Open Issues on the Statistical Spectrum Characterization of Random Vandermonde Matrices

International audienceRecently, analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle have been proposed in the literature. Vandermonde matrices play an important role in signal processing and wireless applications, among which the multiple-antenna channel modeling, precoding or sparse sampling theory. Recent investigations allowed to extend the combinatorial approach usually exploited to characterize the spectral behavior of large random matrices with independent and identically distributed (i.i.d.) entries to Vandermonde structured matrices, under fairly broad assumptions on the entries distributions. While in several cases explicit expressions of the moments of the associated Gram matrix, as well as more advanced models involving the Vandermonde matrix could be provided, several issues are still open in the spectral behavior characterization, with applications either in signal processing (deconvolution, compressed sensing) and/or wireless communications (capacity estimation, topology information retrieving, etc)

MIMO RADAR MODELING THROUGH RANDOM VANDERMONDE MATRICES

International audienceA MIMO radar system is conveniently modeled via random matrices, and its optimal design strongly relies on spectral properties of the matrix exploited to build the model itself. We offer a way to model a High Resolution Radar (HRR) detection in the MIMO case, based on recent results on the asymptotic spectral analysis of random Vandermonde matrices with entries lying on the unit circle. Achievability of compact-form expressions for the design parameters sought for in the multiple-transmitter-multiple-receiver case is investigated, and together with the results of such a starting analysis, some open mathematical questions that arise from the new model formulation are listed and discussed

Forcing scale invariance in multipolarization SAR change detection

This paper considers the problem of coherent (in the sense that both amplitudes and relative phases of the polarimetric returns are used to construct the decision statistic) multi-polarization SAR change detec- tion starting from the availability of image pairs exhibiting possible power mismatches/miscalibrations. The principle of invariance is used to characterize the class of scale-invariant decision rules which are insensitive to power mismatches and ensure the Constant False Alarm Rate (CFAR) property. A maximal invariant statistic is derived together with the induced maximal invariant in the parameter space which significantly compress the data/parameters domain. A Generalized Likelihood Ratio Test (GLRT) is synthesized both for the cases of two- and three-polarimetric channels. Interestingly, for the two-channel case, it is based on the comparison of the condition number of a data-dependent matrix with a suitable threshold. Some additional invariant decision rules are also proposed. The performance of the considered scale-invariant structures is compared to those from two non- invariant counterparts using both simulated and real radar data. The results highlight the robustness of the proposed method and the performance tradeoff involve

1 Capacity Scaling of Wireless Networks with Inhomogeneous Node Density: Lower Bounds

Abstract — We consider static ad hoc wireless networks comprising significant inhomogeneities in the node spatial distribution over the area, and analyze the scaling laws of their transport capacity as the number of nodes increases. In particular, we consider nodes placed according to a shot-noise Cox process, which allows to model the clustering behavior usually recognized in large-scale systems. For this class of networks, we propose novel scheduling and routing schemes which approach previously computed upper bounds to the per-flow throughput as the number of nodes tends to infinity. I. INTRODUCTION AND RELATED WORK In their seminal work, Gupta and Kumar [1] evaluated the capacity of a static ad-hoc wireless network consisting of n nodes randomly placed over a finite bi-dimensional domain and communicating among them (possibly in a multi-ho