Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
Efficient numerical methods in non-uniform sampling theory
Numerische Mathematik
Wireless Communications: Principles and Practice
Wireless Communications: Principles and Practice
Array Signal Processing: Concepts and Techniques
Array Signal Processing: Concepts and Techniques
DFT/FFT and Convolution Algorithms: Theory and Implementation
DFT/FFT and Convolution Algorithms: Theory and Implementation
Coping with irregular spatio-temporal sampling in sensor networks
ACM SIGCOMM Computer Communication Review
The Semicircle Law, Free Random Variables and Entropy (Mathematical Surveys & Monographs)
The Semicircle Law, Free Random Variables and Entropy (Mathematical Surveys & Monographs)
Channel Capacity Estimation Using Free-Probability Theory
IEEE Transactions on Signal Processing
Performance of Linear Field Reconstruction Techniques With Noise and Uncertain Sensor Locations
IEEE Transactions on Signal Processing - Part I
Reconstruction of Multidimensional Signals From Irregular Noisy Samples
IEEE Transactions on Signal Processing
The impact of frequency-flat fading on the spectral efficiency of CDMA
IEEE Transactions on Information Theory
A random matrix model of communication via antenna arrays
IEEE Transactions on Information Theory
MMSE analysis of certain large isometric random precoded systems
IEEE Transactions on Information Theory
Cognitive radio: brain-empowered wireless communications
IEEE Journal on Selected Areas in Communications
Secured communication over frequency-selective fading channels: a practical vandermonde precoding
EURASIP Journal on Wireless Communications and Networking - Special issue on wireless physical layer security
Estimation of the distribution of randomly deployed wireless sensors
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
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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.