Novel AMUB Sequences for Massive Connection IIoT Systems

In this study, we design novel approximately mutually unbiased bases (AMUBs) sequences with arbitrary lengths and large family sizes for massive connection systems. Sequences with low correlations are highly demanded for many wireless communications systems, including Industrial Internet of Things (IIoT) systems for various applications. While many sets of sequences have been designed in the past decades, the requirement of large family size, i.e., the number of available sequences for massive connection systems has not yet been addressed. It is well known that mutually unbiased-based (MUB) sequences process desired correlation properties with large family sizes. However, the family size based on the current construction methods is limited by the length of the MUB sequences. In real applications, the longer length may lead to higher overhead and affect the overall transmission rate. This drawback makes MUB sequences have limited applications for industrial massive connection systems. In this article, we modified the original sequences generator of MUB from a quadratic polynomial to a cubic polynomial to further increase the family size. To generate AMUB sequences with arbitrary lengths, we then proposed a construction method based on the exponential sums over finite fields, and optimized the continuous peak-to-average power ratio (PAPR) of the proposed AMUB sequences for real applications. Given the dimension of MUB M, the proposed method can increase M times the number of available sequences. Meanwhile, the length restrictions in MUB sequence construction are removed. Theoretical cross-correlation (CC) bounds are provided and show low correlations of the proposed sequences. The low CC, PAPR, and increased family size of the proposed sequences are then verified by numerical results.