Author

# Anuj Puri

Other affiliations: University of California, Bell Labs

Bio: Anuj Puri is an academic researcher from University of California, Berkeley. The author has contributed to research in topics: Timed automaton & Reachability. The author has an hindex of 13, co-authored 17 publications receiving 2892 citations. Previous affiliations of Anuj Puri include University of California & Bell Labs.

##### Papers

More filters

••

TL;DR: This work has implemented a decision feedback equalizer for all sub-channels followed by periodic block-type pilots and compared the performances of all schemes by measuring bit error rates with 16QAM, QPSK, DQPSK and BPSK as modulation schemes, and multipath Rayleigh fading and AR based fading channels as channel models.

Abstract: Channel estimation techniques for OFDM systems based on a pilot arrangement are investigated. Channel estimation based on a comb type pilot arrangement is studied through different algorithms for both estimating the channel at pilot frequencies and interpolating the channel. Channel estimation at pilot frequencies is based on LS and LMS methods while channel interpolation is done using linear interpolation, second order interpolation, low-pass interpolation, spline cubic interpolation, and time domain interpolation. Time-domain interpolation is obtained by passing to the time domain by means of IDFT (inverse discrete Fourier transform), zero padding and going back to the frequency domain by DFT (discrete Fourier transform). In addition, channel estimation based on a block type pilot arrangement is performed by sending pilots in every sub-channel and using this estimation for a specific number of following symbols. We have also implemented a decision feedback equalizer for all sub-channels followed by periodic block-type pilots. We have compared the performances of all schemes by measuring bit error rates with 16QAM, QPSK, DQPSK and BPSK as modulation schemes, and multipath Rayleigh fading and AR based fading channels as channel models.

1,551 citations

••

29 May 1995TL;DR: It is proved that the reachability problem is undecidable for timed automata augmented with a single stopwatch, and an (optimal) PSPACE reachability algorithm is given for the case of initialized rectangular automata.

Abstract: Hybrid automata model systems with both digital and analog components, such as embedded control programs. Many verification tasks for such programs can be expressed as reachability problems for hybrid automata. By improving on previous decidability and undecidability results, we identify the precise boundary between decidability and undecidability of the reachability problem for hybrid automata. On the positive side, we give an (optimal) PSPACE reachability algorithm for the case of initialized rectangular automata, where all analog variables follow trajectories within piecewise-linear envelopes and are reinitialized whenever the envelope changes. Our algorithm is based on the construction of a timed automaton that contains all reachability information about a given initialized rectangular automaton. The translation has practical significance for verification, because it guarantees the termination of symbolic procedures for the reachability analysis of initialized rectangular automata. The translation also preserves the $\omega$-languages of initialized rectangular automata with bounded nondeterminism. On the negative side, we show that several slight generalizations of initialized rectangular automata lead to an undecidable reachability problem. In particular, we prove that the reachability problem is undecidable for timed automata augmented with a single stopwatch.

685 citations

03 Oct 1996

TL;DR: It is shown that for hybrid automata with rectangular inclusions, the reachability question can be answered in a finite number of steps and that an $\omega$-automata game with the chain acceptance condition can be solved as a mean payoff game.

Abstract: A continuous system has a continuous state space and an evolution law given by a differential or a difference equation. A discrete event system is modeled by an automaton which changes state in response to events. A hybrid system contains both continuous and discrete event sub-systems. In this thesis we study some theoretical problems in the design and analysis of hybrid systems and discrete event systems.
We first consider the reachability question for a hybrid system--is a target state reachable from an initial state? We show that for hybrid automata with rectangular inclusions, the reachability question can be answered in a finite number of steps. Hybrid systems with more general dynamics can be reduced to hybrid systems with rectangular inclusions using abstractions.
We next consider an Automated Vehicle Highway System (AVHS) design. We consider the safety question: can there be a collision between two vehicles on the AVHS? We show that the AVHS is safe provided the controllers in the vehicles satisfy a set of constraints. The constraints require the reach set $Reach\sb{f}(X\sb0,t$)--the set of states reached after time t starting from an initial set $X\sb0$ for a differential inclusion $\dot x\ \in\ f(x$)--to satisfy a simple criterion. We show that this problem is equivalent to solving an optimal control problem.
We then consider some computational questions for differential inclusions. For a Lipschitz differential inclusion $\dot x\ \in\ f(x$), we give a method to compute an arbitrary close approximation of $Reach\sb{f}(X\sb0,t$). For a differential inclusion $\dot x\ \in\ f(x$), and any $\epsilon>$ 0, we define a finite sample graph $A\sp{\epsilon}$. Using graph $A\sp{\epsilon}$, we can compute the $\epsilon$-invariant sets of the differential inclusion--the sets that remain invariant under $\epsilon$-perturbations in f.
We also consider some dynamical games played on graphs. The synthesis and the control problem for $\omega$-automata can be formulated as a game between two players. We discuss games on $\omega$-automata and the payoff games. We show that $\omega$-automata games do not necessarily have a value when restricted to positional strategies. We exhibit a bound on the amount of memory required to play these games. We then consider the discounted and mean payoff games. We present the successive approximation and the policy iteration algorithm for solving payoff games. We then show that an $\omega$-automata game with the chain acceptance condition can be solved as a mean payoff game. Solving a chain game is equivalent to solving the model checking problem for propositional $\mu$-calculus. Hence, the policy iteration method can be used to model check $\mu$-calculus formula. This is at present the most efficient algorithm for model checking propositional $\mu$-calculus.

