Detection of signals by information theoretic criteria: general asymptotic performance analysis

Abstract

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 (AIC). Although it has been gaining much popularity and has been used in a variety of problems, the performance of information theoretic criteria-based estimators for the unknown number of sources has not been sufficiently 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. In addition, 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.

Tomography Sar Imaging Strategy Based on Block-Sparse Model

“…Then the support set of cardinality is increased one by one by selecting a new column-block's index in each iteration and forms a support set of cardinality K at the end. Here, the sparsity K is obtained by information theoretic criteria (ITC) [25]. The steps of BOMP algorithm are described as follows:…”

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

“…In particular, for signal strength below this threshold, the probability thatθ M L is a reliable estimate of θ is significantly smaller than 1. However, with high probability, such signals will not be detected, since they will not satisfy condition (12). The accuracy of the estimated location of the MLE breakdown is shown in figure 6, see also section VI.…”

“…Note that our method is closely related to the algorithm proposed in [6], though our analysis is more extensive, including an appropriate threshold for the corresponding GLRT, and a theoretical analysis of the asymptotic properties of the algorithm. Our algorithm is also related to the parametric MDL [12], which takes the form…”

An investigation of several typical model selection criteria for detecting the number of signals

“…Associated with this model, a key problem which has received much attention in signal processing literature (e.g., Refs. [1,17,18,20,21]) is to determine the number of source signals based on an observed sequence x(t), t = 1, 2, . .…”

“…[1] and followed by Refs. [17][18][19][20][21][22], AIC [245][246][247][248][249][250][251][252][253][254][255] and minimum description length (MDL) [23] were introduced to determine the number of signals with efforts on approximating the underestimation (or overestimation) probability and asymptotical consistency under an infinite N . Moreover, recent progress in random matrix theory demonstrates the existence of a phase transition threshold (for the eigenvalues of the covariance), below which the effective number of signals is reduced [10][11][12]22] under the limit N, n → ∞ with n/N → c, where n is the dimensionality of observations, and c > 0 is a constant.…”