Binary Golay Spreading Sequences and Reed-Muller Codes for Uplink Grant-Free NOMA

Non-orthogonal multiple access (NOMA) is an emerging technology for massive connectivity in machine-type communications (MTC). In code-domain NOMA, non-orthogonal spreading sequences are uniquely assigned to all devices, where active ones attempt a grant-free access to a system. In this paper, we study a set of user-specific, non-orthogonal, binary spreading sequences for uplink grant-free NOMA. Based on binary Golay complementary sequences, each spreading sequence provides the peak-to-average power ratio (PAPR) of at most 3 dB for multicarrier transmission. Exploiting the theoretical connection to Reed-Muller codes, we conduct a probabilistic analysis to search for a permutation set for Golay sequences, which presents theoretically bounded low coherence for the spreading matrix. Simulation results confirm that the maximum PAPR of transmitted multicarrier signals via the spreading sequences is significantly lower than those for random bipolar, Gaussian, and pseudo-random sequences. Thanks to the low coherence, the performance of compressed sensing (CS) based joint channel estimation and multiuser detection using the spreading sequences turns out to be superior or similar to those for random bipolar, Gaussian, pseudo-random, and Zadoff-Chu sequences. The binary Golay spreading sequences have only two phases regardless of the sequence length, which can make them suitable for low cost MTC devices.