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Area of Interest

My general areas of research lie in the areas of signal processing, DSP, digital communications and information theory. In particular these include (but not limited to) the topical areas of adaptive filtering, time-frequency analysis and representations for non stationary signals specifically AM?FM type signals, co-channel signal separation, MAI suppression in multi-user communications, aerial image enhancement in optical lithography

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Prior Research

### 1. Resolution Enhancement for Optical Nanolithography

Current trends in optical lithography require optical resolution in the sub-wavelength regimes to enable printing of smaller feature sizes. Some of the existing approaches toward attaining this goal such are : (a) decreasing the wavelength, (b) manufacturing lenses with larger numerical apertures and (c) tighter process control. These approaches, however, are not without their own problems and their potential for pushing smaller feature sizes have been more or less exhausted. In these sub-wavelength regimes, the band-limitedness of conventional optics attenuates higher frequencies in the mask (reticle) and this results in a loss of resolution. Hence the need for resolution enhancement techniques that will enable sub-wavelength resolution. Imaging Interferometric lithography (IIL) is one such RET that is based on a wavelength division multiplexing approach towards the attainment of the ultimate spatial frequency resolution afforded by optics.

IIL specifically combines off-axis illumination (OAI) with multiple exposures and pupil plane filtering to implement frequency downshifting of higher frequencies in the mask so that they can be transmitted through the optical system without attenuation and then shifted back. For smaller numerical apertures, the DC frequency term may be lost and a reference beam may need to be introduced at the pupil plane but for present optical systems with very large numerical apertures this may not be necessary. In essence, IIL is the optical equivalent of a modulated filterbank that is commonly used in frequency division multiple access (FDMA) communication systems. The frequency parsing scheme. i.e., the division of spatial frequency among the on-axis and off-axis exposures, used in IIL plays a critical role in terms of resolution and an improper choice for the relevant parameters may result in undesirable artifacts in the aerial image. Some of these artifacts in particular will result in circuit failure in the underlying printed circuit or leakage currents. The ratios of exposure dosages or energies between the on-axis exposure and the off-axis exposure or the reference beam determine the aerial image contrast. Prior IIL experiments have demonstrated the resolution enhancement capabilities of IIL in isolated parameter settings. However, a common platform for parameter optimization in IIL that would enable us to study the resolution limits of IIL is presently lacking.

The goal of the research in this MURI program, funded through a ARO sponsored grant and performed in collaboration with CHTM, University of New Mexico, is to develop a common optimization platform and strategies for parameter optimization as it applies to IIL specifically towards: (a) determining optimal frequency parsing strategies, (b) establishing performance or error metrics for optimization, (c) optimization of the exposure energies to obtain optimal aerial image contrast, (d) optimal use of pupil filtering to alleviate abrupt changes in the mask error enhancement figure (MEEF), (e) catastrophic error checking to eliminate undesirable solutions. This project also looks at the application of this optimization platform in the microscopy problem, i.e., the inverse problem of IIL, where our goal is to reconstruct the mask image from aerial ../Images of each exposure obtained via a CCD camera. This optimization platform will enable the detailed study and comparison of IIL with other RET methods and also enable the study of IIL based hybrid approaches.

Graduate students: (a) Eric Wu, (b) Mark Tridhavee.

### 2. Energy Operators and Energy Demodulation

Energy separation and demodulation, energy demodulation for large deviations, energy demodulation in noise, multi-component AM?FM signal separation and demodulation, co-channel and adjacent channel signal separation, co-channel-voice speaker separation, algebraic separation of mixtures of periodic signals, estimation of multiple periodicities in noise, periodic algebraic separation and energy based demodulation (PASED), energy demodulation of CPM signals, component enumeration for multi-component AM?FM signals using generalized energy operators.

Graduate Students : Malay Gupta.

### 3. Cost Effective Solution for Design of DRFM Systems

Existing digital radio frequency memory (DRFM) devices used in radar systems operate at very high carrier frequency and bandwidth specifications. Signal processing at these very high data rates is typically done using analog heterodyning to reduce the processing to a intermediate frequency (IF) and via custom made A/D and D/A devices that operate at very high data rates. These devices are considerably expensive when several of these devices are used in conjunction in a system. The goal of the research in this project, funded via a grant from the Air force research labs (AFRL), Kirtland and the Big Crow program, is to develop DSP hardware techniques that will allow the use of commercial of the shelf components (COTS) to design these systems so that they are cost effective. The project specifically looks at the use of multirate signal processing methods such as analog-digital hybrid fillterbanks and bandwidth compression using multirate frequency transformations to (a) reduce the sampling rate and (b) to compress the bandwidth for reduction of the sampling rate for subsequent processing. The eventual goal is to develop guidelines for the design of A/D and D/A devices for very high data rates using COTS components. The techniques developed here will also be useful in a software receiver based communications application, specifically in wideband CDMA, where we need to transform the received signal from passband to a manageable IF. Design issues considered particularly relevant in radar applications such as range and velocity gating and cost-effective implementation in a FPGA environment are considered.

