Nonconvex Utility Ontimization Method For Multi-user Millimeter Wave Communication System

Accompanied with the rapid development of science and technology in the age of internet and information,mobile data traffic presents an explosive growth mode,and the limitation of bandwidth resources has become a bottleneck restricting the rapid development of wireless network.Therefore,more efficient utilization of unused frequency band resources becomes critical.Multicast technology by way of delivering the same information to multiple recipients,can reduce with multiple recipients at the same time listen to or view the same resource of network traffic,such as live sporting events,regularly updated software and advertising push practical application can greatly reduce the bandwidth required.Not only that,the millimeter wave system can provide 30G-300 Ghz bandwidth,which can greatly alleviate the current shortage of bandwidth.Therefore,it is significant to study the combination of millimeter-wave communication system and multicast technology(i.e.,millimeter-wave multicast communication system).In this paper,we fully understand the current situation of the research on multicast technology,millimeter-wave communication and millimeter-wave multicast communication system at home and abroad,and mainly do the following aspects:(1)Aiming at the drawback that the alternating optimization method can not guarantee convergence to the static point and the penalty function method will make the objective function tend to be ill conditioned,we propose a Penalty Dual Decomposing(PDD)algorithm to solve the nonconvex problem with coupled constraints.The core steps of PDD algorithm involving the use of BSUM algorithm to solve the AL problem comes from the decomposition of the subproblems,and the degree of violation of the constraint as a measure of PDD algorithm in the adaptive switching between AL method and penalty function method criterion,the benefits of doing so is to find a suitable penalty coefficient to ensure the convergence of the PDD algorithm.By solving the optimality conditions of nonconvex nonsmooth problems,this paper theoretically proves the Karush-Kuhn-Tucker convergence of the PDD algorithm under the Robinson condition.Finally,in order to extend the applicability of the algorithm,the updating method of dual variables and penalty coefficients in the basic PDD algorithm is improved,and KKT convergence certificate of the improved algorithm is also given.(2)A high efficient beamforming scheme is proposed based on PDD algorithm to minimize the transmission power in the multi-group multicasting communication system.Due to the high coupling of variables between the target function and the SINR function,you first need to be decoupled by introducing new variables and equivalent transformation of the original problem.Secondly,by using the gradient descent method and block coordinate descent method,the subproblems of the decomposition of the augmented Lagrangian function are solved respectively.Finally,the feasibility of the proposed scheme is simulated.The experimental results show that the proposed algorithm can achieve very fast convergence speed and excellent performance performance in solving the problem of minimization of transmission power.(3)Aiming at maximizing minimum fairness problem in millimeter wave multicast communication system,a new hybrid precoding scheme based on PDD algorithm framework is designed in this paper.In order to solve this problem,the augmented Lagrange function can be decomposed into optimization subproblems of multiple variables by using constrained concave convex optimization and BSUM algorithm,and then a simple algorithm can be designed respectively.At the same time,this paper also considers the optimization scheme of maximizing minimum fairness problem with fully digital precoding.Using fully digital precoding MMF problem,which can be further reduced to a number of precoding and coupling variables combined optimization problem,and then based on the upper bound of the AL function and the problem of structure design of low complexity algorithm are obtained.Finally verified by simulation in this paper,the proposed hybrid precoding scheme is very close to fully digital precoding performance,and the design of digital precoding scheme in terms of convergence and the performance is better than positive semidefinite relaxation algorithm and penalty block successive upperbound minimization algorithm.