Seyed Alireza Razavi

High-resolution cyclic spectrum reconstruction from sub-Nyquist samples

In this paper, the problem of reconstruction of Spectral Correlation Function (SCF) from sub-Nyquist samples is studied. We will first propose a novel formulation for the problem and then employ two two-dimensional greedy like sparse signal recovery algorithms, namely Compressive Sampling Matching Pursuit (CoSaMP) and Iterative Hard Thresholding (IHT), for the recovery of the sparse SCF. The achievable resolution of the proposed methods is shown to be significantly higher than the existing methods and therefore the methods can be applied to signals with fine frequency components. Comprehensive simulation results shows that the method can efficiently reconstruct the SCF of a signature-embedded OFDM signal, which has applications in cognitive radio systems.

Review: Variable selection in linear regression: Several approaches based on normalized maximum likelihood

The use of the normalized maximum likelihood (NML) for model selection in Gaussian linear regression poses troubles because the normalization coefficient is not finite. The most elegant solution has been proposed by Rissanen and consists in applying a particular constraint for the data space. In this paper, we demonstrate that the methodology can be generalized, and we discuss two particular cases, namely the rhomboidal and the ellipsoidal constraints. The new findings are used to derive four NML-based criteria. For three of them which have been already introduced in the previous literature, we provide a rigorous analysis. We also compare them against five state-of-the-art selection rules by conducting Monte Carlo simulations for families of models commonly used in signal processing. Additionally, for the eight criteria which are tested, we report results on their predictive capabilities for real life data sets.

AR order selection in the case when the model parameters are estimated by forgetting factor least-squares algorithms

During the last decades, the use of information theoretic criteria (ITC) for selecting the order of autoregressive (AR) models has increased constantly. Because the ITC are derived under the strong assumption that the measured signals are stationary, it is not straightforward to employ them in combination with the forgetting factor least-squares algorithms. In the previous literature, the attempts for solving the problem were focused on the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the predictive least squares (PLS). In connection with PLS, an ad hoc criterion called SRM was also introduced. In this paper, we modify the predictive densities criterion (PDC) and the sequentially normalized maximum likelihood (SNML) criterion such that to be compatible with the forgetting factor least-squares algorithms. Additionally, we provide rigorous proofs concerning the asymptotic approximations of four modified ITC, namely PLS, SRM, PDC and SNML. Then, the four criteria are compared by simulations with the modified variants of BIC and AIC.

On the use of Kolmogorov structure function for periodogram smoothing

In a recent series of papers, it was shown how the periodogram can be smoothed by thresholding the estimated cepstral coefficients either with a carefully designed uniformly most powerful unbiased test (UMPUT), or with the Bayesian information criterion (BIC). In this paper, we devise a fully automatic scheme that selects the threshold by using the Kolmogorov structure function (KSF). For the numerical examples taken from the previous literature, the newly proposed method compares favorably with the existing schemes.

Optimally Distinguishable Distributions: a New Approach to Composite Hypothesis Testing With Applications to the Classical Linear Model

The newest approach to composite hypothesis testing proposed by Rissanen relies on the concept of optimally distinguishable distributions (ODD). The method is promising, but so far it has only been applied to a few simple examples. We derive the ODD detector for the classical linear model. In this framework, we provide answers to the following problems that have not been previously investigated in the literature: i) the relationship between ODD and the widely used Generalized Likelihood Ratio Test (GLRT); ii) the connection between ODD and the information theoretic criteria applied in model selection. We point out the strengths and the weaknesses of the ODD method in detecting subspace signals in broadband noise. Effects of the subspace interference are also evaluated.

Composite hypothesis testing by optimally distinguishable distributions

Relying on optimally distinguishable distributions (ODD), it was defined very recently a new framework for the composite hypothesis testing. We resort to the linear model to investigate the performances of the ODD detector and to compare it with the widely used generalized likelihood ratio test (GLRT). As the ODD concept is very new, its application to models with nuisance parameters was not discussed in the previous literature. The present study attempts to fill the gap by proposing a modified ODD criterion to accommodate the practical case of unknown noise variance.

Analysis of an information theoretic criterion for cepstral nulling

Cepstral nulling, one of the newest methods for smoothing the peri-odogram, amounts to turning to zero the cepstrum estimates whose magnitudes are smaller than a threshold. Up to now, the performance of various thresholding schemes was evaluated only empirically. In this paper, we analyze theoretically a slightly modified variant of a thresholding criterion which is based on Kolmogorov structure function (KSF). The motivation of this work is twofold: (i) KSF expression is more complicated than formulas of other criteria; (ii) KSF derivation relies on novel concepts from information theory which are not well-known in the signal processing community. We illustrate the theoretical results by numerical examples.

Application of optimally distinguishable distributions to the detection of subspace signals in Gaussian noise of unknown level

A detection method based on optimally distinguishable distributions (ODD) was introduced recently. However, ODD testing as it was originally formulated has an important limitation because it does not accommodate models with nuisance parameters. This paper demonstrates how the difficulty can be circumvented in the case of subspace signals in Gaussian noise of unknown level. The key point is to define a partition of the parameter space. To this end, we analyze two different methods, and we choose one of them as basis for the new ODD detector. The performance of the detector is compared with that of the GLRT (generalized likelihood ratio test). Additionally, we compute the confidence indexes which are part of the ODD methodology.

A novel method for improving fairness over multiaccess channels

It is known that the orthogonal multiple access (OMA) guarantees for homogeneous networks, where all users have almost the same received power, a higher degree of fairness (in rate) than that provided by successive interference cancellation (SIC). The situation changes in heterogeneous networks, where the received powers are very disparate, and SIC becomes superior to OMA. In this paper, we propose to partition the network into (almost) homogeneous subnetworks such that the users within each subnetwork employ OMA, and SIC is utilized across subnetworks. The newly proposed scheme is equivalent to partition the users into ordered groups. The main contribution is a practical algorithm for finding the ordered partition that maximizes the minimum rate. We also give a geometrical interpretation for the rate-vector yield by our algorithm. Experimental results show that the proposed strategy leads to a good tradeoff between fairness and the asymptotic multiuser efficiency.