The Kolmogorov mapping theorem in signal processing

Since the publication in 1957 of the work of Andrei Kolmogorov 181 in mapping a function of multiple variables by means functions of a single variable, many mathematicians and engineers try , with different degree of success and not without controversy 1191. to find the direct application of it to multiple extremes problems, rooting of multivariate polynomials, neural networks and pattern recognition. This paper revisits the theorem from the optic of a generalised architecture for signal processing 1281. It is envisaged the high potential of the theorem to handle either linear or non-linear processing problems. A specific implementation following the main guide-lines of the theorem is reported, as well as some preliminary results concerning the design, implementation and performance of non-linear systems. The applications cover non linear transmission channels for communications, instantaneous companders and prediction of chaotic series.Peer ReviewedPostprint (published version

Overview of Constrained PARAFAC Models

In this paper, we present an overview of constrained PARAFAC models where the constraints model linear dependencies among columns of the factor matrices of the tensor decomposition, or alternatively, the pattern of interactions between different modes of the tensor which are captured by the equivalent core tensor. Some tensor prerequisites with a particular emphasis on mode combination using Kronecker products of canonical vectors that makes easier matricization operations, are first introduced. This Kronecker product based approach is also formulated in terms of the index notation, which provides an original and concise formalism for both matricizing tensors and writing tensor models. Then, after a brief reminder of PARAFAC and Tucker models, two families of constrained tensor models, the co-called PARALIND/CONFAC and PARATUCK models, are described in a unified framework, for $N^{th}$ order tensors. New tensor models, called nested Tucker models and block PARALIND/CONFAC models, are also introduced. A link between PARATUCK models and constrained PARAFAC models is then established. Finally, new uniqueness properties of PARATUCK models are deduced from sufficient conditions for essential uniqueness of their associated constrained PARAFAC models

Separation of SSR signals by array processing in multilateration systems

Location and identification of cooperating aircraft in the airport area (and beyond) may be implemented by multilateration (MLAT) systems using the secondary surveillance radar (SSR) mode S signals. Most of these signals, spontaneously emitted from on-board mode S transponders at a fixed carrier frequency, arrive randomly at the receiving station, as well as many mode A/C replies from legacy transponders still in use. Several SSR signals are, then, overlapped in multiple aircraft situations. Therefore, the aim of this work is the separation of overlapped SSR signals, i.e., signals superimposed in time at receiving stations. We improve the MLAT receiving station by replacing the single antenna by an array of m elements and using array signal processing techniques. In the literature, several algorithms address the general source separation problem, but a very few of them are specifically designed for a mixture of overlapping SSR replies. Unfortunately, all of them have either some shortcomings, or an expensive computational cost, or no simple practical implementation. In this paper, we use the time sparsity property of the sources to propose more reliable, simpler, and more effective algorithms based on projection techniques to separate multiple SSR signals. Real recorded signals in a live environment are used to demonstrate the effectiveness of our method

Constant & time-varying hedge ratio for FBMKLCI stock index futures

This paper examines hedging strategy in stock index futures for Kuala Lumpur Composite Index futures of Malaysia. We employed two different econometric methods such as-vector error correction model (VECM) and bivariate generalized autoregressive conditional heteroskedasticity (BGARCH) models to estimate optimal hedge ratio by using daily data of KLCI index and KLCI futures for the period from January 2012 to June 2016 amounting to a total of 1107 observations. We found that VECM model provides better results with respect to estimating hedge ratio for spot month futures and one-month futures, while BGACH shows better for distance futures. While VECM estimates time invariant hedge ratio, the BGARCH shows that hedge ratio changes over time. As such, hedger should rebalance his/her position in futures contract time to time in order to reduce risk exposure

Sensor array processing: localisation of wireless sources

In this thesis, various subspace array processing techniques for wireless source localisation are presented and investigated in the following three aspects. First, in the environment of indoor optical wireless communications, the paths of different sources and/or from different reflectors may impinge on the receiver from closely spaced directions with a high probability. In this case, the ranges of the paths, together with their directions, are important especially for isolating the desired source from the interferers. A blind multi-source localisation approach, which can be used as a channel estimator in the receiver of a communication system, is proposed for direction, range, and path gain estimation. Utilising the above channel parameter estimates, two subspace multibeam beamformers are also presented to achieve complete interference cancellation. Second, in applications such as wireless sensor networks and ubiquitous computing, both the location and orientation of an array are important parameters of interest to be estimated. Hence, array localisation and orientation estimation approaches are proposed for two cases. In the first case, a number of sources of known locations are employed to estimate these parameters of a receiver array. In the second case, a receiver array is utilised to estimate these parameters of multiple sources with each one being a transmitter array. Last, when sources operate in the near field of an array, the spherical wave propagation model needs to be considered. A problem associated with such a scenario is source localisation under the wideband assumption, where the wavefront of a baseband signal varies when traversing through the sensors of the array. Two novel approaches with the employment of the subcovariance of the received signal and the rotation of the array reference point are proposed to localise multiple sources under the wideband assumption. Throughout the thesis, computer simulation studies are presented for evaluating the performance of the proposed approaches.Open Acces