The capacity region of the asynchronous Gaussian vector multiple-access channel

Verdu determined the capacity region of the symbol-asynchronous two-user Gaussian multiple-access channel. In this channel, the symbol periods for the users do not coincide at the receiver and each user is only allowed to linearly modulate a fixed signature waveform in each symbol period. In, we extended Verdu's result to the case where each user modulates K orthonormal waveforms and the transmitters know the mutual offset at the receiver. In this paper, we derive a capacity region expression for the case where each user is allowed to modulate a set of orthonormal waveforms in each symbol period and the users do not know the mutual offset. We also provide theorems that allow us to numerically compute the capacity region to any desired degree of accuracy.