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Based on Orthogonal Chaotic Vector Shift Keying (OCVSK) system and Multilevel Code-Shifted Differential Chaos Shift Keying (MCS-DCSK) system, a new Multilevel Code-Shifted Differential Chaos Shift Keying (OMCS-DCSK) modulation system is proposed and designed in this paper. New orthogonal chaotic signal sets are generated using Gram-Schmidt algorithm and Walsh code function then these signals are used for bearing information bits to achieve higher data rate and better bandwidth efficiency compared with the conventional DCSK communication system. The bit error rate (BER) analysis of the OMCS-DCSK system over additive white Gaussian noise (AWGN) and multipath Rayleigh fading channel is derived and compared with the simulation results. Also, the spectral and complexity analysis of the system are presented and compared with the conventional DCSK systems. The results show that the proposed system outperforms OCVSK and MCS-DCSK in BER performance and spectral efficiency. [ABSTRACT FROM AUTHOR]

In this paper we consider the variants of Gram-Schmidt such as Classical Gram-Schmidt and Modified Gram-Schmidt algorithms. It is shown that for problems of dimension more than two the round-off error of operation q1Tq2 has more propagation in both of algorithms. To cure this difficulty we will present an algorithm, namely Optimized Modified Gram-Schmidt algorithm. Numerical examples indicate the accuracy of this algorithm. We show that this method can improve the loss of orthogonality of the orthogonalization in some ill-conditioned cases. [ABSTRACT FROM AUTHOR]

The classical Gram-Schmidt algorithm for computing the QR factorization of a matrix X requires at least one pass over the current orthogonalized matrix Q as each column of X is added to the factorization. When Q becomes so large that it must be maintained on a backing store, each pass involves the costly transfer of data from the backing store to main memory. However, if one orthogonalizes the columns of X in blocks of m columns, the number of passes is reduced by a factor of 1/m. Moreover, matrix-vector products are converted into matrix-matrix products, allowing level-3 BLAS cache performance. In this paper we derive such a block algorithm and give some experimental results that suggest it can be quite effective for large scale problems, even when the matrix X is rank degenerate. [ABSTRACT FROM AUTHOR]