A randomized bias technique for the importance sampling simulation of Bayesian equalizers

Iltis, R.A.

doi:10.1109/26.380142

Cited by 19 publications

(42 citation statements)

References 15 publications

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“…Applications to systems analysis in communications can be found in [87], [88], and [78]. In recent years, the mathematical tools found in LDT have been used to design and evaluate importance sampling simulations [69], [82], [52], [29], [14], [70], [33], [60], [65], [61], [30], [31], [28], [89], [43], [34], [46], [9]. This work was pioneered by Cottrell et al [46], and developed into a coherent simulation strategy by Sadowsky, Bucklew, and others [70], [33], [61], [69], [52], [78].…”

Section: Large Deviation Theorymentioning

confidence: 99%

“…Hence, IS is a powerful simulation tool, and has attracted interest in many areas. Applications in digital communications include direct-sequence spread-spectrum systems [11], [28], avalanche photodiodes [29]- [31], networks and queues [32]- [35], false alarms [36]- [39], [27], [40], fiber repeaters [24], Viterbi decoders [15], [16], [14], [18], sequential decoders [41], [12], equalizers [42], [43], detection of scale problems [44], multidimensional and multilevel systems [13], [45], Markov processes [46], coherent optical systems [47], and general communication systems [48]- [57], [14], [58]- [62], [26], [63], [19], [37], [64]. Interestingly, IS has been less intensively studied in the statistical literature where some examples can be found in [65], [66], [1], [67], [2], and [68].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quick simulation: a review of importance sampling techniques in communications systems

Smith

Shafi²,

Gao

1997

IEEE J. Select. Areas Commun.

252

158

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Importance sampling (IS) is a simulation technique which aims to reduce the variance (or other cost function) of a given simulation estimator. In communication systems, this usually, but not always, means attempting to reduce the variance of the bit error rate (BER) estimator. By reducing the variance, IS estimators can achieve a given precision from shorter simulation runs; hence the term "quick simulation." The idea behind IS is that certain values of the input random variables in a simulation have more impact on the parameter being estimated than others. If these "important" values are emphasized by sampling more frequently, then the estimator variance can be reduced. Hence, the basic methodology in IS is to choose a distribution which encourages the important values. This use of a "biased" distribution will, of course, result in a biased estimator if applied directly in the simulation. However, there is a simple procedure whereby the simulation outputs are weighted to correct for the use of the biased distribution, and this ensures that the new IS estimator is unbiased. Hence, the "art" of designing quick simulations via IS is entirely dependent on the choice of biased distribution. Over the last 50 years, IS techniques have flourished, but it is only in the last decade that coherent design methods have emerged. The outcome of these developments is that at the expense of increasing technical content, modern techniques can offer substantial runtime saving for a very broad range of problems. In this paper, we present a comprehensive history and survey of IS methods. In addition, we offer a guide to the strengths and weaknesses of the techniques, and hence indicate which techniques are suitable for various types of communications systems. We stress that simple approaches can still yield useful savings, and so the simulation practitioner as well as the technical researcher should consider IS as a possible simulation tool.

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Section: Large Deviation Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quick simulation: a review of importance sampling techniques in communications systems

Smith

Shafi²,

Gao

1997

IEEE J. Select. Areas Commun.

252

158

View full text Add to dashboard Cite

show abstract

“…Although the boundary described in Proposition 2 is only exact in the limit case of infinite SNR, our empirical experience, and others such as [18], have shown that for the SNRs on the order of 10-20 dB, the true Bayesian boundary is closely approximated by the asymptotic multiple hyperplane form, and the two forms are often indistinguishable.…”

Section: Remarkmentioning

confidence: 88%

“…As , Iltis [18] has shown that a necessary condition for a point is (21) where denotes an arbitrary vector in the subspace orthogonal to ,…”

Section: Bayesian Decision Feedback Equalizermentioning

confidence: 99%

“…The optimal Bayesian decision boundary, however, is a hypersurface in the observation space [11]. It can be shown that asymptotically, as the SNR tends to infinity, the Bayesian hypersurface becomes piecewise linear and is made up of a set of hyperplanes [18]. In practice, at large rather than infinite SNR, the performance difference between Bayesian decision boundary and a piecewise linear approximation is negligible.…”

Section: Introduction Ementioning

confidence: 99%

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Asymptotic Bayesian decision feedback equalizer using a set of hyperplanes

Chen

Mulgrew

Hanzo

2000

IEEE Trans. Signal Process.

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Abstract-We present a signal space partitioning technique for realizing the optimal Bayesian decision feedback equalizer (DFE). It is known that when the signal-to-noise ratio (SNR) tends to infinity, the decision boundary of the Bayesian DFE is asymptotically piecewise linear and consists of several hyperplanes. The proposed technique determines these hyperplanes explicitly and uses them to partition the observation signal space. The resulting equalizer is made up of a set of parallel linear discriminant functions and a Boolean mapper. Unlike the existing signal space partitioning technique of Kim and Moon, which involves complex combinatorial search and optimization in design, our design procedure is simple and straightforward, and guarantees to achieve the asymptotic Bayesian DFE.Index Terms-Asymptotic decision boundary, Bayesian decision feedback equalizer, signal space partition.

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Approximating the Bayesian Decision Boundary for Channel Equalisation Using Subset Radial Basis Function Network

Chng

Mulgrew

Chen

et al. 1997

Mathematics of Neural Networks

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The aim of this paper is to examine the application of radial basis function (RBF) network to realise the decision function of a symbol-decision equaliser for digital communication system. The paper rst study the Bayesian equaliser's decision function to show that the decision function is nonlinear and has a structure identical to the RBF model. To implement the full Bayesian equaliser using RBF network however requires very large complexity which is not feasible for practical applications. To reduce the implementation complexity, we propose a model selection technique to choose the important centres of the RBF equaliser. Our results indicate that reduced-sized RBF equaliser can be found with no signicant degradation in performance if the subset models are selected appropriately.

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A randomized bias technique for the importance sampling simulation of Bayesian equalizers

Cited by 19 publications

References 15 publications

Quick simulation: a review of importance sampling techniques in communications systems

Quick simulation: a review of importance sampling techniques in communications systems

Asymptotic Bayesian decision feedback equalizer using a set of hyperplanes

Approximating the Bayesian Decision Boundary for Channel Equalisation Using Subset Radial Basis Function Network

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