Bayesian compressive sensing framework for spectrum reconstruction in Rayleigh fading channels

Compressive sensing (CS) is a novel digital signal processing technique that has found great interest in many applications including communication theory and wireless communications. In wireless communications, CS is particularly suitable for its application in the area of spectrum sensing for cognitive radios, where the complete spectrum under observation, with many spectral holes, can be modeled as a sparse wide-band signal in the frequency domain. Considering the initial works performed to exploit the benefits of Bayesian CS in spectrum sensing, the fading characteristic of wireless communications has not been considered yet to a great extent, although it is an inherent feature for all sorts of wireless communications and it must be considered for the design of any practically viable wireless system. In this paper, we extend the Bayesian CS framework for the recovery of a sparse signal, whose nonzero coefficients follow a Rayleigh distribution. It is then demonstrated via simulations that mean square error significantly improves when appropriate prior distribution is used for the faded signal coefficients and thus, in turns, the spectrum reconstruction improves. Different parameters of the system model, e.g., sparsity level and number of measurements, are then varied to show the consistency of the results for different cases

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

A Vector Channel Based Approach to MIMO Radar Waveform Design for Extended Targets

Radar systems have been used for many years for estimating, detecting, classifying, and imaging objects of interest (targets). Stealthier targets and more cluttered environments have created a need for more sophisticated radar systems to gain more precise information about the radar environment. Because modern radar systems are largely defined in software, adaptive radar systems have emerged that tailor system parameters such as the transmitted waveform and receiver filter to the target and environment in order to address this need. The basic structure of a radar system exhibits many similarities to the structure of a communication system. Recognizing the parallel composition of radar systems and information transmission systems, initial works have begun to explore the application of information theory to radar system design, but a great deal of work still remains to make a full and clear connection between the problems addressed by radar systems and communication systems. Forming a comprehensive definition of this connection between radar systems and information transmission systems and associated problem descriptions could facilitate the cross-discipline transfer of ideas and accelerate the development and improvement of new system design solutions in both fields. In particular, adaptive radar system design is a relatively new field which stands to benefit from the maturity of information theory developed for information transmission if a parallel can be drawn to clearly relate similar radar and communication problems. No known previous work has yet drawn a clear parallel between the general multiple-input multiple-output (MIMO) radar system model considering both the detection and estimation of multiple extended targets and a similar multiuser vector channel information transmission system model. The goal of this dissertation is to develop a novel vector channel framework to describe a MIMO radar system and to study information theoretic adaptive radar waveform design for detection and estimation of multiple radar targets within this framework. Specifically, this dissertation first provides a new compact vector channel model for representing a MIMO radar system which illustrates the parallel composition of radar systems and information transmission systems. Second, using the proposed framework this dissertation contributes a compressed sensing based information theoretic approach to waveform design for the detection of multiple extended targets in noiseless and noisy scenarios. Third, this dissertation defines the multiple extended target estimation problem within the framework and proposes a greedy signal to interference-plus-noise ratio (SINR) maximizing procedure based on a similar approach developed for a collaborative multibase wireless communication system to optimally design wave forms in this scenario

Compressively characterizing high-dimensional entangled states with complementary, random filtering

The resources needed to conventionally characterize a quantum system are overwhelmingly large for high- dimensional systems. This obstacle may be overcome by abandoning traditional cornerstones of quantum measurement, such as general quantum states, strong projective measurement, and assumption-free characterization. Following this reasoning, we demonstrate an efficient technique for characterizing high-dimensional, spatial entanglement with one set of measurements. We recover sharp distributions with local, random filtering of the same ensemble in momentum followed by position---something the uncertainty principle forbids for projective measurements. Exploiting the expectation that entangled signals are highly correlated, we use fewer than 5,000 measurements to characterize a 65, 536-dimensional state. Finally, we use entropic inequalities to witness entanglement without a density matrix. Our method represents the sea change unfolding in quantum measurement where methods influenced by the information theory and signal-processing communities replace unscalable, brute-force techniques---a progression previously followed by classical sensing.Comment: 13 pages, 7 figure