Orthogonal digital waveform set for multidimensional signaling and multiuser communications with matched filter receivers

This paper proposes a design of digital waveform sets, which can be used as transmitter signature waveforms for multidimensional signaling and/or multiuser communications. The aim is to design a set of quasiorthogonal digital waveforms with prescribed specifications in time and frequency domains, optimized with respect to the given channels. It will be shown that the digital waveform set design problem can be formulated as a constrained nonlinear optimization problem. For bandwidth efficiency, all the digital waveforms in the set are designed in such a way that, the overall frequency response from each transmitter to the corresponding receiver has approximately the same desired spectral shape in a prescribed passband; To minimize intersymbol interference and cochannel interference, all the digital waveforms in the set are constrained to have low values of weighted (by the channel) autocorrelation at nonzero translates of multiple symbol interval and low values of weighted (by the channel) crosscorrelation at all translates of multiple symbol interval. Numerical results are presented to demonstrate the effectiveness of the proposed design.