Generating software for MUB complementary sequence constructions

Abstract

This master thesis has been performed at the Department of Informatics, University of Bergen between February and November 2015. The work has been supervised by Professor Matthew G. Parker as a part of the research interest within complementary construction using mutually unbiased bases. This project is an attempt in the line of the study to improve the set size of the complementary sequences while keeping the upper bound of PAPR as low as possible and also maintaining the pairwise distinguishability. To perform this task, seeding the recursive construction with optimal mutually-unbiased bases in dimension 2 and 3 was used in this study. To use the MUB-based sequences in OFDM containing systems, we generated program codes that constructed distinct arrays and sequences for dimension 2 and 3 seeding by MUBs with and without linear offset. The codes were produced in MATLAB environment. The codes for both dimensions have delivered satisfactory results. The results for lower iterations have also matched with the manually calculated values based on theory. Various strategies were used to increase the software speed as well as to decrease the resource demand, but still to run the codes for higher iterations there needs advanced and professional computing solutions such as supercomputers. It has been attempted to generate the codes with maximum possible flexibility so that they can be used for other dimensions with minor adjustments. The codes have also the capability of conversion to other programming languages.