Saeed Gazor

Multiple antenna spectrum sensing in cognitive radios

In this paper, we consider the problem of spectrum sensing by using multiple antenna in cognitive radios when the noise and the primary user signal are assumed as independent complex zero-mean Gaussian random signals. The optimal multiple antenna spectrum sensing detector needs to know the channel gains, noise variance, and primary user signal variance. In practice some or all of these parameters may be unknown, so we derive the generalized likelihood ratio (GLR) detectors under these circumstances. The proposed GLR detector, in which all the parameters are unknown, is a blind and invariant detector with a low computational complexity. We also analytically compute the missed detection and false alarm probabilities for the proposed GLR detectors. The simulation results provide the available traded-off in using multiple antenna techniques for spectrum sensing and illustrates the robustness of the proposed GLR detectors compared to the traditional energy detector when there is some uncertainty in the given noise variance.

Speech probability distribution

It is demonstrated that the distribution of speech samples is well described by Laplacian distribution (LD). The widely known speech distributions, i.e., LD, Gaussian distribution (GD), generalized GD, and gamma distribution, are tested as four hypotheses, and it is proved that speech samples during voice activity intervals are Laplacian random variables. A decorrelation transformation is then applied to speech samples to approximate their multivariate distribution. To do this, speech is decomposed using an adaptive Karhunen-Loeve transform or a discrete cosine transform. Then, the distributions of speech components in decorrelated domains are investigated. Experimental evaluations prove that the statistics of speech signals are like a multivariate LD. All marginal distributions of speech are accurately described by LD in decorrelated domains. While the energies of speech components are time-varying, their distribution shape remains Laplacian.

Hybrid adaptive fuzzy identification and control of nonlinear systems

We present a combined direct and indirect adaptive control scheme for adjusting an adaptive fuzzy controller, and adaptive fuzzy identification model parameters. First, using adaptive fuzzy building blocks, with a common set of parameters, we design and study an adaptive controller and an adaptive identification model that have been proposed for a general class of uncertain structure nonlinear dynamic systems. We then propose a hybrid adaptive (HA) law for adjusting the parameters. The HA law utilizes two types of errors in the adaptive system, the tracking error and the modeling error. Performance analysis using a Lyapunov synthesis approach proves the superiority of the HA law over the direct adaptive (DA) method in terms of faster and improved tracking and parameter convergence. Furthermore, this is achieved at negligible increased implementation cost or computational complexity. We prove a theorem that shows the properties of this hybrid adaptive fuzzy control system, i.e., bounds for the integral of the squared errors, and the conditions under which these errors converge asymptotically to zero are obtained. Finally, we apply the hybrid adaptive fuzzy controller to control a chaotic system, and the inverted pendulum system.

An adaptive KLT approach for speech enhancement

An adaptive Karhunen-Loeve transform (KLT) tracking-based algorithm is proposed for enhancement of speech degraded by colored additive interference. This algorithm decomposes noisy speech into its components along the axes of a KLT-based vector space of clean speech. It is observed that the noise energy is disparately distributed along each eigenvector. These energies are obtained from noise samples gathered from silence intervals between speech samples. To obtain these silence intervals, we proposed an efficient voice activity detector based on outputs of the principle component eigenfilter; the greatest eigenvalue of speech KLT. Enhancement is performed by modifying each KLT component due to its noise and clean speech energies. The objective is to minimize the produced distortion when residual noise power is limited to a specific level. At the end, the inverse KLT is performed and an estimation of the clean signal is synthesized. Our listening tests indicated that 71% of our subjects preferred the enhanced speech by the above method over former methods of enhancement of speech degraded by computer generated white Gaussian noise. Our method was preferred by 80% of our subjects when we processed real samples of noisy speech gathered from various environments.

Multiple Peer-to-Peer Communications Using a Network of Relays

We consider an ad hoc wireless network consisting of d source-destination pairs communicating, in a pairwise manner, via R relaying nodes. The relay nodes wish to cooperate, through a decentralized beamforming algorithm, in order to establish all the communication links from each source to its respective destination. Our communication strategy consists of two steps. In the first step, all sources transmit their signals simultaneously. As a result, each relay receives a noisy faded mixture of all source signals. In the second step, each relay transmits an amplitude- and phase-adjusted version of its received signal. That is each relay multiply its received signal by a complex coefficient and retransmits the so-obtained signal. Our goal is to obtain these complex coefficients (beamforming weights) through minimization of the total relay transmit power while the signal-to-interference-plus-noise ratio (SINR) at the destinations are guaranteed to be above certain predefined thresholds. Although such a power minimization problem is not convex, we use semidefinite relaxation to turn this problem into a semidefinite programming (SDP) problem. Therefore, we can efficiently solve the SDP problem using interior point methods. Our numerical examples reveal that for high network data rates, our space division multiplexing scheme requires significantly less total relay transmit power compared to other orthogonal multiplexing schemes, such as time-division multiple access schemes.

