Gang Shi

A Relationship Between Time-Reversal Imaging and Maximum-Likelihood Scattering Estimation

Time-reversal methods have attracted increasing interest recently. The so-called computational time-reversal approach creates an image of the illuminated scene by computing the back-propagated field and is useful for detecting and estimating targets in the scene. In Shi and Nehorai [ldquoMaximum Likelihood Estimation of Point Scatterers for Computational Time-Reversal Imaging,rdquo Communications in Information and Systems, vol. 5, no. 2, pp. 227-256, 2005], we estimated point scatterers by maximum-likelihood estimate (MLE) using the Born-approximated physical model, as well as the Foldy-Lax model. In this correspondence, we further find an explicit relationship between energy-based basic time-reversal imaging and the MLE approach: the time-reversal imaging function differs by only a scaling factor from the likelihood imaging function using the estimated scattering potential when a single-scatterer model is employed. Furthermore, this scaling factor is a function of the imaging position only. We show that, as a result, time-reversal imaging has a near-far problem that tends to produce a weaker image for areas further away from the imaging arrays, whereas the MLE-based image is more balanced. Experimental results confirm this conclusion.

Cramér–Rao Bound Analysis on Multiple Scattering in Multistatic Point-Scatterer Estimation

The resolution improvements of time reversal methods through exploiting nonhomogeneous media have attracted much interest recently with broad applications, including underwater acoustics, radar, detection of defects in metals, communications, and destruction of kidney stones. In this paper, we analyze the effect of inhomogeneity generated by multiple scattering among point scatterers under a multistatic sensing setup. We derive the Crameacuter-Rao bounds (CRBs) on parameters of the scatterers and compare the CRBs for multiple scattering using the Foldy-Lax model with the reference case without multiple scattering using the Born approximation. We find that multiple scattering could significantly improve the estimation performance of the system and higher order scattering components actually contain much richer information about the scatterers. For the case where multiple scattering is not possible, e.g., where only a single target scatterer exists in the illuminated scenario, we propose the use of artificial scatterers, which could effectively improve the estimation performance of the target despite a decrease in the degrees of freedom of the estimation problem due to the introduced unknown parameters of the artificial scatterers. Numerical examples demonstrate the advantages of the artificial scatterers

Meta-Regression of Gene-Environment Interaction in Genome-Wide Association Studies

Genome-wide association studies (GWAS) have created heightened interest in understanding the effects of gene-environment interaction on complex human diseases or traits. Applying methods for analyzing such interaction can help uncover novel genes and identify environmental hazards that influence only certain genetically susceptible groups. However, the number of interaction analysis methods is still limited, so there is a need to develop more efficient and powerful methods. In this paper, we propose two novel meta-analysis methods of studying gene-environment interaction, based on meta-regression of estimated genetic effects on the environmental factor. The two methods can perform joint analysis of a single nucleotide polymorphisms (SNP) main and interaction effects, or analyze only the effect of the interaction. They can readily estimate any linear or non-linear interactions by simply modifying the gene-environment regression function. Thus, they are efficient methods to be applied to different scenarios. We use numerical examples to demonstrate the performance of our methods. We also compare them with two other methods commonly used in current GWAS, i.e., meta-analysis of SNP main effects (MAIN) and joint meta-analysis of SNP main and interaction effects (JMA). The results show that our methods are more powerful than MAIN when the interaction effect exists, and are comparable to JMA in the linear or quadratic interaction cases. In the numerical examples, we also investigate how the number of the divided groups and the sample size of the studies affect the performance of our methods.

A Relationship Between Time-Reversal Imaging and Maximum Likelihood Scattering Estimation

Time-reversal methods have attracted increasing interest recently with broad applications. In the so-called physical time-reversal methods, a transducer array first records a signal emitted by sources or reflected by targets, then it transmits the time-reversed and complex conjugated version of the measurements back into the medium. It was shown that the back-propagated wave would refocus around the locations of the sources or scatterers. This is attractive in many applications in which the energy of waves needs to be physically focused at the desired destinations, e.g., in secure communications or biomedical applications. Another way of employing the refocusing property is computational time-reversal imaging, in which the back-propagation process is simulated in a computer instead of implemented in a real medium. The power of the simulated back-propagated wave is used as the imaging metric, and the generated image can be applied to target detection and estimation, etc. In this paper, we derive an explicit relationship between the power-based computational time-reversal imaging, also called basic time-reversal imaging, and maximum likelihood estimate (MLE) of the scattering potential. We show that the metrics of the two imaging methods, though originate from different physical quantities, differ by only a scaling factor, which is a function of imaging position. We conclude that the time-reversal imaging has a nearfar problem producing weaker image for the area that is further away from the imaging arrays, whereas the MLE-based image of the scattering potential is a more balanced thanks to the inherent appropriate scaling

