Many methods form manifold learning have been proposed recently to accurately embed some high dimensional sets of points into low dimensional space. Most of these methods make assumptions about the spectral support of the high dimensional space being sampled and the consistency of these assumptions over time. Additionally, most of these methods do not directly incorporate a means of assessing the embedding in terms of probability distributions for estimation and detection purposes. Finally, most of these methods do not take into consideration noise in the estimation of the true underlying space. We propose a new method using sparse coherence-based estimation of distributions of points sampled from a high dimensional space that iteratively refines its notion of the support of the space. This approach will enable a new method of estimation, detection, and identification risk analysis and mitigation in a general class of image analysis problems.

Recently there has been much interest in design of systems to manage signal and noise environments adaptively with resource strategies that are optimized for detection performance. These approaches are particularly important for scenarios where the noise environment can change and therefore affect the amount of resources necessary for detection and estimation. A common way to manage these tradeoffs uses a min-max estimation strategy to handle the worst case signal and noise distribution and set resources and detection thresholds accordingly. In many of these approaches however, the difficulty of setting the number of resources to achieve the min-max bound for the worst case probability are difficult to gauge. We propose an approach that considers resource allocation as a problem in sparse approximation. The idea is to measure the current probability distribution and adapt to stay within the worst case bound while using the minimum number of resources necessary.

Many sensing scenarios involve tradeoff between diverse sets of constraints that involve measuring and parameterizing some high dimensional sensing environment trade-space to give minimal estimation risk. Integrating and simplifying these tradeoffs is a daunting task, particularly in the context where the underlying assumptions of signal and noise distributions can result from complex statistical models and these models can evolve in time. Thus we need a strategy to reduce the complexity of the measurement process, parameterize the tradeoff space, and adapt to dynamic changes as the sensing scenarios evolve. We propose using coherence of the measurement process as a means of characterizing both the resource trade-space and the estimation process. We will use gradients in the coherence resource trade space to find the minimum estimator risk over some local sensing space and show how this process can adapt the process to global changes when they occur.

This chapter includes the following topics: Historical Overview of Maxwell's Equations Review of Maxwell-Heaviside-Hertz Equations Solution of Maxwell's Equations Radiation and Reception Properties of Point Source Antennas Radiation and Reception Properties of Electrically Small Dipole-like Structures Radiation and Reception Properties of Finite-Sized Dipole-like Structures Transient Responses from Different Antenna Shapes Measured Impulse Responses of Some Representative Structures Conclusion

This chapter includes the following topics: Introduction Direct Data Domain Least Squares Procedures Main Beam Constraints for Prevention of Signal Cancellation Minimum Norm Property of the Optimum Weights Conclusion

This chapter includes the following topics: Problem Formulation Transformation Matrix to Compensate for Undesired Electromagnetic Effects Direction of Arrival Estimation Adaptive Processing Using a Single Snapshot from a Nonuniformly Spaced Array Operating in the Presence of Mutual Coupling and Near-Field Scatterers DOA Estimation Using a Phased Array Located on a Conformal Hemispherical Surface Conclusion

Currently there are many DOD applications where warfighters are asked to make critical decisions based on environmental conditions that are highly complex and where there is incomplete knowledge of the local conditions. An example of such a situation is that of the theater commander who must deploy his C2/ISR assets such as communications and sensing platforms without complete knowledge of the local electromagnetic environment and its effect on his ability to maintain good information exchange and reconnaissance data for his forces. This type of situation falls into a broad class of problems where decision theory and complex physical models must interact for optimal performance such as investment analysis, weather prediction, and organizational dynamics. Such problems have been cast in the mathematical framework of "partial observability" where only some components of the environment are known. We thus we need to model the uncertainty of the environment and weigh our actions accordingly. The approach conventionally used for such optimization is a Partially Observable Markov Decision Process (POMPD) where we can model both our situational knowns and unknowns and come up with the best actions to take based on our model of what we know and do not know. We propose to develop a distributed computational framework that manages the complexity of such a process for large system optimization and provide an approach to parallelize and maintain operation for the system as more information and updates to our underlying environmental models change.

