The capacity region of the symbol-asynchronous Gaussian multiple-access channel with orthogonal signaling

Verdu determined the capacity region of the symbol-asynchronous two-user Gaussian multiple-access channel. In this channel, each user modulates a fixed waveform in each symbol period and the symbol periods for the users do not coincide at the receiver. First, he explicitly evaluated the capacity region of this class of multiple-access channels in the case where the transmitters know the offset. The result was also extended to the case where the transmitters have no knowledge of the offset. In this paper, we extend the result to the case where each user modulates K orthogonal waveforms and the transmitters know the offset. In addition, the users' orthogonal waveforms are not assumed to be identical. Similar to the case where each user is allowed to modulate a fixed waveform, the result holds regardless of whether or not the transmitters are frame-asynchronous. We later extend the result to certain situations where the transmitters do not know the offset.