Efficient Beamspace Eigen-Based Direction of Arrival Estimation schemes

The Multiple SIgnal Classification (MUSIC) algorithm developed in the late 70\u27s was the first vector subspace approach used to accurately determine the arrival angles of signal wavefronts impinging upon an array of sensors. As facilitated by the geometry associated with the common uniform linear array of sensors, a root-based formulation was developed to replace the computationally intensive spectral search process and was found to offer an enhanced resolution capability in the presence of two closely-spaced signals. Operation in beamspace, where sectors of space are individually probed via a pre-processor operating on the sensor data, was found to offer both a performance benefit and a reduced computationa1 complexi ty resulting from the reduced data dimension associated with beamspace processing. Little progress, however, has been made in the development of a computationally efficient Root-MUSIC algorithm in a beamspace setting. Two approaches of efficiently arriving at a Root-MUSIC formulation in beamspace are developed and analyzed in this Thesis. In the first approach, a structura1 constraint is placed on the beamforming vectors that can be exploited to yield a reduced order polynomial whose roots provide information on the signal arrival angles. The second approach is considerably more general, and hence, applicable to any vector subspace angle estimation algorithm. In this approach, classical multirate digital signal processing is applied to effectively reduce the dimension of the vectors that span the signal subspace, leading to an efficient beamspace Root-MUSIC (or ESPRIT) algorithm. An auxiliaay, yet important, observation is shown to allow a real-valued eigenanalysis of the beamspace sample covariance matrix to provide a computational savings as well as a performance benefit, particularly in the case of correlated signal scenes. A rigorous theoretical analysis, based upon derived large-sample statistics of the signal subspace eigenvectors, is included to provide insight into the operation of the two algorithmic methodologies employing the real-valued processing enhancement. Numerous simulations are presented to validate the theoretical angle bias and variance expressions as well as to assess the merit of the two beamspace approaches

Space Time MUSIC: Consistent Signal Subspace Estimation for Wide-band Sensor Arrays

Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an essential task in sonar, radar, acoustics, biomedical and multimedia applications. Many state of the art wide-band DOA estimators coherently process frequency binned array outputs by approximate Maximum Likelihood, Weighted Subspace Fitting or focusing techniques. This paper shows that bin signals obtained by filter-bank approaches do not obey the finite rank narrow-band array model, because spectral leakage and the change of the array response with frequency within the bin create \emph{ghost sources} dependent on the particular realization of the source process. Therefore, existing DOA estimators based on binning cannot claim consistency even with the perfect knowledge of the array response. In this work, a more realistic array model with a finite length of the sensor impulse responses is assumed, which still has finite rank under a space-time formulation. It is shown that signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying MUSIC-type (ST-MUSIC) estimators to the dominant eigenvectors of the wide-band space-time sensor cross-correlation matrix. A novel Maximum Likelihood based ST-MUSIC subspace estimate is developed in order to recover consistency. The number of sources active at each frequency are estimated by Information Theoretic Criteria. The sample ST-MUSIC subspaces can be fed to any subspace fitting DOA estimator at single or multiple frequencies. Simulations confirm that the new technique clearly outperforms binning approaches at sufficiently high signal to noise ratio, when model mismatches exceed the noise floor.Comment: 15 pages, 10 figures. Accepted in a revised form by the IEEE Trans. on Signal Processing on 12 February 1918. @IEEE201

Karhunen-Loeve eigenvalue problems in cosmology: how should we tackle large data sets?

