  This work studies the uplink of grant-free low data-rate massive
machine-to-machine communications (mMTC) where devices are only active
sporadically, which requires a joint activity and data detection at the
receiver. We develop an adaptive decision feedback detector along with an
$l_0$-norm regularized activity-aware recursive least-squares algorithm that
only require pilot symbols. An iterative detection and decoding scheme based on
low-density parity-check (LDPC) is also devised for signal detection in mMTC.
Simulations show the performance of the proposed approaches against existing
schemes.
