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On the complementary nature of the signature matrices with orthogonal subsets for overloaded CDMA

Very recently, the signature matrices with orthogonal subsets (SMOS) being an efficient construction for uncoded overloaded CDMA has been proposed providing both low complex decoding and favorable error performance for noisy transmission. In this paper, we discuss its complementary feature. While for synchronous transmission the correlation twin tree hierarchy of the matrix serves to offer the errorfree decoding in the absence of noise, another outcome in terms of the complementary feature can also be realized for asynchronous transmission. Accordingly, addition of a delay (of less than a chip period) in transmission of the ternary subsets as compared to the binary significantly reduces the level of interference on specific signatures of the largest (binary) subset. Moreover, for the delay being half chip, a maximum of 50% signatures of the binary subset validates the optimal nature of bit error rate (BER) without affecting the sub-optimal nature of the rest. Also, the interesting features like periodic nature of the optimality and presence of equivalent delay pairs (EDP) are verified through simulations.