Detecting the number of sources is a well known and a well investigated problem. In this problem, the number of sources impinging on an array of sensors is to be estimated. The common approach for solving this problem is to use an information theoretic criterion like the Minimum Description Length (MDL), or the Akaike Information Criterion. Although gaining much popularity and being used in a variety of problems, the performance of information theoretic criteria based estimators for the unknown number of sources has not been su#ciently studied, yet. In the context of array processing, the performance of such estimators were analyzed only for the special case of Gaussian sources where no prior knowledge of the array structure, if given, is used. Based on the theory of misspecified models, this paper presents a general asymptotic analysis of the performance of any information theoretic criterion based estimator, and especially of the MDL estimator. In particular, the performance of the MDL estimator which assumes Gaussian sources and structured array when applied to Gaussian sources is analyzed. Also, it is shown that the performance of a certain MDL estimator is not very sensitive to the actual distribution of the source signals. However, appropriate use of prior knowledge about the array geometry can lead to significant improvement in the performance of the MDL estimator. Simulation results show good fit between the empirical and the theoretical results.

Abstract — In electromagnetic source analysis it is necessary to determine how many sources are required to describe the EEG or MEG adequately. Model selection procedures (MSP’s, or goodness of fit procedures) give an estimate of the required number of sources. Existing and new MSP’s are evaluated in different source and noise settings: two sources which are close or distant, and noise which is uncorrelated or correlated. The commonly used MSP residual variance is seen to be ineffective, that is it often selects too many sources. Alternatives like the adjusted Hotelling’s test, Bayes information criterion, and the Wald test on source amplitudes are seen to be effective. The adjusted Hotelling’s test is recommended if a conservative approach is taken, and MSP’s such as Bayes information criterion or the Wald test on source amplitudes are recommended if a more liberal approach is desirable. The MSP’s are applied to empirical data (visual evoked fields). I.

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In recentyears space-division multiple access (SDMA) has been suggested in order to increase the capacity of a cellular mobile communication system and to simultaneously combat the losses due to multipath and interference. This is achieved by using spatial diversityintroduced byanantenna array and therefore SDMA can easily be implemented as an additional component into existing systems that use time- and/or frequency-division multiple access. An importantcharacteristic of an SDMA system is the direction of arrival of the differentwavefronts impinging on the antenna array which can be obtained from well known high resolution methods that exploit knowledge of the signal or noise subspace. As the scenario is time-varying the subspaces will also change with time and therefore they have to be tracked to avoid repetitive computation of them at each time step. This subspace tracking has been the topic of many research papers over the last years but all of them only deal with snapshot vectors. On the other hand, many existing mobile communication systems have a TDMA component so that a whole burst of data is transmitted during one periodically recurring time slot. Unfortunately, the existing algorithms for subspace tracking do not work with burst-wise data. Therefore weintroduce three algorithms that are based on known tracking algorithms for snapshot vectors which are extended to work with bursty data. Another important problem is the estimation of the current number of waveforms impinging on the antenna array because only exact knowledge of that number ensures correct estimation of the directions of arrival. In a mobile communication system, however, this number may rapidly change because of the varying number of reflections of the signal. We therefore propose an efficient al...

A new approach is presented to the array signal processing problem of detecting the number of incident signals in unknown coloured noise environments with banded covariance structure.

Abstract — In this correspondence, we focus on the performance analysis of the widely-used minimum description length (MDL) source enumeration technique in array processing. Unfortunately, available theoretical analysis exhibit deviation from the simulation results. We present an accurate and insightful performance analysis for the probability of missed detection. We also show that the statistical performance of the MDL is approximately the same under both deterministic and stochastic signal models. Simulation results show the superiority of the proposed analysis over available results. Index Terms — Minimum description length (MDL), source enumeration, performance analysis, deterministic signal. EDICS Category: SAM-PERF, SAM-SDET I. INTRODUCTION AND PRELIMINARIES MDL [1], is one of the most successful methods for determining the number of present signals in array processing and channel

Introduction Array processiRK or more accurately, sensor array processi5W i the processiP of output siput' from an array of sensors located atdiK6PR t poi ts i spacei a wavefield. The purpose of array processiN i to extract usefuliful'--5K5' from therecei edsi5K5-- such as the number and locati-- of thesi'K1 sources, the propagatio velo y of waves, as well as the spectral properti5 of thesi'--5N6 Array processiN techniK6-- have been employed for data collecti[ i volvi5 many types of wave phenomena. Insei1W6 exploratiW for example, arrays of seiWP6N'[K6 are used to collect geophysih' data to study the physiN-- characteri6R--' of the earth'si nteri5W Inpassi e (li'[KEP----'i sonar, arrays of hydrophones are used to collect data generated by underwater sound sources so that a diP5K'[KKK map of the background sound power can be determiWW1 In radar, areceiK ie array of antenna elements i used toli5E6 to the return caused by the reflecti'[ of targetsigets'5PK6 by the electromagne

Abstract—Detection of the number of signals embedded in noise is a fundamental problem in signal and array processing. This paper focuses on the non-parametric setting where no knowledge of the array manifold is assumed. First, we present a detailed statistical analysis of this problem, including an analysis of the signal strength required for detection with high probability, and the form of the optimal detection test under certain conditions where such a test exists. Second, combining this analysis with recent results from random matrix theory, we present a new algorithm for detection of the number of sources via a sequence of hypothesis tests. We theoretically analyze the consistency and detection performance of the proposed algorithm, showing its superiority compared to the standard minimum description length (MDL)-based estimator. A series of simulations confirm our theoretical analysis. Index Terms—Detection, number of signals, random matrix theory, statistical hypothesis tests, Tracy–Widom distribution.

Determining the number of sources is a fundamental problem in many scientific fields. In this paper we consider the non-parametric 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.

Determining the number of sources in a received wave-field is a well known and a well investigated problem. In this problem, the number of sources impinging on an array of sensors is to be estimated. The common approach for solving this problem is to use an information theoretic criterion like the Minimum Description Length (MDL), or the Akaike Information Criterion. Under the assumption that the transmitted signals are Gaussian, the MDL estimator takes both simple and intuitive form. Therefore, this estimator is commonly used even when the signals known to be non-Gaussian communication signals. However, its ability to resolve signals (resolution capacity) is limited by the number of sensors, minus one. In this paper, we study the MDL estimator that is based the correct, non-Gaussian signal distribution of digital signals. We show that this approach leads to both improved performance and improved resolution capacity, that is - the number of signals that can be detected by the resulting MDL processor is larger than the number of array sensors. In addition, a novel asymptotic performance analysis, which can be used to predict the performance of the MDL estimator analytically, is presented. Simulation results support the theoretical conclusions.