151 citations

••

TL;DR: It is shown that the standard approach for performing reachability analysis is not correct when the clocks drift even by a very small amount, and an algorithm for computing R*(T,Z0) is presented and shown to be robust with respect to various types of modeling errors.

Abstract: Timed automata are an important model for specifying and analyzing real-time systems. The main analysis performed on timed automata is the reachability analysis. In this paper we show that the standard approach for performing reachability analysis is not correct when the clocks drift even by a very small amount. Our formulation of the reachability problem for timed automata is as follows: we define the set R^*(T,Z_0)=\cap_{\eps>0}\reach(T_\eps,Z_0) where T_\eps is obtained from timed automaton T by allowing an \eps drift in the clocks. R^*(T,Z_0) is the set of states which can be reached in the timed automatonT from the initial states in Z_0 when the clocks drift by an infinitesimally small amount. We present an algorithm for computing R^*(T,Z_0) and provide a proof of its correctness. We show that R^*(T,Z_0) is robust with respect to various types of modeling errors. To prove the correctness of our algorithm, we need to understand the dynamics of timed automata—in particular, the structure of the limit cycles of timed automata.

127 citations

##### Cited by

More filters

••

27 Jul 1996TL;DR: The goal is to demonstrate that concepts from the theory of discrete concurrent systems can give insights into partly continuous systems, and that methods for the verification of finite-state systems can be used to analyze certain systems with uncountable state spaces.

Abstract: We summarize several recent results about hybrid automata. Our goal is to demonstrate that concepts from the theory of discrete concurrent systems can give insights into partly continuous systems, and that methods for the verification of finite-state systems can be used to analyze certain systems with uncountable state spaces.

1,900 citations

••

TL;DR: HyTech is a symbolic model checker for linear hybrid automata, a subclass of hybrids that can be analyzed automatically by computing with polyhedral state sets that combines automaton transitions for capturing discrete change with differential equations for capturing continuous change.

Abstract: A hybrid system consists of a collection of digital programs that interact with each other and with an analog environment. Examples of hybrid systems include medical equipment, manufacturing controllers, automotive controllers, and robots. The formal analysis of the mixed digital-analog nature of these systems requires a model that incorporates the discrete behavior of computer programs with the continuous behavior of environment variables, such as temperature and pressure. Hybrid automata capture both types of behavior by combining finite automata with differential inclusions (i.e. differential inequalities). HyTech is a symbolic model checker for linear hybrid automata, an expressive, yet automatically analyzable, subclass of hybrid automata. A key feature of HyTech is its ability to perform parametric analysis, i.e. to determine the values of design parameters for which a linear hybrid automaton satisfies a temporal requirement.

1,092 citations

••

TL;DR: This paper addresses basic OFDM and related modulations, as well as techniques to improve the performance of OFDM for wireless communications, including channel estimation and signal detection, time- and frequency-offset estimation and correction, peak-to-average power ratio reduction, and multiple-input-multiple-output (MIMO) techniques.

Abstract: Orthogonal frequency-division multiplexing (OFDM) effectively mitigates intersymbol interference (ISI) caused by the delay spread of wireless channels. Therefore, it has been used in many wireless systems and adopted by various standards. In this paper, we present a comprehensive survey on OFDM for wireless communications. We address basic OFDM and related modulations, as well as techniques to improve the performance of OFDM for wireless communications, including channel estimation and signal detection, time- and frequency-offset estimation and correction, peak-to-average power ratio reduction, and multiple-input-multiple-output (MIMO) techniques. We also describe the applications of OFDM in current systems and standards.

915 citations

••

01 Jul 2000

TL;DR: It is shown that interesting classes of hybrid systems can be abstracted to purely discrete systems while preserving all properties that are definable in temporal logic.

Abstract: A hybrid system is a dynamical system with both discrete and continuous state changes. For analysis purposes, it is often useful to abstract a system in a way that preserves the properties being analysed while hiding the details that are of no interest. We show that interesting classes of hybrid systems can be abstracted to purely discrete systems while preserving all properties that are definable in temporal logic. The classes that permit discrete abstractions fall into two categories. Either the continuous dynamics must be restricted, as is the case for timed and rectangular hybrid systems, or the discrete dynamics must be restricted, as is the case for o-minimal hybrid systems. In this paper, we survey and unify results from both areas.

893 citations

•

[...]

Qualcomm

^{1}TL;DR: In this article, a multiple-access MIMO WLAN system that employs MIMI, OFDM, and TDD was proposed, which employs a channel structure with a number of configurable transport channels, supports multiple rates and transmission modes, which are configurable based on channel conditions and user terminal capabilities.

Abstract: A multiple-access MIMO WLAN system that employs MIMO, OFDM, and TDD. The system (1) uses a channel structure with a number of configurable transport channels, (2) supports multiple rates and transmission modes, which are configurable based on channel conditions and user terminal capabilities, (3) employs a pilot structure with several types of pilot (e.g., beacon, MIMO, steered reference, and carrier pilots) for different functions, (4) implements rate, timing, and power control loops for proper system operation, and (5) employs random access for system access by the user terminals, fast acknowledgment, and quick resource assignments. Calibration may be performed to account for differences in the frequency responses of transmit/receive chains at the access point and user terminals. The spatial processing may then be simplified by taking advantage of the reciprocal nature of the downlink and uplink and the calibration.

759 citations