Jacket Transform And Its Application In Wireless Cooperative Communication

Matrix theory which widely used in engineering fields is the important theoretical basis of many disciplines, also is an irreplaceable mathematical tool. Hadamard matrix as a widely used matrix has an extremely important position. On the basis of center weighted Hadamard matrix, Lee Moon Ho conceived the concept of "Jacket Matrix" in1989. The main properties of the Jacket matrix are that its inverse can be obtained by the processes of element-wise inverse or block-wise inverse and its row/column is orthogonal. This kind of matrix can be widely used in signal processing, image compression, communication and other fields. Most of interesting matrices, such as Hadamard matrix, DFT, DCT, all belong to Jacket matrices family. In summary, the thesis is organized as follows.The research of Jacket matrix theory is to focus this matrix along with other orthogonal matrices and their applications to orthogonal codes and signal processing and to create more efficient algorithms. The combination of abstract algebra, combinatorial mathematics and the matrix theory knowledge, we propose a new construction of Jacket matrix based on finite Abelian group, which expand the Jacket matrix family. Exploiting the well-known Kronecker product of sparse matrices and the relationship of successively lower-order Jacket matrices, a fast Jacket construction algorithms are investigated in detail. The results indicate the presented algorithms perform quite well at decreasing the computation complexity.For the application of Jacket transform, we propose a multi-user cooperative communication coding scheme based on Jacket transform. In order to improve the performance of the system, the transmitter use OFDM technology in cooperative communication system. Our scheme replaces the DFT for the Jacket transform in OFDM modulator, so that the resulting OFDM symbols are orthogonal with simple modulation and demodulation, and the signal is flexible. A cooperative coding scheme is performed on relay nodes and the signal matrix has the special form of Alamouti code at the receiver. The proposed scheme enhances diversity gain of the system, while reducing signal interference with a good performance. At the same time, the system implementation is simple.