A soft voice activity detector based on a Laplacian-Gaussian model

A new voice activity detector (VAD) is developed in this paper. The VAD is derived by applying a Bayesian hypothesis test on decorrelated speech samples. The signal is first decorrelated using an orthogonal transformation, e.g., discrete cosine transform (DCT) or the adaptive Karhunen-Loeve transform (KLT). The distributions of clean speech and noise signals are assumed to be Laplacian and Gaussian, respectively, as investigated recently. In addition, a hidden Markov model (HMM) is employed with two states representing silence and speech. The proposed soft VAD estimates the probability of voice being active (VBA), recursively. To this end, first the a priori probability of VBA is estimated/predicted based on feedback information from the previous time instance. Then the predicted probability is combined/updated with the new observed signal to calculate the probability of VBA at the current time instance. The required parameters of both speech and noise signals are estimated, adaptively, by the maximum likelihood (ML) approach. The simulation results show that the proposed soft VAD that uses a Laplacian distribution model for speech signals outperforms the previous VAD that uses a Gaussian model.

Speckle Noise Reduction of Medical Ultrasound Images in Complex Wavelet Domain Using Mixture Priors

Speckle noise is an inherent nature of ultrasound images, which may have negative effect on image interpretation and diagnostic tasks. In this paper, we propose several multiscale nonlinear thresholding methods for ultrasound speckle suppression. The wavelet coefficients of the logarithm of image are modeled as the sum of a noise-free component plus an independent noise. Assuming that the noise-free component has some local mixture distribution (MD), and the noise is either Gaussian or Rayleigh, we derive the minimum mean squared error (MMSE) and the averaged maximum (AMAP) estimators for noise reduction. We use Gaussian and Laplacian MD for each noise-free wavelet coefficient to characterize their heavy-tailed property. Since we estimate the parameters of the MD using the expectation maximization (EM) algorithm and local neighbors, the proposed MD incorporates some information about the intrascale dependency of the wavelet coefficients. To evaluate our spatially adaptive despeckling methods, we use both real medical ultrasound and synthetically introduced speckle images for speckle suppression. The simulation results show that our method outperforms several recently and the state-of-the-art techniques qualitatively and quantitatively.

Wavelet-Domain Medical Image Denoising Using Bivariate Laplacian Mixture Model

In this paper, we proposed novel noise reduction algorithms that can be used to enhance image quality in various medical imaging modalities such as magnetic resonance and multidetector computed tomography. The noisy captured 3-D data are first transformed by discrete complex wavelet transform. Using a nonlinear function, we model the data as the sum of the clean data plus additive Gaussian or Rayleigh noise. We use a mixture of bivariate Laplacian probability density functions for the clean data in the transformed domain. The MAP and minimum mean-squared error (MMSE) estimators allow us to efficiently reduce the noise. The employed prior distribution is mixture and bivariate, and thus accurately characterizes the heavy-tail distribution of clean images and exploits the interscale properties of wavelets coefficients. In addition, we estimate the parameters of the model using local information; as a result, the proposed denoising algorithms are spatially adaptive, i.e., the intrascale dependency of wavelets is also well exploited in the enhancement process. The proposed approach results in significant noise reduction while the introduced distortions are not noticeable as a result of accurate statistical modeling. The obtained shrinkage functions have closed form, are simple in implementation, and efficiently enhances data. Our experiments on CT images show that among our derived shrinkage functions usually BiLapGausMAP produces images with higher peak SNR. However, BiLapGausMMSE is preferred especially for CT images, which have high SNRs. Furthermore, BiLapRayMAP yields better noise reduction performance for low SNR MR datasets such as high-resolution whole heart imaging while BiLapGauMAP results in better performance in MR data with higher intrinsic SNR such as functional cine data.

Speech enhancement employing Laplacian-Gaussian mixture

A new, efficient speech enhancement algorithm (SEA) is developed in this paper. In this low-complexity SEA, a noisy speech signal is first decorrelated and then the clean speech components are estimated from the decorrelated noisy speech samples. The distributions of clean speech and noise signals are assumed to be Laplacian and Gaussian, respectively. The clean speech components are estimated either by maximum likelihood (ML) or minimum-mean-square-error (MMSE) estimators. These estimators require some statistical parameters derived from speech and noise. These parameters are adaptively extracted by the ML approach during the active speech or silence intervals, respectively. In addition, a voice activity detector (VAD) that uses the same statistical model is employed to detect whether the speech is active or not. The simulation results show that our SEA approach performs as well as a recent high efficiency SEA that employs the Wiener filter. The computational complexity of this algorithm is very low compared with existing SEAs with low computational complexity.

Generalized sliding FFT and its application to implementation of block LMS adaptive filters

This paper has two contributions. First, the concept of the generalized sliding fast Fourier transform (GSFFT) as an efficient implementation of the hopping FFT is introduced. Application of the GSFFT is broad and not limited to what has been considered in this paper. The frequency domain block LMS (FBLMS) adaptive filters are then revised, and their implementations for block lengths less than the length of the adaptive filter are studied. The GSFFT and the available pruned FFTs are used to give an efficient implementation of these filters. In the particular case of the block length equal to one, where the FBLMS algorithm reduces to the frequency domain LMS (FLMS) algorithm, it is shown that the latter can be implemented with the order of M complexity, where M is the length of the adaptive filter. >