On the sparsity for random access in machine type communications under frequency-selective fading

In this paper, we study random access for machine type communications (MTC). In particular, we consider a preamble detection method that can exploit the sparsity of active devices over frequency-selective fading channels to detect multiple preambles in random access. In order to understand the impact of various design parameters and channels, we analyze the performance in terms of the average number of successful preambles when a compressive sensing (CS) based approach is used for the preamble detection. For example, through the analysis, we can see that the performance of the CS-based estimation for the preamble detection can be limited by the length of the channel impulse response (CIR).