Reconstruction of the join time-delay Doppler-scale reflectivity density in the wide-band regime. A frame theory based approach

The inverse scattering problem concerning the determination of the joint time-delayDoppler-scale reflectivity density characterizing continuous target environments is addressed by recourse to the generalized frame theory. A reconstruction formula,involving the echoes of a frame of outgoing signals and its corresponding reciprocalframe, is developed. A ‘‘realistic’’ situation with respect to the transmission ofa finite number of signals is further considered. In such a case, our reconstruction formula is shown to yield the orthogonal projection of the reflectivity density onto a subspace generated by the transmitted signals.

Waveform-independent frame-timing acquisition for UWB signals

In this paper, the problem of frame-level symboltiming acquisition for UWB signals is addressed. The main goalis the derivation of a frame-level timing estimator which does notrequire any prior knowledge of neither the transmitted symbolsnor the received template waveform. The independence withrespect to the received waveform is of special interest in UWBcommunication systems, where a fast and accurate estimation ofthe end-to-end channel response is a challenging and computationallydemanding task. The proposed estimator is derived under theunconditional maximum likelihood criterion, and because of thelow power of UWB signals, the low-SNR assumption is adopted. Asa result, an optimal frame-level timing estimator is derived whichoutperforms existing acquisition methods in low-SNR scenarios.

On the inverse windowed Fourier transform

The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion.

The continuous wavelet transform as a maximum entropy solution of the corresponding inverse problem

The continuous wavelet transform is obtained as a maximumentropy solution of the corresponding inverse problem. It is well knownthat although a signal can be reconstructed from its wavelet transform,the expansion is not unique due to the redundancy of continuous wavelets.Hence, the inverse problem has no unique solution. If we want to recognizeone solution as "optimal", then an appropriate decision criterion hasto be adopted. We show here that the continuous wavelet transform is an"optimal" solution in a maximum entropy sense.

On wideband deconvolution using wavelet transform

A discussion on the expression proposed in [1]–[3]for deconvolving the wideband density function is presented. Weprove here that such an expression reduces to be proportionalto the wideband correlation receiver output, or continuous wavelettransform of the received signal with respect to the transmittedone. Moreover, we show that the same result has been implicitlyassumed in [1], when the deconvolution equation is derived. Westress the fact that the analyzed approach is just the orthogonalprojection of the density function onto the image of the wavelettransform with respect to the transmitted signal. Consequently,the approach can be considered a good representation of thedensity function only under the prior knowledge that the densityfunction belongs to such a subspace. The choice of the transmittedsignal is thus crucial to this approach.

Asymptotic equivalence between the unconditional maximum likelihood and the square-law nonlinearity symbol timing estimation

This paper provides a systematic approach to theproblem of nondata aided symbol-timing estimation for linearmodulations. The study is performed under the unconditionalmaximum likelihood framework where the carrier-frequencyerror is included as a nuisance parameter in the mathematicalderivation. The second-order moments of the received signal arefound to be the sufficient statistics for the problem at hand and theyallow the provision of a robust performance in the presence of acarrier-frequency error uncertainty. We particularly focus on theexploitation of the cyclostationary property of linear modulations.This enables us to derive simple and closed-form symbol-timingestimators which are found to be based on the well-known squaretiming recovery method by Oerder and Meyr. Finally, we generalizethe OM method to the case of linear modulations withoffset formats. In this case, the square-law nonlinearity is foundto provide not only the symbol-timing but also the carrier-phaseerror.

ML estimator and hybrid beamformer for multipath and interference mitigation in GNSS receivers

This paper addresses the estimation of the code-phase(pseudorange) and the carrier-phase of the direct signal received from a direct-sequence spread-spectrum satellite transmitter. Thesignal is received by an antenna array in a scenario with interferenceand multipath propagation. These two effects are generallythe limiting error sources in most high-precision positioning applications.A new estimator of the code- and carrier-phases is derivedby using a simplified signal model and the maximum likelihood(ML) principle. The simplified model consists essentially ofgathering all signals, except for the direct one, in a component withunknown spatial correlation. The estimator exploits the knowledgeof the direction-of-arrival of the direct signal and is much simplerthan other estimators derived under more detailed signal models.Moreover, we present an iterative algorithm, that is adequate for apractical implementation and explores an interesting link betweenthe ML estimator and a hybrid beamformer. The mean squarederror and bias of the new estimator are computed for a numberof scenarios and compared with those of other methods. The presentedestimator and the hybrid beamforming outperform the existingtechniques of comparable complexity and attains, in manysituations, the Cramér–Rao lower bound of the problem at hand.

NDA waveform estimation in the low-SNR regime

This correspondence addresses the problem of nondata-aidedwaveform estimation for digital communications. Based on the unconditionalmaximum likelihood criterion, the main contribution of this correspondenceis the derivation of a closed-form solution to the waveform estimationproblem in the low signal-to-noise ratio regime. The proposed estimationmethod is based on the second-order statistics of the received signaland a clear link is established between maximum likelihood estimation andcorrelation matching techniques. Compression with the signal-subspace isalso proposed to improve the robustness against the noise and to mitigatethe impact of abnormals or outliers.

