  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.
