  In this letter, we study a two-user downlink asynchronous non-orthogonal
multiple access (ANOMA) with limited feedback. We employ the max-min criterion
for the power allocation and derive the closed-form expressions for the upper
and lower bounds of the max-min rate. It is demonstrated that ANOMA can achieve
the same or even higher average maxmin rate with a lower feedback rate compared
with NOMA. Moreover, we propose a quantizer optimization algorithm which
applies to both NOMA and ANOMA. Simulation results show that the optimized
quantizer significantly improves the average max-min rate compared with the
conventional uniform quantizer, especially in the scenario with a low feedback
rate.
