Pilot Signal Design for Compressive Sensing Based Random Access in Machine-Type Communications

In machine-type communications (MTC), a number of devices are present in a cell, but only a few of them attempt to access by sending preambles or pilots. For the sparse activity of devices, compressive sensing (CS) can be applied for joint detection of active devices and estimation of channel profiles. In this paper, a theoretical connection between pilots and the coherence of a CS measurement matrix is revealed for CS-based detection and estimation. Then, the Zadoff-Chu (ZC) and the power residue (PR) sequences are studied as potential candidates for pilot signals in CS-based random access. It is also shown that the CS measurement matrices from the ZC- and the PR-based pilots have theoretically bounded low coherence, which presents a theoretical guarantee of reliable recovery performance. Simulation results demonstrate that the proposed deterministic pilots outperform random binary and complex-valued pilots for CS-based random access in MTC.