Search Method for Identifying Permutation Sequence Groups of Maximum Size with Specified Cross-Correlation Level for IC-FSCM Modulation

The paper considers methods for modulating signals with a spread spectrum based on signals with linear frequency modulation CSS (Chirp Spread Spectrum). One of the methods of data coding based on CSS signals is the cyclic frequency shift of the LFM pulse known as Frequency Shift Chirp Modulation (FSCM). The Interleaved Chirp FSCM (IC-FSCM) modulation method uses a set of permutation sequences of the LFM pulse segments to encode additional information bits. It has a higher spectral efficiency compared to the FSCM method. The minimum level of cross-correlation between the signals obtained by using different permutation sequences is essential. We propose a search method for identifying groups of permutation sequences with a specified maximum level of cross-correlation, which involves representing the matrix of cross-correlation between sequences as a graph and searching for complete subgraphs of maximum size within this graph using the Bron-Kerbosch algorithm. As a result of applying the algorithm, groups of sequences have been identified that enable us to increase the number of additional bits in a symbol to 5 without increasing the level of cross-correlation between symbols. Additionally, we have reduced the level of cross-correlation between symbols when the number of additional bits is set to 3 and 4. The characteristics of the found sequences and the distribution of error probability among the main and additional bits of the symbol have been analyzed.