Estimation of MIMO transmit-antenna number using higher-order moments based hypothesis testing

This letter proposes a higher-order-moment based hypothesis testing algorithm to estimate the transmit-antenna number for multiple-input multiple-output (MIMO) systems. Exploiting the asymptotic normal distribution of the moments composed by noise eigenvalues, the proposed algorithm improves the estimation performance for low signal-to-noise ratios (SNRs). Moreover, since the empirical distribution of the moments converges quickly to the normal distribution when the number of samples increases, our algorithm can make a reliable estimation in a sample starved condition. Computer simulations are provided to demonstrate that the proposed algorithm outperforms the conventional algorithms

Applied stochastic eigen-analysis

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2007The first part of the dissertation investigates the application of the theory of large random matrices to high-dimensional inference problems when the samples are drawn from a multivariate normal distribution. A longstanding problem in sensor array processing is addressed by designing an estimator for the number of signals in white noise that dramatically outperforms that proposed by Wax and Kailath. This methodology is extended to develop new parametric techniques for testing and estimation. Unlike techniques found in the literature, these exhibit robustness to high-dimensionality, sample size constraints and eigenvector misspecification. By interpreting the eigenvalues of the sample covariance matrix as an interacting particle system, the existence of a phase transition phenomenon in the largest (“signal”) eigenvalue is derived using heuristic arguments. This exposes a fundamental limit on the identifiability of low-level signals due to sample size constraints when using the sample eigenvalues alone. The analysis is extended to address a problem in sensor array processing, posed by Baggeroer and Cox, on the distribution of the outputs of the Capon-MVDR beamformer when the sample covariance matrix is diagonally loaded. The second part of the dissertation investigates the limiting distribution of the eigenvalues and eigenvectors of a broader class of random matrices. A powerful method is proposed that expands the reach of the theory beyond the special cases of matrices with Gaussian entries; this simultaneously establishes a framework for computational (non-commutative) “free probability” theory. The class of “algebraic” random matrices is defined and the generators of this class are specified. Algebraicity of a random matrix sequence is shown to act as a certificate of the computability of the limiting eigenvalue distribution and, for a subclass, the limiting conditional “eigenvector distribution.” The limiting moments of algebraic random matrix sequences, when they exist, are shown to satisfy a finite depth linear recursion so that they may often be efficiently enumerated in closed form. The method is applied to predict the deterioration in the quality of the sample eigenvectors of large algebraic empirical covariance matrices due to sample size constraints.I am grateful to the National Science Foundation for supporting this work via grant DMS-0411962 and the Office of Naval Research Graduate Traineeship awar

Online Modeling and Tuning of Parallel Stream Processing Systems

Writing performant computer programs is hard. Code for high performance applications is profiled, tweaked, and re-factored for months specifically for the hardware for which it is to run. Consumer application code doesn\u27t get the benefit of endless massaging that benefits high performance code, even though heterogeneous processor environments are beginning to resemble those in more performance oriented arenas. This thesis offers a path to performant, parallel code (through stream processing) which is tuned online and automatically adapts to the environment it is given. This approach has the potential to reduce the tuning costs associated with high performance code and brings the benefit of performance tuning to consumer applications where otherwise it would be cost prohibitive. This thesis introduces a stream processing library and multiple techniques to enable its online modeling and tuning. Stream processing (also termed data-flow programming) is a compute paradigm that views an application as a set of logical kernels connected via communications links or streams. Stream processing is increasingly used by computational-x and x-informatics fields (e.g., biology, astrophysics) where the focus is on safe and fast parallelization of specific big-data applications. A major advantage of stream processing is that it enables parallelization without necessitating manual end-user management of non-deterministic behavior often characteristic of more traditional parallel processing methods. Many big-data and high performance applications involve high throughput processing, necessitating usage of many parallel compute kernels on several compute cores. Optimizing the orchestration of kernels has been the focus of much theoretical and empirical modeling work. Purely theoretical parallel programming models can fail when the assumptions implicit within the model are mis-matched with reality (i.e., the model is incorrectly applied). Often it is unclear if the assumptions are actually being met, even when verified under controlled conditions. Full empirical optimization solves this problem by extensively searching the range of likely configurations under native operating conditions. This, however, is expensive in both time and energy. For large, massively parallel systems, even deciding which modeling paradigm to use is often prohibitively expensive and unfortunately transient (with workload and hardware). In an ideal world, a parallel run-time will re-optimize an application continuously to match its environment, with little additional overhead. This work presents methods aimed at doing just that through low overhead instrumentation, modeling, and optimization. Online optimization provides a good trade-off between static optimization and online heuristics. To enable online optimization, modeling decisions must be fast and relatively accurate. Online modeling and optimization of a stream processing system first requires the existence of a stream processing framework that is amenable to the intended type of dynamic manipulation. To fill this void, we developed the RaftLib C++ template library, which enables usage of the stream processing paradigm for C++ applications (it is the run-time which is the basis of almost all the work within this dissertation). An application topology is specified by the user, however almost everything else is optimizable by the run-time. RaftLib takes advantage of the knowledge gained during the design of several prior streaming languages (notably Auto-Pipe). The resultant framework enables online migration of tasks, auto-parallelization, online buffer-reallocation, and other useful dynamic behaviors that were not available in many previous stream processing systems. Several benchmark applications have been designed to assess the performance gains through our approaches and compare performance to other leading stream processing frameworks. Information is essential to any modeling task, to that end a low-overhead instrumentation framework has been developed which is both dynamic and adaptive. Discovering a fast and relatively optimal configuration for a stream processing application often necessitates solving for buffer sizes within a finite capacity queueing network. We show that a generalized gain/loss network flow model can bootstrap the process under certain conditions. Any modeling effort, requires that a model be selected; often a highly manual task, involving many expensive operations. This dissertation demonstrates that machine learning methods (such as a support vector machine) can successfully select models at run-time for a streaming application. The full set of approaches are incorporated into the open source RaftLib framework