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ABSTRACT: In this paper, we study the problem of linearly equalizing the multiple-input multiple-output (MIMO) communications channels from an H<sup>∞</sup> point of view. H<sup>∞</sup> estimation theory has been recently introduced as a method for designing filters that have acceptable performance in the face of model uncertainty and lack of statistical information on the exogenous signals. In this paper, we obtain a closed-form solution to the square MIMO linear H<sup>∞</sup> equalization problem and parameterize all possible H<sup>∞</sup>-optimal equalizers. In particular, we show that, for minimum phase channels, a scaled version of the zero-forcing equalizer is H<sup>∞</sup>-optimal. The results also indicate an interesting dichotomy between minimum phase and nonminimum phase channels: for minimum phase channels the best causal equalizer performs as well as the best noncausal equalizer, whereas for nonminimum phase channels, causal equalizers cannot reduce the estimation error bounds from their a priori values. Our analysis also suggests certain remedies in the nonminimum phase case, namely, allowing for finite delay, oversampling, or using multiple sensors. For example, we show that H<sup>∞</sup> equalization of nonminimum phase channels requires a time delay of at least l units, where l is the number of nonminimum phase zeros of the channel.
IEEE Transactions on Signal Processing 03/2006; · 2.63 Impact Factor
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ABSTRACT: In recent work, we have shown how least-squares estimation problems for arbitrary nonstationary processes can be speeded up by using the notion of an index of nonstationarity and a corresponding generalized Levinson algorithm. It was also shown that when the nonstationary processes have constant-parameter state-space models, the generalized Levinson algorithms reduce to the generalized Chandrasekhar equations. In this paper we shall show that the explicit equations of the above algorithms can be replaced by certain implicitly defined J-orthogonal transformation procedures, where J is a signature matrix (zero everywhere except for 1's on the diagonal). In the state-space case, these methods yield the previously-derived fast square-root algorithms of Morf and Kailath.
01/2006: pages 81-91;
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ABSTRACT: A thermal system is developed to rapidly characterize the linewidth sensitivity of advanced resists to process temperature variations in the photolithographic manufacturing sequence. This thermal array consists of a 77 grid of individually programmable heating zones distributed within a thermal cycling apparatus. It is used to improve the quality and quantity of data for determining the optimal thermal conditions by effectively producing equivalent operating conditions besides the spatially controlled temperature. The system is demonstrated for the optimization of the post-apply and post-exposure thermal-processing conditions for chemically amplified photoresists used in the fabrication of quartz photomasks .
Applied Physics A 01/2005; 80(4):899-902. · 1.63 Impact Factor
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ABSTRACT: In recent years, soft iterative decoding techniques have been shown to greatly improve the bit error rate performance of various communication systems. For multiantenna systems employing space-time codes, however, it is not clear what is the best way to obtain the soft information required of the iterative scheme with low complexity. In this paper, we propose a modification of the Fincke-Pohst (sphere decoding) algorithm to estimate the maximum a posteriori probability of the received symbol sequence. The new algorithm solves a nonlinear integer least squares problem and, over a wide range of rates and signal-to-noise ratios, has polynomial-time complexity. Performance of the algorithm, combined with convolutional, turbo, and low-density parity check codes, is demonstrated on several multiantenna channels. The results for systems that employ space-time modulation schemes seem to indicate that the best performing schemes are those that support the highest mutual information between the transmitted and received signals, rather than the best diversity gain.
IEEE Transactions on Wireless Communications 12/2004; · 2.59 Impact Factor
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ABSTRACT: Communication systems transmitting over frequency-selective channels generally employ an equalizer to recover the transmitted sequence corrupted by intersymbol interference (ISI). Most practical systems use a training sequence to learn the channel impulse response and thereby design the equalizer. An important issue is determining the optimal amount of training: too little training and the channel is not learned properly, too much training and there is not enough time available to transmit data before the channel changes and must be learned anew. We use an information-theoretic approach to find the optimal parameters in training-based transmission schemes for channels described by a block-fading model. The optimal length of the training interval is found by maximizing a lower bound on the training-based channel capacity. When the transmitter is capable of providing two distinct transmission power levels (one for training and one for data transmission), the optimal length of the training interval is shown to be equal to the length of the channel. Further, we show that at high SNR, training-based schemes achieve the capacity of block-fading frequency selective channels, whereas at low SNR, they are highly suboptimal.
IEEE Transactions on Signal Processing 10/2004; · 2.63 Impact Factor
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ABSTRACT: A design procedure for feedforward filters is proposed to improve the tracking performance of existing closed-loop systems. A parametric model is not required because it directly utilizes the frequency response of the closed-loop system, which can be measured accurately. This frequency-shaping approach enables the tradeoff between the quality of model-matching and the size of control efforts by adjusting weighting filters. Time domain specifications can be specified indirectly by approximating them in the frequency domain. The procedure is intuitively simple for SISO systems. Generalization for MIMO systems is possible by formulating convex optimization problems. A feedforward filter is designed and implemented on a nanopositioning system for semiconductor manufacturing, to improve its transient response.
