Twin tree hierarchy: a regularized approach to construction of signature matrices for overloaded CDMA

We consider two crucial problems to feature a new set of Signature Matrices with Orthogonal Subsets (SMOS) for overloaded Code Division Multiple Access (CDMA). The first one concerns whether the existence of non-ternary version of SMOS is realizable, and if so, what difference lies in the pattern of interference and error performance, as compared to ternary. The second one is about identifying the superior one. To address the first, we propose the 2k-ary SMOS, where the binary alphabets in each of the k constituent (orthogonal) subsets are unique. Despite the similarity in twin tree hierarchy of interference, its non-uniformity brings contrast to the analysis, and outcome including the existence of optimal signatures. In response to the second, based on the behavior of interference, the whole set is split into 2k number of subsets thereby segregating the simulations too. At higher loading, where for larger and smaller subsets the superiority is detected for the 2k-ary and ternary respectively, counterintuitive deviations are noticed once the loading gets reduced. For the maximization in user capacity to be 50%, superiority is featured by the 2k-ary, but beyond, it becomes a conditional entity. To validate, we present few logical anomalies and trade-off involving suitable operational metrics followed by rigorous simulations.