On the symbol asynchronous Gaussian multiple-access channel

We consider the symbol asynchronous Gaussian multiple access channel in which each user is allowed to linearly modulate a set of orthogonal waveforms and the symbol periods for each user are not aligned at the receiver. This models the case in which asynchronous users may employ quadrature signaling in a multiple access scenario. The case in which each user is only allowed to linearly modulate a fixed waveform in each symbol period was considered by Verdu. He explicitly evaluated the capacity region of this class of multiple access channels for the case where the transmitters know the symbol period offset and also extended it to the case where the transmitters have no knowledge of the offset. In this paper, we characterize the capacity region for the scenario in which each user is allowed to modulate K orthogonal waveforms and the users know the symbol period offset. We note that the orthogonal waveforms need not be identical for both users. 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.