Orthogonal space-time block coding over time-selective fading channels: a PIC detector for the Gi systems

All the orthogonal space-time block coding (O-STBC) schemes are based on the following assumption: the channel remains static over the entire length of the codeword. However, time selective fading channels do exist, and in many cases the conventional O-STBC detectors can suffer from a large error floor in the high signal-to-noise ratio (SNR) cases. This paper addresses such an issue by introducing a parallel interference cancellation (PIC) based detector for the Gi coded systems (i=3 and 4).

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.

Random orthogonal matrix simulation

This paper introduces a method for simulating multivariate samples that have exact means, covariances, skewness and kurtosis. We introduce a new class of rectangular orthogonal matrix which is fundamental to the methodology and we call these matrices L matrices. They may be deterministic, parametric or data specific in nature. The target moments determine the L matrix then infinitely many random samples with the same exact moments may be generated by multiplying the L matrix by arbitrary random orthogonal matrices. This methodology is thus termed “ROM simulation”. Considering certain elementary types of random orthogonal matrices we demonstrate that they generate samples with different characteristics. ROM simulation has applications to many problems that are resolved using standard Monte Carlo methods. But no parametric assumptions are required (unless parametric L matrices are used) so there is no sampling error caused by the discrete approximation of a continuous distribution, which is a major source of error in standard Monte Carlo simulations. For illustration, we apply ROM simulation to determine the value-at-risk of a stock portfolio.

An elastic net orthogonal forward regression algorithm

In this paper we propose an efficient two-level model identification method for a large class of linear-in-the-parameters models from the observational data. A new elastic net orthogonal forward regression (ENOFR) algorithm is employed at the lower level to carry out simultaneous model selection and elastic net parameter estimation. The two regularization parameters in the elastic net are optimized using a particle swarm optimization (PSO) algorithm at the upper level by minimizing the leave one out (LOO) mean square error (LOOMSE). Illustrative examples are included to demonstrate the effectiveness of the new approaches.

A modified PNN algorithm with optimal PD modeling using the orthogonal least squares method

In this paper a modified algorithm is suggested for developing polynomial neural network (PNN) models. Optimal partial description (PD) modeling is introduced at each layer of the PNN expansion, a task accomplished using the orthogonal least squares (OLS) method. Based on the initial PD models determined by the polynomial order and the number of PD inputs, OLS selects the most significant regressor terms reducing the output error variance. The method produces PNN models exhibiting a high level of accuracy and superior generalization capabilities. Additionally, parsimonious models are obtained comprising a considerably smaller number of parameters compared to the ones generated by means of the conventional PNN algorithm. Three benchmark examples are elaborated, including modeling of the gas furnace process as well as the iris and wine classification problems. Extensive simulation results and comparison with other methods in the literature, demonstrate the effectiveness of the suggested modeling approach.

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.

Elastic net orthogonal forward regression

An efficient two-level model identification method aiming at maximising a model׳s generalisation capability is proposed for a large class of linear-in-the-parameters models from the observational data. A new elastic net orthogonal forward regression (ENOFR) algorithm is employed at the lower level to carry out simultaneous model selection and elastic net parameter estimation. The two regularisation parameters in the elastic net are optimised using a particle swarm optimisation (PSO) algorithm at the upper level by minimising the leave one out (LOO) mean square error (LOOMSE). There are two elements of original contributions. Firstly an elastic net cost function is defined and applied based on orthogonal decomposition, which facilitates the automatic model structure selection process with no need of using a predetermined error tolerance to terminate the forward selection process. Secondly it is shown that the LOOMSE based on the resultant ENOFR models can be analytically computed without actually splitting the data set, and the associate computation cost is small due to the ENOFR procedure. Consequently a fully automated procedure is achieved without resort to any other validation data set for iterative model evaluation. Illustrative examples are included to demonstrate the effectiveness of the new approaches.

Nonlinear identification using orthogonal forward regression with nested optimal regularization

An efficient data based-modeling algorithm for nonlinear system identification is introduced for radial basis function (RBF) neural networks with the aim of maximizing generalization capability based on the concept of leave-one-out (LOO) cross validation. Each of the RBF kernels has its own kernel width parameter and the basic idea is to optimize the multiple pairs of regularization parameters and kernel widths, each of which is associated with a kernel, one at a time within the orthogonal forward regression (OFR) procedure. Thus, each OFR step consists of one model term selection based on the LOO mean square error (LOOMSE), followed by the optimization of the associated kernel width and regularization parameter, also based on the LOOMSE. Since like our previous state-of-the-art local regularization assisted orthogonal least squares (LROLS) algorithm, the same LOOMSE is adopted for model selection, our proposed new OFR algorithm is also capable of producing a very sparse RBF model with excellent generalization performance. Unlike our previous LROLS algorithm which requires an additional iterative loop to optimize the regularization parameters as well as an additional procedure to optimize the kernel width, the proposed new OFR algorithm optimizes both the kernel widths and regularization parameters within the single OFR procedure, and consequently the required computational complexity is dramatically reduced. Nonlinear system identification examples are included to demonstrate the effectiveness of this new approach in comparison to the well-known approaches of support vector machine and least absolute shrinkage and selection operator as well as the LROLS algorithm.

A proof of van Aubel's theorem using orthogonal vectors

We show how two linearly independent vectors can be used to construct two orthogonal vectors of equal magnitude in a simple way. The proof that the constructed vectors are orthogonal and of equal magnitude is a good exercise for students studying properties of scalar and vector triple products. We then show how this result can be used to prove van Aubel's theorem that relates the two line segments joining the centres of squares on opposite sides of a plane quadrilateral.

Simple piecewise geodesic interpolation of simple and Jordan curves with applications

We explicitly construct simple, piecewise minimizing geodesic, arbitrarily fine interpolation of simple and Jordan curves on a Riemannian manifold. In particular, a finite sequence of partition points can be specified in advance to be included in our construction. Then we present two applications of our main results: the generalized Green’s theorem and the uniqueness of signature for planar Jordan curves with finite p -variation for 1⩽p<2.