We define and characterise selfnegadual generalised quadratic booleanfunctions by establishing a link, both to the multiplicative order of symmetric binary matrices, and also to the Hermitian self-dual -linear codes....
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We define and characterise selfnegadual generalised quadratic booleanfunctions by establishing a link, both to the multiplicative order of symmetric binary matrices, and also to the Hermitian self-dual -linear codes. This facilitates a novel way to classify Hermitian self-dual -linear codes.
generalised boolean functions are useful in the design of programmable logic arrays. In this paper a heuristic algorithm suitable to minimise such functions is presented. The algorithm generates an irredundant cover b...
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generalised boolean functions are useful in the design of programmable logic arrays. In this paper a heuristic algorithm suitable to minimise such functions is presented. The algorithm generates an irredundant cover by using a local approach to select generalised prime implicants. A benefit of such a method is that the preliminary generation of the set of all the generalised prime implicants is not required. Experimental results are presented, showing a favourable comparison with an already established minimisation algorithm as far as computing speed is concerned.
Spatial modulation (SM) is a new paradigm of multiple-input multiple-output (MIMO) systems. Recently, it is observed that SM training sequences derived from corss Z-complementary pairs (CZCPs) lead to optimal channel ...
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Spatial modulation (SM) is a new paradigm of multiple-input multiple-output (MIMO) systems. Recently, it is observed that SM training sequences derived from corss Z-complementary pairs (CZCPs) lead to optimal channel estimation performance over frequency-selective channels. Recent paper by Liu et al. discussed only perfect CZCPs. In this paper, we focus on non-perfect CZCPs. We introduce the term cross Z-complementary ratio and re-categorise the CZCPs, both perfect and non-perfect, based on that. We propose a systematic construction of CZCPs based on generalized booleanfunctions (GBFs). We further extend the lengths of the CZCPs by using the insertion method. The proposed CZCPs are all of new lengths of the form 2(alpha)10(beta)26(gamma) + 2(alpha >= 1), 10(beta) + 2, 26(gamma) + 2 and 10(beta)26(gamma) + 2. Finally we propose optimal binary CZCPs having parameters (12,5) and (24,11) from binary Barker sequences. These CZCPs are also extended to (12N, 5N)- CZCPs and (24N, 11N)- CZCPs, where N is the length of a binary Golay complementary pair (GCP). We also found a new structural property of binary CZCPs and concluded all binary GCPs are also CZCPs. Finally, we give some numerical simulations to confirm that depending on the number of multi-paths, the proposed CZCPs can be used to design SM training matrix which attains the minimum mean square error.
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