IEEE Transactions on Control Systems Technology 10/2004; · 1.77 Impact Factor
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ABSTRACT: This paper proposes the use of multivariable control methods to design a thermal platform for processing semiconductor substrates (semiconductor wafers and/or quartz reticles for photomasks) that far exceeds conventional methods in performance and flexibility. A thermal processing module for lithography applications is presented and demonstrated. The module comprises numerous (49) small, disjoint, and independently controlled heating elements capable of precise substrate spatial temperature control. The module also has a low thermal mass that allows for rapid element temperature variation, and hence transient control of substrate temperature. In addition, the module integrates active baking and chilling in a single unit, eliminating the need for substrate transfer between separate baking and chilling units and the temperature control limitations associated with it. The module is compared to a current state-of-the-art commercial system and shown to provide a factor of two improvement in transient temperature uniformity control on a six in quartz reticle using "hand-tuned" control techniques. A linear-quadratic regulator (LQR) feedback controller is also demonstrated and shown to provide peak-to-peak reticle temperature uniformity that does not exceed 1.6°C throughout the transient bake.
IEEE Transactions on Control Systems Technology 08/2004; · 1.77 Impact Factor
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ABSTRACT: We approach the multiple input multiple output (MIMO) decision feedback equalization (DFE) problem in digital communications from an H<sup>∞</sup> estimation point of view. Using the standard (and simplifying) assumption that all previous decisions are correct, we obtain an explicit parameterization of all H<sup>∞</sup> optimal DFEs. In particular, we show that, under the above assumption, minimum mean square error (MMSE) DFEs are H<sup>∞</sup> optimal. The H<sup>∞</sup> approach also suggests a method for dealing with errors in previous decisions.
IEEE Transactions on Signal Processing 04/2004; · 2.63 Impact Factor
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ABSTRACT: We approach "nite impulse response (FIR) equalization problem from an H# perspective. First, we formulate the calculation of the optimal H# performance for a given equalization setting as a semide"nite programming (SDP) problem. H# criterion provides a set of FIR equalizers with di!erent optimality properties. Among these, we formulate the calculation of risk-sensitive or minimum entropy FIR "lter as the constrained analytic centring problem and mixed H#/H# problem as another SDP. We provide examples to illustrate the procedures we described. # 2001 Elsevier Science B.V. All rights reserved.
10/2003;
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ABSTRACT: Many communications systems employ training, ie, the transmission of known signals, so that the channel parameters may be learned at the receiver. This has a dual effect: too little training and the channel is improperly learned, too much training and there is no time left for data transmission before the channel changes. We use an information-theoretic approach to find the optimal amount of training for frequency selective channels described by a block-fading model. When the training and data powers are allowed to vary, we show that the optimal number of training symbols is equal to the length of the channel impulse response. When the training and data powers are instead required to be equal, the optimal number of symbols may be larger. We further show that at high SNR training-based schemes are capable of capturing most of the channel capacity, whereas at low SNR they are highly suboptimal
Acoustics, Speech, and Signal Processing, 2001. Proceedings. (ICASSP '01). 2001 IEEE International Conference on; 02/2001
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ABSTRACT: As an alternative to existing techniques and algorithms, we
investigate the merit of the H<sup>∞</sup> approach to the linear
equalization of communication channels. We first give the formulation of
all causal H<sup>∞</sup> equalizers using the results of and then
look at the finite delay ease. We compare the risk-sensitive
H<sup>∞</sup> equalizer with the MMSE equalizer with respect to
both the average and the worst-case BER performances and illustrate the
improvement due to the use of the H<sup>∞</sup> equalizer
IEEE Transactions on Signal Processing 12/2000; · 2.63 Impact Factor
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ABSTRACT: We develop array algorithms for H<sup>∞</sup> filtering.
These algorithms can be regarded as the Krein space generalizations of H
<sup>2</sup> array algorithms, which are currently the preferred method
fur implementing H<sup>2</sup> filters. The array algorithms considered
include two main families: square-root array algorithms, which are
typically numerically more stable than conventional ones, and fast array
algorithms which, when the system is time-invariant, typically offer an
order of magnitude reduction in the computational effort. Both have the
interesting feature that one does not need to explicitly check for the
positivity conditions required for the existence of H<sup>∞</sup>
filters, as these conditions are built into the algorithms themselves.
