Search

Summary: The hybrid precoding problem is considered a Frobenius norm reduction problem for the narrowband channel in a millimeter wave (mmWave) with multiple inputs and outputs (mmWave MIMO). This work proposes a hybrid distributed online and alternating convex optimization (HDO‐ACO) algorithm to improve hybrid precoding (HP), interpreted as a trace minimization problem. HDO‐ACO alternately determines the digital and analog precoders to reduce the trace by keeping the other constant. Initially, HDO‐ACO uses Lagrange's method to determine the digital precoding subproblem. Then, it uses the integrated distributed online convex optimization and alternating minimization algorithm in the analog precoder design. In the HP method, the digital and analog precoders are iteratively updated until the highest number of iterations or convergence is reached. But this hybrid precoding method requires an initial analog precoding matrix input to begin the iteration. The algorithms converge gradually and fall into a suboptimal solution when the initial analog precoding matrix is set randomly. Hence, an initial value acceleration‐based heuristic approach is used in the HDO‐ACO alternating minimization algorithm that calculates the initial feasible value of an alternating minimization method using channel conditions. The simulation results of the proposed HDO‐ACO algorithm are presented under bit error rate (BER), spectral efficiency (SE), and convergence behavior by comparing it with modified block coordinate descent–HP (MBCD‐HP), manifold optimization–alternating minimization (MO‐AltMin), and semi‐definite relaxation‐based alternating optimization (SDR‐AO). The proposed HDO‐ACO attains maximum SE and less BER than other hyper‐precoding designs. [ABSTRACT FROM AUTHOR]

This paper is concerned with several variants of the Hermitian and skew-Hermitian splitting iteration method to solve a class of complex symmetric linear systems. Theoretical analysis shows that several Hermitian and skew-Hermitian splitting based iteration methods are unconditionally convergent. Numerical experiments from an n-degree-of-freedom linear system are reported to illustrate the efficiency of the proposed methods. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The application of the complex quadratic form as the decision boundary for complex‐valued data classification is described. This function is always real when its matrix is Hermitian. Thus, a simple sign function to classify the input data is used. This matrix is obtained through an iterative learning process similar to the Rosenblatt algorithm. The concept of the Frobenius matrix norm is used to prove that the proposed learning algorithm converges if a solution exists. This approach is different from other complex‐valued neural networks that use optimisation techniques or feature mapping. An artificial neuron that uses a complex quadratic form as the decision boundary is called a complex quadratic neural unit. [ABSTRACT FROM AUTHOR]