In this paper, we design a low complexity linear MMSE decoder to recover the signal transmitted by M mobile users to a base station equipped with N receiving antennas, arranged as a uniform linear array (ULA). The angles of arrival are supposed to be uniformly distributed. As the dimension increases, it is hard to invert the system and therefore recent results on random matrix theory and polynomial expansion detectors are helpful to approximate the optimum linear MMSE receiver. Simulation results confirm the validity of this approximation.

Different types of convolution operations involving large Vandermonde matrices are considered. The convolutions parallel those of large Gaussian matrices and additive and multiplicative free convolution, and include additive and multiplicative convolution of Vandermonde matrices and deterministic diagonal matrices, and cases where two independent Vandermonde matrices are involved. It is also shown that the convergence of any combination of Vandermonde matrices is almost sure. The convolutions are divided into two types: those which depend on the phase distribution of the Vandermonde matrices, and those which depend only on the spectra of the matrices. A general criterion is presented to find which type applies for any given convolution. A simulation is presented, verifying the results. Implementations of the presented convolutions are provided and discussed. The implementation is based on the technique of Fourier-Motzkin elimination, and is quite general as it can be applied to virtually any combination of Vandermonde matrices. Connections with related matrices, such as Toeplitz and Hankel matrices, are also discussed.

In this paper, we derive the explicit series expansion of the eigenvalue distribution of various models, namely the case of noncentral Wishart distributions, as well as correlated zero mean Wishart distributions. The tools used extend those of the free probability framework, which have been quite successful for high dimensional statistical inference (when the size of the matrices tends to infinity), also known as free deconvolution. This contribution focuses on the finite Gaussian case and proposes algorithmic methods to compute the moments. Cases where asymptotic results fail to apply are also discussed.

The distribution of randomly deployed wireless sensors plays an important role in the quality of the methods used for data acquisition and signal reconstruction. Mathematically speaking, the estimation of the distribution of randomly deployed sensors can be related to computing the spectrum of Vandermonde matrices with non-uniform entries. In this paper, we use the recent free deconvolution framework to recover, in noisy environments, the asymptotic moments of the structured random Vandermonde matrices and relate these moments to the distribution of the randomly deployed sensors. Remarkably, the results are valid in the finite case using only a limited number of sensors and samples.

Many low bit-depth images are compactly expressed in terms of runlength-based representations. This paper discusses methods for processing such images directly in runlength-represented form and how this can improve processing times for image processing operations. The primary focus in the analysis is on image compression operations, but an explanation of the overall scheme for runlength-based processing is also presented. Tradeoffs between processing times and compression ratio for runlength-based image compression algorithms are discussed. Sketches of runlength-based compression algorithms for some widely used image standards are given, and the algorithms are compared with raster-based counterparts. Important design features needed in implementations of runlength-based image processing are discussed. The main application areas of runlength-based image processing are also explained.

Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde matrices play an important role in signal processing and wireless applications such as direction of arrival estimation, precoding, and sparse sampling theory, just to name a few. Within this framework, we extend classical freeness results on random matrices with independent and identically distributed (i.i.d.) entries and show that Vandermonde structured matrices can be treated in the same vein with different tools. We focus on various types of matrices, such as Vandermonde matrices with and without uniform phase distributions, as well as generalized Vandermonde matrices. In each case, we provide explicit expressions of the moments of the associated Gram matrix, as well as more advanced models involving the Vandermonde matrix. Comparisons with classical i.i.d. random matrix theory are provided, and deconvolution results are discussed. We review some applications of the results to the fields of signal processing and wireless communications.

Situations in many fields of research, such as digital communications, nuclear physics and mathematical finance, can be modelled with random matrices. When the matrices get large, free probability theory is an invaluable tool for describing the asymptotic behaviour of many systems. It will be explained how free probability can be used to estimate covariance matrices. Multiplicative free deconvolution is shown to be a method which can aid in expressing limit eigenvalue distributions for sample covariance matrices, and to simplify estimators for eigenvalue distributions of covariance matrices.

This demonstration shows how one can build advanced web applications by embedding user interaction elements inside the graphical application using the RIM framework for image processing. This framework was developed for high-performance image processing applications, in particular web map applications. The framework is described further at the conference poster stand, and in upcoming publications. MobileHCI06 participants can try out the application for themselves at the conference.