Constructions of Binary Signature Sets With Optimal Odd Total Squared Correlation and Their Application to Device Activity Detection

Massive machine type communication (mMTC) is one of the core components of 6G communication systems to fulfil the demand of massive connectivity of billions of Internet-of-Things (IoT) devices. Due to its various advantages, grant-free random access schemes are considered as a promising technique to implement mMTC. The key to grant-free random access is active device detection at the base station. In this paper, firstly we introduce the odd total squared correlation (OTSC) of binary signature sets, then derive a corresponding lower bound. Systematic constructions of optimal signature sets based on the known odd periodic complementary sets (OPCS), almost binary sequences, large Kasami subsets and ideal sequences are presented, which are all optimal with respect to the derived OTSC lower bound. Next, it is demonstrated that the optimal OTSC signature sets can be effectively used in massive device activity detection. Using efficient approximate message passing with minimum mean squared error (AMP-MMSE) algorithm, it is shown that the sensing matrices arising from OTSC-optimal signature sets and periodic total squared correlation (PTSC)-optimal signature sets performs better than the popular Gaussian random matrix.