Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification

Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input {\it a-priori}. However, individual system components are often described by surrogate models rather than density functions. In order to apply stochastic spectral methods in hierarchical uncertainty quantification, we first propose to construct physically consistent closed-form density functions by two monotone interpolation schemes. Then, by exploiting the special forms of the obtained density functions, we determine the generalized polynomial-chaos basis functions and the Gauss quadrature rules that are required by a stochastic spectral simulator. The effectiveness of our proposed algorithm is verified by both synthetic and practical circuit examples.Comment: Published by IEEE Trans CAD in May 201

Multi-User Detection for the Optical Code Division Multiple Access (OCDMA): Optical Parallel Interference Cancellation (OPIC)

Optical Code Division Multiple Access (OCDMA) has recently been proposed as an alternative to frequency and time based multiple access methods for the next generation high-speed optical fiber networks. This is because such system offers a large bandwidth. Based on the vast amount of bandwidth available in optical line, OCDMA system has received much attention in fiber optic Local Area Network (LAN) where the traffic is typically bursty. However, Multiple Access Interference (MAl), which is originated from other simultaneous users, severely limits the capacity of the system. In addition, the need for dynamic threshold in the Conventional Correlation Receiver (CCR) is a very demanding requirement particularly in the high speed LANs. To overcome the stated problems, Optical Parallel Interference Cancellation is used throughout this thesis. Optical Hard Limiter (OHL) has been placed at the front of the OPIC receiver to reduce the effect of MAl and fixed threshold is used to overcome the problem of dynamic threshold. The study carried out using theoretical and simulation. The results reveal that, OPJC system is attractive technology for next generation optical networks. The drawback of OPIC is the increases in the demand for hardware in each receiver. As a result, it requires more complex hardware, higher processing time and cost. To overcome these difficulties, an efficient method is proposed called, One Stage Optical Parallel Interference Cancellation (OS-OPIC) which is based mainly on the OPIC. Performance analysis of the proposed design is done using Optical Orthogonal Code (OOC) as a signature sequence and a new expression for error probability is demonstrated. It is shown that, the proposed method is effective to reduce the hardware complexity, processing time and cost while maintaining the same BER at the cost of increasing threshold value

Model order reduction of fully parameterized systems by recursive least square optimization

This paper presents an approach for the model order reduction of fully parameterized linear dynamic systems. In a fully parameterized system, not only the state matrices, but also can the input/output matrices be parameterized. The algorithm presented in this paper is based on neither conventional moment-matching nor balanced-truncation ideas. Instead, it uses “optimal (block) vectors” to construct the projection matrix, such that the system errors in the whole parameter space are minimized. This minimization problem is formulated as a recursive least square (RLS) optimization and then solved at a low cost. Our algorithm is tested by a set of multi-port multi-parameter cases with both intermediate and large parameter variations. The numerical results show that high accuracy is guaranteed, and that very compact models can be obtained for multi-parameter models due to the fact that the ROM size is independent of the number of parameters in our approach

Stochastic Testing Simulator for Integrated Circuits and MEMS: Hierarchical and Sparse Techniques

Process variations are a major concern in today's chip design since they can significantly degrade chip performance. To predict such degradation, existing circuit and MEMS simulators rely on Monte Carlo algorithms, which are typically too slow. Therefore, novel fast stochastic simulators are highly desired. This paper first reviews our recently developed stochastic testing simulator that can achieve speedup factors of hundreds to thousands over Monte Carlo. Then, we develop a fast hierarchical stochastic spectral simulator to simulate a complex circuit or system consisting of several blocks. We further present a fast simulation approach based on anchored ANOVA (analysis of variance) for some design problems with many process variations. This approach can reduce the simulation cost and can identify which variation sources have strong impacts on the circuit's performance. The simulation results of some circuit and MEMS examples are reported to show the effectiveness of our simulatorComment: Accepted to IEEE Custom Integrated Circuits Conference in June 2014. arXiv admin note: text overlap with arXiv:1407.302

Uncertainty quantification for integrated circuits: Stochastic spectral methods

Due to significant manufacturing process variations, the performance of integrated circuits (ICs) has become increasingly uncertain. Such uncertainties must be carefully quantified with efficient stochastic circuit simulators. This paper discusses the recent advances of stochastic spectral circuit simulators based on generalized polynomial chaos (gPC). Such techniques can handle both Gaussian and non-Gaussian random parameters, showing remarkable speedup over Monte Carlo for circuits with a small or medium number of parameters. We focus on the recently developed stochastic testing and the application of conventional stochastic Galerkin and stochastic collocation schemes to nonlinear circuit problems. The uncertainty quantification algorithms for static, transient and periodic steady-state simulations are presented along with some practical simulation results. Some open problems in this field are discussed.MIT Masdar Program (196F/002/707/102f/70/9374

MEMS Accelerometers

Micro-electro-mechanical system (MEMS) devices are widely used for inertia, pressure, and ultrasound sensing applications. Research on integrated MEMS technology has undergone extensive development driven by the requirements of a compact footprint, low cost, and increased functionality. Accelerometers are among the most widely used sensors implemented in MEMS technology. MEMS accelerometers are showing a growing presence in almost all industries ranging from automotive to medical. A traditional MEMS accelerometer employs a proof mass suspended to springs, which displaces in response to an external acceleration. A single proof mass can be used for one- or multi-axis sensing. A variety of transduction mechanisms have been used to detect the displacement. They include capacitive, piezoelectric, thermal, tunneling, and optical mechanisms. Capacitive accelerometers are widely used due to their DC measurement interface, thermal stability, reliability, and low cost. However, they are sensitive to electromagnetic field interferences and have poor performance for high-end applications (e.g., precise attitude control for the satellite). Over the past three decades, steady progress has been made in the area of optical accelerometers for high-performance and high-sensitivity applications but several challenges are still to be tackled by researchers and engineers to fully realize opto-mechanical accelerometers, such as chip-scale integration, scaling, low bandwidth, etc

Multi-User Detection for the Optical Code Division Multiple Access (OCDMA): Optical Parallel Interference Cancellation (OPIC)

Optical Code Division Multiple Access (OCDMA) has recently been proposed as an alternative to frequency and time based multiple access methods for the next generation high-speed optical fiber networks. This is because such system offers a large bandwidth. Based on the vast amount of bandwidth available in optical line, OCDMA system has received much attention in fiber optic Local Area Network (LAN) where the traffic is typically bursty. However, Multiple Access Interference (MAl), which is originated from other simultaneous users, severely limits the capacity of the system. In addition, the need for dynamic threshold in the Conventional Correlation Receiver (CCR) is a very demanding requirement particularly in the high speed LANs. To overcome the stated problems, Optical Parallel Interference Cancellation is used throughout this thesis. Optical Hard Limiter (OHL) has been placed at the front of the OPIC receiver to reduce the effect of MAl and fixed threshold is used to overcome the problem of dynamic threshold. The study carried out using theoretical and simulation. The results reveal that, OPJC system is attractive technology for next generation optical networks. The drawback of OPIC is the increases in the demand for hardware in each receiver. As a result, it requires more complex hardware, higher processing time and cost. To overcome these difficulties, an efficient method is proposed called, One Stage Optical Parallel Interference Cancellation (OS-OPIC) which is based mainly on the OPIC. Performance analysis of the proposed design is done using Optical Orthogonal Code (OOC) as a signature sequence and a new expression for error probability is demonstrated. It is shown that, the proposed method is effective to reduce the hardware complexity, processing time and cost while maintaining the same BER at the cost of increasing threshold value