Research On The Pseudo Noise Communication Technology Based On The Frame Theory

CDMA system is the most common pseudo noise communication system. In CDMA system, every user will be assigned a unique sequence. The signals sent by users will be multiplied by these sequences, and all the spread spectrum signals will be added together and 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 sequences. The multiple access interference has a great impact on the performance of the CDMA system. The interference will be reduced by choosing the codebooks which have good structure, and the impact to the system can also be softened and the capacity of the system can be enlarged by adopting multi-user detection technology. So, the codebook designing and multi-user detection are the two hotspots in this area, which have theoretical significance and practical value.In frame theory, grassmannian frame has the minimal coherence between elements in the frames with same dimension and size. The optimal grassmannian frame also named as equiangular tight frame, the elements'coherence of which are all the same. The CDMA codebook which is constituted by optimal grassmannian frame is called optimal grassmannian sequence. When the optimal grassmannian sequence is used in CDMA system, the inter-user interference is minimized 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 dissertation studies the frame theory, analyses the structure of grassmannian frame, and proposes the new construction methods which is based on the best antipodal spherical codes and an improved genetic algorithm. Compared with the already exist algorithms, the new algorithms have higher dimensional adaptability and faster convergent rate. Then a pre-processing method is presented on the account of the optimal grassmannian sequence structural features and the high inter-user interference of overloaded CDMA system. This method is applied to extract the users' information which can be optimally detected before multi-user detection. Compared with simply applying multi-user detection, new method can make the error rate of the system lower, and improve the system performance.This dissertation mainly contains four parts:the first part introduces the basic concept of the CDMA system, provides the channel mode, and analyses the already exist spread spectrum codes and multi-user detection technology; the second part introduces the basic knowledge of frame theory, analyses several kinds of frames with special structures; the third part provides the definition of grassmannian frame and optimal grassmannian frame, also their structural features, illustrates several existing construction methods of grassmannian frame, and proposes two new construction methods which is based on the best antipodal spherical codes and an improved genetic algorithm; the forth part introduces the WBE (Welch Bound Equality) sequence and the optimal grassmannian sequence and their features, and proposes a pre-processing method for multi-user detection on the basis of optimal grassmannian sequence.