However, since H<sup>∞</sup> square-root algorithms predominantly
use J-unitary transformations, rather than the unitary transformations
required in the H<sup>2</sup> case, further investigation is needed to
determine the numerical behavior of such algorithms
IEEE Transactions on Automatic Control 05/2000; · 2.11 Impact Factor
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Acoustics, Speech, and Signal Processing, 2000. ICASSP '00. Proceedings. 2000 IEEE International Conference on; 02/2000
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ABSTRACT: We study the design of synthesis filters in noisy filter bank
systems using an H<sup>∞</sup> estimation point of view. The
H<sup>∞</sup> approach is most promising in situations where the
statistical properties of the disturbances (arising from quantization,
compression, etc.) in each subband of the filter bank are unknown, or
are too difficult to model and analyze. For arbitrary analysis polyphase
matrices, standard state-space H<sup>∞</sup> techniques can be
employed to obtain numerical solutions. When the synthesis filters are
restricted to being FIR, as is often the case in practice, the design
can be cast as a finite-dimensional semi-definite program. In this case,
we can effectively exploit the inherent non-uniqueness of the
H<sup>∞</sup> solution to optimize for an additional average
performance and thus obtain mixed H<sup>2</sup>/H<sup>∞</sup>
optimal FIR synthesis filters
Acoustics, Speech, and Signal Processing, 2000. ICASSP '00. Proceedings. 2000 IEEE International Conference on; 02/2000 · 4.63 Impact Factor
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ABSTRACT: This paper derives an expression for the optimal error
nonlinearity in adaptive filter design. Using an energy conservation
relation, and some typical assumptions, the choice of the error function
is optimized by minimizing the mean-square deviation subject to a fixed
rate of convergence. The resulting optimal choice is shown to subsume
earlier results as special cases
Acoustics, Speech, and Signal Processing, 2000. ICASSP '00. Proceedings. 2000 IEEE International Conference on; 02/2000 · 4.63 Impact Factor
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ABSTRACT: We study the design of multiuser detectors from an H/sup /spl infin// point of view. The H/sup /spl infin// approach is most appropriate in the situations where the statistical properties of the disturbances are not known or are too hard to model and analyze. The design of the H/sup /spl infin// optimal FIR multiuser detectors can be efficiently performed using numerical methods. Exploiting the inherent non-uniqueness of the H/sup /spl infin// solution, we additionally optimize for an average performance thus obtaining mixed H/sup 2//H/sup /spl infin// optimal multiuser detector. Recursive solutions, allowing for computationally efficient implementation of the decision-feedback detectors, is discussed.
Signals, Systems and Computers, 2000. Conference Record of the Thirty-Fourth Asilomar Conference on; 02/2000
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ABSTRACT: We propose a new space-time multiuser receiver for CDMA wireless systems. The receiver is based on the fixed-lag smoothed estimator which occurs in the well-researched area of state-space estimation. The receiver can work with long codes as opposed to most other multiuser detectors that require cyclic spreading codes. It is also naturally suited for adaptation and can be used with time-varying (Doppler spread) multipath channels. All the desired users are decoded simultaneously with little decoding delay. The approach assumes that a reliable channel estimate is available which in practice can be obtained from training symbols. We also briefly study the computational complexity of the receiver.
Signals, Systems and Computers, 2000. Conference Record of the Thirty-Fourth Asilomar Conference on; 02/2000
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ABSTRACT: Decentralized control is shown through analysis and
experimentation to be an appropriate strategy for wafer temperature
control in certain multizone rapid thermal processing (RTP) systems. An
input-output controllability analysis is conducted to illustrate that
the direction associated with the reference command (set-point)
corresponding to a spatially uniform temperature trajectory
specification is nearly in alignment with the “most”
controllable direction associated with the maximum singular value for a
multiple concentric lamp configuration. Consequently, the control
structure need not alter the directionality of the plant and, thus, can
be achieved by a simple decentralized controller where the lamps are
paired individually to sensors to achieve a multiloop structure where
all interactions are not taken explicitly into account. This result is
shown to produce acceptable performance even for an ill-conditioned
plant since the directions corresponding to the smaller singular values
are irrelevant to the uniform temperature control criteria. Moreover,
straightforward nonmodel-based tuning of the controller is enabled due
to the simplicity of the decentralized control structure
IEEE Transactions on Semiconductor Manufacturing 06/1999; · 0.72 Impact Factor
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ABSTRACT: A thermal cycling system for baking and chilling semiconductor
wafers is presented for photoresist processing applications. The
proposed unit differs from conventional systems as the bake and chill
steps are conducted sequentially within the same module without
substrate movement. The unit includes a circulating fluid that can be
switched between hot and cold reservoirs and serves as the dominant
means for heat transfer. A set of thermoelectric devices is used in
conjunction with the hot/cold fluid to provide a distributed amount of
heat to the wafer for uniformity and transient temperature control.
Experimental results are provided to demonstrate temperature uniformity
during both transient and steady-state operation
IEEE Transactions on Semiconductor Manufacturing 06/1999; · 0.72 Impact Factor
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ABSTRACT: We study the design of synthesis filters in noisy filter bank
systems using an H<sup>∞</sup> point of view. For unitary analysis
polyphase matrices we obtain an explicit expression for the minimum
achievable disturbance attenuation. Numerical examples and comparisons
with existing methods are also included
Acoustics, Speech, and Signal Processing, 1999. Proceedings., 1999 IEEE International Conference on; 04/1999 · 4.63 Impact Factor