Since cosmology is no longer "the data-starved science", the problem of how to best analyze large data sets has recently received considerable attention, and Karhunen-Loeve eigenvalue methods have been applied to both galaxy redshift surveys and Cosmic Microwave Background (CMB) maps. We present a comprehensive discussion of methods for estimating cosmological parameters from large data sets, which includes the previously published techniques as special cases. We show that both the problem of estimating several parameters jointly and the problem of not knowing the parameters a priori can be readily solved by adding an extra singular value decomposition step. It has recently been argued that the information content in a sky map from a next generation CMB satellite is sufficient to measure key cosmological parameters (h, Omega, Lambda, etc) to an accuracy of a few percent or better - in principle. In practice, the data set is so large that both a brute force likelihood analysis and a direct expansion in signal-to-noise eigenmodes will be computationally unfeasible. We argue that it is likely that a Karhunen-Loeve approach can nonetheless measure the parameters with close to maximal accuracy, if preceded by an appropriate form of quadratic "pre-compression". We also discuss practical issues regarding parameter estimation from present and future galaxy redshift surveys, and illustrate this with a generalized eigenmode analysis of the IRAS 1.2 Jy survey optimized for measuring beta=Omega^{0.6}/b using redshift space distortions.Comment: 15 pages, with 5 figures included. Substantially expanded with worked COBE examples for e.g. the multiparameter case. Available from http://www.sns.ias.edu/~max/karhunen.html (faster from the US), from http://www.mpa-garching.mpg.de/~max/karhunen.html (faster from Europe) or from [email protected]

Advanced array processing techniques and systems

Research and development on smart antennas, which are recognized as a promising technique to improve the performance of mobile communications, have been extensive in the recent years. Smart antennas combine multiple antenna elements with a signal processing capability in both space and time to optimize its radiation and reception pattern automatically in response to the signal environment. This paper concentrates on the signal processing aspects of smart antenna systems. Smart antennas are often classified as either switched-beam or adaptive-array systems, for which a variety of algorithms have been developed to enhance the signal of interest and reject the interference. The antenna systems need to differentiate the desired signal from the interference, and normally requires either a priori knowledge or the signal direction to achieve its goal. There exists a variety of methods for direction of arrival (DOA) estimation with conflicting demands of accuracy and computation. Similarly, there are many algorithms to compute array weights to direct the maximum radiation of the array pattern toward the signal and place nulls toward the interference, each with its convergence property and computational complexity. This paper discusses some of the typical algorithms for DOA estimation and beamforming. The concept and details of each algorithm are provided. Smart antennas can significantly help in improving the performance of communication systems by increasing channel capacity and spectrum efficiency, extending range coverage, multiplexing channels with spatial division multiple access (SDMA), and compensating electronically for aperture distortion. They also reduce delay spread, multipath fading, co-channel interference, system complexity, bit error rates, and outage probability. In addition, smart antennas can locate mobile units or assist the location determination through DOA and range estimation. This capability can support and benefit many location-based services including emergency assistance, tracking services, safety services, billing services, and information services such as navigation, weather, traffic, and directory assistance

High-resolution sonar DF system

One of the fundamental problems of sonar systems is the determination of the bearings of underwater sources/targets. The classical solution to this problem, the 'Conventional Beamformer', uses the outputs from the individual sensors of an acoustic array to form a beam which is swept across the search sector. The resolution of this method is limited by the beam width and narrowing this beam to enhance the resolution may have some practical problems, especially in low frequency sonar, because of the physical size of the array needed. During the past two decades an enormous amount of work has been done to develop new algorithms for resolution enhancements beyond that of the Conventional Beamformer. However, most of these methods have been based on computer simulations and very little has been published on the practical implementation of these algorithms. One of the main reasons for this has been the lack of hardware that can handle the relatively heavy computational load of these algorithms. However, there have been great advances in semiconductor and computer technologies in the last few years which have led to the availability of more powerful computational and storage devices. These devices have opened the door to the possibility of implementing these high-resolution Direction Finding (DF) algorithms in real sonar systems. The work presented in this thesis describes a practical implementation of some of the high-resolution DF algorithms in a simple sonar system that has been designed and built for this purpose. [Continues.

