  We propose an improvement of the random spreading approach with polar codes
for unsourced multiple access. Each user encodes its message by a polar code,
and the coded bits are then spread using a random spreading sequence. The
proposed approach divides the active users into different groups, and employs
different power levels for each group in such a way that the average power
constraint is satisfied. We formulate and solve an optimization problem to
determine the number of groups, and the number of users and power level of each
group. Extensive simulations show that the proposed approach outperforms the
existing methods, especially when the number of active users is large.
