Multiplicative Superposition Research Articles

Receiver Design and Performance Analysis of Multiplicative Superposition Signaling Scheme for Heterogeneous-Speed Users

On the two-user multiple-input multiple-output (MIMO) broadcast channel, when one user with low mobility (called the static user) knows the exact channel state information (CSI) whereas the other user with high mobility (called the dynamic user) does not know CSI, a novel multiplicative superposition signaling scheme could obtain additive degree of freedom. Based on this novel signaling scheme, different types of receivers over an two-Heterogeneous-Speed-User MIMO broadcast channel are investigated in this study. At the dynamic user, the non-coherent maximum likelihood detection (NCMLD) is used. At the static user, we propose two hard detection scheme based on NCMLD-ML and NCMLD-Minimum-Mean-Square-Error (MMSE), respectively. We derive the union bound of the symbol error rate for the optimal hard detection scheme and the upper bound of that for the MMSE-based hard detection scheme. To avoid the error-propagation problem in the hard detection schemes, we also propose a low-complexity soft detection scheme based on the conditional expectation and MMSE (CE-MMSE). Simulation results show that the NCMLD-ML scheme outperforms the NCMLD-MMSE scheme and CE-MMSE scheme. Furthermore, CE-MMSE scheme has a better error performance than NCMLD-MMSE in the low signal-to-noise ratio region at the expense of higher complexity which is inconsiderable when compared with NCMLD-ML scheme. The numerical and simulation results verify the correctness of the theoretical analysis.

Interpretation of visible moiré between repetitive periodic-like gratings in the image domain.

An image domain approach to the interpretation of visible moiré phenomena in repetitive grating multiplicative superposition has been proposed. The local frequency method provides the instantaneous period and orientation of generated moiré. These parameters of the moiré have been sorted into real and pseudo patterns by the Fourier expansions analysis. With the combination of these two steps, the concept "equivalent period contribution threshold" has been introduced. It is found that different thresholds bring different integral domains and results for the calculation of average intensities of generated moiré waveforms. This proves that different thresholds would introduce different average intensity distribution (macrostructure effects) in different moiré patterns. With the local intensity variation (microstructure effects), the human eye would confuse different macrostructure effects but only consider them the same. The interpretation is that the macrostructure versus microstructure effects garble discernment of the human eye and result in different visible moiré phenomena. This is significant for visible moiré effects in various repetitive grating (both of cosinusoidal and binary patterns) superpositions in the image domain. It also presents and summarizes the coexistence of real and pseudo moirés in repetitive, periodic-like layer superposition.

A corotational flat triangular element for large strain analysis of thin shells with application to soft biological tissues

A flat triangular element for the nonlinear analysis of thin shells is presented. The formulation relies on (i) a polar decomposition based corotational framework and (ii) a core-element kinematic description adopting the multiplicative superposition of membrane and bending actions. The resulting element is a refined yet simple three-node displacement-based triangle accounting for thickness extensibility and initial shell curvature, and equipped with a fully consistent tangent stiffness. Numerical tests involving shell structures made of rubber-like materials or fibred biological tissues show the effectiveness of the proposed element and its suitability to problems characterized by large displacements, large rotations, large membrane strains and bending. A Matlab toolkit implementing the present formulation is provided as supplementary material.

An image domain approach to the interpretation of the visible moiré phenomenon

An approach to the interpretation of the visible moiré phenomenon in the image domain has been proposed. The analysis of the Fourier series expansion presents an initial criterion for distinguishing the real moiré and pseudo-moiré cases. A geometric calculation of the superposed grating lines is utilized to obtain the parameters for describing the real and pseudo-moiré cases. On the basis of the study, the average intensities of the waveforms of the real moiré and pseudo-moiré cases are calculated in order to provide the interpretation. It indicates that different moiré cases result from the garbled discernment of human eyes, which is introduced by the microstructure versus macrostructure effects. The variations of intensity and average intensity in the microstructure result in the confusion of the average intensities of the real moiré and pseudo-moiré waveforms. The interpretation is significant for the visible real and pseudo-moiré effects, both in the multiplicative superposition and in the additive superposition composed from periodic cosinusoidal gratings and binary gratings in the image domain. The approach also considers the coexistence of the real moiré and pseudo-moiré cases. The rule for their coexistence has been summarized in the image domain.

Product Superposition for MIMO Broadcast Channels

This paper considers the multiantenna broadcast channel without transmit-side channel state information. For this channel, it has been known that when all receivers have channel state information (CSIR), the degrees of freedom (DoFs) cannot be improved beyond what is available via time-division multiple access. The same is true if none of the receivers possess CSIR. This paper shows that an entirely new scenario emerges when receivers have unequal CSIR. In particular, orthogonal transmission is no longer DoF optimal when one receiver has CSIR and the other does not. A multiplicative superposition is proposed for this scenario and shown to attain the optimal DoFs under a wide set of antenna configurations and coherence lengths. Two signaling schemes are constructed based on the multiplicative superposition. In the first method, the messages of the two receivers are carried in the row and column spaces of a matrix, respectively. This method works better than orthogonal transmission while reception at each receiver is still interference-free. The second method uses coherent signaling for the receiver with CSIR, and Grassmannian signaling for the receiver without CSIR. This second method requires interference cancellation at the receiver with CSIR, but achieves higher DoF than the first method.

