Design of digital waveform set for multiuser CDMA communications with matched filter receivers

This paper presents a new approach for the design of a set of bandwidth-efficient quasiorthogonal digital filters which can be used as signature waveforms for multiuser CDMA communication systems. The design problem is formulated in such a way when matched filter is used at the receiver end, the overall impulse response from the transmitter to the receiver will approximated be a Nyquist pulse. It will be shown that the digital waveform set design problem can be converted to a constrained nonlinear minimax optimization problem. For bandwidth efficiency, all the digital waveforms in the set are designed to have approximately the same desired magnitude spectral shape in a prescribed passband. To minimize intersymbol and cochannel interferences, all the digital waveforms in the set are constrained to have low autocorrelation at nonzero translates of multiple symbol intervals and low cross correlation at all translates of multiple symbol intervals. Methods to solve the proposed optimization problem are discussed. A demodulation scheme with the proposed matched filter receiver is briefly outlined. Numerical results are presented to demonstrate the effectiveness of the proposed method.