User Activity Detection for Irregular Repetition Slotted Aloha Based MMTC

Irregular repetition slotted aloha (IRSA) is a grant-free random access protocol for massive machine-type communications, in which users transmit replicas of their packet in randomly selected resource blocks within a frame. In this paper, we first develop a novel Bayesian user activity detection (UAD) algorithm for IRSA, which exploits both the sparsity in user activity as well as the underlying structure of IRSA transmissions. Next, we derive the Cramér-Rao bound (CRB) on the mean squared error in channel estimation. We empirically show that the channel estimates obtained as a by-product of the proposed UAD algorithm achieves the CRB. Then, we analyze the signal to interference plus noise ratio achieved by the users, accounting for UAD, channel estimation errors, and pilot contamination. Finally, we illustrate the impact of these non-idealities on the throughput of IRSA via Monte Carlo simulations. For example, in a system with 1500 users and 10% of the users being active per frame, a pilot length of as low as 20 symbols is sufficient for accurate user activity detection. In contrast, using classical compressed sensing approaches for UAD would require a pilot length of about 346 symbols. Our results reveal crucial insights into dependence of UAD errors and throughput on parameters such as the length of the pilot sequence, the number of antennas at the BS, the number of users, and the signal to noise ratio.