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22
Statistical Performance Analysis of MDL Source Enumeration
- in Array Processing, IEEE
"... 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 insigh ..."
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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
Rank Estimation and Redundancy Reduction of High-Dimensional Noisy Signals with Preservation of Rare Vectors
- IEEE Trans. Signal Proc
, 2007
"... In this paper, we address the problem of redundancy-reduction of high-dimensional noisy signals that may contain anomaly (rare) vectors, which we wish to preserve. For example, when applying redundancy reduction techniques to hyperspectral images, it is essential to preserve anomaly pixels for targe ..."
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In this paper, we address the problem of redundancy-reduction of high-dimensional noisy signals that may contain anomaly (rare) vectors, which we wish to preserve. For example, when applying redundancy reduction techniques to hyperspectral images, it is essential to preserve anomaly pixels for target detection purposes. Since rare-vectors contribute weakly to the ℓ2-norm of the signal as compared to the noise, ℓ2-based criteria are unsatisfactory for obtaining a good representation of these vectors. The proposed approach combines ℓ2 and ℓ ∞ norms for both signal-subspace and rank determination and considers two aspects: One aspect deals with signal-subspace estimation aiming to minimize the maximum of data-residual ℓ2-norms, denoted as ℓ2,∞, for a given rank conjecture. The other determines whether the rank conjecture is valid for the obtained signal-subspace by applying Extreme Value Theory results to model the distribution of the noise ℓ2,∞-norm. These two operations are performed alternately using a suboptimal greedy algorithm, which makes the proposed approach practically plausible. The algorithm was applied on both synthetically simulated data and on a real hyperspectral image producing better results than common ℓ2-based methods. Index Terms Signal-subspace rank, singular value decomposition (SVD), minimum description length (MDL), anomaly detection, dimensionality reduction, redundancy reduction, hyperspectral images. 2 I.
Blind Channel Equalization With Colored Sources Based On Second-Order . . .
- IEEE TRANS. SIGNAL PROC
, 2001
"... We consider the blind equalization and estimation of single-user, multichannel models from the second-order statistics of the channel output when the channel input statistics are colored but known. By exploiting certain results from linear prediction theory, we generalize the algorithm of Tong et al ..."
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Cited by 5 (1 self)
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We consider the blind equalization and estimation of single-user, multichannel models from the second-order statistics of the channel output when the channel input statistics are colored but known. By exploiting certain results from linear prediction theory, we generalize the algorithm of Tong et al., which was derived under the assumption of a white transmitted sequence. In particular, we show that all one needs to estimate the channel to within an unitary scaling constant, and thus to find its equalizers, is a) that a standard channel matrix have full column rank, and b) a vector of the input signal and its delays have positive definite lag zero autocorrelation. An algorithm is provided to determine the equalizer under these conditions. We argue that because this algorithm makes explicit use of the input statistics, the equalizers thus obtained should outperform those obtained by other methods that neither require, nor exploit, the knowledge of the input statistics. Simulation results are provided to verify this fact.
Constrained Optimization Methods for Direct Blind Equalization
"... Abstract—Constrained optimization techniques are studied in this paper for direct design of linear multichannel equalizers. Novel blind algorithms are derived by minimizing the equalizer’s output variance subject to appropriate constraints. The constraints are chosen to guarantee no desired signal c ..."
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Abstract—Constrained optimization techniques are studied in this paper for direct design of linear multichannel equalizers. Novel blind algorithms are derived by minimizing the equalizer’s output variance subject to appropriate constraints. The constraints are chosen to guarantee no desired signal cancellation, and their parameters are jointly optimized to maximize the signal component at the output. The resulting blind algorithm was observed to have near optimal performance at high signal-tonoise ratio, i.e., close to the performance of the trained minimum mean-square-error receiver. Also, the proposed method is not sensitive to the color of the transmitted sequence. Analytical expressions are derived to quantify the algorithm’s performance. Index Terms — Blind equalization, constrained optimization, multichannel equalization.
FAST AND EFFECTIVE MODEL ORDER SELECTION METHOD TO DETERMINE THE NUMBER OF SOURCES IN A LINEAR TRANSFORMATION MODEL
"... This paper formally introduces the method named as RAE (ratio of adjacent eigenvalues) for model order selection, and proposes a new approach combining the recently developed SORTE (Second ORder sTatistic of the Eigenvalues) and RAE in the context for determining the number of sources in a linear tr ..."
