  Recent studies have numerically demonstrated the possible advantages of the
asynchronous non-orthogonal multiple access (ANOMA) over the conventional
synchronous non-orthogonal multiple access (NOMA). The ANOMA makes use of the
oversampling technique by intentionally introducing a timing mismatch between
symbols of different users. Focusing on a two-user uplink system, for the first
time, we analytically prove that the ANOMA with a sufficiently large frame
length can always outperform the NOMA in terms of the sum throughput. To this
end, we derive the expression for the sum throughput of the ANOMA as a function
of signal-to-noise ratio (SNR), frame length, and normalized timing mismatch.
Based on the derived expression, we find that users should transmit at full
powers to maximize the sum throughput. In addition, we obtain the optimal
timing mismatch as the frame length goes to infinity. Moreover, we
comprehensively study the impact of timing error on the ANOMA throughput
performance. Two types of timing error, i.e., the synchronization timing error
and the coordination timing error, are considered. We derive the throughput
loss incurred by both types of timing error and find that the synchronization
timing error has a greater impact on the throughput performance compared to the
coordination timing error.