Macrocell multiple-input multiple-output system analysis

We develop a semi-deterministic semi-stochastic channel model for the multiple-input multiple-output (MIMO) system under the macrocell environment with local-to-mobile and local-to-base scatterers. We show that employing closely-spaced antennas (e.g., phased array) at the base station is capable of achieving diversity via the local-to-base scatterers, which avoids impractical large aperture requirement for the spatial diversity at the base station. We evaluate the system performance in terms of ergodic capacity, average pairwise error probability (PEP), and signal-to-noise ratio (SNR); derive closed-form expressions for lower and upper bounds on the capacity and PEP; and show that the capacity, multiplexing and diversity gains are limited by the number of multipaths around the base station. The base-station array affects the lower bound on the capacity and the upper bound on the error probability through the same metric; thus, optimal design of the base station array based on this metric will optimize the two different information theoretic measures simultaneously. The fading correlation matrix also appears in the two bounds in the same form. To improve the performance of the macrocell MIMO system, we propose using artificial scatterers and discuss optimal design issues. Numerical examples demonstrate the accuracy of our analytical results and tightness of performance bounds.

Cramer-Rao Bound Analysis on Multiple Scattering in Multistatic Point Scatterer Estimation

The resolution improvements of time reversal methods through exploiting nonhomogeneous media have attracted much interest recently with broad applications, including underwater acoustics, radar, detection of defects in metals, communications, and destruction of kidney stones. In this paper, we analyze the effect of inhomogeneity generated by multiple scattering among point scatterers under a multistatic sensing setup. We derive the Crameacuter-Rao bounds (CRBs) on parameters of the scatterers and compare the CRBs for multiple scattering using the Foldy-Lax model with the reference case without multiple scattering using the Born approximation. We find that multiple scattering could significantly improve the estimation performance of the system and higher order scattering components actually contain much richer information about the scatterers. For the case where multiple scattering is not possible, e.g., where only a single target scatterer exists in the illuminated scenario, we propose the use of artificial scatterers, which could effectively improve the estimation performance of the target despite a decrease in the degrees of freedom of the estimation problem due to the introduced unknown parameters of the artificial scatterers. Numerical examples demonstrate the advantages of the artificial scatterers

Genome-wide meta-regression of gene-environment interaction

Understanding the effects of gene-environment interaction on complex human diseases or traits in genome-wide association studies (GWAS) can help uncover novel genes and identify environmental hazards that influence only certain genetically susceptible groups. Thus there is a pressing need to develop efficient and powerful interaction analysis methods. In this paper, we propose a novel meta-analysis method of gene-environment interaction, based on meta-regression (MR-M&I). Compared with existing meta-analysis methods, MR-M&I allows for heterogeneity in the environmental factor (E) by dividing the subjects in each study into groups according to the distribution of E. Moreover, it can readily estimate linear or non-linear interactions, and thus it is more generally applicable to different scenarios. We use numerical examples to demonstrate the performance of MR-M&I and compare it with two commonly used methods in current GWAS. The results show that MR-M&I is more powerful than the other methods.

Macrocell multiple-input multiple-output system with local-to-mobile and local-to-base scatterers

We develop a semi-deterministic semi-stochastic channel model for a multiple-input multiple-output (MIMO) system under the macrocell environment with local-to-mobile and local-to-base scatterers, and show that the channel capacity, multiplexing gain and diversity gain are multipath limited in the sense that they are limited by the number of multipaths around the base station. We derive a lower bound on the ergodic capacity and an upper bound on the average pairwise error detection probability. It is shown that the base-station array affects the two different information theoretic measures through the same metric, and the fading correlation matrix also appears in the two bounds with the same form. Numerical examples show the tightness of the two bounds.