Cross-Complementary Pairs for Optimal Training in Spatial Modulation over Frequency Selective Channels
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The contributions of this paper are twofold: Firstly, we introduce a novel class of sequence pairs, called "cross-complementary pairs (CCPs)". Unlike a Golay complementary pair (GCP) which must be transmitted in two non-interfering channels, a CCP may be transmitted in two non-orthogonal channels and hence proper design should be conducted to minimize the cross-interference of the two constituent sequences. Properties and systematic constructions (from selected GCPs) of perfect CCPs are presented in this paper. Secondly, we show that CCPs can be utilized as a key component in designing training sequences for spatial modulation (SM) systems. In spite of a massive body of literature on SM, little has been understood on broadband SM training design. We prove and validate through simulation that our proposed SM training sequences derived from CCPs lead to optimal channel estimation performance over frequency-selective channels.
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