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This paper formally introduces the method named as RAE (ratio of adjacent eigenvalues) for model order selection, and proposes a new approach combining the recently developed SORTE (Second ORder sTatistic of the Eigenvalues) and RAE in the context for determining the number of sources in a linear transformation model. The underlying rationale for the combination discovered through sufficient simulations is that SORTE overestimated the true order in the model and RAE underestimated the true order when the signal to noise ratio (SNR) was low. Simulations further showed that after the new method, called RAESORTE, was optimized, the true number of sources was almost correctly estimated even when the SNR was-10 dB, which is extremely difficult for any other model order selection methods; moreover, RAE took much less time than SORTE known as computational efficiency. Hence, RAE and RAESORTE appear promising for the real-time and real world signal processing. Index Terms—Linear transformation model, model order selection, number of sources, ratio of adjacent eigenvalues, signal to noise ratio 1.
DETERMINISTIC MIMO CHANNEL ORDER ESTIMATION BASED ON CANONICAL CORRELATION ANALYSIS
"... Channel order estimation is a critical step in blind channel identification/equalization algorithms. In this paper, a new criterion for channel order estimation of multiple-input multiple-output (MIMO) channels is presented. The proposed method relies on the reformulation of the blind equalization p ..."
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Cited by 2 (0 self)
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Channel order estimation is a critical step in blind channel identification/equalization algorithms. In this paper, a new criterion for channel order estimation of multiple-input multiple-output (MIMO) channels is presented. The proposed method relies on the reformulation of the blind equalization problem as a set of nested canonical correlation analysis (CCA) problems, whose solutions are given by a generalized eigenvalue (GEV) problem. In particular, the channel order estimates are obtained from the multiplicity of the largest generalized eigenvalue of the successive GEVs. Unlike previous approaches, the performance of the proposed method is good even in the cases of small data sets, colored signals, and channels with small head and tails terms, which is illustrated by means os some numerical examples. 1.
ON-LINE ORDER SELECTION FOR COMMUNICATIONS
"... We address the problem of on-line order determination for communications and show that penalized partial likelihood criterion provides a suitable likelihood framework for the problem by allowing correlations among samples and online processing ability. An on-line, efficient order selection scheme is ..."
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We address the problem of on-line order determination for communications and show that penalized partial likelihood criterion provides a suitable likelihood framework for the problem by allowing correlations among samples and online processing ability. An on-line, efficient order selection scheme is developed assuming that the observations can be modeled by a finite normal mixture model without imposing any additional conditions on the unknown system, such as linearity. Channel equalization by finite normal mixtures is considered as an example for which correct order determination is critical and examples are presented to show the application and effectiveness of the approach. 1.
A Semi-Blind Channel Estimation Technique Based on Second-Order Blind Method for CDMA Systems
"... Abstract—This paper aims at studying a semi-blind channel estimation scheme based on the subspace method or a carefully weighted linear prediction approach. The corresponding (composite) semi-blind cost functions result from a linear combination of the training-based cost function and a blind cost f ..."
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Abstract—This paper aims at studying a semi-blind channel estimation scheme based on the subspace method or a carefully weighted linear prediction approach. The corresponding (composite) semi-blind cost functions result from a linear combination of the training-based cost function and a blind cost function. For each blind method, we show how to calculate the asymptotic estimation error. Therefore, by minimizing this error, we can properly tune the-dimensional regularizing vector introduced in the composite semi-blind criterion (for active users in the uplink). The asymptotic estimation error minimization is a-variable minimization problem, which is a complex issue with which to deal. We explicitly show under what conditions this problem boils down to single-variable minimization problems. Our discussion is not limited to theoretical analyses. Simulation results performed in a realistic context [universal mobile telecommunication system—time division duplex (UMTS-TDD) mode] are provided. In particular, we conclude about the potential of the proposed approach in real communication systems. Index Terms—CDMA, channel estimation, linear prediction, MIMO, regularizing, semi-blind, subspace method, uplink. I.
Approved as to style and content by:
, 2014
"... This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has ..."
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This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has
