Number-Theoretic Sequence Design for Uncoordinated Autonomous Multiple Access in Relay-Assisted Machine-Type Communications

Terminal relaying is expected to offer an effective means for realizing machine-type communications (MTC) in wireless cellular networks. In the absence of channel quality indicators, the effective utilization of relaying terminals (RTs) requires a mechanism by which RTs can autonomously assign available resource blocks (RBs) to potentially large numbers of uncoordinated MTC devices with minimal conflicts. Unlike random RB assignments, which do not offer performance guarantees, using prescribed RB assignment sequences provides an opportunity for obtaining performance gains. However, realizing these gains requires optimizing RB assignments over a large set of lengthy sequences. One technique for selecting assignment sequences is based on an exhaustive search of exponential complexity over sequences generated by multiplicative cyclic groups. This technique restricts the number of RBs to be prime minus one and does not consider sequences generated using other group operations. In this paper, we use group isomorphism to eliminate the constraint on the number of RBs and to show that the optimal assignment sequences generated by a specific cyclic group are globally optimal over the set of all cyclically generated sequences. We develop a greedy algorithm with polynomial complexity for the sequential selection of RB assignment sequences in systems with large numbers of RTs and arbitrary device distributions. This algorithm is further simplified by invoking the graphical representation of cyclic groups. The resulting algorithm is more efficient and thus suitable for generating assignment sequences for relay-assisted massive multiple access Internet-of-Things systems. Numerical results show that the performance of the sequences generated by the greedy algorithms is comparable to that of those generated by exhaustive search, but with much less computational cost.