Antenna Selection Method of Maximizing Secrecy Rate for Green Secure Spatial Modulation

In secure spatial modulation systems, an active antenna-group (AAG) selection of maximizing the average secrecy rate (SR) is proposed to avoid the disadvantage that conventional AAG selection scheme of minimizing bit error ratio at desired receiver may lead to a substantial SR loss. However, due to the limited active antenna pattern and finite-alphabet inputs, it is very hard for us to optimize the SR without closed-form expression. To address the two issues, first, by exploiting the relationship between minimum mean-square error and mutual information, the expression of SR in the low signal-to-noise ratio (SNR) region is derived. Using the expression, the problem of maximizing SR (Max-SR), called Max-SR I, is converted to integer programming problem. In the high SNR region, we derive an asymptotical lower bound for SR, and find the fact that the Max-SR can be reduced to maximizing the difference of Bob's minimum Euclidean distance and Eve's one, called Max-SR II. Through this conclusion, we can find the relationship between SR and bit-error rate. Furthermore, Max-SR III is proposed to overcome the disadvantage of the SR performance loss for the above two asymptotical algorithms in the moderate SNR region, where an approximate expression is exploited as the efficient metric to design AAG. Numerical results show that the SR performance of the proposed Max-SR III is close to that of optimal exhaustive search method, and the Max-SR I and Max-SR II can achieve acceptable SR performance with extremely low complexity.