An application of multi-wavelet packets in digital communications

Bandwidth efficiency and the ability to combat the effects of frequency selective channels are critical in the design of digital modulation schemes. To improve bandwidth utilization and to avoid ISI caused by time dispersion in the channel, a new multi-wavelet packet modulation (MWPM) scheme is proposed. The MWPM is based on orthogonal multi-wavelet packets (MWP). In particular, the orthogonality in MWP is exploited to guarantee the demodulation of the overlapped MWP coded signals in time and frequency domains. A practical implementation of the MWPM transceiver is proposed by employing matrix filter banks. For MWP with multiplicity r, the bandwidth efficiency is increased r times compared to scalar wavelet packet modulation or the conventional FFT based OFDM system. Similarly, as these prototype schemes, the MWPM is implementable either as a binary or a multilevel scheme. As a multi-carrier modulation, MWPM can mitigate the time dispersiveness in the channel effectively because the symbol duration can be extended as required by the flexible structure of MWPM. Using two orthogonal MWPs introduced by J. Geronimo et al. (see J. Approx. Theory, vol.78, p.373-401, 1994) and C. Chui and J. Lian (Ctr. for Approximation Theory, 1995), the corresponding MWPM are constructed. The performance for these MWPM in AWGN and flat Rayleigh fading channels is analyzed and simulated using binary phase shift keying (BPSK) in each subcarrier. The simulation results demonstrate the effectiveness of the proposed MWPM scheme.