Design of non-uniform filter bank transmultiplexer with canonical signed digit filter coefficients

Design of non-uniform filter bank transmultiplexer (NUFB TMUX) with canonical signed digit (CSD) coefficients is presented. NUFB TMUX is preferred in a multicarrier communication system when applications with different data rates are to be multiplexed. If the filter coefficients are represented in CSD format, the hardware complexity of the NUFB TMUX can be reduced. A continuous coefficient NUFB TMUX is designed and the coefficients of the filters are synthesised in CSD format using genetic algorithm (GA). Separate objective functions are formulated for the fitness evaluation of the filters. Chromosomes are encoded as ternary digit strings. New crossover and mutation techniques are introduced to preserve the canonical property of the signed power of two (SPT) representations. For the fast convergence of the GA, position-dependent probability of mutation is used. Simulation results show that the CSD coefficient NUFB TMUX designed using the proposed algorithm has better signal-to-interference ratio (SIR) than that of continuous coefficient NUFB TMUX and CSD coefficient NUFB TMUX obtained by rounding. Frequency responses of its filters are better than that of the filters in CSD coefficient NUFB TMUX obtained by rounding and comparable with that of continuous coefficient NUFB TMUX.