  We consider a multiple-access channel where the users are powered from
batteries having non-negligible internal resistance. When power is drawn from
the battery, a variable fraction of the power, which is a function of the power
drawn from the battery, is lost across the internal resistance. Hence, the
power delivered to the load is less than the power drawn from the battery. The
users consume a constant power for the circuit operation during transmission
but do not consume any power when not transmitting. In this setting, we obtain
the maximum sum-rates and achievable rate regions under various cases. We show
that, unlike in the ideal battery case, the TDMA (time-division multiple
access) strategy, wherein the users transmit orthogonally in time, may not
always achieve the maximum sum-rate when the internal resistance is non-zero.
The users may need to adopt a hybrid NOMA-TDMA strategy which combines the
features of NOMA (non-orthogonal multiple access) and TDMA, wherein a set of
users are allocated fixed time windows for orthogonal single-user and
non-orthogonal joint transmissions, respectively. We also numerically show that
the maximum achievable rate regions in NOMA and TDMA strategies are contained
within the maximum achievable rate region of the hybrid NOMA-TDMA strategy.
