A theoretical foundation for pre-detection fusion of sensors is needed if the United States Air Force is to ever field a system of distributed and layered sensors that can detect and perform parameter estimation of complex, extended targets in difficult interference environments, without human intervention, in near real-time. This research is relevant to the United States Air Force within its layered sensing and cognitive radar/sensor initiatives. The asymmetric threat of the twenty-first century introduces stressing sensing conditions that may exceed the ability of traditional monostatic sensing systems to perform their required intelligence, surveillance and reconnaissance missions. In particular, there is growing interest within the United States Air Force to move beyond single sensor sensing systems, and instead begin fielding and leveraging distributed sensing systems to overcome the inherent challenges imposed by the modern threat space. This thesis seeks to analyze the impact of integrating target echoes in the angular domain, to determine if better detection and ranking performance is achieved through the use of a distributed sensor network. Bespoke algorithms are introduced for detection and ranking ISR missions leveraging a distributed network of radio-frequency sensors: the first set of bespoke algorithms area based upon a depth-based nonparametric detection algorithm, which is to shown to enhance the recovery of targets under lower signal-to-noise ratios than an equivalent monostatic radar system; the second set of bespoke algorithms are based upon random matrix theoretic and concentration of measure mathematics, and demonstrated to outperform the depth-based nonparametric approach. This latter approach shall be shown to be effective across a broad range of signal-to-noise ratios, both positive and negative.

Spectrum sensing is a fundamental component of cognitive radio (CR). How to promptly sense the presence of primary users (PUs) is a key issue to a CR network. The time requirement is critical in that violating it will cause harmful interference to the PU, leading to a system-wide failure. The motivation of this paper is to provide an effective spectrum sensing method to detect PUs as soon as possible. In the language of streaming-based real-time data processing, short time means small data. In this paper, we propose a cumulative spectrum sensing method dealing with limited sized data. A novel method of covariance matrix estimation is utilized to approximate the true covariance matrix. The theoretical analysis is derived based on McDiarmid's concentration inequalities and random matrix theory to support the claims of detection performance. Comparisons between the proposed method and other traditional approaches, judged by the simulation using a captured digital TV (DTV) signal, show that this proposed method can operate either using smaller data or working under a lower signal-to-noise ratio (SNR) environment.

This letter presents an experimental demonstration of software-defined-radio-based wireless tomography using computer-hosted radio devices called Universal Software Radio Peripheral (USRP). This experimental brief follows our vision and previous theoretical study of wireless tomography that combines wireless communication and RF tomography to provide a novel approach to remote sensing. Automatic data acquisition is performed inside an RF anechoic chamber. Semidefinite relaxation is used for phase retrieval, and the Born iterative method is utilized for imaging the target. Experimental results are presented, validating our vision of wireless tomography.

An ultrawideband (UWB) multiple input/multiple output (MIMO) cognitive radar has been developed and demonstrated for the first time. Field-programmable gate array (FPGA) is used for waveform-level computing, while waveform optimization is accomplished in CPU. Working as a closed loop, convex optimization is applied to jointly design (arbitrary) transmitted waveforms and the receiving filters in response to the varying wireless environment. Multiple targets localization in the presence of interference is demonstrated. Shown in the experiment, performance improvement is obvious in all interference patterns.

This letter presents a novel single-step approach for self-coherent tomography using semidefinite relaxation. Phase retrieval for scattered fields is not required. The general solver can be used to solve the corresponding convex optimization problem and image the target. Both man-made and experimental data is exploited to demonstrate the performance of the proposed approach. The imaging results illustrate the benefit of bringing the state-of-the-art mathematics to inverse scattering or diffraction tomography.

In this paper we introduce a novel non-parametric depth-based method for the target detection problem in noisy environments under nominal signal-to-noise ratios. Specifically, a distributed sensor network comprised of multiple transceivers is considered. Each sensor is able to transmit and receive a single tone; which is passed to a super sensor where the data is formed into a multistatic response matrix via a pre-detection fusion algorithm. An algorithm is introduced for the determination of the presence of a target in the background medium. The detection performance versus signal-to-noise ratio is developed for a given false alarm rate and compared to a typical monostatic sensor. The depth-based method is shown to improve upon the performance of a single sensor by a considerable margin.

This paper proposes potential approaches to detect the weak target in the presence of strong disturbance. The disturbance consists of strong clutter and white Gaussian noise. The target and clutter are assumed to lie in the corresponding subspaces. The algorithms of subspace matching in the linear and kernel subspaces are derived respectively. The leading eigenvector matching that is the subspace with rank one is investigated as well. The simulation is done for two sensor arrays based on the characteristics of the clutter environment. The results from the simulation show the potential and promising uses of the proposed algorithms to detect the weak target.