Traditional computing uses transistors and binary logic in order to perform computing operations. This approach has proved successful as long as the number of transistors per integrated circuit can be scaled to accommodate increasing speed and heat requirements. Unfortunately, this approach does not allow speeds above the limit where the size of the transistors approaches the limit of the integrated circuit substrates' molecular size. In this condition, electrons cannot reliably be contained within the boundaries separating one transistor from the next and increasingly small circuits become impractical. The current solution to this dilemma is to increase the number of functional units on an integrated circuit and thereby eliminate the need for increasingly small transistors. However whether we increase the number of functional units or the speed, there are inherent limitations in the number of transistors we can put onto one chip. We therefore look to another functional approach to generate the next generation of integrated circuits. We therefore look to using the molecules and elementary particles themselves as a means of computation. In order to accomplish molecular computation we need to modify the model of traditional computation from a transistor based binary method to analog based arbitrary basis model. This approach is not unknown since optical computation among other has used analog processing for highly parallel computation. The issue with molecular and quantum computing methods has traditionally been that understanding the state the computing function itself is often subject to high degree uncertainty. This uncertainty is not unexpected since the number of possible states that can exist when electromagnetic energy interrogates a collection of molecules, atoms, or electrons is quite large. In order to develop a method of representing these states we use a partially observable Markov decision process. We will then develop a finite state machine approach to computation based on a model for our molecular or quantum system.

Classical detection theory for sensing relies on fixed target illumination and independent identically distributed noise for target and clutter characterization. Unfortunately in many cases such as sensing and communications in urban or atmospheric scenarios, we encounter much more complex clutter and target conditions due to scattering from multiple sources. As a result we must envision a new sensing scheme to combat noise not handled by classical sensing methods. We will therefore develop framework whereby we can use the waveform to manage the physical scattering process such that our return statistics conform to the classical detection assumption such as independent identically distributed data. We will first describe how to use a well known set of waveforms in the context of a given aperture and how these waveforms propagate when we consider the wideband multi-frequency nature of the waveform. To accomplish this we will characterize different apertures in the context of varying amounts of instantaneous bandwidth and center frequency using coherence length and coherence time of the waveform in the aperture. We will then characterize the scattering process in the same context and show how the waveform must be designed using coherence principles of the scattering environment. Finally will show how our waveform process improves our discrimination performance and conclude with a detection example of this process.

Conventional radar signal processing techniques approximate multipath as a linear process. Unfortunately, such an approach results in poor detection performance and because the model for the interference does not accurately represent the physical scattering process. We instead propose a method that uses the flexibility of waveform design for a given aperture to linearize the physical scattering phenomenon. This allows us to successfully detect targets using a Wiener matched filter approach in high multipath conditions.

RF image formation is a computationally expensive process due to the excessive amount of instantaneous RF bandwidth required to form imagery for high resolution. As a result the size weight and power of traditional devices designed to compute imagery in RF apertures is quite high. We therefore propose a method that allows us to compute RF imagery using an analog fiber diffraction grating in conjunction with electro-optical modulators, traditional analog RF phase shifters and a spatial light modulator.

Conventional RF image formation relies on a fixed waveform set that is based largely on obtaining maximum resolution for a given amount of bandwidth present in a waveform. However, the correlation process for a given waveform set varies widely depending on the cross correlation properties of the waveform and the geometry of the aperture interrogating the object to be imaged. We propose a method that maximizes quality of the imagery being reconstructed based by first using an orthogonal basis to minimize the unwanted correlation response for the waveform. We then shape the frequency and temporal correlation response of the waveform for a given target using a rate distortion criteria and demonstrate the performance of the method.

This chapter includes the following topics: Introduction Received Signal Model Without Spatial Diversity Use of the Matrix Pencil Method for Identification of Multipath Components Simulation Results Conclusion