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In many situations, telecommunication engineers are faced with the problem of extracting information from the network. This corresponds in many cases to infer on functionals of spectrum of random matrices with only a limited knowledge on the statistics of the matrix entries. Here, the inference on the spectrum of random matrices is realized by moments method. In its full generality, the problem requires...
In this paper, we derive the explicit series expansion of the eigenvalue distribution of various models, namely the case of non-central Wishart distributions as well as one sided correlated zero mean Wishart distributions. The tools used are borrowed from the free probability framework which have been quite successful for high dimensional statistical inference (when the size of the matrices tends...
We present a novel blind identification and source separation method for linear multi input single output (MISO) convolutive systems driven by PAM sources. The method is based on the distribution estimation of the differences of pairs of outputs. We show that the most likely differences are the ones corresponding to the columns of the mixing matrix (upto a sign). The columns can be arranged in the...
In this paper, a new kind of fuzzy relation equations (FREs for short) A0R* x = b is first introduced, and then the problem of solving solution to the FREs is discussed, where A is an mtimesn matrix, x and b are an n and an m dimension column vectors, respectively. More specifically, its solvability and unique solvability are investigated, the corresponding necessary and sufficient conditions are...
This paper considers the problem of estimating a discrete signal from its convolution with a pulse consisting of a sequence of independent and identically distributed Gaussian random variables. We derive lower bounds on the length of a random pulse needed to stably reconstruct a signal supported on [1, n]. We will show that a general signal can be stably recovered from convolution with a pulse of...
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...
This paper proposes a single-channel audio source decomposition method that integrates perceptual quality criteria into source separation. Unlike the existing methods, the proposed method applies a perceptually weighted non-negative matrix factorization on log-frequency spectrogram of the mixed signal. The weights are adaptively calculated for each critical band based on a perceptual model described...
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