[Formula Omitted]-Dimensional ESPRIT-Type Algorithms for Strictly Second-Order Non-Circular Sources and Their Performance Analysis

High-resolution parameter estimation algorithms designed to exploit the prior knowledge about incident signals from strictly second-order (SO) noncircular (NC) sources allow for a lower estimation error and can resolve twice as many sources. In this paper, we derive the [Formula Omitted] [Formula Om...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2014-09, Vol.62 (18), p.4824
Main Authors: Steinwandt, Jens, Roemer, Florian, Haardt, Martin, Galdo, Giovanni Del
Format: Article
Language:English
Subjects:
Algorithms
Estimating techniques
Noise
Parameter estimation
Online Access:Get full text
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Summary:High-resolution parameter estimation algorithms designed to exploit the prior knowledge about incident signals from strictly second-order (SO) noncircular (NC) sources allow for a lower estimation error and can resolve twice as many sources. In this paper, we derive the [Formula Omitted] [Formula Omitted] NC Standard ESPRIT and the [Formula Omitted] [Formula Omitted] NC Unitary ESPRIT algorithms that provide a significantly better performance compared to their original versions for arbitrary source signals. They are applicable to shift-invariant [Formula Omitted] [Formula Omitted] antenna arrays and do not require a centro-symmetric array structure. Moreover, we present a first-order asymptotic performance analysis of the proposed algorithms, which is based on the error in the signal subspace estimate arising from the noise perturbation. The derived expressions for the resulting parameter estimation error are explicit in the noise realizations and asymptotic in the effective signal-to-noise ratio (SNR), i.e., the results become exact for either high SNRs or a large sample size. We also provide mean squared error (MSE) expressions, where only the assumptions of a zero mean and finite SO moments of the noise are required, but no assumptions about its statistics are necessary. As a main result, we analytically prove that the asymptotic performance of both [Formula Omitted] [Formula Omitted] NC ESPRIT-type algorithms is identical in the high-effective SNR regime. Finally, a case study shows that no improvement from strictly non-circular sources can be achieved in the special case of a single source.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2014.2342673