Secrecy-Capacity-Optimization-Artificial-Noise in Large-Scale MIMO: Ergodic Lower Bound on Secrecy Capacity and Optimal Power Allocation

The security of wireless information transmission in large-scale multi-input and multioutput (MIMO) is the focus of research in wireless communication. Recently, a new artificial noise—SCO-AN which shows no orthogonality to the channel, is proposed to overcome the shortcomings of traditional artificial noise. In the previous research, the optimization function of SCO-AN is not convex, and its extremum cannot be obtained. Usually, nonconvex optimization algorithms or iterative relaxation algorithms are used to get the maximum value of the optimization objective function. Nonconvex optimization algorithms or iterative relaxation algorithms are greatly affected by the initial value, and the extremum cannot be obtained by a nonconvex optimization algorithm or iterative relaxation algorithm. In this paper, we creatively apply the strong law of large numbers to obtain the optimal value of the optimization function of SCO-AN under the condition of large-scale MIMO: the strong law of large numbers is applied to obtain the ergodic lower bound (ELB) expression of SC for SCO-AN. The power allocation (PA) problem of the SCO-AN system is discussed. We use a statistical method to get the formula for calculating the optimal power distribution coefficient of the SCO-AN system. The transmitter can use the optimal power ratio of PA to distribute the transmitted power without using the PA algorithm. The effect of imperfect channel state information is discussed. Through simulation, we found that more power should be generated for SCO-AN if the channel estimation is imperfect and the proposed method can achieve better security performance in the large-scale MIMO system.