  A key challenge of massive MTC (mMTC), is the joint detection of device
activity and decoding of data. The sparse characteristics of mMTC makes
compressed sensing (CS) approaches a promising solution to the device detection
problem. However, utilizing CS-based approaches for device detection along with
channel estimation, and using the acquired estimates for coherent data
transmission is suboptimal, especially when the goal is to convey only a few
bits of data.
  First, we focus on the coherent transmission and demonstrate that it is
possible to obtain more accurate channel state information by combining
conventional estimators with CS-based techniques. Moreover, we illustrate that
even simple power control techniques can enhance the device detection
performance in mMTC setups.
  Second, we devise a new non-coherent transmission scheme for mMTC and
specifically for grant-free random access. We design an algorithm that jointly
detects device activity along with embedded information bits. The approach
leverages elements from the approximate message passing (AMP) algorithm, and
exploits the structured sparsity introduced by the non-coherent transmission
scheme. Our analysis reveals that the proposed approach has superior
performance compared to application of the original AMP approach.
