Asymptotically Optimal Blind Calibration of Uniform Linear Sensor Arrays for Narrowband Gaussian Signals

An asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband Gaussian signals is proposed. Rather than taking the direct Maximum Likelihood (ML) approach for joint estimation of all the unknown model parameters, which leads to a multi-dimensional optimization problem with no closed-form solution, we revisit Paulraj and Kailath's (P-K's) classical approach in exploiting the special (Toeplitz) structure of the observations' covariance. However, we offer a substantial improvement over P-K's ordinary Least Squares (LS) estimates by using asymptotic approximations in order to obtain simple, non-iterative, (quasi-)linear Optimally-Weighted LS (OWLS) estimates of the sensors gains and phases offsets with asymptotically optimal weighting, based only on the empirical covariance matrix of the measurements. Moreover, we prove that our resulting estimates are also asymptotically optimal w.r.t. the raw data, and can therefore be deemed equivalent to the ML Estimates (MLE), which are otherwise obtained by joint ML estimation of all the unknown model parameters. After deriving computationally convenient expressions of the respective Cram\'er-Rao lower bounds, we also show that our estimates offer improved performance when applied to non-Gaussian signals (and/or noise) as quasi-MLE in a similar setting. The optimal performance of our estimates is demonstrated in simulation experiments, with a considerable improvement (reaching an order of magnitude and more) in the resulting mean squared errors w.r.t. P-K's ordinary LS estimates. We also demonstrate the improved accuracy in a multiple-sources directions-of-arrivals estimation task.Comment: in IEEE Transactions on Signal Processin

The influence of random element displacement on DOA estimates obtained with (Khatri-Rao-)root-MUSIC

Although a wide range of direction of arrival (DOA) estimation algorithms has been described for a diverse range of array configurations, no specific stochastic analysis framework has been established to assess the probability density function of the error on DOA estimates due to random errors in the array geometry. Therefore, we propose a stochastic collocation method that relies on a generalized polynomial chaos expansion to connect the statistical distribution of random position errors to the resulting distribution of the DOA estimates. We apply this technique to the conventional root-MUSIC and the Khatri-Rao-root-MUSIC methods. According to Monte-Carlo simulations, this novel approach yields a speedup by a factor of more than 100 in terms of CPU-time for a one-dimensional case and by a factor of 56 for a two-dimensional case

Efficient and Robust Signal Detection Algorithms for the Communication Applications

Signal detection and estimation has been prevalent in signal processing and communications for many years. The relevant studies deal with the processing of information-bearing signals for the purpose of information extraction. Nevertheless, new robust and efficient signal detection and estimation techniques are still in demand since there emerge more and more practical applications which rely on them. In this dissertation work, we proposed several novel signal detection schemes for wireless communications applications, such as source localization algorithm, spectrum sensing method, and normality test. The associated theories and practice in robustness, computational complexity, and overall system performance evaluation are also provided

High-resolution Direction-of-Arrival estimation

Direction of Arrival (DOA) estimation is considered one of the most crucial problems in array signal processing, with considerable research efforts for developing efficient and effective direction-finding algorithms, especially in the transportation industry, where the demand for an effective, real-time, and accurate DOA algorithm is increasing. However, challenges must be addressed before real-world deployment can be realised. Firstly, there is the requirement for fast computational time for real-time detection. Secondly, there is a demand for high-resolution and accurate DOA estimation. In this thesis, two state-of-the-art DOA estimation algorithms are proposed and evaluated to address the challenges. Firstly, a novel covariance matrix reconstruction approach for single snapshot DOA estimation (CbSS) was proposed. CbSS was developed by exploiting the relationship between the theoretical and sample covariance matrices to reduce estimation error for a single snapshot scenario. CbSS can resolve accurate DOAs without requiring lengthy peak searching computational time by computationally changing the received sample covariance matrix. Simulation results have verified that the CbSS technique yields the highest DOA estimation accuracy by up to 25.5% compared to existing methods such as root-MUSIC and the Partial Relaxation approach. Furthermore, CbSS presents negligible bias when compared to the existing techniques in a wide range of scenarios, such as in multiple uncorrelated and coherent signal source environments. Secondly, an adaptive diagonal-loading technique was proposed to improve DOA estimation accuracy without requiring a high computational load by integrating a modified novel and adaptive diagonal-loading method (DLT-DOA) to further improve estimation accuracy. An in-depth simulation performance analysis was conducted to address the challenges, with a comparison against existing state-of-the-art DOA estimation techniques such as EPUMA and MODEX. Simulation results verify that the DLT-DOA technique performs up to 8.5% higher DOA estimation performance in terms of estimation accuracy compared to existing methods with significantly lower computational time. On this basis, the two novel DOA estimation techniques are recommended for usage in real-world scenarios where fast computational time and high estimation accuracy are expected. Further research is needed to identify other factors that could further optimize the algorithms to meet different demands

Signal direction-of-arrival and amplitude estimation for multiple-row bathymetric sidescan sonars

Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 1998In practical applications with bathymetric sidescan sonars, the multipath reflections and other directional interferences are the key limiting factors for a better performance. This thesis proposes a new scheme to deal with the interferences using a multiple-row bathymetric sidescan sonar. Instead of smoothing the measurements over some time or angle intervals, which was previously widely investigated, we resolve the multipath interferences from the direct signal. Two approaches on signal direction-of-arrival DOA and amplitude estimation are developed, the correlated signal direction estimate CSDE for three-row systems and the ESPRIT-based method. These approaches are compared using different sonar data models, including a stochastic model from the statistical analysis on bottom scattering and a coherent model from the analysis on interference field; the simulations show the ESPRIT-based approach is quite robust at the angular separation of 100 between two sources and at the signal-to-noise ratio above 10dB except for highly coherent or temporally correlated signals, for which CSDE works very well. The computer simulation results and the discussions on practical algorithm implementation indicate the proposed scheme can be applied to a real multiple-row bathymetric sidescan sonar. With the capability to simultaneously resolve two or more directional signals, the new sonar model should work better for a wider variety of practical situations in shallow water with out significant increase of the system cost.Funding supporting my thesis research project was provided by the Office of Naval Research ONR

Sensor array signal processing : two decades later

Caption title.Includes bibliographical references (p. 55-65).Supported by Army Research Office. DAAL03-92-G-115 Supported by the Air Force Office of Scientific Research. F49620-92-J-2002 Supported by the National Science Foundation. MIP-9015281 Supported by the ONR. N00014-91-J-1967 Supported by the AFOSR. F49620-93-1-0102Hamid Krim, Mats Viberg

Array processing based on time-frequency analysis and higher-order statistics

Ph.DDOCTOR OF PHILOSOPH