医用超音波における散乱体分布の高解像かつ高感度な画像化に関する研究

Ultrasound imaging as an effective method is widely used in medical diagnosis andNDT (non-destructive testing). In particular, ultrasound imaging plays an important role in medical diagnosis due to its safety, noninvasive, inexpensiveness and real-time compared with other medical imaging techniques. However, in general the ultrasound imaging has more speckles and is low definition than the MRI (magnetic resonance imaging) and X-ray CT (computerized tomography). Therefore, it is important to improve the ultrasound imaging quality. In this study, there are three newproposals. The first is the development of a high sensitivity transducer that utilizes piezoelectric charge directly for FET (field effect transistor) channel control. The second is a proposal of a method for estimating the distribution of small scatterers in living tissue using the empirical Bayes method. The third is a super-resolution imagingmethod of scatterers with strong reflection such as organ boundaries and blood vessel walls. The specific description of each chapter is as follows: Chapter 1: The fundamental characteristics and the main applications of ultrasound are discussed, then the advantages and drawbacks of medical ultrasound are high-lighted. Based on the drawbacks, motivations and objectives of this study are stated. Chapter 2: To overcome disadvantages of medical ultrasound, we advanced our studyin two directions: designing new transducer improves the acquisition modality itself, onthe other hand new signal processing improve the acquired echo data. Therefore, the conventional techniques related to the two directions are reviewed. Chapter 3: For high performance piezoelectric, a structure that enables direct coupling of a PZT (lead zirconate titanate) element to the gate of a MOSFET (metal-oxide semiconductor field-effect transistor) to provide a device called the PZT-FET that acts as an ultrasound receiver was proposed. The experimental analysis of the PZT-FET, in terms of its reception sensitivity, dynamic range and -6 dB reception bandwidth have been investigated. The proposed PZT-FET receiver offers high sensitivity, wide dynamic range performance when compared to the typical ultrasound transducer. Chapter 4: In medical ultrasound imaging, speckle patterns caused by reflection interference from small scatterers in living tissue are often suppressed by various methodologies. However, accurate imaging of small scatterers is important in diagnosis; therefore, we investigated influence of speckle pattern on ultrasound imaging by the empirical Bayesian learning. Since small scatterers are spatially correlated and thereby constitute a microstructure, we assume that scatterers are distributed according to the AR (auto regressive) model with unknown parameters. Under this assumption, the AR parameters are estimated by maximizing the marginal likelihood function, and the scatterers distribution is estimated as a MAP (maximum a posteriori) estimator. The performance of our method is evaluated by simulations and experiments. Through the results, we confirmed that the band limited echo has sufficient information of the AR parameters and the power spectrum of the echoes from the scatterers is properly extrapolated. Chapter 5: The medical ultrasound imaging of strong reflectance scatterers based on the MUSIC algorithm is the main subject of Chapter 5. Previously, we have proposed a super-resolution ultrasound imaging based on multiple TRs (transmissions/receptions) with different carrier frequencies called SCM (super resolution FM-chirp correlation method). In order to reduce the number of required TRs for the SCM, the method has been extended to the SA (synthetic aperture) version called SA-SCM. However, since super-resolution processing is performed for each line data obtained by the RBF (reception beam forming) in the SA-SCM, image discontinuities tend to occur in the lateral direction. Therefore, a new method called SCM-weighted SA is proposed, in this version the SCM is performed on each transducer element, and then the SCM result is used as the weight for RBF. The SCM-weighted SA can generate multiple B-mode images each of which corresponds to each carrier frequency, and the appropriate low frequency images among them have no grating lobes. For a further improvement, instead of simple averaging, the SCM applied to the result of the SCM-weighted SA for all frequencies again, which is called SCM-weighted SA-SCM. We evaluated the effectiveness of all the methods by simulations and experiments. From the results, it can be confirmed that the extension of the SCM framework can help ultrasound imaging reduce grating lobes, perform super-resolution and better SNR(signal-to-noise ratio). Chapter 6: A discussion of the overall content of the thesis as well as suggestions for further development together with the remaining problems are summarized.首都大学東京, 2019-03-25, 博士（工学）首都大学東