Machine-type communication (MTC) services are expected to be an integral part of the future cellular systems. A key challenge of MTC, especially for the massive MTC (mMTC), is the detection of active devices among a large number of devices. The sparse characteristics of mMTC makes compressed sensing (CS) approaches a promising solution to the device detection problem. CS-based techniques are shown to outperform conventional device detection approaches. However, utilizing CS-based approaches for device detection along with channel estimation and using the acquired estimates for coherent data transmission may not be the optimal approach, especially for the cases where the goal is to convey only a few bits of data. In this work, we propose a non-coherent transmission technique for the mMTC uplink and compare its performance with coherent transmission. Furthermore, we demonstrate that it is possible to obtain more accurate channel state information by combining the conventional estimators with CS-based techniques.