### 4.Signal Environment Analysis

Modern radar systems and both analog/digital communication systems use a wide variety of modulation techniques to make effective use of power/bandwidth resources and to combat channel impairments such as fading and multipath. The problem of determining the type of modulation used in a system, i.e., modulation classification (MC) is one problem of importance both from a civilian communications perspective in terms of spectral monitoring and smart receiver applications and for several military surveillance applications. Existing methods for solving this problem range from maximum likelihood approaches, neural network related approaches, classification based on higher-order statistics, cyclostationarity based approaches to fuzzy logic based approaches. Each of these approaches has its own advantage and problems. Neural network based approaches are sensitive to the training set, require prior knowledge of input statistics and are unable to adapt to changes. Approaches that employ higher-order cummulants to maximize a contrast function to separate the sources that produce the modulated signals suffer from local minima that do not provide adequate separation between sources. Approaches that are optimal in a specific sense but not tractable from a complexity viewpoint are not desirable.

Machine learning based pattern recognition and data classification has recently been applied to several communication problems such as multiuser detection and power control in CDMA systems. These techniques that include support vector machines (SVM) do not place any restrictions on statistical characteristics of the input data and are based upon minimizing an empirical risk. Recently a SVM based approach has been applied towards classification of modulation types in a radar setting. Specifically, information theoretic criteria such as mutual information or relative entropy can be applied to rank/order the features used for classification according to their importance.

The goal of the research in this AFRL, Kirtland funded project is to first complete a survey of existing approaches towards solving the MC problem. We also will look at the application of machine learning based approaches to the more general problem of signal environment analysis that will determine parameters of the received signal such as the number of components present, fading, multipath, bandwidth and modulation type. This will be accomplished by using a combination of machine learning based methods, cyclic cummulant and cyclic power spectral density analysis, and feature extraction based on information theoretic criteria.

### 5. Airline Wire Quality Monitor

The research goal of this project, sponsored by Management Scientific Inc, was to develop a multisensor approach towards monitoring the quality of wiring aboard an aircraft. The first step of the project involved a complete survey of imaging, chemical, electromagnetic, gas, heat and a host of other sensors that may be applicable to the problem. The second stage of the project involved data collection and integration of the multisensor data in an appropriate format into a PDA that can be connected to a network for data analysis.

### 6. Design of Cost Effective DRFM Systems

Multi-rate frequency transformations, bandwidth compression and noise shaping, reduced sampling rate requirement for digital radio frequency memory devices, A/D & D/A design for very high sampling rates.

Graduate Students : David Boutte (AFRL).

### 7. MAI Reduction in DSSS-CDMA

Adaptive IIR normalized lattice filtering for reduction of MAI in DS?CDMA systems, subspace-MOE based MAI suppression, ICA-based MAI reduction, prior ICA-based MAI suppression, joint MAC and physical layer design for WLAN and structure-less networks, virtual infrastructure (VI) for covering networks with the minimum redundancy and overhead.

Graduate students: (a) Ryan Shoup, (b) Saeid Taheri, (c) Malay Gupta.

### 8. Modulation Classification

Robust recognition and classification of analog and digital modulation via support vector machines and other machine learning algorithms. Multiuser detection using machine learning approaches.

Graduate Students: David Boutte (AFRL).

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Current Research

### 1.Discrete Fractional Fourier Transform

Fractional Fourier Transform (FRFT), discrete rotational Fourier Transform (DRFT), discrete Fractional Fourier Transform (DFRFT), time-frequency analysis of multi-component chirp signals via the DFRFT, subspace methods for multi-component parameter estimation, modified fractional spectrograms based on the DFRFT, a unified framework for time-frequency analysis of non stationary signals, time-frequency multiplexing, multi-component signal separation, other applications of the DFRFT. SAR Vibrometry using the DFRFT and subspace methods

### 2. Wideband FM Demodulation

Adaptive linear predictive frequency tracking, multirate frequency transformations, wideband speech formant demodulation, wideband image demodulation, wideband CPM demodulation for satellite communications.