages, 8 figure