Performance analysis of ESPRIT-type algorithms for non-circular sources

Steinwandt, Jens; Roemer, Florian; Haardt, Martin

doi:10.1109/icassp.2013.6638407

Cited by 20 publications

(28 citation statements)

References 15 publications

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“…Note that the exchange matrix M used in [17,18] to facilitate the real-valued implementation of NC unitary ESPRIT is not a requirement for the NC-ESPRIT here. We define the augmented measurement matrix x (nc) (t) as (23) to correspond with [17,18].…”

Section: A Motivationmentioning

confidence: 99%

“…In other words, the complex symbol amplitudes of signals lie on a line in the I/Q diagram, which may correspond to BPSK, offset QPSK, and PAM [18]. Consequently, the source symbol snapshot vector can be decomposed as [17] …”

Section: Problem Formulationmentioning

confidence: 99%

“…We define the augmented measurement matrix x (nc) (t) as (23) to correspond with [17,18]. Substituting (1) and (9) into (23) yields…”

Section: A Motivationmentioning

confidence: 99%

“…In order to take advantage of the benefits associated with the NC sources, we apply widely linear processing and define the augmented measurement data vector x (nc) (t) according to [17,18] as…”

Section: A Motivationmentioning

confidence: 99%

“…The NC signals, such as binary phase shift keying (BPSK), offset quadrature phase shift keying (QPSK), pulse-amplitude modulation (PAM), and amplitude shift keying (ASK) modulated signals, have been widely used in many modern communication systems. By using the NC properties of the received signals, a number of improved subspace-based DOA estimators have been proposed, such as the NC-MUSIC [14], NC-root-MUSIC [15], NC-ESPRIT [16], and NC unitary ESPRIT [17,18]. The NC ESPRIT-like algorithms can double the array aperture and reduce the estimation errors.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Direction-of-arrival estimation for noncircular sources via structured least squares–based esprit using three-axis crossed array

Shi

Cheng

2015

IEEE Trans. Aerosp. Electron. Syst.

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A structured least squares (SLS)-based ESPRIT algorithm for direction-of-arrival (DOA) estimation of strictly second-order noncircular signals using a crossed array is devised in this paper. Unlike the conventional ESPRIT for noncircular signals, which employs the least squares or total least squares, the proposed solution is able to exploit the overlapping structure of the subarray configurations to efficiently solve the shift-invariant equations (SIEs), ending up with the SLS solution for a three-axis crossed array. Moreover, an additional constraint requiring the SIEs of the three linear subarrays directed along the x-, y-, and z-axes to share the same set of eigenvectors is applied to solve the rank-deficiency problem. Consequently, the proposed approach provides more accurate DOA estimates, and its superiority over existing ESPRIT schemes is demonstrated via computer simulations.

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Section: A Motivationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

“…We define the augmented measurement matrix x (nc) (t) as (23) to correspond with [17,18]. Substituting (1) and (9) into (23) yields…”

Section: A Motivationmentioning

confidence: 99%

Section: A Motivationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Direction-of-arrival estimation for noncircular sources via structured least squares–based esprit using three-axis crossed array

Shi

Cheng

2015

IEEE Trans. Aerosp. Electron. Syst.

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A Spectral Mask - Based on Method for Applying into Generalized Sidelobe Canceller Beamformer

Nguyen

Anh

The

2023

Lecture Notes in Networks and Systems

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Robustness and performance analysis of subspace-based DOA estimation for rectilinear correlated sources in CES data model

Abeida

Delmas

2021

Signal Processing

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This paper focuses on a theoretical performance analysis of subspace-based algorithms for the localization of spatially correlated rectilinear sources embedded in circular complex elliptically symmetric (C-CES) distributed noise model and also when the observations are non-circular CES (NC-CES) distributed with dependent scatter matrices on the direction of arrival (DOA) parameters. A perturbation analysis has been performed to derive closed-form expressions for the asymptotic covariance matrices of DOA estimates for non-circular subspacebased algorithms in two CES data models. Robustness of subspace-based algorithms is theoretical evaluated using robust covariance matrix estimators (instead of the sample covariance matrix (SCM)). We prove, for the first time, interpretable closed-form expressions of the asymptotic variance of the estimated DOA of two equi-power correlated sources, which allows us to derive a number of properties describing the DOA variance's dependence on signals parameters and non-Gaussian distribution of the noise. Different robustness properties are theoretically analyzed. In particular, we prove in the framework of NC-CES distributed observations, that Tyler's M -estimator enhances the performance for heavy-tailed distributions w.r.t. the SCM, with negligible loss in performance for circular Gaussian distributed observations. Finally, some Monte Carlo illustrations are given for quantifying this robustness and specifying the domain of validity of our theoretical asymptotic results.

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Performance analysis of ESPRIT-type algorithms for non-circular sources

Cited by 20 publications

References 15 publications

Direction-of-arrival estimation for noncircular sources via structured least squares–based esprit using three-axis crossed array

Direction-of-arrival estimation for noncircular sources via structured least squares–based esprit using three-axis crossed array

A Spectral Mask - Based on Method for Applying into Generalized Sidelobe Canceller Beamformer

Robustness and performance analysis of subspace-based DOA estimation for rectilinear correlated sources in CES data model

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