Asymptotically Optimal Blind Calibration of Uniform Linear Sensor Arrays for Narrowband Gaussian Signals

An asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband Gaussian signals is proposed. Rather than taking the direct Maximum Likelihood (ML) approach for joint estimation of all the unknown model parameters, which leads to a multi-dimensional optimization problem with no closed-form solution, we revisit Paulraj and Kailath's (P-K's) classical approach in exploiting the special (Toeplitz) structure of the observations' covariance. However, we offer a substantial improvement over P-K's ordinary Least Squares (LS) estimates by using asymptotic approximations in order to obtain simple, non-iterative, (quasi-)linear Optimally-Weighted LS (OWLS) estimates of the sensors gains and phases offsets with asymptotically optimal weighting, based only on the empirical covariance matrix of the measurements. Moreover, we prove that our resulting estimates are also asymptotically optimal w.r.t. the raw data, and can therefore be deemed equivalent to the ML Estimates (MLE), which are otherwise obtained by joint ML estimation of all the unknown model parameters. After deriving computationally convenient expressions of the respective Cram\'er-Rao lower bounds, we also show that our estimates offer improved performance when applied to non-Gaussian signals (and/or noise) as quasi-MLE in a similar setting. The optimal performance of our estimates is demonstrated in simulation experiments, with a considerable improvement (reaching an order of magnitude and more) in the resulting mean squared errors w.r.t. P-K's ordinary LS estimates. We also demonstrate the improved accuracy in a multiple-sources directions-of-arrivals estimation task.Comment: in IEEE Transactions on Signal Processin

Time-Domain Based Embeddings for Spoofed Audio Representation

Anti-spoofing is the task of speech authentication. That is, identifying genuine human speech compared to spoofed speech. The main focus of this paper is to suggest new representations for genuine and spoofed speech, based on the probability mass function (PMF) estimation of the audio waveforms' amplitude. We introduce a new feature extraction method for speech audio signals: unlike traditional methods, our method is based on direct processing of time-domain audio samples. The PMF is utilized by designing a feature extractor based on different PMF distances and similarity measures. As an additional step, we used filter-bank preprocessing, which significantly affects the discriminative characteristics of the features and facilitates convenient visualization of possible clustering of spoofing attacks. Furthermore, we use diffusion maps to reveal the underlying manifold on which the data lies. The suggested embeddings allow the use of simple linear separators to achieve decent performance. In addition, we present a convenient way to visualize the data, which helps to assess the efficiency of different spoofing techniques. The experimental results show the potential of using multi-channel PMF based features for the anti-spoofing task, in addition to the benefits of using diffusion maps both as an analysis tool and as an embedding tool

BLIND DECONVOLUTION VIA THE GENERALIZED CHARACTERISTIC FUNCTION

ABSTRACT Blind deconvolution is aimed at recovering an unknown signal that has been distorted in transmission through an unknown channel. In this work we present a new tool for blind equalization, exploiting a statistical independence criterion based on the log-characteristic function (also termed the Second Generalized Characteristic Function (SGCF)). More specifcally, the criterion is based on the empirical difference between the joint SGCF and the sum of marginal SGCFs. evaluated at pre-selected "processing points". We consider the case of a linear. time invariant (over blocks), possibly nonminimum-phase distortive channel. Using a nonlinear (possibly Weighted) Least-Squares (WLS) approach for minimizing the criterion, we propose an iterative batchprocessing-type algorithm for updating a Finite Impulse Response (FIR) "channel inversion"-type equalizer. The algorithm's performance is compared in simulation to the performance attained by Shalvi-Weinstein kurtosis maximization approach, as well as to the optimal performance attainable by an FIR equalizer (assuming a known channel)