Robust non-orthogonal space-time block codes over highly correlated channels: a generalisation

Little has so far been reported on the robustness of non-orthogonal space-time block codes (NO-STBCs) over highly correlated channels (HCC). Some of the existing NO-STBCs are indeed weak in robustness against HCC. With a view to overcoming such a limitation, a generalisation of the existing robust NO-STBCs based on a 'matrix Alamouti (MA)' structure is presented.

A robust non-orthogonal space-time block code for four transmit antennas

Several non-orthogonal space-time block coding (NO-STBC) schemes have recently been proposed to achieve full rate transmission. Some of these schemes, however, suffer from weak robustness: their channel matrices will become ill conditioned in the case of highly correlated channels (HCC). To address this issue, this paper derives a family of robust NO-STBC schemes for four Tx antennas based on the worst case of HCC. These codes turned out to be a superset of Jafarkhani's quasi-orthogonal STBC codes. A computationally affordable linear decoder is also proposed. Although these codes achieve a similar performance to the non-robust schemes under normal channel conditions, they offer a strong robustness against HCC (although possibly yielding a poorer performance). Finally, computer simulations are presented to verify the algorithm design.

Space-time block coding for four transmit antennas over time-selective fading channels: orthogonal or non-orthogonal design?

The paper deals with an issue in space time block coding (STBC) design. It considers whether, over a time-selective channel, orthogonal STBC (O-STBC) or non-orthogonal STBC (NO-STBC) performs better. It is shown that, under time-selectiveness, once vehicle speed has risen above a certain value, NO-STBC always outperforms O-STBC across the whole SNR range. Also, considering that all existing NO-STBC schemes have been investigated under quasi-static channels only, a new simple receiver is derived for the NO-STBC system under time-selective channels.

Non-orthogonal version of the arbitrary polygonal C-grid and a new diamond grid

Quasi-uniform grids of the sphere have become popular recently since they avoid parallel scaling bottle- necks associated with the poles of latitude–longitude grids. However quasi-uniform grids of the sphere are often non- orthogonal. A version of the C-grid for arbitrary non- orthogonal grids is presented which gives some of the mimetic properties of the orthogonal C-grid. Exact energy conservation is sacrificed for improved accuracy and the re- sulting scheme numerically conserves energy and potential enstrophy well. The non-orthogonal nature means that the scheme can be used on a cubed sphere. The advantage of the cubed sphere is that it does not admit the computa- tional modes of the hexagonal or triangular C-grids. On var- ious shallow-water test cases, the non-orthogonal scheme on a cubed sphere has accuracy less than or equal to the orthog- onal scheme on an orthogonal hexagonal icosahedron. A new diamond grid is presented consisting of quasi- uniform quadrilaterals which is more nearly orthogonal than the equal-angle cubed sphere but with otherwise similar properties. It performs better than the cubed sphere in ev- ery way and should be used instead in codes which allow a flexible grid structure.

Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation

An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport generates meshes that keep the same connectivity as the original mesh, making them suitable for r-adaptive simulations, in which the equations of motion can be solved in a moving frame of reference in order to avoid mapping the solution between old and new meshes and to avoid load balancing problems on parallel computers. The semi-implicit solution of the Monge-Ampère type equation involves a new linearisation of the Hessian term, and exponential maps are used to map from old to new meshes on the sphere. The determinant of the Hessian is evaluated as the change in volume between old and new mesh cells, rather than using numerical approximations to the gradients. OT meshes are generated to compare with centroidal Voronoi tesselations on the sphere and are found to have advantages and disadvantages; OT equidistribution is more accurate, the number of iterations to convergence is independent of the mesh size, face skewness is reduced and the connectivity does not change. However anisotropy is higher and the OT meshes are non-orthogonal. It is shown that optimal transport on the sphere leads to meshes that do not tangle. However, tangling can be introduced by numerical errors in calculating the gradient of the mesh potential. Methods for alleviating this problem are explored. Finally, OT meshes are generated using observed precipitation as a monitor function, in order to demonstrate the potential power of the technique.

Orthogonal space-time block codes for free-space IM/DD optical links

Use of orthogonal space-time block codes (STBCs) with multiple transmitters and receivers can improve signal quality. However, in optical intensity modulated signals, output of the transmitter is non-negative and hence standard orthogonal STBC schemes need to be modified. A generalised framework for applying orthogonal STBCs for free-space IM/DD optical links is presented.

Orthogonal space–time block codes for free-space IM/DD optical links

Use of orthogonal space-time block codes (STBCs) with multiple transmitters and receivers can improve signal quality. However, in optical intensity modulated signals, output of the transmitter is non-negative and hence standard orthogonal STBC schemes need to be modified. A generalised framework for applying orthogonal STBCs for free-space IM/DD optical links is presented.

