Identify more non-golay complementary sequences for OFDM with low PMEPR using multi-dimensional root pairs

Recently, sub-root pairs and sequences are introduced to identify Davis-Jedwab (DJ) codes, non-Davis-Jedwab (non-DJ) Golay complementary sequences (GCS) and non-Golay complementary sequences (non-GCS) for OFDM with low PMEPR. In this paper, we extend sub-root pairs to super-root pairs. A discrete version of super-root pairs called multi-dimensional root pairs are used to build arbitrarily interleaving Boolean functions of long length. The newly identified arbitrarily interleaving Boolean functions can produce more non-DJ GCS and non-GCS with PMEPR at most pre-chosen positive number not always being a power of 2. In this way, we propose an efficient method to identify more codes with low PMEPR for OFDM.