Orthogonally multiplexed communication is a bandwidth efficient modulation format that places independent QAM symbols on orthogonal pulses. With the traditional approach, this provides a uniform decomposition of the bandwidth allowing for variable compensation techniques within each subband tailored to the channel distortion peculiar to that band. In this dissertation, we propose orthonormal wavelet basis functions for the orthogonal pulses. In particular, dyadic wavelets are used to provide a nonuniform decomposition of the data bandwidth while M-band wavelets are used to generate a uniform decomposition. All the fundamental characterization of these new waveforms is provided and it is shown that digital filter banks enable an efficient discrete time implementation.
These filter banks are studied in detail resulting in the identification and solution of a number of practical problems encountered with FIR filter realizations. Most importantly, an even order FIR filter bank is developed for applications requiring linear phase. We then evaluate candidate pulse designs and make the important connection between the Meyer scaling function and the Nyquist communication pulse. In the dyadic case, we derive an analytical form for the square root raised cosine wavelet. Additionally, this allows us to prove several results in extending the Meyer scaling function to the M-band case. We finally use function approximation to the Meyer scaling function to design linear phase FIR filters for use in the new even order filter bank.
As an application for the newly developed waveforms, we introduce a unified framework for spread spectrum communication. In particular,dimensionality in time is obtained with traditional DSPN having a scaling function chip pulse, dimensionality in time-frequency is obtained with dyadic wavelets and dimensionality in frequency is achieved with M-band wavelets. An optimum filter is developed which operates on the coefficients obtained by projecting the received signal upon the basis functions defining the waveforms. The performance of this filter is evaluated for additive interference channels. It is shown that concentrating the interference to a minimum number of waveform coordinates and applying an excision strategy is near optimum yielding processing gains well in excess of the bandwidth expansion estimate.