Reduced-Rank MDL Method for Source Enumeration in High-Resolution Array Processing

Huang, Lei; Wu, Shunjun; Li, Xia

doi:10.1109/tsp.2007.899344

Cited by 76 publications

(54 citation statements)

References 22 publications

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“…The performance of the AIC estimator was also studied in various works, see [15], [35] and references therein. It was shown that its main source of error is model order overestimation by exactly one signal (9) where is given by (10) and . In [34] and [35], expressions for this overestimation probability were derived, which require numerical evaluation of a possibly high dimensional integral (although [34] also presented approximations to these high dimensional integrations).…”

Section: B Previous Workmentioning

confidence: 99%

“…In the nonparametric setting, where no assumptions on the array manifold or on the desired signal waveforms are made, two of the most common estimators for this problem are the AIC and the MDL estimators, both derived from information theoretic considerations [29]. Information theoretic criteria have also been used to derive estimators in parametric settings, where the array manifold is assumed known, as in [28] and [30], or when other information is available, such as explicit knowledge of the waveform of the desired signal or some shift invariance properties of the sensor array response, as in [9] and [10]. Most of these estimators require the eigendecomposition of the sample covariance matrix.…”

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confidence: 99%

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Nonparametric Detection of Signals by Information Theoretic Criteria: Performance Analysis and an Improved Estimator

Nadler

2010

IEEE Trans. Signal Process.

146

116

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Abstract-Determining the number of sources from observed data is a fundamental problem in many scientific fields. In this paper we consider the nonparametric setting, and focus on the detection performance of two popular estimators based on information theoretic criteria, the Akaike information criterion (AIC) and minimum description length (MDL). We present three contributions on this subject. First, we derive a new expression for the detection performance of the MDL estimator, which exhibits a much closer fit to simulations in comparison to previous formulas. Second, we present a random matrix theory viewpoint of the performance of the AIC estimator, including approximate analytical formulas for its overestimation probability. Finally, we show that a small increase in the penalty term of AIC leads to an estimator with a very good detection performance and a negligible overestimation probability.

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Section: B Previous Workmentioning

confidence: 99%

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confidence: 99%

Nonparametric Detection of Signals by Information Theoretic Criteria: Performance Analysis and an Improved Estimator

Nadler

2010

IEEE Trans. Signal Process.

146

116

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“…Some popular algorithms for parameter estimation, such as MUSIC and ESPRIT, assume that the number of signals is a-priori known. These methods rely on non-parametric or semi-parametric algorithms to detect the number of sources [8], [14], [15], [27], [31], [33], [16], [22], [18]. Other approaches, often more computationally intensive, perform joint detection and estimation using the full knowledge of the array geometry [20], [2], [1], [6].…”

Section: Introductionmentioning

confidence: 99%

Parametric joint detection-estimation of the number of sources in array processing

Arkind

Nadler

2010

2010 IEEE Sensor Array and Multichannel Signal Processing Workshop

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Detection of the number of signals and estimation of their directions of arrival (DOAs) are fundamental problems in signal array processing. In this paper we present three main contributions to this problem.First, we show that there is an explicit relation between model selection and the breakdown phenomena of the Maximum Likelihood estimator (MLE). Second, we provide a simple formula for the location of the breakdown of the MLE, using tools from extreme value theory. This gives an explicit formula for the signal strength required for reliable detection. Third, we apply these results and propose a new joint detection-estimation algorithm with state-of-the-art performance. We present computer simulations that demonstrate the performance of our algorithm, compared to other popular methods. Index Termsjoint detection-estimation, statistical hypothesis tests, extreme value theory, MLE breakdown phenomena.

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“…To localize the sources by using a superresolution method and then suppress the interference sources and noise, it is crucial to determine the number of sources first. In the literature, source enumeration (SE) and direction finding (DF) have been extensively studied, such as in [1]- [8]. To enhance the DF accuracy, a number of methods have been suggested by using a priori knowledge of the signals.…”

Section: Introductionmentioning

confidence: 99%

MMSE-Based MDL Method for Accurate Source Number Estimation

Mao

2009

IEEE Signal Process. Lett.

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Abstract-In civilian communication systems, the signature sequence of the desired signal in training phase is known to the receiver. In this letter, using the mutual information, we bridge the probability density function and minimum mean-square error (MMSE) between the observed data and training sequence of the desired signal, and then employ the MMSE to construct a minimum description length (MDL) criterion for accurate source enumeration. Numerical results demonstrate that the proposed method is superior to existing MDL methods in terms of detection performance particularly for small number of snapshots and/or source angular separation.Index Terms-Eigenvalue decomposition, minimum description length, sensor array processing, source number estimation.

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Reduced-Rank MDL Method for Source Enumeration in High-Resolution Array Processing

Cited by 76 publications

References 22 publications

Nonparametric Detection of Signals by Information Theoretic Criteria: Performance Analysis and an Improved Estimator

Nonparametric Detection of Signals by Information Theoretic Criteria: Performance Analysis and an Improved Estimator

Parametric joint detection-estimation of the number of sources in array processing

MMSE-Based MDL Method for Accurate Source Number Estimation

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