Exhaled nitric oxide and influencing factors in a random population sample

The aim of the current study was to determine the impact and interaction of important influencing factors on the fraction of exhaled nitric oxide (FeNO). FeNO was measured in a population-based sample of 1250 middle-aged subjects from the KORA F4 cohort (Augsburg, Germany). Analysis of covariance models was performed including the factors age, height, FVC, FEV(1), sex, current smoking status, recent respiratory tract infection, and respiratory allergy. Geometric mean (SD as factor; 95% confidence interval as factor) FeNO was 13.9 (1.9; 1.033) ppb. FeNO significantly depended on age, height, smoking, infection and allergy. Smoking reduced FeNO by 21%, while infection and allergy led to increases by 9 and 11%, respectively. Increases in age by 10 years and in height by 10 cm were associated with increases of FeNO by 15 and 10%, respectively. Non-smokers demonstrated independent multiplicative superposition of factors affecting FeNO while the effect of allergy was virtually eliminated in smokers without infection. We conclude that in middle-aged non-smokers the effects of infection, age and height can be easily taken into account and do not significantly disturb the effect of respiratory tract allergies on FeNO. In current smokers, however, effects were heterogeneous and information on smoking intensity seems to be useful for better adjustment.

Variational approach to moiré pattern synthesis.

Moiré phenomena occur when two or more images are nonlinearly combined to create a new superposition image. Moiré patterns are patterns that do not exist in any of the original images but appear in the superposition image, for example as the result of a multiplicative superposition rule. The topic of moiré pattern synthesis deals with creating images that when superimposed will reveal certain desired moiré patterns. Conditions that ensure that a desired moiré pattern will be present in the superposition of two images are known; however, they do not specify these images uniquely. The freedom in choosing the superimposed images can be exploited to produce various degrees of visibility and ensure desired properties. Performance criteria for the images that measure when one superposition is better than another are introduced. These criteria are based on the visibility of the moire patterns to the human visual system and on the digitization that takes place when the images are presented on discrete displays. We propose to resolve the freedom in moire synthesis by choosing the images that optimize the chosen criteria.

Quasiself‐similar Cantor gratings and their diffraction

We use the impedance method to study the far-field diffraction of a transmission grating characterized by a Cantor density function. This density function is obtained from a multiplicative superposition of periodic functions. Intensity patterns for different configurations are shown when randomization and filtering of some periodic components are introduced. These results relate the geometric–statistical properties of the grating with its scattered fields; this is the randomness to diffraction. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 20: 393–397, 1999.

Quasiself-similar Cantor gratings and their diffraction

We use the impedance method to study the far-field diffraction of a transmission grating characterized by a Cantor density function. This density function is obtained from a multiplicative superposition of periodic functions. Intensity patterns for different configurations are shown when randomization and filtering of some periodic components are introduced. These results relate the geometric–statistical properties of the grating with its scattered fields; this is the randomness to diffraction. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 20: 393–397, 1999.

Diffraction by a Fractal Transmittance Obtained from a Multiplicative Superposition of Periodical Rectangular Functions

The Fraunhofer region of one-dimensional fractal diffraction grating is studied when this grating is defined using a set of scaled periodical (and rectangular) functions. The fractal structure is obtained through a Cantor density function, which is defined from an incremental product of such periodical components. Each of these components can be filtered individually and so, the corresponding intensity pattern can be evaluated. A mathematical foundation for such decomposition is developed using the concept of characteristic (or indicator) function of a set. Graphic results are shown and the partial self-similarity of lateral intensity distribution calculated in any transversal plane to the optical axis for a certain value of magnification. With these results, fractal, periodical and intrinsic periodical domains can be distinguished to characterize the intensity patterns. The self-similarity of intensity distributions and the contrast of that function are calculated for different states of the Cantor transmittance.

Adaptive image estimation based on multiplicative superposition

A nonlinear adaptive filtering approach is applied to the problem of estimating images corrupted by multiplicative noise. With a pointwise digital model of multiplicative noise, the problem of obtaining a minimum mean squared error estimate of a true image from an observed noisy image and the statistical properties of the degrading noise field is posed. The approach presented in this paper is to perform image estimation with locally adaptive estimating operators that display the property of multiplicative superposition. Optimal point and multipoint adaptive estimating operators are formulated. Image processing algorithms are developed based on the calculation of local statistics estimates, Taylor series approximations to optimal formulas, and the normalization of data by local multiplicative sample means. Both adaptive and edge-adaptive implementations are investigated. The image processing results of single-point and two-point algorithms are given; the resulting images are noise-smoothed both visually and in mean squared error. The image processing algorithms are compared with other known methods of multiplicative filtering and estimation such as adaptive homomorphic point filtering.

Generation of moiré by nonlinear transfer characteristics

The intermodulation of signal frequencies, or moiré, is an effect generally encountered in situations in which periodic or quasi-periodic structures are superimposed. Most familiar are the striking low-frequency patterns achieved by the multiplicative superposition of two structures. In other situations, the intermodulation of signal frequencies may be caused by nonlinear distortions of an input signal. This can be a desired feature in measuring applications or a noise source in transmission or display. Effects of nonlinear transfer characteristics on input signals consisting of more than one frequency are shown. The dependence of resulting moiré frequencies on the nonlinearity is evaluated, and common nonlinearities are compared by simulating a moiré topography experiment.