Clutter has a strong interference on target detection. Different statistical model should be applied to specific situation. In this paper, we propose a function of covariance matrix based algorithm to detect target under clutter environment. The statistical covariance matrices with and without target are usually different, thus we can find the target present or absent. The advantage of proposed algorithm is it works effectively with limited sample data when target signal strength is very weak. The probabilities of detection versus SNR and ROC curves using sinusoidal target on Rayleigh distribution clutter model, log-normal distribution clutter model, and Weibull distribution clutter model show that the algorithm is valid for different clutter models. (6 pages)

Spectrum sensing is a fundamental problem in cognitive radio. We propose a function of covariance matrix based detection algorithm for spectrum sensing in cognitive radio network. Monotonically increasing property of function of matrix involving trace operation is utilized as the cornerstone for this algorithm. The advantage of proposed algorithm is it works under extremely low signal-to-noise ratio, like lower than -30 dB with limited sample data. Theoretical analysis of threshold setting for the algorithm is discussed. A performance comparison between the proposed algorithm and other state-of-the-art methods is provided, by the simulation on captured digital television (DTV) signal.

Spectrum sensing is a cornerstone in cognitive radio. Covariance matrix based method has been widely used in spectrum sensing. As is well-known that the covariance matrix of white noise is proportional to the identity matrix which is sparse. On the other hand, the covariance matrix of signal is usually low-rank. Robust principal component analysis (PCA) has been proposed recently to recover the low-rank matrix which is corrupted by a sparse matrix with arbitrarily large magnitude non-zero entries. In this paper, robust PCA for spectrum sensing is proposed based on the sample covariance matrix. The received signal will be divided into two segments. Robust PCA will be applied to extract the low-rank matrices from the sample covariance matrices of both segments. The primary user's signal is detected if the discrepancy between the recovered low-rank matrices is smaller than a predefined threshold. The simulations are done both on the simulated and captured DTV signal. Also, the simulations that robust PCA is taken as a de-noising process for sample covariance matrix are also implemented in this paper.

Digital Radar Transceivers providing precise digital control over waveform amplitude, frequency and phase is critical for modern Phased Array Radar systems. A Plug-and-Play (PNP) Transceiver was developed to support the Air Force's objective to develop a Hybrid Multiple Input Multiple Output (MIMO) Phased Array Radar (HMPAR) system, where the full array is partitioned into multiple sub-arrays which can be driven by mission specific waveforms. This PNP Radar Transceiver has been integrated with the Lockheed Martin's Portable Search and Target Acquisition Radar (PSTAR) antenna array. Advanced Radar capabilities including transmit-receive digital beam-steering, direct digital L-band receiver and real-time digital signal processing with the integrated system have been successfully demonstrated. This paper discusses the overall PNP Radar Transceiver concept and highlights the successful phased-array test results when integrated with the PSTAR array.

The detection of small targets against a background of clutter and interference has long been a challenge to the designer of radar systems. Whilst much progress has been made, there is still a strong motivation to improve performance even further. Specifically here, the detection of targets that are both weak and extended where the signal-to-noise ratios (SNR) is negative is considered. This work examines a novel diversity based coherent integration technique where the coherence is partial.

This paper propose a function of covariance matrix based spectrum sensing approach for cognitive radio systems. The statistical covariance of signal and noise are usually different, so a binary hypothesis test on covariance matrix is employed to determine the existence of primary user. Collaborative sensing scenario is introduced for the proposed algorithm, in which each sensor only needs limited sample data for calculation and sends mediate result to fusion center. A performance comparison among different rational functions is provided, which shows different functions in this algorithm may have similar or distinct performance. So it is important to choose an appropriate function. The proposed algorithm has a reliable performance in very low signal-to-noise ratio (SNR) condition, and outperforms the Estimator-Correlator (EC) approach.

Spectrum sensing has been put forward to make more efficient use of scarce radio frequency spectrum. The leading eigenvector of the sample covariance matrix has been applied to spectrum sensing under the frameworks of PCA and kernel PCA. In this paper, spectrum sensing with subspace matching is proposed. The subspace is comprised of the eigenvectors corresponding to dominant non-zero eigenvalues of the sample covariance matrix. That is, several eigenvectors are applied to spectrum sensing other than the only use of leading one. The distance between the subspaces is measured by the projection Frobenius norm. The simulations are done based on the simulated and captured DTV signals.

Compressive sensing concepts have potential applications to multiple RADAR problems, which include Moving Target Indication, and RADAR imaging in two and three spatial dimensions. Currently known sufficient conditions for reliable sparse signal reconstruction do not seem to be directly applicable or practical for some traditional RADAR problems. But experiments and mathematical invariance properties of some reconstruction methods indicate that useful products can often be obtained using these methods for circumstances outside the usual conditions.