Sequential Joint Detection and Estimation: Optimum Tests and Applications

Yılmaz, Yasin; Li, Shang; Wang, Xiaodong

doi:10.1109/tsp.2016.2582469

Cited by 23 publications

(15 citation statements)

References 45 publications

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“…Our perspective on the problem has been motivated by the success of joint design frameworks such as joint detection and estimation [22]- [27] and joint detection and decoding [28]- [30]. The work in [23] considers a binary hypothesis testing problem in which only one of the hypothesis is composite, i.e., it contains an unknown random parameter whose prior distribution is assumed to be known.…”

Section: A Motivation and Related Workmentioning

confidence: 99%

“…For a fixed modulation classification rule δ, the optimization problem in (P1) with the new cost function is written as (27) After some manipulation, we get (28) It is now clear from (28) that the optimal symbol decoder is given by the MAP rule, i.e., φ ( )…”

Section: Extensionmentioning

confidence: 99%

“…Having identified the symbol decoder, we proceed with the derivation of the modulation classification rule. By inserting MAP based symbol decoders into the objective function (27), the problem reduces to…”

Section: Map (•)mentioning

confidence: 99%

See 2 more Smart Citations

Optimal Joint Modulation Classification and Symbol Decoding

Kazikli

Dulek

Gezici

2019

IEEE Trans. Wireless Commun.

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In this paper, modulation classification and symbol decoding problems are jointly considered and optimal strategies are proposed under various settings. In the considered framework, there exist a number of candidate modulation formats and the aim is to decode a sequence of received signals with an unknown modulation scheme. To that aim, two different formulations are proposed. In the first formulation, the prior probabilities of the modulation schemes are assumed to be known and a formulation is proposed under the Bayesian framework. This formulation takes a constrained approach in which the objective function is related to symbol decoding performance whereas the constraint is related to modulation classification performance. The second formulation, on the other hand, addresses the case in which the prior probabilities of the modulation schemes are unknown, and provides a method under the minimax framework. In this case, a constrained approach is employed as well; however, the introduced performance metrics differ from those in the first formulation due to the absence of the prior probabilities of the modulation schemes. Finally, the performance of the proposed methods is illustrated through simulations. It is demonstrated that the proposed techniques improve the introduced symbol detection performance metrics via relaxing the constraint(s) on the modulation classification performance compared with the conventional techniques in a variety of system configurations.

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Section: A Motivation and Related Workmentioning

confidence: 99%

Section: Extensionmentioning

confidence: 99%

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Optimal Joint Modulation Classification and Symbol Decoding

Kazikli

Dulek

Gezici

2019

IEEE Trans. Wireless Commun.

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“…Moreover, Yilmaz et al (2016) provided an optimal sequential joint detection and estimation framework for multiple hypotheses which is based on a state space model. That approach uses, similarly to (Yilmaz et al, 2014), an overall cost function consisting of a weighted combination of detection and estimation errors.…”

Section: Introductionmentioning

confidence: 99%

Bayesian sequential joint detection and estimation

Reinhard

Fauß

Zoubir

2018

Sequential Analysis

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Joint detection and estimation refers to deciding between two or more hypotheses and, depending on the test outcome, simultaneously estimating the unknown parameters of the underlying distribution. This problem is investigated in a sequential framework under mild assumptions on the underlying random process. We formulate an unconstrained sequential decision problem, whose cost function is the weighted sum of the expected run-length and the detection/estimation errors. Then, a strong connection between the derivatives of the cost function with respect to the weights, which can be interpreted as Lagrange multipliers, and the detection/estimation errors of the underlying scheme is shown. This property is used to characterize the solution of a closely related sequential decision problem, whose objective function is the expected run-length under constraints on the average detection/estimation errors. We show that the solution of the constrained problem coincides with the solution of the unconstrained problem with suitably chosen weights. These weights are characterized as the solution of a linear program, which can be solved using efficient off-the-shelf solvers. The theoretical results are illustrated with two example problems, for which optimal sequential schemes are designed numerically and whose performance is validated via Monte Carlo simulations.2. The hypothesis H i , i = 0, 1, as well as the random parameter Θ i do not change during the observation period of X N .3. A sufficient static t n (x n ) in a state space (E t , E t ) exists such thatThe sufficient statistic has a transition kernel of the formand some initial statistic t 0 .4. The two hypotheses are separable, i.e.,5. The second order moment of the random parameter Θ exists and is finite, i.e., E[Θ 2 ] <∞ .Note that this implies, that the conditional second order moment E[Θ 2 | A] exist and is finite for all events A with non-zero probability.

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“…Some popular techniques to address this problem include reformulating the composite detection problem as a pure estimation problem [12], while the maximum a posteriori estimate was shown to provide a solution to the joint detection and estimation problem in a Bayesian context [13]. The problem has also been addressed in a sequential setting, where the objective is to minimize the number of samples subject to a constraint on the combined detection and estimation cost [14], [15]. The generalized sequential probability ratio test was presented in [16], where a decision was obtained using the maximum likelihood estimate of the unknown parameter.…”

Section: Introductionmentioning

confidence: 99%

Sequential joint signal detection and signal-to-noise ratio estimation

Fauß

Nagananda

Zoubir

et al. 2017

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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The sequential analysis of the problem of joint signal detection and signal-to-noise ratio (SNR) estimation for a linear Gaussian observation model is considered. The problem is posed as an optimization setup where the goal is to minimize the number of samples required to achieve the desired (i) type I and type II error probabilities and (ii) mean squared error performance. This optimization problem is reduced to a more tractable formulation by transforming the observed signal and noise sequences to a single sequence of Bernoulli random variables; joint detection and estimation is then performed on the Bernoulli sequence. This transformation renders the problem easily solvable, and results in a computationally simpler sufficient statistic compared to the one based on the (untransformed) observation sequences. Experimental results demonstrate the advantages of the proposed method, making it feasible for applications having strict constraints on data storage and computation.

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Sequential Joint Detection and Estimation: Optimum Tests and Applications

Cited by 23 publications

References 45 publications

Optimal Joint Modulation Classification and Symbol Decoding

Optimal Joint Modulation Classification and Symbol Decoding

Bayesian sequential joint detection and estimation

Sequential joint signal detection and signal-to-noise ratio estimation

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