Maximum likelihood estimation of position in GNSS

In this letter, we obtain the Maximum LikelihoodEstimator of position in the framework of Global NavigationSatellite Systems. This theoretical result is the basis of a completelydifferent approach to the positioning problem, in contrastto the conventional two-steps position estimation, consistingof estimating the synchronization parameters of the in-viewsatellites and then performing a position estimation with thatinformation. To the authors’ knowledge, this is a novel approachwhich copes with signal fading and it mitigates multipath andjamming interferences. Besides, the concept of Position–basedSynchronization is introduced, which states that synchronizationparameters can be recovered from a user position estimation. Weprovide computer simulation results showing the robustness ofthe proposed approach in fading multipath channels. The RootMean Square Error performance of the proposed algorithm iscompared to those achieved with state-of-the-art synchronizationtechniques. A Sequential Monte–Carlo based method is used todeal with the multivariate optimization problem resulting fromthe ML solution in an iterative way.

On the q=1/2 non-extensive maximum entropy distribution

A detailed mathematical analysis on the q = 1/2 non-extensive maximum entropydistribution of Tsallis' is undertaken. The analysis is based upon the splitting of such adistribution into two orthogonal components. One of the components corresponds to theminimum norm solution of the problem posed by the fulfillment of the a priori conditionson the given expectation values. The remaining component takes care of the normalizationconstraint and is the projection of a constant onto the Null space of the "expectation-values-transformation"

A non-extensive maximum entropy based regulations method for bad conditioned inverse problems

A regularization method based on the non-extensive maximum entropy principle is devised. Special emphasis is given to the q=1/2 case. We show that, when the residual principle is considered as constraint, the q=1/2 generalized distribution of Tsallis yields a regularized solution for bad-conditioned problems. The so devised regularized distribution is endowed with a component which corresponds to the well known regularized solution of Tikhonov (1977).

Frames: a maximum entropy statistical estimate of the inverse problem

A maximum entropy statistical treatment of an inverse problem concerning frame theory is presented. The problem arises from the fact that a frame is an overcomplete set of vectors that defines a mapping with no unique inverse. Although any vector in the concomitant space can be expressed as a linear combination of frame elements, the coefficients of the expansion are not unique. Frame theory guarantees the existence of a set of coefficients which is “optimal” in a minimum norm sense. We show here that these coefficients are also “optimal” from a maximum entropy viewpoint.

Complete DNA sequence of Kuraishia capsulata illustrates novel genomic features among budding yeasts (Saccharomycotina)

The numerous yeast genome sequences presently available provide a rich source of information for functional as well as evolutionary genomics but unequally cover the large phylogenetic diversity of extant yeasts. We present here the complete sequence of the nuclear genome of the haploid-type strain of Kuraishia capsulata (CBS1993(T)), a nitrate-assimilating Saccharomycetales of uncertain taxonomy, isolated from tunnels of insect larvae underneath coniferous barks and characterized by its copious production of extracellular polysaccharides. The sequence is composed of seven scaffolds, one per chromosome, totaling 11.4 Mb and containing 6,029 protein-coding genes, ~13.5% of which being interrupted by introns. This GC-rich yeast genome (45.7%) appears phylogenetically related with the few other nitrate-assimilating yeasts sequenced so far, Ogataea polymorpha, O. parapolymorpha, and Dekkera bruxellensis, with which it shares a very reduced number of tRNA genes, a novel tRNA sparing strategy, and a common nitrate assimilation cluster, three specific features to this group of yeasts. Centromeres were recognized in GC-poor troughs of each scaffold. The strain bears MAT alpha genes at a single MAT locus and presents a significant degree of conservation with Saccharomyces cerevisiae genes, suggesting that it can perform sexual cycles in nature, although genes involved in meiosis were not all recognized. The complete absence of conservation of synteny between K. capsulata and any other yeast genome described so far, including the three other nitrate-assimilating species, validates the interest of this species for long-range evolutionary genomic studies among Saccharomycotina yeasts.

Comparative transcriptomics of early dipteran development

BACKGROUND: Modern sequencing technologies have massively increased the amount of data available for comparative genomics. Whole-transcriptome shotgun sequencing (RNA-seq) provides a powerful basis for comparative studies. In particular, this approach holds great promise for emerging model species in fields such as evolutionary developmental biology (evo-devo). RESULTS: We have sequenced early embryonic transcriptomes of two non-drosophilid dipteran species: the moth midge Clogmia albipunctata, and the scuttle fly Megaselia abdita. Our analysis includes a third, published, transcriptome for the hoverfly Episyrphus balteatus. These emerging models for comparative developmental studies close an important phylogenetic gap between Drosophila melanogaster and other insect model systems. In this paper, we provide a comparative analysis of early embryonic transcriptomes across species, and use our data for a phylogenomic re-evaluation of dipteran phylogenetic relationships. CONCLUSIONS: We show how comparative transcriptomics can be used to create useful resources for evo-devo, and to investigate phylogenetic relationships. Our results demonstrate that de novo assembly of short (Illumina) reads yields high-quality, high-coverage transcriptomic data sets. We use these data to investigate deep dipteran phylogenetic relationships. Our results, based on a concatenation of 160 orthologous genes, provide support for the traditional view of Clogmia being the sister group of Brachycera (Megaselia, Episyrphus, Drosophila), rather than that of Culicomorpha (which includes mosquitoes and blackflies).