In orthogonal frequency division multiplexing （OFDM） systems, time and frequency synchronization are two critical elements for guaranteeing the orthogonality of OFDM subcarriers. Conventionally, with the employment ...In orthogonal frequency division multiplexing （OFDM） systems, time and frequency synchronization are two critical elements for guaranteeing the orthogonality of OFDM subcarriers. Conventionally, with the employment of pseudo-noise （PN） sequences in preamble design, the preamble information is not fully utilized in both symbol timing offset acquisition and carrier frequency offset estimation. In this article, a new synchronization algorithm is proposed for jointly optimizing the time and frequency synchronization. This algorithm uses polynomial sequences as synchronization preamble instead of PN sequences. Theoretical analysis and simulation results indicate that the proposed algorithm is much more accurate and reliable than other existing methods.展开更多
Recently people proved that every f∈C[0, 1] can be uniformly approximated by polynomial sequences {P_n}, {Q_n} such for any x∈[0,1] and n=1,2,…that Q_n(x)<Q_(n+1)(x)<f(x)<P_(n+1)(x)<P_n(x). For example...Recently people proved that every f∈C[0, 1] can be uniformly approximated by polynomial sequences {P_n}, {Q_n} such for any x∈[0,1] and n=1,2,…that Q_n(x)<Q_(n+1)(x)<f(x)<P_(n+1)(x)<P_n(x). For example, Xie and Zhou showed that one can construct such monotone polynomial sequences which do achieve the best uniform approximation rate for a continuous func- tion. Actually they obtained a result as ‖P_n(x)-Q_n(x)‖≤42E_n (f), (1) which essentially improved a conclusion in Gal and Szabados. The present paper, by optimal procedure, improves this inequality to ‖[P_n(x)-Q_n(x)‖≤(18+ε)E_n(f), where εis any positive real number.展开更多
In this paper, we present a fast and fraction free procedure for computing the inertia of Bezout matrix and we can determine the numbers of different real roots and different pairs of conjugate complex roots of a pol...In this paper, we present a fast and fraction free procedure for computing the inertia of Bezout matrix and we can determine the numbers of different real roots and different pairs of conjugate complex roots of a polynomial equation with integer coefficients quickly based on this result.展开更多
In this paper, a multiplicity-preserving triangular set decomposition algorithm is proposed for a system of two polynomials, which involves only computing the primitive polynomial remainder sequence of two polynomials...In this paper, a multiplicity-preserving triangular set decomposition algorithm is proposed for a system of two polynomials, which involves only computing the primitive polynomial remainder sequence of two polynomials once and certain GCD computations. The algorithm decomposes the unmixed variety defined by two polynomials into square free and disjoint （for non-vertical components, see Definition 4） algebraic cycles represented by triangular sets which may have negative multiplicities. Thus, the authors can count the multiplicities of the non-vertical components. In the bivariate case, the amthors give a complete algorithm to decompose tile system into zeros represented by triangular sets with multiplicities. The authors also analyze the complexity of the algorithm in the bivariate ease. The authors implement the algorithm and show the effectiveness of the method with extensive experiments.展开更多
基金supported by Korean Electronics and Telecommunications Research Institute,the Hi-Tech Research and Development Program of China(2006AA01Z283)the Natural Science Foundation of China(60772113)
文摘In orthogonal frequency division multiplexing （OFDM） systems, time and frequency synchronization are two critical elements for guaranteeing the orthogonality of OFDM subcarriers. Conventionally, with the employment of pseudo-noise （PN） sequences in preamble design, the preamble information is not fully utilized in both symbol timing offset acquisition and carrier frequency offset estimation. In this article, a new synchronization algorithm is proposed for jointly optimizing the time and frequency synchronization. This algorithm uses polynomial sequences as synchronization preamble instead of PN sequences. Theoretical analysis and simulation results indicate that the proposed algorithm is much more accurate and reliable than other existing methods.
文摘Recently people proved that every f∈C[0, 1] can be uniformly approximated by polynomial sequences {P_n}, {Q_n} such for any x∈[0,1] and n=1,2,…that Q_n(x)<Q_(n+1)(x)<f(x)<P_(n+1)(x)<P_n(x). For example, Xie and Zhou showed that one can construct such monotone polynomial sequences which do achieve the best uniform approximation rate for a continuous func- tion. Actually they obtained a result as ‖P_n(x)-Q_n(x)‖≤42E_n (f), (1) which essentially improved a conclusion in Gal and Szabados. The present paper, by optimal procedure, improves this inequality to ‖[P_n(x)-Q_n(x)‖≤(18+ε)E_n(f), where εis any positive real number.
文摘In this paper, we present a fast and fraction free procedure for computing the inertia of Bezout matrix and we can determine the numbers of different real roots and different pairs of conjugate complex roots of a polynomial equation with integer coefficients quickly based on this result.
基金partially supported by NKBRPC under Grant No.2011CB302400the National Natural Science Foundation of China under Grant Nos.11001258,60821002,91118001+1 种基金SRF for ROCS,SEMChina-France cooperation project EXACTA under Grant No.60911130369
文摘In this paper, a multiplicity-preserving triangular set decomposition algorithm is proposed for a system of two polynomials, which involves only computing the primitive polynomial remainder sequence of two polynomials once and certain GCD computations. The algorithm decomposes the unmixed variety defined by two polynomials into square free and disjoint （for non-vertical components, see Definition 4） algebraic cycles represented by triangular sets which may have negative multiplicities. Thus, the authors can count the multiplicities of the non-vertical components. In the bivariate case, the amthors give a complete algorithm to decompose tile system into zeros represented by triangular sets with multiplicities. The authors also analyze the complexity of the algorithm in the bivariate ease. The authors implement the algorithm and show the effectiveness of the method with extensive experiments.
