Number-Theoretic Sequence Design for Uncoordinated Resource Block Assignments in Relay-Assisted Machine-Type Communication Systems

Terminal relaying offers effective means for realizing machine-type communication (MTC) systems. However, coordinating these relaying terminals (RTs) becomes a cumbersome task as the number of RTs increases. In the absence of channel state information, the efficient utilization of RTs requires a mechanism by which RTs can autonomously assign available resource blocks (RBs) to large numbers of uncoordinated MTC devices with minimal conflicts. Unlike random RB assignments, using prescribed assignment sequences provides an opportunity for obtaining performance gains. However, realizing these gains requires optimizing RB assignments over a large set of 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 RB assignment sequence length and does not consider sequences generated using other group operations.In this thesis, we use group isomorphism to eliminate the constraint on the sequence length 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 also develop a greedy algorithm with polynomial complexity for the sequential selection of assignment sequences in systems with large numbers of RTs. This algorithm is further simplified by invoking the graphical representation of cyclic groups to enable its application in massive MTC systems. To further improve performance, we extend the RB assignment sequences set by considering multi-generator sequences. In particular, the Chinese remainder theorem (CRT) is used to combine cyclically-generated sequences into longer ones. This combining process introduces additional degrees of freedom in sequence generation, thereby enriching the set of assignment sequences. We then use group isomorphism to show that the set of pseudonoise maximal length sequences (M-sequences) constitutes a subset of the cyclically-generated sequences set and that their performance is upper bounded by that of cyclically-generated and CRT-based sequences. This isomorphism is also used to extend the ease of generation property of M-sequences to their corresponding cyclically-generated supersets. Finally, we compare the correlation properties of CRT-based, Zadoff-Chu (ZC), and M-sequences and discuss the applicability of the CRT-based sequences for synchronization signalling in practical systems with large carrier frequency offsets.