EM Algorithm for Multiple Wideband Source Localization

A computationally efficient algorithm using the expectation-maximization (EM) algorithm for multiple wideband source localization in the near field of a sensor array/area is addressed in this thesis. Our idea is to decompose the observed sensor data, which is a superimposition of multiple sources, into the individual components in the frequency domain and then estimate the corresponding location parameters associated with each component separately. Instead of the conventional alternating projection (AP) method, we propose to adopt the EM algorithm in this work; our new method involves two steps, namely Expectation (E-step) and Maximization (M-step). In the E-step, the individual incident source waveforms are estimated. Then, in the M-step, the maximum likelihood estimates of the source location parameters are obtained. These two steps are executed iteratively and alternatively until the pre-defined convergence is reached. The computational complexity comparison between our proposed EM algorithm and the existing AP scheme is investigated. It is shown through Monte Carlo simulations that the computational complexity of the proposed EM algorithm is significantly lower than that of the existing AP algorithm

Unified Capacity Limit of Non-coherent Wideband Fading Channels

In non-coherent wideband fading channels where energy rather than spectrum is the limiting resource, peaky and non-peaky signaling schemes have long been considered species apart, as the first approaches asymptotically the capacity of a wideband AWGN channel with the same average SNR, whereas the second reaches a peak rate at some finite critical bandwidth and then falls to zero as bandwidth grows to infinity. In this paper it is shown that this distinction is in fact an artifact of the limited attention paid in the past to the product between the bandwidth and the fraction of time it is in use. This fundamental quantity, called bandwidth occupancy, measures average bandwidth usage over time. For all signaling schemes with the same bandwidth occupancy, achievable rates approach to the wideband AWGN capacity within the same gap as the bandwidth occupancy approaches its critical value, and decrease to zero as the occupancy goes to infinity. This unified analysis produces quantitative closed-form expressions for the ideal bandwidth occupancy, recovers the existing capacity results for (non-)peaky signaling schemes, and unveils a trade-off between the accuracy of approximating capacity with a generalized Taylor polynomial and the accuracy with which the optimal bandwidth occupancy can be bounded.Comment: Accepted for publication in IEEE Transactions on Wireless Communications. Copyright may be transferred without notic

Off-the-Grid Line Spectrum Denoising and Estimation with Multiple Measurement Vectors

Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is the spectrally-sparse signal, which is composed of a small number of spectral atoms with arbitrary frequencies on the unit interval. In this paper we study the problem of line spectrum denoising and estimation with an ensemble of spectrally-sparse signals composed of the same set of continuous-valued frequencies from their partial and noisy observations. Two approaches are developed based on atomic norm minimization and structured covariance estimation, both of which can be solved efficiently via semidefinite programming. The first approach aims to estimate and denoise the set of signals from their partial and noisy observations via atomic norm minimization, and recover the frequencies via examining the dual polynomial of the convex program. We characterize the optimality condition of the proposed algorithm and derive the expected convergence rate for denoising, demonstrating the benefit of including multiple measurement vectors. The second approach aims to recover the population covariance matrix from the partially observed sample covariance matrix by motivating its low-rank Toeplitz structure without recovering the signal ensemble. Performance guarantee is derived with a finite number of measurement vectors. The frequencies can be recovered via conventional spectrum estimation methods such as MUSIC from the estimated covariance matrix. Finally, numerical examples are provided to validate the favorable performance of the proposed algorithms, with comparisons against several existing approaches.Comment: 14 pages, 10 figure

A Comparative Analysis of Deterministic Detection and Estimation Techniques for MIMO SFCW Radars

In this paper, the problem of the joint estimation of the range and azimuth of multiple targets in a multiple-input multiple-output stepped-frequency continuous wave radar system is investigated. Three deterministic algorithms solving it through an iterative beam cancellation procedure are described; moreover, an iterative technique, based on the expectation-maximization algorithm, is developed with the aim of refining their estimates. The accuracy achieved by all the considered algorithms is assessed on the basis of the raw data acquired from a low power wideband radar device. Our results evidence that these algorithms achieve similar accuracies, but at the price of different computational efforts

Multiple Signal Classification for Determining Direction of Arrival of Frequency Hopping Spread Spectrum Signals

This research extends a MUSIC algorithm to determine DOA of FHSS signals. All incident FHSS signals have unknown DOA and use PSK. Conventional MUSIC algorithm involves multiple MUSIC estimation for all frequency bins. On the other hand, the extended development is meant to execute a single MUSIC algorithm of observations on multiple frequency bins or hops. The new extension shows better performance compared to the conventional MUSIC execution at different SNR levels. Both have the same power accumulation at the true angles of arrival. However, the new development has lower side lobes and hence helps avoid false detections. In addition, the new development has lower side lobes variance resulting in lower error of false detections compared to the normal execution. Simulation results show that the new extension is sensitive to the SNR values and number of samples taken at each frequency bin. However, it is less sensitive to the possible number of frequency hops or hop set and number of array sensors