A Sum Capacity Optimization Analysis Of Multiple Access Channels With Noise

Multiple-access channel(MAC)has a high value for research as a common uplink channel for most practical communication system.And the Multiple-access technology is the key technology of each generation of communication technology.So it's significant to obtain a general multiple access technology design theory based on the maximum sum capacity constraint.At first,this paper summaries almost all former studies in theoretical field of multiple access channel.And the theoretical sum capacity and capacity region is showed separately and those capacity of different conventional multiple access technologies are compared.Then,an one-dimensional innovate discrete input continuous output memoryless channel model is proposed.And a general capacity formulation is derived.the maximum of this formulation is very difficult.Thus,a new method based on concatenated channel is proposed and then a maximum method of each concatenated channel is studied.In the first part,this paper introduces a complete proof of the binary multi-user extreme theoretical sum capacity through the way of the simplicity receiving entropy's distribution.And in this study,the condition of discrete channel outputs apply the Gaussian Distribution is proved based on the central-limit theorem.In the second part,the channel transition probability are divided into three general form to study its impact on the channel capacity and obtain the theory of maximum sum capacity condition.Then,the results of optimal mapping scheme and capacity of limited number of users are derived by using the method of solution space optimization.In this method,the optimal constellation points are obtained through numerical searching algorithm.At last,the nuerical results is generalized to a general situation based on mathematical induction.In one-dimensional situation these two schemes are analyzed comprehensively,and the maximum sum capacity they can achieve are obtained and shown with the relation of number of users,the proof of the uniqueness of optimal constellation design of each user.In end of the paper,the situation of two-dimensional channel modal is introduced based on the previous one-dimensional conclusion.The numerical result of limited users is also pointed out.but the conclusion of general case in two-dimensional modal is not derived out.but we got a special solution when the number of users is even.and a set of general solution can be derived though the coordinate transformation of the special solution's relative coordinate position.