Optimized Pilot Design for Joint Compressive Sensing Multi-user and Channel Detection in Massive MTC

Massive machine-type communication (MTC) with sporadically transmitted small packets and a low data rate requires new designs on the PHY and MAC layer with light transmission overhead. Compressive sensing (CS) based multi-user detection (MUD) is able to jointly detect active users and estimate their channel/data through random access with low overhead by exploiting sparsity, i.e., the nature of sporadic transmissions in massive MTC. In this paper, we propose a novel pilot design approach that leads to good user activity and channel detection performance for CS-based MTC systems. Capitalizing on the total squared coherence of pilot sequences and convex relaxation, we derive an efficient algorithm which improves the quality of the pilot sequences. The proposed design exhibits superior performance in relation to the random pilot design and the tight-frame based design in the literature, which is revealed by our numerical investigation in various settings.