  This paper studies the performance of a transmission and reception scheme for
massive access under some practical challenges. One challenge is the near-far
problem, i.e., an access point often receives signals from different
transmitting devices at vastly different signal strengths. Another challenge is
that the signals from different devices may be subject to arbitrary, analog,
and heterogeneous delays. This paper considers a fully asynchronous model which
is more realistic than the frame or symbol level synchrony needed in most
existing work. A main theorem characterizes the asymptotic scaling of the
codelength with the number of devices, a device delay upper bound, and the
dynamic range of received signal strengths across devices. The scaling result
suggests potential advantages of grouping devices with similar received signal
strengths and letting the groups use time sharing. The performance of the
proposed scheme is evaluated using simulations with and without grouping.
