This paper proposes relay selection techniques for XOR physical layer network coding with MMSE based non-linear precoding in MIMO bi-directional wireless relaying networks. The proposed selection techniques are derived on the different assumption about characteristics of the MMSE based non-linear precoding in the wireless network. We show that the signal to noise power ratio (SNR) is dependent on the product of all the eigenvalues in the channels from the terminals to relays. This paper shows that the best selection techniques in all the proposed techniques is to select a group of the relays that maximizes the product. Therefore, the selection technique is called “product of all eigenvalues (PAE)” in this paper. The performance of the proposed relay selection techniques is evaluated in a MIMO bi-directional wireless relaying network where two terminals with 2 antennas exchange their information via relays. When the PAE is applied to select a group of the 2 relays out of the 10 relays where an antenna is placed, the PAE attains a gain of more than 13dB at the BER of 10-3.

In the shadow theory, a new description and a physical mean at a low grazing limit of incidence on gratings in the two dimensional scattering problem have been discussed. In this paper, by applying the shadow theory to the three dimensional problem of multilayered dielectric periodic gratings, we formulate the oblique primary excitation and introduce the scattering factors through our analytical method, by use of the matrix eigenvalues. In terms of the scattering factors, the diffraction efficiencies are defined for propagating and evanescent waves with linearly and circularly polarized incident waves. Numerical examples show that when an incident angle becomes low grazing, only specular reflection occurs with the reflection coefficient -1, regardless of the incident polarization. It is newly found that in a circularly polarized incidence case, the same circularly polarized wave as the incident wave is specularly reflected at a low grazing limit.

Let M(y) be a matrix whose entries are polynomial in y, λ(y) and v(y) be a set of eigenvalue and eigenvector of M(y). Then, λ(y) and v(y) are algebraic functions of y, and λ(y) and v(y) have their power series expansionsλ(y) = β0 + β1 y + + βk yk + (βj C),(1) v(y) = γ0 + γ1 y + + γk yk + (γj Cn), (2)provided that y=0 is not a singular point of λ(y) or v(y). Several algorithms are already proposed to compute the above power series expansions using Newton's method (the algorithm in [4]) or the Hensel construction (the algorithm in[5],[12]). The algorithms proposed so far compute high degree coefficients βk and γk, using lower degree coefficients βj and γj (j=0,1,,k-1). Thus with floating point arithmetic, the numerical errors in the coefficients can accumulate as index k increases. This can cause serious deterioration of the numerical accuracy of high degree coefficients βk and γk, and we need to check the accuracy. In this paper, we assume that given matrix M(y) does not have multiple eigenvalues at y=0 (this implies that y=0 is not singular point of λ(y) or v(y)), and presents an algorithm to estimate the accuracy of the computed power series βi,γj in (1) and (2). The estimation process employs the idea in [9] which computes a coefficient of a power series with Cauchy's integral formula and numerical integrations. We present an efficient implementation of the algorithm that utilizes Newton's method. We also present a modification of Newton's method to speed up the procedure, introducing tuning parameter p. Numerical experiments of the paper indicates that we can enhance the performance of the algorithm by 1216%, choosing the optimal tuning parameter p.

An algorithm for the sound projection using multiple sources is presented. The source strength vector is obtained by using a fast estimation approach instead of the conventional eigenvalue decomposition (EVD) method. The computation load is therefore greatly reduced, which makes the algorithm more efficient in practical applications.

We consider the problem of estimating one- and two-dimensional direction of arrivals for arbitrary plane waves in an incoherent/coherent source environment. For the one-dimensional case, we use matrix pencil (MP) method developed by Y. Hua for signal-poles estimation. We then extend this method to estimate the two-dimensional direction of arrivals (2D-DOA), resulting in the "Extended Matrix Pencil" (EMP) method. This method can be applied successfully as much for an incoherent source environment as for a coherent source environment. To study the performance of these methods, in both cases results are compared with the "Total Least Squares-Estimation of Signal Parameters via Rotational Invariance Techniques" (TLS-ESPRIT) and the "Spatial Smoothing-TLS-ESPRIT" (SS-TLS-ESPRIT) methods. The results show that the MP method estimates the DOA more accurately and better than the TLS-ESPRIT and the SS-TLS-ESPRIT, even with few snapshots. Simulation results show that the EMP method, presented in this paper, estimates the 2-DOA better than the other two methods used for comparison.

In the usual optical flow detection, the gradient constraint, which expresses the relationship between the gradient of the image intensity and its motion, is combined with the least-squares criterion. This criterion means assuming that only the time derivative of the image intensity contains noise. In this paper, we assume that all image derivatives contain noise and derive a new optical flow detection technique. Since this method requires the knowledge about the covariance matrix of the noise, we also discuss a method for its estimation. Our experiments show that the proposed method can compute optical flow more accurately than the conventional method.

It is shown that for a class of interval matrices we can estimate the location of eigenvalues in a very simple way. This class is characterized by the property that eigenvalues of any real linear combination of member matrices are all real and thus includes symmetric interval matrices as a subclass. Upper and lower bounds for each eigenvalue of such a class of interval matrices are provided. This enables us to obtain Hurwitz stability conditions and Schur ones for the class of interval matrices and positive definiteness conditions for symmetric interval matrices.