Mostafa Kaveh

Exact symbol error probability of a Cooperative network in a Rayleigh-fading environment

In a distributed spatial diversity wireless system, not all antennas are located at one station as in classical transmit diversity systems, but are dispersed at different, possibly mobile, stations in the network. Transmit diversity is created when the selected stations assist a sender by relaying its information signal to the destination. In this letter, we present an exact average symbol error rate analysis for the distributed spatial diversity wireless system with K amplifying relays in a Rayleigh-fading environment. The average symbol error rate formula allows us to clearly illustrate the advantage that the distributed diversity system has in overcoming the severe penalty in signal-to-noise ratio caused by Rayleigh fading. Using simple bounds on the probability of error, we show that the cooperative network presented in this letter achieves full diversity order.

Coherent signal-subspace processing for the detection and estimation of angles of arrival of multiple wide-band sources

This paper presents a method of constructing a single signal subspace for high-resolution estimation of the angles of arrival of multiple wide-band plane waves. The technique relies on an approximately coherent combination of the spatial signal spaces of the temporally narrow-band decomposition of the received signal vector from an array of sensors. The algorithm is presented, and followed by statistical simulation examples. The performance of the technique is contrasted with other suggested methods and statistical bounds in terms of the determination of the correct number of sources (detection), bias, and variance of estimates of the angles.

Fourth-order partial differential equations for noise removal

A class of fourth-order partial differential equations (PDEs) are proposed to optimize the trade-off between noise removal and edge preservation. The time evolution of these PDEs seeks to minimize a cost functional which is an increasing function of the absolute value of the Laplacian of the image intensity function. Since the Laplacian of an image at a pixel is zero if the image is planar in its neighborhood, these PDEs attempt to remove noise and preserve edges by approximating an observed image with a piecewise planar image. Piecewise planar images look more natural than step images which anisotropic diffusion (second order PDEs) uses to approximate an observed image. So the proposed PDEs are able to avoid the blocky effects widely seen in images processed by anisotropic diffusion, while achieving the degree of noise removal and edge preservation comparable to anisotropic diffusion. Although both approaches seem to be comparable in removing speckles in the observed images, speckles are more visible in images processed by the proposed PDEs, because piecewise planar images are less likely to mask speckles than step images and anisotropic diffusion tends to generate multiple false edges. Speckles can be easily removed by simple algorithms such as the one presented in this paper.

The statistical performance of the MUSIC and the minimum-norm algorithms in resolving plane waves in noise

This paper presents an asymptotic statistical analysis of the null-spectra of two eigen-assisted methods, MUSIC [1] and Minimum-Norm [2], for resolving independent closely spaced plane waves in noise. Particular attention is paid to the average deviation of the null-spectra from zero at the true angles of arrival for the plane waves. These deviations are expressed as functions of signal-to-noise ratios, number of array elements, angular separation of emitters, and the number of snapshots. In the case of MUSIC. an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise. This result is validated by Monte Carlo simulations.

Behavioral analysis of anisotropic diffusion in image processing

In this paper, we analyze the behavior of the anisotropic diffusion model of Perona and Malik (1990). The main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem, so its behavior can be analyzed based on the shape of the corresponding energy surface. We show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem. It is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space. We give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima. The mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts: one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator, and the other that flows normally to the edges and thus acts as an enhancement operator.

A space-time correlation model for multielement antenna systems in mobile fading channels

Analysis and design of multielement antenna systems in mobile fading channels require a model for the space-time cross correlation among the links of the underlying multiple-input multiple-output (MIMO) channel. In this paper, we propose a general space-time cross-correlation function for mobile frequency nonselective Rice fading MIMO channels, in which various parameters of interest such as the angle spreads at the base station and the user, the distance between the base station and the user, mean directions of the signal arrivals, array configurations, and Doppler spread are all taken into account. The new space-time cross-correlation function includes all the relevant parameters of the MIMO fading channel in a clean compact form, suitable for both mathematical analysis and numerical calculations/simulations. It also covers many known correlation models as special cases. We demonstrate the utility of the new space-time correlation model by clarifying the limitations of a widely accepted correlation model for MIMO fading channels. As another application, we quantify the impact of nonisotropic scattering around the user, on the capacity of a MIMO fading channel.

