Research On Framework Structure And Its Application In Communication

Before the user information is transmitted to the channel in CDMA system,the data will be spread spectrum encoding and each user's spreading code sequence is unique.All the spread spectrum signals will be transmitted in a common channel.On the receiving end,the information sent by the users will be demodulated from the received signals by the same spreading sequence.Due to the redundancy between the spreading codes,there will be multiple access interference in the system.The multiple access interference has a great impact on the performance of the CDMA system.The interference can be reduced by choosing a codebook of good structure,and the impact to the system can also be decreased by adopting multi-user detection technology.So,the codebook designing and multi-user detection are always the most important parts in communication system.In framework theory,Grassmannian frame has the minimal coherence between elements in the frames with same dimension.The optimal Grassmannian frame also named as equiangular tight frame,and the coherence of each two elements are all the same.In CDMA system,the spreading codebook based on Grassmannian frame can reduce multiple access interference of each user efficiently.And when the active users change,the interference is only related to the number of the active users.However,optimal Grassmannian frames exist only when the dimension m and the number of column vector N take certain values,and the construction is very difficult.This paper studies the framework theory,analyses the structure of Grassmannian frame,and proposes a new construction method which is based on Steiner system.Compared with the existing algorithms,the new method can construct a high dimension equiangular tight frame to satisfy more users in the system as many as possible.Then,on the receiving end,an optimization decision method based on two-valued decision is proposed,which can reduce the computational complexity of the system effectively,and the system has a good bit error rate.The paper mainly contains four parts:the first part introduces the basic concept of spread spectrum communication system,provides the channel model of CDMA system,and introduces several common multi-user detection technology in CDMA system;the second part introduces the basic knowledge of space and collection,and makes a clear definition of framework,analyses several kinds of frameworks with special structures;the third part provides the definition of Grassmannian frames and their structural features,analyses the existence conditions of Grassmannian frame.Then,several existing construction methods of Grassmannian frame is illustrated and a new construction method of equiangular tight frame based on Steiner system is proposed;the forth part illustrates several common spread spectrum codes in CDMA system,introduces the concept of welch bound,then,elaborates the WBE(Welch Bound Equality)sequence and the optimal Grassmannian sequence and their features,and an optimization decision method based on two-valued detection is improved.