Symmetric Capacity and Signal Design for L-out-of-K Symbol-Synchronous CDMA Gaussian Channels

We consider the symbol-synchronous Gaussian L-out-of-K code-division multiaccess channel, and obtain the capacity region and the upper and lower bounds to the symmetric capacity. The capacity region is found to be the same with or without frame synchronism. The lower bound depends on the signature waveforms through the eigenvalues of the SNR-weighted crosscorrelation matrix. We find a sufficient condition for the signature waveform set to maximize this lower bound and give an algorithm to construct a set of signature waveforms satisfying the sufficient condition.