Finite sample size effect on minimum variance beamformers: optimum diagonal loading factor for large arrays

Mestre, Xavier; Lagunas, M.A.

doi:10.1109/tsp.2005.861052

Cited by 171 publications

(155 citation statements)

References 29 publications

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“…Taking the above limit and recalling (3.54) and In comparison to the approach used here, note that [35] characterizesQ 1 as a part of the study of the SINR at the MPDR output. The deterministic equivalentQ 1 obtained therein is given in terms of the unique solution B 0 (in a certain set) to…”

Section: Asymptotic Analysis Of Power Estimatorsmentioning

confidence: 99%

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The development and application of random matrix theory in adaptive signal processing in the sample deficient regime

Pajovic¹

2014

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This thesis studies the problems associated with adaptive signal processing in the sample deficient regime using random matrix theory. The scenarios in which the sample deficient regime arises include, among others, the cases where the number of observations available in a period over which the channel can be approximated as timeinvariant is limited (wireless communications), the number of available observations is limited by the measurement process (medical applications), or the number of unknown coefficients is large compared to the number of observations (modern sonar and radar systems). Random matrix theory, which studies how different encodings of eigenvalues and eigenvectors of a random matrix behave, provides suitable tools for analyzing how the statistics estimated from a limited data set behave with respect to their ensemble counterparts.The applications of adaptive signal processing considered in the thesis are (1) adaptive beamforming for spatial spectrum estimation, (2) tracking of time-varying channels and (3) equalization of time-varying communication channels. The thesis analyzes the performance of the considered adaptive processors when operating in the deficient sample support regime. In addition, it gains insights into behavior of different estimators based on the estimated second order statistics of the data originating from time-varying environment. Finally, it studies how to optimize the adaptive processors and algorithms so as to account for deficient sample support and improve the performance.In particular, random matrix quantities needed for the analysis are characterized in the first part. In the second part, the thesis studies the problem of regularization in the form of diagonal loading for two conventionally used spatial power spectrum estimators based on adaptive beamforming, and shows the asymptotic properties of the estimators, studies how the optimal diagonal loading behaves and compares the estimators on the grounds of performance and sensitivity to optimal diagonal load-3 ing. In the third part, the performance of the least squares based channel tracking algorithm is analyzed, and several practical insights are obtained. Finally, the performance of multi-channel decision feedback equalizers in time-varying channels is characterized, and insights concerning the optimal selection of the number of sensors, their separation and constituent filter lengths are presented. First of all, I am deeply indebted to my research supervisor and mentor Dr. James Preisig for offering me this wonderful opportunity and being so much helpful on every step on this long journey. Jim, thank you for giving me lot of academic freedom and making sure at the same time that I do not get lost in the wealth of opportunities I was presented to. Thank you for teaching me to seek insights in every mathematical expression and repeatedly asking for intuition and physical interpretation behind every analytical result. Thank you for being so supportive outside of academia and research when life faced me with...

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Section: Asymptotic Analysis Of Power Estimatorsmentioning

confidence: 99%

“…The probability density function of the MPDR output when the received signal is complex Gaussian and at most two signals are present in the sensed field is studied in [37]. The work in [35] characterizes the expected value of the signal-to-interference-plus-noise ratio (SINR)…”

Section: Introductionmentioning

confidence: 99%

The development and application of random matrix theory in adaptive signal processing in the sample deficient regime

Pajovic¹

2014

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“…Through this paper, a detailed literature survey is made on the various bearing estimation techniques and algorithms till date. These many estimation algorithms which are available in the literature have different capabilities and limitations [2]- [3]. The DOA estimation problem in some cases, is first solved by estimation methods of the number of sources [4]- [5]- [6] and then applying a high-resolution method to estimate the angular position of these sources.…”

Section: Introductionmentioning

confidence: 99%

Beamforming for Direction-of-Arrival (DOA) Estimation-A Survey

Krishnaveni¹,

Kesavamurthy²,

Aparna.³

2013

IJCA

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Direction-of-Arrival (DOA) estimation plays a vital role in many applications. Beamforming is the most prominent technique to estimate DOA. In this survey, a study of various beamforming techniques and algorithms to estimate the direction of arrival of a signal is made. An assessment on the background robust algorithms using Nyquist sampling rate and its Compressive sensing alternative is done. It is known that Bearing estimation algorithms obtain only a small number of direction of arrivals (DOAs) within the entire angle domain, when the sources are spatially sparse. Hence, it may be concluded that, the methods those specifically exploits this spatial sparsity property is advantageous. These methods use a very small number of measurements in the form of random projections of the sensor data along with one full waveform recording at one of the sensors.

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“…These approaches efficiently calculate the loading factor. Other variable-loading based robust beamformers are also proposed in [8,9]. Motivated by a similar idea, the authors in [10,11] introduced different optimization formulation and proposed solutions that are based on semi-definite programming.…”

Section: Introductionmentioning

confidence: 99%

“…Since the direction of the signal-of-interest (SOI) is nearer to the presumed look-direction, it is possible to distinguish the null's direction associated to the SOI from the interferences. Although numerous capon beamforming algorithms have been proposed [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15], all these algorithms suffer from the problem of saturation in the output SINR as the input SNR increases.…”

Section: Introductionmentioning

confidence: 99%

Robust Adaptive Beamforming Based on Covariance Matrix Reconstruction for Look Direction Mismatch

Mallipeddi¹,

Lie²,

Razul³

et al. 2011

PIER Letters

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Abstract-The performance degradation in traditional adaptive beamformers can be attributed to the imprecise knowledge of the array steering vector and inaccurate estimation of the covariance matrix. The inaccurate estimation of the covariance matrix is due to the limited data samples and presence of desired signal components in the training data. The mismatch between the actual and presumed steering vectors can be mainly due to the error in the look direction estimate. In this paper, we propose a novel algorithm to estimate the look direction and to reconstruct the covariance matrix so that near optimal performance without the effect of saturation can be achieved as the input SNR increases. Numerical results also show that all existing beamforming algorithms suffer from saturation effect as the input SNR increases.

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Finite sample size effect on minimum variance beamformers: optimum diagonal loading factor for large arrays

Cited by 171 publications

References 29 publications

The development and application of random matrix theory in adaptive signal processing in the sample deficient regime

The development and application of random matrix theory in adaptive signal processing in the sample deficient regime

Beamforming for Direction-of-Arrival (DOA) Estimation-A Survey

Robust Adaptive Beamforming Based on Covariance Matrix Reconstruction for Look Direction Mismatch

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