Spatio-temporally modulated impedance surfaces can be good candidates for generation of radiating waves with arbitrary eigenstates by breaking momentum and energy conservations. Here, we present a ...theoretical framework based on the holographic technique and generalized Floquet-wave expansion to analyze spatio-temporally modulated impedance surfaces. The holographic technique estimates the required impedance distribution to achieve the desired momentum. Injecting temporal modulation deviates the eigenvalues and changes the radiation frequency. Using the proposed analytical model, the eigenvalues can be calculated accurately in the presence of space and time modulations. Consequently, it is possible to predict the propagation mechanism of bounded and radiation states. It has been shown that, imposition of temporal modulation causes the Doppler-shift effect and nonreciprocal responses in the hologram. By plotting the antenna dispersion diagram, and observing the asymmetric displacement of dispersion curve due to temporal modulation, the system nonreciprocity can be verified. The beam scanning properties of these structures have also been investigated.
In this paper, an approach for the adaptive detection of a hypothesized signal in unknown multivariate Gaussian interference-plus-noise is considered under conditions where the set of signal space ...eigenvalues of the interference-plus-noise covariance matrix of the training samples and the test vector may be mismatched. The detector is required to have the constant false alarm rate (CFAR) property under these conditions. The proposed approach uses two sets of interference-plus-noise data: First, vectors from a reference set, typically from range cells in the vicinity of the test cell that have the same interference-plus-noise covariance matrix C as the test vector, and second, vectors from a training set that are used to compute the weights for interference suppression in the test vector and the reference vectors. Because the matrices C and Σ are unknown, the average power level of the residual interference in the test cell and reference cells after interference suppression is unknown. The adaptive matched filter statistic at the test cell is normalized by the sample mean of similar statistics for the reference cells to evaluate the detection statistic, which is shown to have the CFAR property. The detection performance of the CFAR detector is analyzed and the effect of mismatches in the eigenvalues of the covariance matrices C and Σ is shown to be characterized by a single random variable ρ, defined as the signal-to-interference-plus-noise ratio loss factor. Sample results are provided for purposes of illustration.
This article is concerned with the following spectral problem: to find a positive function φ∈C1(Ω) and λ∈R such that q(x)φ′(x)+∫ΩJ(x,y)φ(y)dy+a(x)φ(x)+λφ(x)=0forx∈Ω, where Ω⊂R is a non-empty domain ...(open interval), possibly unbounded, J is a positive continuous kernel, and a and q are continuous coefficients. Such a spectral problem naturally arises in the study of nonlocal population dynamics models defined in a space–time varying environment encoding the influence of a climate change through a spatial shift of the coefficient. In such models, working directly in a moving frame that matches the spatial shift leads to consider a problem where the dispersal of the population is modeled by a nonlocal operator with a drift term. Assuming that the drift q is a positive function, for rather general assumptions on J and a, we prove the existence of a principal eigenpair (λp,φp) and derive some of its main properties. In particular, we prove that λp(Ω)=limR→+∞λp(ΩR), where ΩR=Ω∩(−R,R) and λp(ΩR) corresponds to the principal eigenvalue of the truncation operator defined in ΩR. The proofs especially rely on the derivation of a new Harnack type inequality for positive solutions of such problems.
Two difference schemes for Begli-Torvik models are constructed in the article, depending on the order of the fractional derivative. The eigenvalues are calculated for important special cases ...encountered in practical problems. Comparison is made with other values obtained by other methods.
Searching for the explicit solutions of the potential function in an arbitrary resistor network is important but difficult in physics. We investigate the problem of potential formula in an arbitrary ...m × n globe network of resistors, which has not been resolved before (the previous study only calculated the resistance). In this paper, an exact potential formula of an arbitrary m × n globe network is discovered by means of the Recursion-Transform method with current parameters (RT-I). The key process of RT method is to set up matrix equation and to transform two-dimensional matrix equation into one-dimensional matrix equation. In order to facilitate practical application, we deduced a series of interesting results of potential by means of the general formula, and the effective resistance between two nodes in the m × n globe network is derived naturally by making use of potential formula.
We establish exact relations between the winding of "energy" (eigenvalue of Hamiltonian) on the complex plane as momentum traverses the Brillouin zone with periodic boundary condition, and the ...presence of "skin modes" with open boundary conditions in non-Hermitian systems. We show that the nonzero winding with respect to any complex reference energy leads to the presence of skin modes, and vice versa. We also show that both the nonzero winding and the presence of skin modes share the common physical origin that is the nonvanishing current through the system.
In this paper, we propose a general framework on the hybrid analog-digital transceiver design for multi-hop communications. For the inclusive purpose, a transceiver model unifying both linear and ...nonlinear transceivers has been taken into account. Various performance metrics, including the most representative capacity and weighted mean-squared error (MSE), have been investigated in a unified manner. In particular, to meet practical needs for the quality of services (QoS), a general eigenvalue power constraint model is introduced, which contains a sum power constraint and box eigenvalue constraints as special cases. Specifically, by carefully designing the auxiliary analog and digital beamformers, the multi-hop transceiver optimization is decomposed into a series of independent sub-problems, where the analog beamformers for different hops are completely decoupled. Based on that, this framework establishes a majorization-minimization (MM) based analog beamformer design algorithm, which is able to handle the complicated weighted unit-modulus matrix optimizations by finding their semi-closed-form solutions. Furthermore, an efficient waterfilling algorithm is proposed for the digital beamformer designs to deal with the difficulties of optimizations subject to the multiple eigenvalue power constraints. The numerical results are provided to demonstrate the performance advantages of the proposed framework.
Abstract
We establish a new upper bound on the spectral radius for the Schur product of two matrices with nonnegative elements by utilizing the eigenvalue inclusion theorem. The new bound is more ...useful in practical applications because it is simply based on the elements of two matrices. Additionally, a numerical example is taken into account to show that, in some circumstances, the result achieved is superior to some previously reported results.
The role of multiple antennas for secure communication is investigated within the framework of Wyner's wiretap channel. We characterize the secrecy capacity in terms of generalized eigenvalues when ...the sender and eavesdropper have multiple antennas, the intended receiver has a single antenna, and the channel matrices are fixed and known to all the terminals, and show that a beamforming strategy is capacity-achieving. In addition, we study a masked beamforming scheme that radiates power isotropically in all directions and show that it attains near-optimal performance in the high SNR regime. Insights into the scaling behavior of the capacity in the large antenna regime as well as extensions to ergodic fading channels are also provided.
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