Linear-wavelet models for non-linear identification applied to a pressure plant

A nonlinear regression structure comprising a wavelet network and a linear term is proposed for system identification. The theoretical foundation of the approach is laid by proving that radial wavelets are orthogonal to linear functions. A constructive procedure for building such models is described and the approach is tested with experimental data.

Validation of ACE-FTS satellite data in the upper troposphere/lower stratosphere (UTLS) using non-coincident measurements

CO, O3, and H2O data in the upper troposphere/lower stratosphere (UTLS) measured by the Atmospheric Chemistry Experiment Fourier Transform Spectrometer(ACE-FTS) on Canada’s SCISAT-1 satellite are validated using aircraft and ozonesonde measurements. In the UTLS, validation of chemical trace gas measurements is a challenging task due to small-scale variability in the tracer fields, strong gradients of the tracers across the tropopause, and scarcity of measurements suitable for validation purposes. Validation based on coincidences therefore suffers from geophysical noise. Two alternative methods for the validation of satellite data are introduced, which avoid the usual need for coincident measurements: tracer-tracer correlations, and vertical tracer profiles relative to tropopause height. Both are increasingly being used for model validation as they strongly suppress geophysical variability and thereby provide an “instantaneous climatology”. This allows comparison of measurements between non-coincident data sets which yields information about the precision and a statistically meaningful error-assessment of the ACE-FTS satellite data in the UTLS. By defining a trade-off factor, we show that the measurement errors can be reduced by including more measurements obtained over a wider longitude range into the comparison, despite the increased geophysical variability. Applying the methods then yields the following upper bounds to the relative differences in the mean found between the ACE-FTS and SPURT aircraft measurements in the upper troposphere (UT) and lower stratosphere (LS), respectively: for CO ±9% and ±12%, for H2O ±30% and ±18%, and for O3 ±25% and ±19%. The relative differences for O3 can be narrowed down by using a larger dataset obtained from ozonesondes, yielding a high bias in the ACEFTS measurements of 18% in the UT and relative differences of ±8% for measurements in the LS. When taking into account the smearing effect of the vertically limited spacing between measurements of the ACE-FTS instrument, the relative differences decrease by 5–15% around the tropopause, suggesting a vertical resolution of the ACE-FTS in the UTLS of around 1 km. The ACE-FTS hence offers unprecedented precision and vertical resolution for a satellite instrument, which will allow a new global perspective on UTLS tracer distributions.

Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

Maximum principles for vectorial approximate minimisers on non-convex functionals

We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance compared to results already existing in the literature is that we have dropped the quasiconvexity assumption of the integrand in the gradient term. The lack of weak Lower semicontinuity is compensated by introducing a nonlinear convergence technique, based on the approximation of the projection onto a convex set by reflections and on the invariance of the integrand in the gradient term under the Orthogonal Group. Maximum Principles are implied for the relaxed solution in the case of non-existence of minimizers and for minimizing solutions of the Euler–Lagrange system of PDE.

A Gaussian-mixture ensemble transform filter

We generalize the popular ensemble Kalman filter to an ensemble transform filter, in which the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian-mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions and the three-dimensional Lorenz-63 model). It is demonstrated that the EGMF is capable of tracking systems with non-Gaussian uni- and multimodal ensemble distributions. Copyright © 2011 Royal Meteorological Society

Application of two-dimensional wavelet transform in near-shore X-band radar images

Among existing remote sensing applications, land-based X-band radar is an effective technique to monitor the wave fields, and spatial wave information could be obtained from the radar images. Two-dimensional Fourier Transform (2-D FT) is the common algorithm to derive the spectra of radar images. However, the wave field in the nearshore area is highly non-homogeneous due to wave refraction, shoaling, and other coastal mechanisms. When applied in nearshore radar images, 2-D FT would lead to ambiguity of wave characteristics in wave number domain. In this article, we introduce two-dimensional Wavelet Transform (2-D WT) to capture the non-homogeneity of wave fields from nearshore radar images. The results show that wave number spectra by 2-D WT at six parallel space locations in the given image clearly present the shoaling of nearshore waves. Wave number of the peak wave energy is increasing along the inshore direction, and dominant direction of the spectra changes from South South West (SSW) to West South West (WSW). To verify the results of 2-D WT, wave shoaling in radar images is calculated based on dispersion relation. The theoretical calculation results agree with the results of 2-D WT on the whole. The encouraging performance of 2-D WT indicates its strong capability of revealing the non-homogeneity of wave fields in nearshore X-band radar images.