A parametric model for the distribution of the angle of arrival and the associated correlation function and power spectrum at the mobile station

One of the main assumptions in Clarkes classic channel model is isotropic scattering, i.e., uniform distribution for the angle of arrival (AOA) of multipath components at the mobile station. However, in many mobile radio channels we encounter nonisotropic scattering, which strongly affects the correlation function and power spectrum of the complex envelope at the mobile receiver. We propose the use of the versatile von Mises (1918) angular distribution, which includes and/or closely approximates important distributions like uniform, impulse, cardioid, Gaussian, and wrapped Gaussian, for modeling the nonuniform AOAs at the mobile. Based on this distribution, the associated correlation function and. power spectrum of the complex envelope at the mobile receiver are derived. The utility of the new results is demonstrated by comparison with the correlation function estimates of measured data.

Reconstructive tomography and applications to ultrasonics

Computer technology has brought about a revolution in radiology. By combining the computer with X rays it is possible (in principle) to obtain tomographic images of any cross section in the human body. These techniques are now used for medical diagnosis in all the major hospitals of the world. But X rays are not the only kind of radiation for which computer-assisted tomography is feasible. Microwaves, electron beams, ultrasound, fast subatomic particles from accelerators, gamma rays from such sources as positron annihilation, and even magnetic fields can also be used. This paper is mainly concerned with ultrasound. Acoustic energy can often give a view of a cross section not available with X rays or other types of radiation. A mapping of acoustic and elastic discontinuities can be expected to give a basically different pattern than a mapping of X-ray absorption and scattering coefficients. Several methods of ultrasonic tomography are discussed including methods based on geometric optics and a Doppler-oriented approach. A major portion of the paper is concerned with introducing ways to take into account diffraction effects. Because of the wavelength differences, these effects are far more important for ultrasound than for X rays.

A new simple model for land mobile satellite channels: first- and second-order statistics

We propose a new shadowed Rice (1948) model for land mobile satellite channels. In this model, the amplitude of the line-of-sight is characterized by the Nakagami distribution. The major advantage of the model is that it leads to closed-form and mathematically-tractable expressions for the fundamental channel statistics such as the envelope probability density function, moment generating function of the instantaneous power, and the level crossing rate. The model is very convenient for analytical and numerical performance prediction of complicated narrowband and wideband land mobile satellite systems, with different types of uncoded/coded modulations, with or without diversity. Comparison of the first- and the second-order statistics of the proposed model with different sets of published channel data demonstrates the flexibility of the new model in characterizing a variety of channel conditions and propagation mechanisms over satellite links. Interestingly, the proposed model provides a similar fit to the experimental data as the well-accepted Loos (1985) model but with significantly less computational burden.

A regularization approach to joint blur identification and image restoration

The primary difficulty with blind image restoration, or joint blur identification and image restoration, is insufficient information. This calls for proper incorporation of a priori knowledge about the image and the point-spread function (PSF). A well-known space-adaptive regularization method for image restoration is extended to address this problem. This new method effectively utilizes, among others, the piecewise smoothness of both the image and the PSF. It attempts to minimize a cost function consisting of a restoration error measure and two regularization terms (one for the image and the other for the blur) subject to other hard constraints. A scale problem inherent to the cost function is identified, which, if not properly treated, may hinder the minimization/blind restoration process. Alternating minimization is proposed to solve this problem so that algorithmic efficiency as well as simplicity is significantly increased. Two implementations of alternating minimization based on steepest descent and conjugate gradient methods are presented. Good performance is observed with numerically and photographically blurred images, even though no stringent assumptions about the structure of the underlying blur operator is made.