Polynomial rooting based frequency offset estimation for MIMO OFDM systems

Based on the frequency domain training sequences, the polynomial-based carrier frequency offset （CFO） estimation in multiple-input multiple-output （ MIMO ） orthogonal frequency division multiplexing （ OFDM ） systems is extensively investigated. By designing the training sequences to meet certain conditions and exploiting the Hermitian and real symmetric properties of the corresponding matrices, it is found that the roots of the polynomials corresponding to the cost functions are pairwise and that both meger CFO and fractional CFO can be estimated by the direct polynomial rooting approach. By analyzing the polynomials corresponding to the cost functions and their derivatives, it is shown that they have a common polynomial factor and the former can be expressed in a quadratic form of the common polynomial factor. Analytical results further reveal that the derivative polynomial rooting approach is equivalent to the direct one in estimation at the same signal-to-noise ratio（SNR） value and that the latter is superior to the former in complexity. Simulation results agree well with analytical results.

Bounds for Polynomial’s Roots from Fiedler and Sparse Companion Matrices for Submultiplicative Matrix Norms

We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial P(X) over the field C[X]. From a n×n Fiedler companion matrix C, sparse companion matrices and triangular Hessenberg matrices are introduced. Then, we identify a special triangular Hessenberg matrix Lr, supposed to provide a good estimation of the roots. By application of Gershgorin’s theorems to this special matrix in case of submultiplicative matrix norms, some estimations of bounds for roots are made. The obtained bounds have been compared to known ones from the literature precisely Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds. According to the starting formel of Lr, we see that the more we have coefficients closed to zero with a norm less than 1, the more the Sparse method is useful.

Polynomial Root Finding on Frequency Estimation with Sub-Nyquist Temporal Sampling

This paper addresses an algebraic approach for wideband frequency estimation with sub-Nyquist temporal sampling. Firstly, an algorithm based on double polynomial root finding procedure to estimate aliasing frequencies and joint aliasing frequencies-time delay phases in multi-signal situation is presentcd. Since the sum of time delay phases determined from the least squares estimation shows the characteristics of the corre- sponding parameters pairs, then the pairmatching method is conducted by combining it with estimated parameters mentioned above. Although the proposed method is computationally simpler than the conventional schemes, simulation results show that it can approach optimum estimation performance.

Bounds for Polynomial’s Roots from Hessenberg Matrices and Gershgorin’s Disks

The goal of this study is to propose a method of estimation of bounds for roots of polynomials with complex coefficients. A well-known and easy tool to obtain such information is to use the standard Gershgorin’s theorem, however, it doesn’t take into account the structure of the matrix. The modified disks of Gershgorin give the opportunity through some geometrical figures called Ovals of Cassini, to consider the form of the matrix in order to determine appropriated bounds for roots. Furthermore, we have seen that, the Hessenbeg matrices are indicated to estimate good bounds for roots of polynomials as far as we become improved bounds for high values of polynomial’s coefficients. But the bounds are better for small values. The aim of the work was to take advantages of this, after introducing the Dehmer’s bound, to find an appropriated property of the Hessenberg form. To illustrate our results, illustrative examples are given to compare the obtained bounds to those obtained through classical methods like Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds.

A search-free near-field source localization method with exact signal model

Most of the near-field source localization methods are developed with the approximated signal model,because the phases of the received near-field signal are highly non-linear.Nevertheless,the approximated signal model based methods suffer from model mismatch and performance degradation while the exact signal model based estimation methods usually involve parameter searching or multiple decomposition procedures.In this paper,a search-free near-field source localization method is proposed with the exact signal model.Firstly,the approximative estimates of the direction of arrival(DOA)and range are obtained by using the approximated signal model based method through parameter separation and polynomial rooting operations.Then,the approximative estimates are corrected with the exact signal model according to the exact expressions of phase difference in near-field observations.The proposed method avoids spectral searching and parameter pairing and has enhanced estimation performance.Numerical simulations are provided to demonstrate the effectiveness of the proposed method.

Graphs with the Same Color-partition as the Complement of lK_1∪(∪C_(u_i))

In this paper, using the properties of chromatic polynomial, we discuss the color-partition of the complement of lK 1∪(∪C u i),and characterize the graph with the same color-partition as the class graph under u i≠4k+2.

Graphs with the Same Color-partition as the Complement of lK1∪(∪Cui)

In this paper, using the properties of chromatic polynomial, we discuss the color-partition of the complement of lK 1∪(∪C u i),and characterize the graph with the same color-partition as the class graph under u i≠4k+2.

A Parallel Algorithm for Finding Roots of a Complex Polynomial

A distribution theory of the roots of a polynomial and a parallel algorithm for finding roots of a complex polynomial based on that theory are developed in this paper. With high parallelism, the algorithm is an im- provement over the Wilf algorithm.