Design of a synchronization scheme for a bandwidth-on-demand multiplexer-demultiplexer pair based on wavelet packet tree filter banks

For a spectrum-efficient, bandwidth-on-demand multiplexer-demultiplexer for a multiuser, multicarrier communication system based on wavelet packet trees for downstream transmission, an innovative scheme for synchronization is proposed which uses a unique sync word at the root of the tree. An example filterbank tree with 8 leaves is used throughout the paper. For this example the creation of the unique 32-bit sync word is described. The multirate signal processing and construction and properties of 25 32×32 matrices required in the multiplexer to find locations of sync words at input ports to cancel the effects of data and insert the 32-bit sync word in a window in the correct location at the root of the tree is described. The ratio of maximum to minimum absolute values of eigenvalues of the matrices is used to ensure well-conditioning, since they must be inverted in the processing