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.

Quasi-overlapping Semi-discrete Schwarz Waveform Relaxation Algorithms: The Hyperbolic Problem

The Schwarz waveform relaxation (SWR) algorithms have many favorable properties and are extensively studied and investigated for solving time dependent problems mainly at a continuous level. In this paper, we consider a semi-discrete level analysis and we investigate the convergence behavior of what so-called semi-discrete SWR algorithms combined with discrete transmission conditions instead of the continuous ones. We shall target here the hyperbolic problems but not the parabolic problems that are usually considered by most of the researchers in general when investigating the properties of the SWR methods. We first present the classical overlapping semi-discrete SWR algorithms with different partitioning choices and show that they converge very slow. We then introduce optimal, optimized, and quasi optimized overlapping semi-discrete SWR algorithms using new transmission conditions also with different partitioning choices. We show that the new algorithms lead to a much better convergence through using discrete transmission conditions associated with the optimized SWR algorithms at the semi-discrete level. In the performed semi-discrete level analysis, we also demonstrate the fact that as the ratio between the overlap size and the spatial discretization size gets bigger, the convergence factor gets smaller which results in a better convergence. Numerical results and experiments are presented in order to confirm the theoretical aspects of the proposed algorithms and providing an evidence of their usefulness and their accuracy.

Algorithms on Sparse Representation

Representation of signals and images in sparse become more interesting for various applications like restoration, compression and recognition. Many researches carried out in the era of sparse representation. Sparse represents signal or image as a few elements from the dictionary atoms. There are various algorithms proposed by researchers for learning dictionary. This paper discuss some of the terms related to sparse like regularization term, minimization, minimization, minimizationfollowed by the pursuit algorithms for solving problem, greedy algorithms and relaxation algorithms. This paper gives algorithmic approaches for the algorithms.