  In massive machine-type communications (mMTC), grant-free access is a key
enabler for a massive number of users to be connected to a base station with
low signaling overhead and low latency. In this paper, a two-stage genetic
algorithm (GA) is proposed to design a new set of user-specific,
non-orthogonal, unimodular sequences for uplink grant-free access. The
first-stage GA is to find a subsampling index set for a partial unitary matrix
that can be approximated to an equiangular tight frame. Then in the
second-stage GA, we try to find a sequence to be masked to each column of the
partial unitary matrix, in order to reduce the peak-to-average power ratio of
the resulting columns for multicarrier transmission. Finally, the masked
columns of the matrix are proposed as new non-orthogonal sequences for uplink
grant-free access. Simulation results demonstrate that the non-orthogonal
sequences designed by our two-stage GA exhibit excellent performance for
compressed sensing based joint activity detection and channel estimation in
uplink grant-free access. Compared to algebraic design, this GA-based design
can present a set of good non-orthogonal sequences of arbitrary length, which
provides more flexibility for uplink grant-free access in mMTC.
